a million storing these individually would be too expensive in memory space.

A1.17.1 Task-A :

The drift parameters for every image are calculated by a linear interpolation
of the entries in the table of drifts for the band, provided by A1.14
uvtComputeDrift, at the relevant time.

A1.17.1a PC mode -

For PC mode data, these interpolated drift parameters are used to apply
identical corrections to centroids of all photon events of the specific frame.
c_x_snr= x_shift + (c_x -x0)*cos$\theta$ \- (c_y -y0)*sin$\theta$ \+ x0
c_y_snr= y_shift + (c_x -x0)*sin$\theta$ \- (c_y -y0)*cos$\theta$ \+ y0

where x0 = x_size/2 & y0 = y_size/2; where the ‘snr’ subscript refers to the
shift and rotation corrected centroids & the (c_x, c_y) are the most recently
updated centroids from the master photon event list from the module
“uvtOpticAssDistCorr” (Sec A1.12). These drift corrected centroid values
(c_x_snr, c_y_snr) for each photon event replace the earlier entries for
centroid values in the master table of events and remain available for
subsequent processing blocks till the very end of execution of the chain. In
case the RAS does not cover the entire time range for the Episode, only the
part with time overlap is retained and the remaining events are discarded
since the drift corrections can not be applied to them. This updated table is
preserved in the sub-directory labeled ‘uvtShiftRot_6.3’ within the product
bundle for the corresponding Episode, in a file named with the suffix ‘_snr’
(see Appendix-9).

Further updating by a later processing (uvtFullFrameAst Module) :

The photon event table finally updated by this uvtShiftRot Module (described
above) gets further refined by a later processing Module carrying out
astrometric corrections by matching detected stars with those in an existing
standard catalogue (module uvtFullFrameAst; Sec. A1.20). A new event table is
generated which adds fresh information regarding coordinates and time while
retaining all the past details, located in the same sub-directory with the
file name having the suffix ‘_radec’.

Five additional columns are appended, which are named ‘RA’, ‘DEC’, ‘MJD_L2’,
‘RA-aaaaa’ & ‘DEC-aaaaa’. The first pair contains the best estimate of the
event coordinates in RA, Dec (ICRS; J2000) system relative to the map centre,
which are the final values obtained from the pipeline run for the
corresponding Episode including Astrometry. The last pair correspond to the
RA, Dec obtained through transformation of event centroids from Detector (X,
Y) system to RA, Dec system using the aspect information from the spacecraft.
In the event of failure of the astrometry block, both sets of coordinates
would be identical.

The column named ‘TIME’ was planned to provide the primary timing information
for each photon event. It is normally populated with SPS_MJD, the absolute
time provided by L1 through calibration of the spacecraft’s on board clock,
through selection of the ‘utcFlag’ to be ON. Alternately, if the UTC switch is
selected to be OFF (when SPS_MJD showed erratic values occasionally), this
‘TIME’ column is populated with the UVIT’s Master clock, and the ‘MJD_L2’
column in the table would still provide estimated absolute time with about
$\sim$ 1 sec accuracy, using local calibration of the UVIT’s Master clock
(carried out within the L2 pipeline, in DataIngest Module – Sec. A1.1). This
enables astronomical variability analysis at time scales shorter than typical
duration of observation episodes which is $\sim$ 2000 seconds under all
circumstances.

The standard bundle of the pipeline products disseminated by the ISSDC
includes this final resulting table (with suffix ‘_radec’), as the event list
table, corresponding to every data set from individual Episodes.

A1.17.1b INT mode -

For INT mode data, individual image frames are first transformed by pixel sub-
division from original size 4800$\times$4800 to 9600$\times$9600\. Then
contents of each of these finer sub-pixels are moved to a new location after
application of the shift and rotation correction using relations similar to
the above. Finally, a 2x2 binning is carried out to bring the array dimensions
back to original level. The process ensures local ‘conservation’ of signals
and adequate handling of ‘Bad Pixels’. At the end, as many drift corrected
image frame products are generated as were available at the input. They are
all in Detector coordinate system (X, Y).

A1.17.2 Task-B :

For the second task of generating Exposure Arrays, at first the relevant
“Template Exposure Array” is accessed from CAL_DB (EXPOSURE_TEMPLATE / band /
mode / window size). Primarily, entries in this array are ‘1’ for all sub-
pixels corresponding to the good pixels within the selected window and ‘0’ for
the rest. For every image qualified for inclusion in making sky image, a
corresponding Exposure Array is generated by applying drift corrections (on
the template array) appropriate for that time instance following the procedure
described in Task-A (A1.17.1b INT mode).

A1.18 uvtFrameIntegration

This Module is called by both the Relative Aspect and Sky Imaging chains for
PC mode data. It is responsible for gridding the photon centroids from
multiple (N_combine) successive frames onto 2-D array/(s). For the RA_PC
chain, a time series of images, Comb_frames, are generated which are used for
identifying individual stars in a subsequent processing stage. For the L2_PC
chain this module is either used to combine all the frames for the Episode
into a single image or construct multiple images by sub- dividing the full
data into smaller time intervals corresponding to ‘pseudo-Episode’-s. The
latter option enables application of corrections for small mis-alignments due
to any temporal effects, in a subsequent processing step (module uvtRegAvg;
Sec. A1.19).

The typical values of the time step ‘T’ corresponding to the selectable
parameter, N_combine, are $\sim$ 1 s and $\sim$ 300 s for RA_PC and L2_PC
chains respectively. Time sequence of images, Comb_frames, are referred to as
4800$\times$4800 “Sig” arrays. The last image would be made with $<$ N_combine
frames in case the Total number of frames is not integer multiple of
N_combine. There is a provision to skip N_discard initial frames to discard
the initial frames either due to any starting disturbance or during a rapid
drift of the pointing. Corresponding sole / sequence of “Exposure” array/s and
“Uncertainty” array/s are also generated in the L2_PC chain. The “Signal”
array/s are obtained by pixel by pixel division of the “Sig” array/s by the
corresponding “Exposure” array/s and the statistical “Uncertainty” array/s are
generated using the “Signal” and “Exposure” array/s (based on square-root of
estimated number of total EFFECTIVE photon events, corrected for the variation
of responsivity on the detector, in each individual pixel and not the actual
number of photon events). The “Exposure” products from this module are stored
in the directory ‘uvtExposureFrames_6.3’ and the rest (Sig, Signal &
Uncertainty) in sub-directories under the directory ‘uvtFrameIntegration_6.3’.

A1.19 uvtRegAvg

This Module is called by both INT & PC versions of the Sky Imaging chain. It
may be noted that in an earlier processing block (PC : uvtFrameIntegration
Module; Sec. A1.18; INT : uvtFindWtdMean for L2_INT (not described here), the
dataset from a specific Episode has either been treated as a whole (‘Episode’)
or in smaller parts (‘pseudo-Episode’) as per user’s choice. Here, the Module
uvtRegAvg, combines the multiple Signal (“Sig”) and Exposure (“Exposure”)
arrays in case ‘pseudo-Episode’ option was exercised in that earlier bloc.
These multiple ‘Sig’ & ‘Exposure’ arrays are combined after determining
relative Shifts and Rotation between them using an algorithm to align detected
brightest point sources from successive ‘Sig’ arrays which were generated
earlier on. The alignment operations are identical for each pair of ‘Sig’ &
‘Exposure’ arrays.

Additionally, for PC mode UV imaging, these combined ‘Sig’ & ‘Exposure’ arrays
are used to generate the output ‘Signal’ & ‘Uncertainty’ arrays in true
“count/second” unit, using the same scheme as described earlier
(uvtFrameIntegration Module; Section A1.18). The same operation is carried out
on the sole pair of ‘Sig’ & ‘Exposure’ arrays in case the ‘Episode’ option was
exercised in the preceding processing block to generate all 3 final products,
viz., ‘Signal’, ‘Exposure’ & ‘Uncertainty’.

At the end of this uvtRegAvg process (irrespective of the choice between
pseudo-Episode / Episode), a single set of sky image, exposure & uncertainty
products are generated which utilize the entire data set for the particular
observation Episode (for a particular combination of Band, Filter & Window
size in one orbit). These final array products Signal (counts/sec), Exposure
(no of frames) & Uncertainty (counts/sec) are of 4800$\times$4800 size and in
Detector coordinate (X, Y) system and stored in the ‘uvtRegAvg_6.3’ directory
(see Appendix-9).

Since the algorithms used in this uvtRegAvg Module for 3 different steps of
processing are identical to those described earlier for other Modules, only
their references are mentioned here. The scheme to find bright point sources
in individual component images (from pseudo-Episodes) is similar to that used
for the Module uvtDetectStar (Sec. A1.10) & to determine relative offset
(shifts and rotation) between them uses the scheme followed for the Module
uvtComputeDrift (Sec. A1.14). Finally, the scheme employed for aligning these
individual images based on the locations of detected point sources, is the
same as followed for the Module uvtShiftRot (Sec. A1.17.1b; Task-A, for INT
mode). It may be noted that the alignment of pseudo-Episodes involves
transformation of image sub-pixels resulting in some loss of angular
precision, unlike alignment among Episodes carried out in the Driver Scheme
(Sec. 3.2.4) in which individual photon centroids are transformed.

A1.20 uvtFullFrameAst

This Module is called by both INT & PC versions of the Sky Imaging chain as
well as the DriverScheme, which determines finer corrections to the sky
coordinates of image products by correlating stars detected in the UV image
with standard astronomical catalogues of stars.

The Module uvtFullFrameAst attempts to improve the accuracy of the aspect of
the UV sky image products generated prior to invoking this Module. The input
images have their sky coordinates determined based on information of
spacecraft attitude (Roll_RA, Roll_DEC, Roll_ROT; ICRS J2000) provided in the
Level-1 Aux data (‘*.att’ file in ‘mL1’ dataset). The typical accuracy of
these coordinates is $\sim$ 45 arc-sec RMS and up to 3 arc-min peak-to-peak.
Hence, there is a large scope for improvement by correlating stars detected in
the image products with standard star catalogues to first determine the
offsets and then applying corresponding corrections.

The algorithm followed is described here. First identify brightest point like
sources detected from the UVIT image (NUV/FUV) and record their RA-Dec (ICRS)
coordinates. They are then correlated with brightest entries in the USNO A2
optical star catalogue within a selected search radius ($\sim$ 3 arc minutes).
The USNO catalogue was reformatted by – (a) retaining stars brighter than 16
magnitude & (b) embedding an indexing scheme to enable very fast search by the
pipeline. ‘Good’ or ‘accidental’ matches of UVIT-USNO pairs are classified
based on a sequence of statistical tests carried out iteratively. At first the
brightest pairs are considered and progressively less bright pairs are also
included for this analysis. If successful in identifying confirmed matches, a
least square method is employed to extract the 3 parameters – shifts along RA
& Dec and a rotation around the centre of the image (similar to the algorithm
described for the Module uvtComputeDrift, Sec. A1.14). The next step is to
apply these corrections (shifts & rotation) to the 3 standard products, viz.,
UV image (‘Signal’), Exposure and Uncertainty arrays. The scheme for
application of these astrometric corrections to the UV image differs between
the case for individual Episode (when sub-division into pseudo-Episodes is not
selected), from that for multi-Episode case. While the astrometric corrections
are applied to centroids of individual photons in the former case, the shift &
rotational transformations are applied on the sub-divided array elements for
the latter.

In the Sky Imaging Chain L2_PC -

When this uvtFullFrameAst Module is called by the Sky Imaging chain L2_PC for
an individual Episode, the corrections are applied to the centroids (RA, Dec)
of each photon event and the master table of events is updated. Two additional
columns are introduced in this master table, which hold the astrometry
corrected coordinates (details given in Sec. A1.17 for Module uvtShiftRot,
Task-A, PC mode). The final UV image is generated by populating these photons
in Signal array of 4800$\times$4800 size. This process ensures minimal loss of
precision (angular resolution) while applying astrometric corrections. Similar
corrections for the Exposure and Uncertainty arrays are implemented by
physical movements of pixel contents as described for Module uvtShiftRot (Sec.
A1.17, Task-A, INT mode; first pixel sub-division from 4800$\times$4800 to
9600$\times$9600; re-gridding individual sub-pixels by applying
transformation; & finally 2x2 binning).

In the Driver Scheme -

When this uvtFullFrameAst Module is called by the Driver Scheme to apply
astrometric corrections to the combined multi-Episode products, all 3 arrays
viz., Signal, Exposure and Uncertainty are handled identically. In this case,
Signal array also undergoes the same scheme of corrections for the two shifts
and the rotation, as implemented for the Exposure and Uncertainty arrays in
the case for individual Episodes described in the preceding para.

In addition to using the optical catalogue USNO A2, bright NUV & FUV source
catalogues from GALEX mission are also used to correlate bright point like
sources from UVIT images. The good matches of UVIT-GALEX pairs are also used
to extract the offset corrections, but they are only recorded in a log file.
The details of star match ‘success’ / ‘failure’ with Optical & UV catalogues
are recorded as HISTORY / COMMENT entries on image HEADERs.

All the image products Signal (counts/sec), Exposure (no of frames) &
Uncertainty (counts/sec) are of 4800$\times$4800 size and in RA-Dec (ICRS;
J2000) coordinate system. They all are stored in the sub- directory named
‘uvtFullFrameAst_6.3’ either below a directory labeled by the specific Episode
(see Appendix-9) or a directory identifying the “group” (Band/ Filter/ Window)
for multi-Episode case (see Appendix-10). In case of failure of this
astrometry block, the set of resulting products contain arrays identical to
pre-astrometry images with adequate qualification in header keywords of the
failure.

The standard bundle of pipeline products archived and disseminated by ISSDC
includes the Signal image product from this Module as final UV sky image in
Astronomical coordinates, corresponding to every Episode generated by the Sky
Imaging chain (L2_PC), as well as combined multi-Episode images generated by
the Driver Scheme for every “group”. The corresponding Exposure and
Uncertainty products are also included.

Appendix 2 : Relative time shifts between the three Bands
In spite of a common Master Clock used by all three Bands of UVIT, the timing
details of detector read out electronics lead to systematic shifts in the time
stamps recorded on individual frames. These shifts depend on the imaging
parameters configured. The relative time shifts most relevant for the pipeline
are between the band used to obtain Relative Aspect Series and the Imaging UV
bands. This has been calibrated (in seconds unit) to be :

t_RAS - t_img = t0_RAS - (-T_Img_frame/ 2)

where ‘t0_RAS’ depends on the band generating RAS, its imaging mode &
parameters; & ‘T_Img_frame’ is the frame integration time of the imaging Band
(NUV / FUV); t0_RAS =-0.427; for drift tracking by VIS band in INT mode; full
512$\times$512 field; t0_RAS = -(T_RAS_frame/2); for drift tracking by NUV
band in PC mode; any window size; where ‘T_RAS_frame’ is the frame integration
time of the tracking Band (NUV).

Appendix 3 : Transformations between the Detector and Spacecraft coordinate
systems

The Detector coordinate system for each band is defined by the X-Y axes of its
electronic sensor (Star-250), and the axis normal to this plane corresponds to
the optic axis of the telescope (either directly as for the FUV & VIS bands,
or via one reflection with a plane surface; see Fig. 1). The rotation angle
about the optic axis is denoted by ‘$\theta$’ in the detector system. The
Spacecraft coordinate system comprise of the axes Roll, Yaw & Pitch which is
defined by the structure of the spacecraft. These two systems are
interconnected through the details of mounting of sub-systems of UVIT on to
the spacecraft’s mechanical interface. Nominally, the optic axis is aligned
parallel to the Roll axis and the (X, Y) and (Yaw, Pitch) are connected
through a single angle of rotation about an axis normal to all these 4 axes.
Similarly, one rotation angle connects any pair of detectors for two bands.
All these angles were initially measured during optical alignment tests in the
laboratory. These were subsequently validated andrefined by in orbit
measurements during the Performance Verification phase.

The transformations between detector (X, Y, $\theta$) and spacecraft (Roll,
Yaw & Pitch) are implemented as matrices for band, BND, as RPYTOXYTHETA_BND,
{BND : FUV / NUV / VIS}, populated with numerical values, along with a
corresponding plate scale. The reverse transformations, XYTHETATORPY_BND, are
generated internally by matrix inversion.

RPYTOXYTHETA_FUV : -0.00249798, 0.29636841, 0.29636841, 0.00249798
RPYTOXYTHETA_NUV : 0.15423, 0.25153, -0.25153, 0.15423
RPYTOXYTHETA_VIS : 0.1627, 0.2400, 0.2400, -0.1627

The above are consistent with the angles between +Y and the -Yaw (measured
CCW) to be +0.483, +31.515 and +34.134 degrees for the FUV, NUV & VIS bands
respectively. They are also consistent with the following directly observable
relations which connect image coordinates of a star in the NUV & VIS detectors
(accounting for slightly different plate scale for VIS; dX & dY are referenced
with respect to the respective array centres) :

dX_NUV = 1.01652 * dX_VIS - 0.04649 * dY_VIS
dY_NUV = - 0.04649 * dX_VIS - 1.01652 * dY_VIS

The corresponding relations connecting image coordinates of a star in the FUV
& VIS detectors are :

dX_FUV = -0.85093 * dX_VIS + 0.56645 * dY_VIS
dY_FUV = 0.56645 * dX_VIS - 0.85093 * dY_VIS

Appendix-4 : Directory structure of merged Level-1 data set (mL1)

-AS1G06_157T01_9000000772uvt_level1_mcap.xml
-AS1G06_157T01_9000000772uvt_level1.mkf

—aux
-AS1G06_157T01_9000000772uvt_level1.tct
—aux1
-AS1G06_157T01_9000000772uvt_level1.att
-AS1G06_157T01_9000000772uvt_level1.gyr
-AS1G06_157T01_9000000772uvt_level1.orb
—aux2
-AS1G06_157T01_9000000772uvt_level1.lbt
—aux3
—AS1G06_157T01_9000000772uvt_level1.orb

-hk
-AS1G06_157T01_9000000772uvt_level1.hk

—uvtF
——DarkF
——uvtF.01
-AS1G06_157T01_9000000772uvtFIIPC00F2_level1.bti
-AS1G06_157T01_9000000772uvtFIIPC00F2_level1.fits
-AS1G06_157T01_9000000772uvtFIIPC00F2_level1.gti
——uvtF.02
-AS1G06_157T01_9000000772uvtFIIPC00F0_level1.bti
-AS1G06_157T01_9000000772uvtFIIPC00F0_level1.fits
-AS1G06_157T01_9000000772uvtFIIPC00F0_level1.gti
——uvtF.03

…

—uvtN
——DarkN
——uvtN.01
-AS1G06_157T01_9000000772uvtNIIPC00F5_level1.bti
-AS1G06_157T01_9000000772uvtNIIPC00F5_level1.fits
-AS1G06_157T01_9000000772uvtNIIPC00F5_level1.gti
——uvtN.02
-AS1G06_157T01_9000000772uvtNIIPC00F0_level1.bti
-AS1G06_157T01_9000000772uvtNIIPC00F0_level1.fits
-AS1G06_157T01_9000000772uvtNIIPC00F0_level1.gti
——uvtN.03

…

—uvtV
——DarkV
——uvtV.01
-AS1G06_157T01_9000000772uvtVIIIM00F2_level1.bti
-AS1G06_157T01_9000000772uvtVIIIM00F2_level1.fits
-AS1G06_157T01_9000000772uvtVIIIM00F2_level1.gti
——uvtV.02
-AS1G06_157T01_9000000772uvtVIIIM00F2_level1.bti
-AS1G06_157T01_9000000772uvtVIIIM00F2_level1.fits
-AS1G06_157T01_9000000772uvtVIIIM00F2_level1.gti
——uvtV.03

…

Appendix-5 : Directory structure of UVIT Calibration Database (CAL_DB)

-change.log
-readme.txt

-AV_PH_ENERGY (scalar)
–FUV
-calibfile.fits
–NUV
-calibfile.fits
–VIS
-calibfile.fits

-BAD_PIXELS (2-D array 512 x 512)
–FUV
—IM
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits
—PC
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits

–NUV
—IM
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits
—PC
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits

–VIS
—IM
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits
—PC
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits

-BIAS_CORR (table : 3 col x 4097 row)
–FUV
—3X3
-calibfile.fits
—5X5
-calibfile.fits

–NUV
—3X3
-calibfile.fits
—5X5
-calibfile.fits

–VIS
—3X3
-calibfile.fits
—5X5
-calibfile.fits

-DARK (2-D array 512 x 512)
-darkend.fits
-darkstart.fits

-DISTORTION (Two 2-D arrays 512 x 512;
…….. first for X axis & second for Y axis)
–DETECTOR
—FUV
-calibfile.fits

—NUV
-calibfile.fits

—VIS
-calibfile.fits

–OPTICS
—FUV
—–F0
-calibfile.fits

…
—–F7
-calibfile.fits

—NUV
—–F0
-calibfile.fits

…
—–F7
-calibfile.fits

—VIS
—–F0
-calibfile.fits

…
—–F5
-calibfile.fits

-EXPOSURE_TEMPLATE (2-D array 1200 x 1200)
–FUV
—IM
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits
—PC
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits

–NUV
—IM
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits
—PC
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits

–VIS
—IM
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits
—PC
—-100X100
-calibfile.fits

…
—-512X512
-calibfile.fits

-FLAT_FIELDS_FILTER (2-D array 512 x 512)
–FUV
—IM
—-F0
-calibfile.fits

…
—-F7
-calibfile.fits

—PC
—-F0
-calibfile.fits

…
—-F7
-calibfile.fits

–NUV
—IM
—-F0
-calibfile.fits

…
—-F7
-calibfile.fits

—PC
—-F0
-calibfile.fits

…
—-F7
-calibfile.fits

–VIS
—IM
—-F0
-calibfile.fits

…
—-F5
-calibfile.fits

—PC
—-F0
-calibfile.fits

…
—-F5
-calibfile.fits

-QE_TEMP (table : 9 col x 20 row)
–FUV
—IM
-calibfile.fits
—PC
-calibfile.fits

–NUV
—IM
-calibfile.fits
—PC
-calibfile.fits

–VIS
—IM
-calibfile.fits
—PC
-calibfile.fits

Appendix-6 Directory structure for DataIngest output (Integration mode; INT)

-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.crcFailedList
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.dataIngestOut
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.info
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.missingFrameList
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.timeCorrection

-Dark
–AS1A03_103T01_9000001132uvtVIIIM00F4_l2_darkbegin.fits
–AS1A03_103T01_9000001132uvtVIIIM00F4_l2_darkend.fits

-SignalFrames
–AS1A03_103T01_9000001132uvtVIIIM00F4_l2_t2734052.8140_f16_di.fits
–AS1A03_103T01_9000001132uvtVIIIM00F4_l2_t2734053.7900_f32_di.fits
–AS1A03_103T01_9000001132uvtVIIIM00F4_l2_t2734054.7670_f48_di.fits

…

…

Appendix-7 Directory structure for DataIngest output (Photon Counting mode;
PC)

-AS1G06_157T01_9000000772uvtFIIPC00F6_l2_di.crcFailedList
-AS1G06_157T01_9000000772uvtFIIPC00F6_l2_di.dataIngestOut
-AS1G06_157T01_9000000772uvtFIIPC00F6_l2_di.events
-AS1G06_157T01_9000000772uvtFIIPC00F6_l2_di.image
-AS1G06_157T01_9000000772uvtFIIPC00F6_l2_di.info
-AS1G06_157T01_9000000772uvtFIIPC00F6_l2_di.missingFrameList
-AS1G06_157T01_9000000772uvtFIIPC00F6_l2_di.timeCorrection

–Dark
-AS1G06_157T01_9000000772uvtFIIPC00F6_l2_darkbegin.fits
-AS1G06_157T01_9000000772uvtFIIPC00F6_l2_darkend.fits

Appendix 8 Directory structure for the outputs from the Relativistic Aspect
Chain for Integration Mode (RA_INT)

DataIngest_6.3

-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.crcFailedList
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.crcFailedList
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.dataIngestOut
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.info
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.missingFrameList
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_di.timeCorrection

-Dark
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_darkbegin.fits
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_darkend.fits

-SignalFrames
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_t2734052.8140_f16_di.fits
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_t2734053.7900_f32_di.fits

…

…

-uvtComputeDrift_6.3
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_dr.fits
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_dr.info
-observation.txt

-uvtRefFrameCal_6.3
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_rfc.info

-Centroid
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_t2734053.790000_f1_rf_centroid.fits
-AS1A03_103T01_9000001132uvtVIIIM00F4_l2_t2734054.767000_f2_rf_centroid.fits

…

…

Appendix 9 : Directory structure for the outputs from the Level-2 Sky Imaging
Chain for Photon Counting Mode (L2_PC)

DataIngest_6.3

-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_di.crcFailedList
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_di.dataIngestOut
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_di.events
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_di.image
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_di.info
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_di.missingFrameList
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_di.timeCorrection

-Dark
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_darkbegin.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_darkend.fits

-uvtExposureFrames_6.3
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000_f1_exp_fi.fits

-uvtFlippedRegImage_6.3
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000_f1_10Per_rg.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000
………………………._f1_expFlipped_rg.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000
………………………._f1_NoiseMapFlipped_rg.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000
………………………._f1_sigFlipped_rg.fits

-uvtFrameIntegration_6.3
–NOISE_MAP
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t2734148.0000
………………………_f1_sig_noise_map_sig.fits
–SignalFrames
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t2734148.0000
………………………_f1_sig_fi.fits
–SignalFrames_DividedWithExposure
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t2734148.0000
………………………_f1_sig_Sig_DividedWithExp.fits

-uvtFullFrameAst_6.3
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_as_Exp.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_as_NoiseMap.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_as_Sig.fits
-star_raDec_frmOptics_catalogueWith_10Stars.txt
-star_raDec_frmOptics_catalogueWith_5Stars.txt
-star_radec.txt

-uvtRADECImage_6.3
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000
…………………………_f1_noise_ra-decnoise.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000
…………………………_f1_sig_ra-decexp.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000_f1_sig_ra-dec.fits

-uvtRegAvg_6.3
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000_f1_exp_regAvg.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000
…………………………_f1_noiseMap_regAvg.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t0.0000_f1_sig_regAvg.fits

-uvtShiftRot_6.3
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_radec.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_snr.fits
-AS1A03_103T01_9000001132uvtNIIPC00F1_l2_t9999.0000_f1_img_fi.fits

Appendix-10 : Top level directories for products from Driver Scheme (with some
additional details for Combined multi-Episode products)

-/FUV_FullFrameAst_F3_W511
–uvtFullFrameAst_6.3
-AS1A03_103T01_9000001132uvtFIIPC00F3_l2_as_Exp.fits
-AS1A03_103T01_9000001132uvtFIIPC00F3_l2_as_NoiseMap.fits
-AS1A03_103T01_9000001132uvtFIIPC00F3_l2_as_Sig.fits
-star_raDec_frmOptics_catalogueWith_5Stars.txt
-star_radec.txt

–/FUV_Final_F3_W511
-F3_W511_FinalImage_Exp.fits
-F3_W511_FinalImage_NoiseMap.fits
-F3_W511_FinalImage_Sig.fits

-/FUV_FullFrameAst_F2_W511
-/FUV_Final_F2_W511
-/NUV_FullFrameAst_F6_W511
-/NUV_Final_F6_W511
-/NUV_FullFrameAst_F3_W511
-/NUV_Final_F3_W511
-/NUV_FullFrameAst_F2_W511
-/NUV_Final_F2_W511
-/NUV_FullFrameAst_F1_W511
-/NUV_Final_F1_W511
-/_RAPC
-/_FUV_10
-/_NUV_10
-/_FUV_9
-/_NUV_9
-/_FUV_8
-/_NUV_8
-/_FUV_7
-/_NUV_7
-/_FUV_6
-/_NUV_6
-/_FUV_5
-/_NUV_5
-/_FUV_4
-/_NUV_4
-/_FUV_3
-/_NUV_3
-/_FUV_2
-/_NUV_2
-/_FUV_1
-/_NUV_1
-/uvit

Appendix-11 : All user selectable parameters

List of all user selectable switch settings and parameters for the pipeline
(through Parameter Interface Library, PIL), are presented in a tabular form
(see Table 7). The sequence of parameters are grouped by : DRIVER_SCHEME and
RA_INT, RA_PC & L2_PC chains. Parameter names in bold font indicate them to be
tweaked frequently by users.

Table 7:  List of all user selectable switch settings and parameters available
through Parameter Interface Library (PIL). The sequence of items are grouped
in the following order : (a) DRIVER_SCHEME and (b) RA_INT, RA_PC & L2_PC
chains. Parameters frequently tweaked by the users are highlighted by bold
font.

Serial | Parameter name | Processing | Suggested | Description | Comments
---|---|---|---|---|---
No. | (bold indicates | Chain | Default | (switch logic: |
| frequently |  | value | ‘1’/‘y’ for ON; |
| tweaked ones) |  |  | ‘0’/‘n’ for OFF) |
| Parameters for | Processing |  |  |
| Driver Scheme | Chain |  |  |
1 | NUVonNUVflag | DRIVER_SCHEME | n | Switch for forcing all drift generations | Turn ON only if
|  |  |  | using NUV only (i.e. ignore all VIS) | VIS data NOT
|  |  |  |  | reliable
2 | FUVonFUVflag | DRIVER_SCHEME | n | Switch for forcing all drift generation | Turn ON only if
|  |  |  | using FUV only (i.e. ignore all VIS & | VIS & NUV
|  |  |  | NUV data). Useful for generating | NOT available
|  |  |  | FUV images only |
3 | thresholdpc | DRIVER_SCHEME | 50 | Parameter related to threshold for star | ‘AVG’ &
|  | (& L2PC-NUV) |  | detection (starting value of ‘p’ in : | ‘SIGMA’ are
|  |  |  | Threshold = AVG + p * SIGMA; ‘p’ is | average and
|  |  |  | gradually decreased iteratively till | standard
|  |  |  | demanded no. of stars are achieved). | deviation of
|  |  |  | Used (1) for aligning UV images from | values (only non-
|  |  |  | different Episodes; & (2) in Astrometry | zero entries
|  |  |  | module. | considered) in
|  |  |  |  | pixels of image
|  |  |  |  | array. Only for
|  |  |  |  | PC mode.
4 | minimumTargetedStars | DRIVER_SCHEME | 6 | Targeted minimum no. of stars | (1) For PC mode
|  | (& RA_INT) |  | (iterations proceed with lower ‘p’ & | & (2) for INT
|  |  |  | detection threshold, till target is | mode.
|  |  |  | achieved) : (1) to align images from |
|  |  |  | different Episodes; & (2) detection of |
|  |  |  | stars in ‘uvtDetectStar’ module (INT |
|  |  |  | mode) |
5 | minimum_targetedstarspc | DRIVER_SCHEME | 5 | Success Criterion for Astrometry stage : |
|  | (& L2PC-NUV) |  | minimum no. of star matches with |
|  |  |  | Catalogue required; |
| Parameters | Processing |  |  |
| common to | Chains |  |  |
| multiple chains |  |  |  |
6 | level1indir | RA_INT, RA_PC, | - | Path to the directory holding Input |
|  | L2_PC, L2_INT |  | Level-1 data |
7 | caldbdir | RA_INT, RA_PC, | - | Path to the directory holding Calibration |
|  | L2_PC, L2_INT |  | Database (CAL_DB) |
8 | level2outdir | RA_INT, RA_PC, | - | Path to the directory holding Calibration |
|  | L2_PC, L2_INT |  | from the Driver Scheme (top level |
|  |  |  | location, below which products appear |
|  |  |  | in a structured manner) |
9 | ZipFlag | RA_INT, RA_PC, | y | Switch to indicate type of L1 data set : | ISSDC
|  | L2_PC, L2_INT |  | ‘tar’ (select ‘n’) or ‘zip’ (select ‘y’) | disseminates in
|  |  |  |  | ‘zip’ format
10 | utcFlag | RA_INT, RA_PC, | n | Switch to select clock for time reference | Must be ‘n’
|  | L2_PC, L2_INT |  | \- ‘y’ : use calibrated Universal Time |
|  |  |  | Clock (UTC); ‘n’ : use UVIT’s Master |
|  |  |  | clock |

… Continued

Table 7:  (Continued) : List of all user selectable switch settings and
parameters available through Parameter Interface Library, PIL.

Serial | Parameter name | Processing | Suggested | Description | Comments
---|---|---|---|---|---
No. |  | Chain | Default |  |
|  |  | value |  |
| Parameters for | RA_INT |  | For ‘drift’ extraction |
| Relative Aspect |  |  | from VIS images |
| Series Chain (INT) |  |  | (in Integration Mode) |
11 | history | RA_INT | y | Switch for history to be written (‘y’) or | Records the
|  |  |  | not (‘n’). History contains all the settings | settings : #11 to
|  |  |  | of the selectable switches & input | #39 as listed in
|  |  |  | parameters with which the Chain has | this table)
|  |  |  | ran. |
12 | clobber | RA_INT | y | Action in case the output directory | Default to erase
|  |  |  | chosen by the user is already existing. If | past contents (if
|  |  |  | clobber is YES (‘y’) then this directory | any)
|  |  |  | will be removed and created afresh by |
|  |  |  | pipeline. If clobber is NO (‘n’) then |
|  |  |  | pipeline will exit with an appropriate |
|  |  |  | error message |
13 | GTI_FLAG | RA_INT | 0 | GTI filtering to be done(1) or not(0). | Must be ’0’ (i.e.
|  |  |  |  | not using GTI
|  |  |  |  | filter)
14 | crcflag | RA_INT | n | Switch to select if CRC check to be | CRC check is
|  |  |  | carried out (‘y’), or not (‘n’). If ‘y’ is | ignored. Bit error
|  |  |  | selected, another switch (‘dropframe’, | rate in general is
|  |  |  | see #20) selects the action : to drop the | very low.
|  |  |  | affected packet alone or all packets for |
|  |  |  | that image frame. |
15 | ManualMode | RA_INT | n | Switch for Manual Mode operation to | Useful only when
|  |  |  | select stars - On(‘y’) or Off(‘n’); | either star field
|  |  |  | [used in “uvtComputeDrift” block]; | very complex or
|  |  |  | enters interactive mode for this block | severe detector
|  |  |  | alone, and the rest of the processes run | artifacts (&
|  |  |  | automatically]. | normal run with
|  |  |  |  | ‘n’ has FAILED)
16 | channel | RA_INT | VIS | Selection of Band for which to run | Normally only
|  |  |  |  | VIS band is used
|  |  |  |  | in Integration
|  |  |  |  | (INT) Mode
17 | junkfileflag | RA_INT | 1 | Switch for handling artifacts of VIS | VIS artifact
|  |  |  | detector (‘horizontal stripes’ etc. in VIS | handler must be
|  |  |  | images) - ‘1’ : ON; ‘0’ : OFF | ON
18 | thresholdforjunkFrame | RA_INT | 5000 | Threshold (pixel ADU) value for | Pixel threshold
|  |  |  | identifying ‘artifacts’ in VIS images | value of VIS
|  |  |  | (Threshold for artifact detection) | artifacts from
|  |  |  |  | experience
19 | darkframeFlag | RA_INT | 1 | Switch for Dark Subtraction: ‘1’ | Dark subtraction
|  |  |  | =substract Dark; ‘0’ = no action | must be ON (‘1’)
20 | dropframe | RA_INT-DataIngest | 0 | Switch to select action if CRC check | Relevant only if
|  |  |  | fails : ‘1’ = entire image frame to be | switch for CRC
|  |  |  | discarded; or ‘0’ = only the individual | test is turned ON
|  |  |  | failed packets (2048 bytes) to be | (‘crcflag’ = ‘y’;
|  |  |  | discarded. | see #14 above)
21 | ThresholdValue | RA_INT | 400000 | Threshold value to identify pixel with | Cosmic Ray
|  |  |  | Cosmic Ray hit (for INT mode) | detection is
|  |  |  |  | effectively OFF
22 | flatfieldFlag | RA_INT | 1 | Flat Field correction Switch : ‘1’= apply | Flat Field
|  |  |  | Flat Field correction; ‘0’= no action | correction must
|  |  |  |  | be ON (‘1’)
23 | Nacc | RA_INT | 1 | Effectively selects the size of the Time | Allowed values
|  |  |  | bin for drift extraction; ‘Nacc’ is the no. | include any
|  |  |  | of successive raw INT mode frames | integer : 1 / 2 / 3 /
|  |  |  | accumulated to generate a single image | 4 … etc. The
|  |  |  | (from which stars are identified) & | value of 1 is
|  |  |  | processed further | optimal for
|  |  |  |  | typical spacecraft
|  |  |  |  | drift.
24 | refineWindow | RA_INT | 15 | Size (pixel unit) of the square window | Selection MUST
|  |  |  | considered (centered on each star | be ‘15’
|  |  |  | candidate in the First-cut list) to further |
|  |  |  | shortlist identifying local maxima |
|  |  |  | (leading to generate Refined list); |

… Continued

Table 7:  (Continued) : List of all user selectable switch settings and
parameters available through Parameter Interface Library, PIL.

Serial | Parameter name | Processing | Suggested | Description | Comments
---|---|---|---|---|---
No. |  | Chain | Default |  |
|  |  | value |  |
25 | centroidWindow | RA_INT | 3 | Size (pixel unit) of the square window | Selection MUST
|  |  |  | used to compute Centroid values (along | be ‘3’
|  |  |  | X & Y axes) for each entry in the |
|  |  |  | Refined list; |
26 | threshold | RA_INT | 10 | Parameter related to threshold for star | ‘AVG’ &
|  |  |  | detection - starting value of ‘p’ in : | ‘SIGMA’ are
|  |  |  | Threshold = AVG + p * SIGMA; ‘p’ is | average and
|  |  |  | gradually decreased iteratively till | standard
|  |  |  | required no. of stars are found. | deviation of
|  |  |  |  | values in pixels
|  |  |  |  | (with outliers
|  |  |  |  | removed) in dark
|  |  |  |  | substracted
|  |  |  |  | image array (for
|  |  |  |  | INT mode only).
27 | framesToBeDiscard | RA_INT | 1 | Number of initial images (each obtained | Valid range of
|  |  |  | by accumulating ‘Nacc’ raw images) to | values : 0/ 1/ 2/
|  |  |  | be ignored (skipped) prior to identifying | … less than the
|  |  |  | the Reference Frame (or its beginning | total no. of
|  |  |  | sample) | images.
|  |  |  |  | Can be used to
|  |  |  |  | skip data patch
|  |  |  |  | with unusually
|  |  |  |  | large drift.
28 | averageFactor | RA_INT | 1 | A second level of Time bin selection : | Valid range of
|  |  |  | centroids of detected stars from selected | values : 1/ 2/ 3/…
|  |  |  | number of successive ‘accumulated’ | etc.
|  |  |  | frames (each comprising of ‘Nacc’ raw | Optimal value for
|  |  |  | frames) are averaged to define the | typical drift is
|  |  |  | Reference Frame & similarly averaged | ‘1’.
|  |  |  | centroid tables for future time bins; |
29 | freqDomainFilterFlag | RA_INT | 2 | Switch to select kind of filtering on the | Default value is
|  |  |  | Drift Series (low pass filtering) : ‘0’= | conservative (by-
|  |  |  | Time domain; ‘1’= Frequency domain; | passing the
|  |  |  | & ‘2’= no Filtering; | filter). Under
|  |  |  |  | special
|  |  |  |  | circumstances,
|  |  |  |  | the filter can be
|  |  |  |  | useful.
30 | freq_value | RA_INT | 0.2 | Cut-off frequency (Hz); | Default is max.
|  |  |  | Relevant only if Frequency domain | allowed,
|  |  |  | filtering is selected; (i.e. | corresponding to
|  |  |  | ‘freqDomainFilterFlag’=‘1’, see #29 | the bandwidth for
|  |  |  | above) | drift extraction
|  |  |  |  | from VIS. Lower
|  |  |  |  | values are valid.
31 | orderPitch | RA_INT | 1 | Polynomial order for filtering time series | Choice is
|  |  |  | of PITCH component of drift | appropriate for
|  |  |  |  | default Time
|  |  |  |  | Window (4 sec).
32 | orderYaw | RA_INT | 1 | Polynomial order for filtering time series | See #31
|  |  |  | of YAW component of drift |
33 | orderRoll | RA_INT | 1 | Polynomial order for filtering time series | See #31
|  |  |  | of ROLL component of drift |
34 | typeFiltering | RA_INT | 2 | Switch for selection among 3 options in | Global option fits
|  |  |  | Time domain filtering : ‘0’= global; | the entire time
|  |  |  | 1=polynomial; 2= local (sliding | series of drift at
|  |  |  | polynomial) ; | once. Local
|  |  |  |  | option fits many
|  |  |  |  | times, using a
|  |  |  |  | sliding Time
|  |  |  |  | Window
|  |  |  |  | (‘deltaTime’ = 4
|  |  |  |  | sec, see #35
|  |  |  |  | below).
35 | deltaTime | RA_INT | 4 | Selection of Time Window for the ‘local’ |
|  |  | (seconds) | option of Time domain filtering; |
|  |  |  | (Relevant only if ‘typeFiltering’=2, see |
|  |  |  | #34 above) |

… Continued

Table 7:  (Continued) : List of all user selectable switch settings and
parameters available through Parameter Interface Library, PIL.

Serial | Parameter name | Processing | Suggested | Description | Comments
---|---|---|---|---|---
No. |  | Chain | Default |  |
|  |  | value |  |
36 | diffDist | RA_INT | 1 | Parameter for drift computation. | Search distance
|  |  |  | Selection of initial search distance (pixel | is gradually
|  |  |  | unit) for identifying star matches among | increased if no
|  |  |  | images from successive time bins; | match is found.
|  |  |  |  | (up to a fixed
|  |  |  |  | max. value).
37 | GenMatchStarsFile_flag | RA_INT | 0 | Switch regarding writing record of star |
|  |  |  | matched star-pair lists from two |
|  |  |  | successive time bins; ‘1’= write & ‘0’= |
|  |  |  | do not write; |
38 | shiftRotDetAlgoFlag | RA_INT | 1 | Switch to select (among 3 available | Equal weights
|  |  |  | options) the scheme for computation of | to each star
|  |  |  | drift. The 3 choices are : (1) Equal | provides uniform
|  |  |  | weight to each star & rotation angle | representation to
|  |  |  |  d_theta, between successive time | the full sky field,
|  |  |  | bins is small; (2) Intensity based | improving
|  |  |  |  weight; (3) d_theta can be large. | precision of the
|  |  |  |  | extracted drift.
39 | flag_thetaComp | RA_INT | 0 | Switch to include or exclude ‘rotation’ |
|  |  |  |  (d_theta), in drift computation; ‘1’ = |
|  |  |  |  d_theta parameter is included along with |
|  |  |  | ‘Xshift’ & ‘Yshift’; & ‘0’ = only ‘Xshift’ |
|  |  |  | & ‘Yshift’ to be extracted; |
| Parameters for | RA_PC |  | For ‘drift’ extraction from |
| Relative Aspect |  |  | NUV /FUV photon event list |
| Series Chain (PC) |  |  | (in Photon Counting Mode) |
40 | historyrapc | RA_PC | y | Switch to retain history or not; (similar | Records settings
|  |  |  | to ‘history’, see #11 above); | of all switches &
|  |  |  |  | parameters for
|  |  |  |  | the RA_PC
|  |  |  |  | Chain (#40 to
|  |  |  |  | #66 as listed in
|  |  |  |  | this table)
41 | clobberrapc | RA_PC | y | Action in case the output directory |
|  |  |  | chosen by the user is already existing; |
|  |  |  | (similar to ‘clobber’, see #12 above); |
42 | GTI_FLAGrapc | RA_PC-DataIngest | 0 | GTI filtering to be done(1) or not(0) | Not using GTI
|  |  |  |  | filter
43 | crcflagrapc | RA_PC | n | Switch to select if CRC check to be | CRC check is
|  |  |  | carried out (‘y’), or not (‘n’). If ‘y’ is | ignored. Bit error
|  |  |  | selected, another switch | rate in general is
|  |  |  | (‘dropframerapc’, see #44) selects the | very low.
|  |  |  | action : to drop the affected packet alone |
|  |  |  | or all packets for that image frame. |
44 | dropframerapc | RA_PC-DataIngest | 0 | Switch to select action if CRC check | Relevant only if
|  |  |  | fails : ‘1’ = entire image frame to be | switch for CRC
|  |  |  | discarded; or ‘0’ = only the individual | test is turned ON
|  |  |  | failed packets (2048 bytes) to be | (‘crcflagrapc’ =
|  |  |  | discarded | ‘y’; see #43
|  |  |  |  | above).
45 | parityFlagrapc | RA_PC | 2 | Switch for qualifying criteria of photon | Default option
|  |  |  | events based on their parity tests; ‘1’= | tests the 2 crucial
|  |  |  | all three words for the event must have | words. The 3-rd
|  |  |  | correct parity, ‘2’= the two words | word holds event
|  |  |  | holding X & Y centroids must have | asymmetry.
|  |  |  | correct parity. | Statistics of
|  |  |  | The option ‘0’ by-passes parity tests | rejected events
|  |  |  | completely. | based correction
|  |  |  |  | is applied to
|  |  |  |  | retain
|  |  |  |  | photometric
|  |  |  |  | accuracy.

… Continued

Table 7:  (Continued) : List of all user selectable switch settings and
parameters available through Parameter Interface Library, PIL.

Serial | Parameter name | Processing | Suggested | Description | Comments
---|---|---|---|---|---
No. |  | Chain | Default |  |
|  |  | value |  |
46 | thresholdMultphrapc | RA_PC | 9999 | Threshold for identifying multiple | Test to identify
|  |  |  | photon events (from asymmetry in the | multi-photon
|  |  |  | event’s 5x5 pixel footprint); | events is turned
|  |  |  | Event with ‘Max-Min’ among 4 corners | OFF.
|  |  |  | above selected ‘thresholdMultphrapc’ | Recommended
|  |  |  | are flagged as multi-photon event. | value to turn the
|  |  |  |  | test ON is ‘100’.
47 | flatfieldFlagrapc | RA_PC | 0 | Switch for applying Flat field correction |
|  |  |  | : ‘1’ = apply; ‘0’ = no action; |
48 | thresholdrapc | RA_PC | 10 | Parameter related to threshold for star | Similar to
|  |  |  | detection (first-cut peaks); Starting value | ‘thresholdpc’, see
|  |  |  | of ‘p’ in : Threshold = AVG + p * | #3 above.
|  |  |  | SIGMA; ‘p’ is gradually decreased |
|  |  |  | iteratively till required no. of stars are |
|  |  |  | found. |
49 | GenMatchStarsFile_flagrapc | RA_PC | 0 | Switch regarding writing record of star | Similar to
|  |  |  | matched star-pair lists; ‘1’= write & | ‘GenMatchStarsF
|  |  |  | ‘0’= do not write; | ile_flag’, see #37
|  |  |  |  | above.
50 | refinedWinSizerapc | RA_PC | 15 | Neighbourhood criteria for identifying | Selection MUST
|  |  |  | stars; (pixel unit) | be ‘15’. Similar to
|  |  |  |  | ‘refineWindow’,
|  |  |  |  | see #24 above.
51 | centroidWinSizerapc | RA_PC | 3 | Size of square box to compute Centroids | Selection MUST
|  |  |  | for detected stars (pixel unit); | be ‘3’. Similar to
|  |  |  |  | ‘centroidWindow’,
|  |  |  |  | see #25 above.
52 | framesDiscardrapc | RA_PC | 2 | Number of initial frames to be discarded | Default choice of
|  |  |  | before initiating accumulation of frames; | ‘2’ is optimal,
|  |  |  | Valid values : 0 / 1 / 2/ … less than total | since only the
|  |  |  | frames. | very first frame is
|  |  |  |  | found to be
|  |  |  |  | ‘disturbed’.
53 | framesComputerapc | RA_PC | 90 ( 3 | Number of successive frames to be | Selection
|  |  | sec per | combined (accumulated) for generating | depends on NUV
|  |  | image) | every image to be used for extracting | brightness of
|  |  |  | drift; (effectively selects the Time bin) | field stars
54 | framesToBeDiscardrapc | RA_PC | 1 | Number of initial ‘combined’ | The default value
|  |  |  | (accumulated) frames to be discarded | ‘1’, ignores
|  |  |  | prior to identifying the Reference Frame | initial 3 sec,
|  |  |  | (or its beginning sample). | which is
|  |  |  | Valid choices are 0 /1 / 2/ 3 …etc., less | appropriate.
|  |  |  | than total data set. | Can be used to
|  |  |  |  | skip data patch
|  |  |  |  | with unusually
|  |  |  |  | large drift.
55 | averageFactorrapc | RA_PC | 1 | A second level of selection to widen the | Optimal value
|  |  |  | Time bin : number of successive | for typical drift is
|  |  |  | ’combined’ (accumulated) frames, whose | ‘1’. Similar to
|  |  |  | star centroids need to be averaged to | ‘averageFactor’,
|  |  |  | construct Reference Frame (& also for | see #28 above.
|  |  |  | subsequent future Time bins) |
|  |  |  | Valid range of numbers : 1/ 2/ 3/… etc. |
|  |  |  | Larger number implies cruder time |
|  |  |  | sampling of drift. |
56 | flag_thetaComprapc | RA_PC | 0 | Switch to include (‘1’) or exclude (‘0’) | Similar to
|  |  |  |  ‘rotation’ (d_theta) in drift | ‘flag_thetaComp’,
|  |  |  | computation; | see #39 above.
57 | diffDistrapc | RA_PC | 1 | Parameter for drift computation. | Search distance is
|  |  |  | Selection of initial search distance (pixel | gradually
|  |  |  | unit) for identifying star matches among | increased if no
|  |  |  | centroids from successive time bins; | match is found.
|  |  |  |  | (up to a fixed
|  |  |  |  | max. value).
|  |  |  |  | Similar to
|  |  |  |  | ‘diffDist’; see
|  |  |  |  | #36 above.

… Continued

Table 7:  (Continued) : List of all user selectable switch settings and
parameters available through Parameter Interface Library, PIL.

Serial | Parameter name | Processing | Suggested | Description | Comments
---|---|---|---|---|---
No. |  | Chain | Default |  |
|  |  | value |  |
58 | freqDomainFilterFlag | RA_PC | 2 | Switch to select kind of low pass | Similar to
| rapc |  |  | filtering on the Drift Series; | ‘freqDomainFilter
|  |  |  |  | Flag’, see #29 above.
59 | freqValuerapc | RA_PC | 0.2 | Cut-off frequency (Hz); (Only for | Similar to
|  |  |  | Frequency domain filtering selection) | ‘freq_value’, see
|  |  |  |  | see #30 above.
60 | orderPitchrapc | RA_PC | 1 | Polynomial order for filtering PITCH | Similar to
|  |  |  | component of drift | ‘orderPitch’, see
|  |  |  |  | see #31 above.
61 | orderYawrapc | RA_PC | 1 | Polynomial order for filtering YAW | See #60
|  |  |  | component of drift |
62 | orderRollrapc | RA_PC | 1 | Polynomial order for filtering ROLL | See #60
|  |  |  | component of drift |
63 | typeFilteringrapc | RA_PC | 2 | Switch for selection among 3 options in | Similar to
|  |  |  | Time domain filtering; | ‘typeFiltering’,
|  |  |  |  | see #34 above.
64 | deltaTimerapc | RA_PC | 4 | Selection of Time Window for the ‘local’ |
|  |  | (seconds) | option of Time domain filtering; |
|  |  |  | (Relevant only if ‘typeFilteringrapc’=2, |
|  |  |  | see #63 above) |
65 | shiftRotDetAlgoFlag | RA_PC | 3 | Switch to select (among 3 available | The 3 algorithms
| rapc |  |  | options) the scheme for computation of | are described for
|  |  |  | drift | ‘shiftRotDetAlgo
|  |  |  |  | Flag’, see #38 above
66 | minimumTargetedStars | RA_PC | 4 | Minimum no. of stars demanded in the | Similar to
| rapc |  |  | module for star detection | ‘minimumTargeted
|  |  |  | (uvtDetectStar; PC mode) | Stars’, see #4 above;
| Parameters for | L2_PC (for |  | For generating NUV /FUV sky |
| Sky Imaging chain | NUV /FUV) |  | images from photon event list |
| (Level2PC) : |  |  | (in Photon Counting Mode) |
67 | historypc | L2_PC-NUV | y | Switch to write history or not; | Records settings
/68 | /historypcfuv | /L2_PC-FUV |  | (similar to ‘history’ in #11 above); | of all switches &
|  |  |  |  | parameters for
|  |  |  |  | the L2_PC Chain
|  |  |  |  | for NUV/ FUV;
|  |  |  |  | (#67/68 to
|  |  |  |  | #119/120 as
|  |  |  |  | listed in this
|  |  |  |  | table)
69 | clobberpc | L2_PC-NUV | y | Action in case the output directory |
/70 | /clobberpcfuv | /L2_PC-FUV |  | chosen by the user is already existing; |
|  |  |  | (similar to ‘clobber’ in #12 above); |
71 | GTI_FLAGpc | L2_PC-NUV | 0 | GTI filtering to be done(1) or not(0) | Not using GTI
/72 | /GTI_FLAGpcfuv | DataIngest |  |  | filter
|  | /L2_PC-FUV |  |  |
|  | DataIngest |  |  |
73 | crcflagpc | L2_PC-NUV | n | Switch to select if CRC check to be | CRC check is
/74 | /crcflagpcfuv | /L2_PC-FUV |  | carried out (‘y’), or not (‘n’). If ‘y’ is | ignored. Bit error
|  |  |  | selected, another switch (‘dropframepc’ | rate in general is
|  |  |  | /‘dropframepcfuv’, see #81/82 below) | very low.
|  |  |  | selects the action : to drop the affected |
|  |  |  | packet alone or all packets for that |
|  |  |  | image frame. |
75 | pathToOutputTarpc | L2_PC-NUV | - | path for storing the output products of | Not relevant
/76 | /pathToOutputTarpc | /L2_PC-FUV |  | L2_PC chain, when run as a stand alone | when running full
| fuv |  |  | chain; | Driver Scheme
77 | parityFlagpc | L2_PC-NUV | 2 | Switch for qualifying criteria of photon | Details similar to
/78 | /parityFlagpcfuv | /L2_PC-FUV |  | events based on their parity tests; | ‘parityFlagrapc’,
|  |  |  |  | see #45 above.
79 | thresholdMultphpc | L2_PC-NUV | 9999 | Threshold for identifying multiple | Test to identify
/80 | /thresholdMultphpcfuv | /L2_PC-FUV |  | photon events. | multi-photon
|  |  |  | Similar to ‘thresholdMultphrapc’, | events is turned OFF
|  |  |  | in #46 above; | Recommended value
|  |  |  |  | to turn it ON is ‘100’.

… Continued

Table 7:  (Continued) : List of all user selectable switch settings and
parameters available through Parameter Interface Library, PIL.

Serial | Parameter name | Processing | Suggested | Description | Comments
---|---|---|---|---|---
No. |  | Chain | Default |  |
|  |  | value |  |
81 | dropframepc | L2_PC-NUV | 0 | Switch to select action if CRC check | Relevant only if
/82 | /dropframepcfuv | DataIngest |  | fails : ‘1’ = entire image frame to be | switch for CRC
|  | /L2_PC-FUV |  | discarded; or ‘0’ = only the individual | test is turned ON
|  | DataIngest |  | failed packets (2048 bytes) to be | (‘crcflagpc’ /
|  |  |  | discarded | ‘crcflagpcfuv’ =
|  |  |  |  | ‘y’; see #73/ #74
|  |  |  |  | above).
83 | thr_One_crpc | L2_PC-NUV | 9999 | Value of the parameter no. 1 for | Cosmic Ray
/84 | /thr_One_crpcfuv | /L2_PC-FUV |  | identifying Cosmic Ray affected frames, | affected frame
|  |  |  | “N”, in equation : threshold = AVG + | identification is
|  |  |  | N*sqrt (AVG) + ST/(sqrt(AVG)) ; | effectively turned
|  |  |  | where AVG= average no of events per | OFF.
|  |  |  | frame; | Recommended
|  |  |  |  | value to turn it
|  |  |  |  | ON is ‘3’.
85 | thr_Two_crpc | L2_PC-NUV | 9999 | Value of the parameter no. 2 for | Cosmic Ray
/86 | /thr_Two_crpcfuv | /L2_PC-FUV |  | identifying Cosmic Ray affected frames, | affected frame
|  |  |  | “ST”; (see ‘thr_One_crpc’ / | detection is
|  |  |  | ‘thr_One_crpcfuv’, #83/ #84 above); | turned OFF.
|  |  |  |  | Recommended
|  |  |  |  | value to turn it
|  |  |  |  | ON is ‘10’.
87 | CentCorr_tobedonepc | L2_PC-NUV | 0 | Switch regarding application of |
/88 | /CentCorr_tobedonepc | /L2_PC-FUV |  | corrections to event centroids due to |
| fuv |  |  | Dark : ‘1’ = apply; ‘0’ = no action |
89 | CentBias_tobedonepc | L2_PC-NUV | 0 | Switch regarding application of |
/90 | /CentBias_tobedonepc | /L2_PC-FUV |  | corrections to event centroids due to |
| fuv |  |  | Bias (FPN) : ‘1’ = apply; |
|  |  |  | ‘0’ = no action |
91 | DetectDist_tobedone | L2_PC-NUV | 1 | Switch for Detector Distortion |
/92 | pc | /L2_PC-FUV |  | correction : ‘1’ = apply; |
| /DetectDist_tobedone |  |  | ‘0’ = no action |
| pcfuv |  |  |  |
93 | OpticDist_tobedone | L2_PC-NUV | 1 | Switch for Detector Distortion |
/94 | pc | /L2_PC-FUV |  | correction : ‘1’ = apply; |
| /OpticDist_tobedone |  |  | ‘0’ = no action |
| pcfuv |  |  |  |
95 | frameIntFlagpc | L2_PC-NUV | 0 | Switch selection for ’Frame Integration’ | Default is
/96 | /frameIntFlagpcfuv | /L2_PC-FUV |  | block : to divide the full data from the | ‘Episode’ case, to
|  |  |  | ‘Episode’ into smaller parts (‘pseudo- | use the full data
|  |  |  | Episode’-s) or not; ‘1’ = divide into | together (i.e. no
|  |  |  | multiple parts (‘pseudo-Episode’ case); | division into
|  |  |  | ‘0’ = all data used together as a | ‘pseudo-
|  |  |  | single set (‘Episode’ case); | Episode’-s).
97 | framesDiscardpc | L2_PC-NUV | 2 | Number of initial frames to be discarded | Valid range of
/98 | /framesDiscardpcfuv | /L2_PC-FUV |  | (prior to gridding photon events into | values : 0/ 1/ 2/
|  |  |  | 2-D array/(s) in ‘Frame Integration’ block) | … less than the
|  |  |  |  | total no. of
|  |  |  |  | images.
|  |  |  |  | Choice optimal,
|  |  |  |  | since only the
|  |  |  |  | very first frame is
|  |  |  |  | found to be
|  |  |  |  | ‘disturbed’.
99 | framesComputepc | L2_PC-NUV | 9400 | Number of successive frames to be | Relevant only if
/100 | /framesComputepcfuv | /L2_PC-FUV | (say) | combined together to form a ‘pseudo- | ‘pseudo-Episode’
|  |  |  | Episode’, in the ‘Frame Integration’ | case is selected
|  |  |  | block. | for dividing the
|  |  |  | Should not exceed the total no. of | full data from the
|  |  |  | frames in the full Episode. | ‘Episode’ into
|  |  |  | In general, the last ‘pseudo-Episode’ | multiple parts
|  |  |  | will consist of fewer no. of frames, when | (i.e.‘frameIntFlagpc’
|  |  |  | total no. is not an integral multiple of | /‘frameIntFlagpcfuv’
|  |  |  | this selection. | =‘1’; see #95 /#96)

… Continued

Table 7:  (Continued) : List of all user selectable switch settings and parameters available through Parameter Interface Library, PIL.  Serial | Parameter name | Processing | Suggested | Description | Comments
---|---|---|---|---|---
No. |  | Chain | Default |  |
|  |  | value |  |
101 | refinedWinSizepc | L2_PC-NUV | 15 | Neighbourhood criteria for identifying | Selection MUST
/102 | /refinedWinSize | /L2_PC-FUV |  | stars (pixel unit); | be ‘15’ (similar to
| pcfuv |  |  |  | ‘refineWindow’,
|  |  |  |  | see #24 above);
103 | centroidWinSizepc | L2_PC-NUV | 3 | Size of square box to compute Centroids | Selection MUST
/104 | /centroidWinSize | /L2_PC-FUV |  | for detected stars (pixel unit); | be ‘3’ (similar to
| pcfuv |  |  |  | ‘centroidWindow’,
|  |  |  |  | see #25 above);
105 | diffDistpc | L2_PC-NUV | 1 | Selection of initial search distance (pixel | Search distance is
/106 | /diffDistpcfuv | /L2_PC-FUV |  | unit) for identifying star matches | gradually
|  |  |  | between a pair of images from ‘pseudo- | increased if no
|  |  |  | Episode’-s; (used for ‘pseudo-Episode’ | match is found
|  |  |  | case in Frame Integration block) | (up to a fixed
|  |  |  |  | max. value).
107 | shiftRotDetAlgo | L2_PC-NUV | 1 | Switch to select (among 3 available | The 3 algorithms
/108 | Flagpc | /L2_PC-FUV |  | options) the algorithm for determining | are similar to
| /shiftRotDetAlgo |  |  | offsets (shift & rotation) between images | those described for
| Flagpcfuv |  |  | from a pair of ‘pseudo-Episode’-s; | ‘shiftRotDetAlgoFlag’,
|  |  |  | (used for ‘pseudo-Episode’ case in | see #38 above
|  |  |  | Frame Integration block) |
109 | flag_thetaComppc | L2_PC-NUV | 0 | Switch to include (‘1’) or exclude (‘0’) | Similar to
/110 | /flag_thetaComp | /L2_PC-FUV |  |  ‘rotation’ (d_theta) in computation | ‘flag_thetaComp’,
| pcfuv |  |  | of offset; (used for ‘pseudo-Episode’ | see #39 above;
|  |  |  | case in Frame Integration block) |
111 | thresholdpc | L2_PC-NUV (& | 50 | Threshold for star detection (first-cut | See details in #3
/112 | /thresholdpcfuv | DRIVER_SCHEME) | /10 | peaks) - starting multiplier, ‘p’, of sigma | above.
|  | /L2_PC-FUV |  | in : Threshold = AVG + p * SIGMA; | The parameter
|  |  |  | [used by Astrometry block; and | ‘thresholdpc’ is
|  |  |  | used for ‘pseudo-Episode’ case in Frame | common to
|  |  |  | Integration block] | Driver Scheme &
|  |  |  |  | L2_PC Chain for
|  |  |  |  | NUV.
113 | database_namepc | L2_PC-NUV | - | Path pointing to star catalogue (USNO |
/114 | /database_name | /L2_PC-FUV |  | A2) database; used for matching stars in |
| pcfuv |  |  | Astrometry block. |
115 | search_algo_for | L2_PC-NUV | 2 | Switch to select type of Search area in |
/116 | FullFrameAstpc | /L2_PC-FUV |  | the star Catalog : ‘1’ = Square box; |
| /search_algo_for |  |  | ‘2’ = Circular; |
| FullFrameAstpcfuv |  |  |  |
117 | Radi_searchpc | L2_PC-NUV | 0.05 | Dimension of Search area (length of | Default choice is
/118 | Radi_searchpcfuv | /L2_PC-FUV |  | square box or radius of circle) to find | based on
|  |  |  | matching stars from Catalogue; | accuracy of
|  |  |  | (in degrees) | spacecraft’s
|  |  |  |  | attitude.
119 | minimum_targeted | L2_PC-NUV | 5 | Success Criterion for Astrometry stage : | The parameter
/120 | starspc | /L2_PC-FUV |  | minimum no. of star matches with | ‘minimum_
| /minimum_targeted |  |  | Catalogue demanded; | targetedstarspc’ is
| starspcfuv |  |  |  | common to
|  |  |  |  | Driver Scheme &
|  |  |  |  | L2_PC Chain for
|  |  |  |  | NUV (see #5 above).

## Acknowledgements

We thank the anonymous referees for their useful suggestions which led to
improvements. The UVIT project is a result of collaboration between IIA,
Bangalore, IUCAA, Pune, TIFR, Mumbai, many centers of the Indian Space
Research Organization (ISRO), and the Canadian Space Agency. We thank these
organizations for their general support. We thank D Bhattacharya for his role
in organizing the pipeline requirements. The Ground Segment software teams of
ISRO at ISAC/URSC, Banglaore, ISTRAC, Bangalore & SAC, Ahmedabad have provided
significant support throughout the development of the pipeline. We gratefully
thank all the members of these teams for their support. We also thank members
of the ASTROSAT Project & the ASTROSAT Science Working Group for their
critical feedbacks. Finally, we thank numerous users of early versions of this
pipeline for their feedbacks.

* (1) Ghosh, S. K., Tandon, S. N., Joseph, P., et al., 2021, JApA, 42, 29
* (2) Kumar, A., Ghosh, S. K., Hutchings, J., et al., 2012, SPIE, 8443, 84431N
* (3) Tandon, S. N., Ghosh, S. K., Hutchings, J. B., et al., 2017a, CSci, 113, 583
* (4) Tandon, S. N., Hutchings, J. B., Ghosh, S. K., et al., 2017b, JApA, 38, 28
* (5) Tandon, S. N., Postma, J., Joseph, P., et al., 2020, AJ, 159, 158
* (6) Tandon, S. N., Subramaniam, A., Girish, V., et al., 2017c, AJ, 154, 128


# Probing the magnetic band gap of the ferromagnetic topological insulator
MnSb2Te4

P. Küppers1, J. Zenner1, S. Wimmer2, G. Springholz2, O. Rader3, M. Liebmann1,
M. Morgenstern1∗ 1II. Institute of Physics B and JARA-FIT, RWTH Aachen
University, 52074 Aachen, Germany  2Institut für Halbleiter- und
Festkörperphysik, Johannes Kepler Universität, Altenberger Straße 69, 4040
Linz, Austria  3Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-
Einstein-Straße 15, 12489 Berlin, Germany

###### Abstract

Mn-rich MnSb2Te4 is a ferromagnetic topological insulator with yet the highest
Curie temperature $T_{\rm C}=45-50$ K. It exhibits a magnetic gap at the Dirac
point of the topological surface state that disappears above $T_{\rm C}$. By
scanning tunneling spectroscopy, we probe this gap at different magnetic
fields and temperatures. We firstly reveal that the gap size shrinks, when an
in-plane magnetic field of up to $B_{\parallel}=3$ T is applied, but does not
close completely as the magnetization is only partially rotated in-plane. This
corroborates the magnetic origin of the gap and the complex magnetic
structure. In addition, we demonstrate significant spatiotemporal fluctuations
of the gap size at temperatures as low as $T_{\rm C}/2$, above which the
remanent magnetization indeed decays. This temperature is close to the
antiferromagnetic transition temperature observed for bulk-type single
crystals of MnSb2Te4, highlighting the important role of competing magnetic
orders in the formation of the favorable ferromagnetic topological insulator.
Our study, thus, provides crucial insights into the complex magnetic gap
opening of topological insulators that is decisive for quantum anomalous Hall
devices.

Corresponding author: M. Morgenstern, email<EMAIL_ADDRESS>
The quantum anomalous Hall effect (QAHE) offers quantized conductance and
lossless transport without the need for an external magnetic field $B$ Onoda03
; CXLiu08 ; YuScience10 . This implies applications, e.g., in metrology
FoxPRB18 . Combining topological insulators (TIs) with transition metal atoms
CXLiu08 ; YuScience10 ; Qiao10 ; Tokura19  led to the QAHE in Cr- and V- doped
(Bi, Sb)2Te3 Chang13 ; CheckelskyNP14 ; KouPRL14 ; BestwickPRL15 ; Kandala2015
with exact quantization down to a precision of $10^{-8}$ ChangCZNM15 ;
GrauerPRB15 ; FoxPRB18 ; GoetzAPL18 ; Okazaki2021 . Fundamentally, the effect
is based on the out-of-plane magnetization of ferromagnetically coupled
transition metal atoms that opens a gap within the topological surface state.
The gap features a non-trivial Chern number via the Berry curvature of the
topological Dirac cone Mong2010 ; Zhang2019 ; CXLiu08 ; YuScience10 ; Qiao10 ;
Tokura19 . Surprisingly, however, the experimental temperatures $T$ required
for observing the QAHE ($T<300$ mK Chang13 ; GrauerPRB15 ) were initially two
orders of magnitude lower than the ferromagnetic transition temperature
$T_{\rm C}\approx 20$ K Zhou2005 ; Figueroa2020 ; CheckelskyNP14 . This has
been improved by modulation doping, i.e., by concentrating the magnetic
dopants in distinct layers of the topological insulator and, thus, reducing
the disorder MogiAPL15 ; Xiao2018 . The QAHE then survives up to $T=2$ K,
still much lower than $T_{\mathrm{C}}$ MogiAPL15 ; Xiao2018 , which is likely
due to fluctuations of the Dirac point energy caused by electrostatic disorder
Chong2020 ; Fijalkowski2021 .

In contrast, intrinsic magnetic topological insulators (MTIs) enabled the
observation of the QAHE up to about $T_{\mathrm{C}}$ DengNatPhys2020 . Such
MTIs consist of MnX2Te4 septuple layers (X=Bi or Sb) with Te-X-Te-Mn-Te-X-Te
stacking Rienks ; HagmannNJP17 ; Wimmer2021  (Fig. 1d). Hence, one extra layer
of MnTe is inserted into each quintuple layer X2Te3 of conventional
topological insulators YuScience10 ; YeNatComm2015 ; LiMPRL15 . This aims at
reducing the disorder compared to randomly substituting X by Cr or V.
Accordingly, even for MnxX2Te3+x with $x<1$, the Mn containing septuple layers
are regularly distributed between unperturbed quintuple layers Hu2020 ; Rienks
. For such MnxBi2Te3+x, the QAHE indeed appeared up to $T\simeq 7$ K (precison
$\approx 10$%), i.e., very close to the magnetic transition at $T=10$ K
DengNatPhys2020 . On the other hand, for MnxBi2Te3+x, the appearance of a
magnetically induced gap in the topological surface state EremeevJAC17 ;
McQueeneyPRM19 ; McQueeneyPRB19 ; OtrokovAFMTI18 ; ChenPRM20 ; Sekine2021  has
remained experimentally controversial Rienks ; Yuan2020 ; OtrokovAFMTI18 ;
PRX1 ; PRX3 , which is likely due to its strong sensitivity on sample
preparation details as well as due to the predominantly antiferromagnetic
coupling of the Mn layers Shikin2021 ; Garnica2022 . In contrast, we have
recently revealed that MnSb2Te4 with slight Mn excess is a ferromagnetic
topological insulator (TI) with record high $T_{\rm C}=45-50$ K and a
pronounced band gap at the Fermi level $E_{\rm F}$ that opens precisely at and
below $T_{\mathrm{C}}$ Wimmer2021 . Moreover, the band gap size $\Delta(T)$
was found to be proportional to the magnetization $M_{\perp}(T)$ perpendicular
to the surface as theoretically expected Rosenberg12 ; Henk2012 . The
behaviour of $M_{\perp}$ is, however rather complex Wimmer2021 ; Ge2021 ;
Lai2021  as it reduces linearly with $T$ between $T_{\mathrm{C}}$ /2 and
$T_{\mathrm{C}}$ and exhibits a non-saturating magnetic moment of $\approx
1.5\,\mu_{\rm B}$ per Mn atom at $B=5$ T Wimmer2021 . In fact, ferromagnetic
MnSb2Te4 with slightly different stoichiometry displays a saturation of the
magnetization ($5\,\mu_{\rm B}$ per Mn atom) at $B=60$ T only Lai2021 . In
addition, nominally stoichiometric MnSb2Te4 shows both ferromagnetism
MurakamiPRB19 ; Ge2021 ; liu2021  and antiferromagnetism McQueeneyPRB19 ;
ChenPRM20 ; liu2021  depending on the synthesis conditions. This complex
magnetic behaviour is most likely related to the partial Mn-Sb exchange within
the septuple layers in the few % regime, which strongly depends on the growth
conditions liu2021 ; Riberolles2021 ; li2021 ; HuarXiv2020 ; Wimmer2021 ;
Lai2021 . On the other hand, it is exactly this Mn-Sb exchange within the Sb
layers that is responsible for the favorable combination of TI and
ferromagnetic properties in Mn-rich MnSb2Te4 Wimmer2021 ; li2021 .

Here, we probe the change of the ferromagnetic gap in epitaxial MnSb2Te4 by
scanning tunneling spectroscopy (STS) as a function of in-plane magnetic
fields $B_{\parallel}$ and at different temperatures. In particular, we
demonstrate that the gap of the topological surface state reduces with
increasing in-plane field that rotates the magnetization towards the surface,
thus decreasing the out-of-plane $M_{\perp}(T)$ (see Fig. 1a–c). Since the gap
size depends dominantly on $M_{\perp}$ Rosenberg12 ; Henk2012 ; Mong2010 ;
Sekine2021 , this result corroborates the magnetic origin of the gap. While
the applied in-plane field rotates the Mn spins preferentially towards the in-
plane direction, a large $B_{\parallel}\simeq 60$ T is required for complete
alignment (Fig. 1c) Wimmer2021 ; Lai2021 . This implies that a moderate
$B_{\parallel}$ leads to a gap reduction with spatial fluctuations instead of
a complete closure of the gap. Indeed, we find that the magnetic gap reduces
with $B_{\parallel}$, but does not close completely up to $B_{\parallel}=3$ T,
where it exhibits significant spatial variation of the gap size. This is
strong additional evidence that the origin of the gap is indeed the
topological Dirac cone. Moreover, we find that the gap slowly fluctuates at
elevated temperatures towards $T_{\rm C}$, where the remanent magnetization
starts to decay. We map the spatiotemporal fluctuations by recording
sequential gap size maps $\Delta(x,y)$ of the same area, featuring lateral
patches of enhanced gap that slowly meander across the surface on the scale of
hours, similar to magnetic domains close to a phase transition Shpyrko2007 ;
Kronseder2015 ; Lachman16 .

Epitaxial MnSb2Te4 films with 200 nm thickness were grown by molecular beam
epitaxy Wimmer2021  and transferred in ultrahigh vacuum to two scanning
tunneling microscopes (STMs) operating down to $T=4.3$ K and $T=6$ K,
respectively Mashoff2009  (Supplementary Section S1). The voltage $V$ is
applied to the sample and the current $I$ is measured via the tip. The
differential conductivity $dI/dV(V)$, proportional to the local density of
states (LDOS) of the sample Morgenstern03 , is recorded by lock-in technique
after opening the feedback loop at voltage $V_{\rm stab}$ and current $I_{\rm
stab}$.

Figure 1:  (a) –(c) Evolution of the topological surface state of
ferromagnetic MnSb2Te4 as a function of an applied $B_{\parallel}$ (left) that
increasingly aligns the spins of the Mn atoms (arrows in the green rectangle)
towards the in-plane direction. (d) Side view of the stick and ball model of
Mn-rich MnSb2Te4 consisting of septuple layers Te-Sb-Te-Mn-Te-Sb-Te with van-
der-Waals gaps between adjacent Te layers (red). Excess Mn atoms (green) are
additionally distributed in the Sb layers (violet). The vertical lines are
guides to the eye. (e) Top view of the first three layers. (f) Atomically
resolved STM image of Mn-rich MnSb2Te4, $V=500$ mV, $I=200$ pA. (g) $dI/dV(V)$
curves recorded at the same position, but at different $B_{\parallel}$ as
marked, $V_{\rm stab}=-100$ mV, $I_{\rm stab}=400$ pA. The dashed line marks
the threshold for the gap determination, i.e. $dI/dV$ values above the line
are not regarded as gap. The band gap closes with increasing $B_{\parallel}$.
(f–g) $T=6$ K.

Figures 1d and e sketch the atomic structure of the epitaxial MnSb2Te4 as
deduced by transmission electron microscopy, X-ray diffraction and Rutherford
backscattering Wimmer2021 . Septuple layers with a Mn layer in the center are
separated by van-der-Waals gaps between adjacent Te layers. Moreover, about
3.5 % of the atoms in the Sb layers are replaced by Mn atoms (green balls in
the violet layers). STM reveals the hexagonal structure of the top Te layer
(Fig. 1f). The height fluctuations up to about 1 Å (RMS roughness: 24 pm),
have been attributed previously to the Mn atoms in the subsurface Sb layer
Wimmer2021 . The $dI/dV$ curves exhibit a band gap at the Fermi level $E_{\rm
F}$ for $B_{\parallel}=0$ T (Fig. 1g, blue curve) Wimmer2021 . At the chosen
fixed surface position, the band gap reduces in size at $B_{\parallel}=1$ T
(red curve) and completely disappears at $B_{\parallel}=3$ T (yellow curve).
This is in line with the expectation that, in first order, the gap size
depends only on the magnetization perpendicular to the surface, while an in-
plane component $M_{\parallel}$ only shifts the position in $k$ space but does
not induce a gap Sekine2021 ; Rosenberg12 ; CXLiu08 ; Henk2012 . The reducing
gap size, thus, indicates that the Mn spins are locally rotated into the plane
by $B_{\parallel}$.

Figure 2:  (a) Histogram of negative $dI/dV$ values resulting from 2500
$dI/dV(V)$ curves covering an area of 625 nm2, red line: exponential fit,
black dashed line: threshold $dI/dV_{78\%}$ used for gap determination (see
text). Inset: full histogram including positive $dI/dV(V)$, $B_{\parallel}=0$
T. (b) Histogram of deduced band gaps $\Delta$ at $B_{\parallel}=0$ T for 5500
$dI/dV(V)$ curves covering 1375 nm2, the blue bar at negative $\Delta$ counts
all spectra without gap, while the bar covering $0-2$ meV excludes these
spectra, $\overline{\Delta}$: average gap value including the blue bar
$\Delta=0$ meV, $\sigma_{\Delta}$: standard deviation. (c) Same as b at
$B_{\parallel}=3$ T for 4600 $dI/dV(V)$ curves covering 1150 nm2. (a–c)
$V=-50$ mV to $50$ mV, $V_{\rm stab}=-140$ mV, $I_{\rm stab}=400$ pA, $T=6$ K.

For quantitative band gap determination, we must consider the noise level of
$dI/dV(V)$ curves. Therefore, we firstly determine a histogram of all
$dI/dV<0$ nS for a $dI/dV(V)$ map after careful calibration of the lock-in
phase (Fig. 2a). We regard the negative $dI/dV$ as noise. The histogram can be
fitted by an exponential function (red line, Fig. 2a). The $dI/dV$ value that
encloses 78 % of the area below the exponential curve, $dI/dV_{78\%}$ (dashed
line, Fig. 2a), serves as threshold, i.e. only voltages $V$ with
$dI/dV(V)<-dI/dV_{78\%}$ are regarded to belong to the gap (Supplementary
Section S2). Figure 2b and c display the histograms of the resulting gap
values $\Delta$ for $B_{\parallel}=0$ T and 3 T, each using several $dI/dV(V)$
maps including $\sim 5000$ curves and covering an area as large as $\sim 1300$
nm2. The mean value $\overline{\Delta}$, that includes curves without gap as
$\Delta=0$ meV, decreases from $\overline{\Delta}(B_{\parallel}=0$ T$)=12.7$
meV to $\overline{\Delta}(B_{\parallel}=3$ T$)=7.8$ meV, i.e. the average gap
reduces, but does not close completely. The absolute gap values depend on the
chosen threshold (Supplementary Section S2), but the threshold is identical
for the two $B_{\parallel}$ and the gap reduction by $B_{\parallel}$ turns out
to be robust for differently chosen thresholds. The percentage of curves
without gap (blue bar at $\Delta<0$ meV, Fig. 2b,c) increases from 5 % to 23
%. This indicates that only about 20% of the Mn spins in the surface area are
rotated in-plane, while the majority is only partially rotated towards the in-
plane direction as evidenced by the reduced $\overline{\Delta}$. In-plane
magnetization data of a ferromagnetic Mn1.00Sb2.09Te3.91 bulk crystal revealed
that $M_{\parallel}$ at $B_{\parallel}=3$ T corresponds to
$2\,\mu_{\mathrm{B}}$/Mn atom only, while $5\,\mu_{\mathrm{B}}$/Mn atom are
achieved at $B_{\parallel}>60$ T Lai2021 . This nicely corroborates the only
partial rotation of Mn moments into the plane at $B_{\parallel}=3$ T as in our
case. Since time reversal symmetry is broken, a tiny gap might also appear for
a magnetization parallel to a topological insulator surface. However,
according to density functional theory calculations of MnBi2Te4, this gap is
an order of magnitude smaller than for surfaces with perpendicular
magnetization Gu2021 . The Dirac point energy $E_{\rm D}(x,y)$ (mid point
energy of the gap) barely changes by applying an in-plane field
($B_{\parallel}=0$ T: $\overline{E}_{D}=1.6$ meV, $\sigma_{E_{\rm D}}=3.5$
meV; $B_{\parallel}=3$ T: $\overline{E}_{D}=1.2$ meV, $\sigma_{E_{\rm D}}=4.0$
meV, Supplementary Section S3). Hence, the change in local magnetization does
not significantly influence the electrostatic potential. The fact that
$\sigma_{E_{\rm D}}<\sigma_{\Delta}$ reveals that magnetic disorder is more
severe than electrostatic potential fluctuations for MnSb2Te4. This is
opposite for Cr-doped (Bi,Sb)2Te3 Chong2020 , where, however, spatial
fluctuations of the magnetization vector $\bf{M}$ are still relevant for the
magnetic field induced phase transition Lachman16 ; Liu2020 .

Figure 3:  (a)–(c) STM images of the same area, each recorded after 2D mapping
of the $dI/dV(V)$ curves that are used to determine the $\Delta(x,y)$ map
shown below. Insets: Larger scale STM images recorded prior to the
$\Delta(x,y)$ maps, red rectangles: areas of main STM image and $\Delta(x,y)$
map below, $V=-500$ mV, $I=250$ pA. (d)–(f) $\Delta(x,y)$ maps of the
identical area as displayed in the main image on top for the three
$B_{\parallel}$ as marked, $V=-100$ mV to $100$ mV, $V_{\rm stab}=-100$ mV,
$I_{\rm stab}=400$ pA, grey areas: gap can not be determined (see text), grey
areas cover (d) 1.7 %, (e) 3.4 %, (f) 0.7 %, (d) $\overline{\Delta}=9.2$ meV,
$\sigma_{\Delta}=7.2$ meV, (e) $\overline{\Delta}=5.1$ meV,
$\sigma_{\Delta}=6.6$ meV, (f) $\overline{\Delta}=3.1$ meV,
$\sigma_{\Delta}=5.5$ meV.

Figure 3 shows $\Delta(x,y)$ maps of the identical area of MnSb2Te4 for three
different $B_{\parallel}$ values (Fig. 3d–f). The area is repeatedly adjusted
by its relative position to step edges as seen in the larger scale STM images
(insets in Fig. 3a–c). Two experimental challenges appeared. Firstly, roughly
2 % of the curves do not exhibit an increasing $dI/dV$ for $0{\,\rm mV}<V<50$
mV, such that $\Delta$ could not be determined Wimmer2021 . The corresponding
positions are colored grey in the $\Delta(x,y)$ maps. The effect is repeatedly
observed for several tips in both STM instruments up to $B_{\parallel}=3$ T
and up to $T=50$ K. The reason is unknown, but might be related to dynamic
trapping of charges from the tunneling current by defects. Secondly, the
conditions for STS were not completely stable during the recording of
$dI/dV(V)$ maps at $B_{\parallel}>0$ T as clusters of unknown origin appeared
on the surface after the maps (Fig. 3c). Such clusters can change the
electrostatic potential and, hence, also $\Delta(x,y)$. Consequently, a
reliable comparison can only be made between Fig. 3d and e, again
demonstrating a reduction of the average gap size $\overline{\Delta}$ with the
magnetic field applied, decreasing from $\overline{\Delta}$ = 9.2 meV at
$B_{\parallel}=0$ T to 5.1 meV at $B_{\parallel}=1$ T, in line with the result
obtained from the histograms (Fig. 2). In the top part of the images,
$\Delta(x,y)$ exhibits a rather homogeneous decrease of the local $\Delta$
with increasing $B_{\parallel}$. However, also regions of local increases are
found (lower left part) that encircle areas with undefined gap (grey regions),
presumably indicating charge trapping. The correlation length of $\Delta(x,y)$
slightly increases from $\xi_{6{\rm K}}(0\,{\rm T})=2.1$ nm to $\xi_{6{\rm
K}}(1\,{\rm T})=2.7$ nm (Supplementary Section S3), being only slightly larger
than the distance between individual Mn atoms within the subsurface Sb layer
$d_{\rm Mn-Mn}\simeq 2$ nm. Hence, it appears that each Mn atom in the Sb
layer contributes significantly to the local gap $\Delta(x,y)$. Figure 3f,
recorded at $B_{\parallel}=3$ T, must be regarded as a largely modified
potential landscape due to the surface contamination found after recording
$\Delta(x,y)$. Indeed, there is no obvious correlation to $\Delta(x,y)$ at
lower $B_{\parallel}$. Nevertheless, the average gap of
$\overline{\Delta}_{6{\rm K}}(3\,{\rm T})=3.1$ meV is further decreased by
about 40% with respect to $\overline{\Delta}_{6{\rm K}}(1\,{\rm T})$. The
average gap $\overline{\Delta}_{6{\rm K}}(3\,{\rm T})$ in this area is
relatively small (compare Fig. 2c), which is due to the large patch without
gap observed in the upper part of the image. The correlation length
$\xi_{6{\rm K}}(3\,{\rm T})=3.0$ nm barely changes compared to
$B_{\parallel}=1$ T. Previously reported magnetization data Wimmer2021  shows
that the in-plane magnetization $M_{\parallel}$ of our MnSb2Te4 films
increases by about 20 % between $B_{\parallel}=1$ T and $B_{\parallel}=3$ T.
Albeit a direct comparison is not straightforward, the changes of band gap and
magnetization are of a very similar strength. Hence, we conclude that the
origin of reduced $\Delta(x,y)$ is dominated by a partial, non-uniform
rotation of the Mn spins into the plane by $B_{\parallel}$ as illustrated in
Fig. 1b. Such a relation between gap and magnetization direction as expected
for ferromagnetic TIs Tokura2019 ; Sekine2021  has never been demonstrated
experimentally before.

Figure 4:  (a) Individual $dI/dV(V)$ curve recorded at $T=4.3$ K (blue line),
$V_{\rm stab}=-100$ mV, $I_{\rm stab}=100$ pA, $B_{\parallel}=0$ T. Red line:
same $dI/dV(V)$ after convolving with the Fermi-Dirac distribution
$f(E,T=22\,{\rm K})$ according to eq. 1. The dashed line indicates the
threshold for gap determination ($-dI/dV_{95\,\%}$) deduced similar as in Fig
2a (Supplementary Section S2). The resulting gap sizes are $\Delta(4.3\,{\rm
K})=13$ meV, $\Delta(22\,{\rm K})=10$ meV. (b) Scatter plot of the relation
$\Delta_{\rm sim}(22\,{\rm K})$ to $\Delta(4.3\,{\rm K})$ for 7500 $dI/dV(V)$
curves recorded at $T=4.3$ K. $\Delta(4.3\,{\rm K})$ results from the recorded
curves via the $-dI/dV_{95\,\%}$ threshold, $\Delta_{\rm sim}(22\,{\rm K})$
results after applying eq. 1. Black line: linear fit. (c) Logarithmic plot of
$R=dI/dV(0\,{\rm mV})/dI/dV(-50\,{\rm mV})$ as function of
$\Delta(4.3\rm{\,K})$ for 7500 $dI/dV(V)$ curves, recorded at $T=4.3$ K and
folded with $f(E,22\,{\rm K})$ according to eq. 1 Wimmer2021 . (d)–(i) Time
series of subsequently recorded $\Delta(x,y)$ maps, $T=21-23$ K continuously
decreasing from d to i. Recording time per image: 4 h. Grey areas (2–6 % of
the images) indicate the positions where $\Delta$ could not be determined. The
dashed circles in e–h mark a similar feature (see text). Measurement
conditions: $V=-100$ mV to $100$ mV, $V_{\rm stab}=-100$ mV, $I_{\rm
stab}=100$ pA, $B_{\parallel}$=0 T.

Next, we probe spatiotemporal fluctuations of the magnetically induced gap
$\Delta(x,y)$. $M_{\perp}(T)$ curves by XMCD Wimmer2021  revealed a
continuous, mostly linear reduction of $M_{\perp}(T)$ for $T>20$ K .
Consequently, we record $\Delta(x,y)$ maps slightly above, at $T=22\pm 1$ K,
in a series of images covering the same area (Fig. 4d–i). Indirect temperature
stabilization led to a lateral drift of $0.2-2$ nm/hour during the
measurements (Supplementary Section S1). The determination of $\Delta$ at
elevated $T$ must consider the Fermi level broadening of the probing tip
Wimmer2021 ; LeeIPNAS2015 ; SessiNC16 ; ChenNJP2015 . Figure 4a shows
$dI/dV(V,T=4.3\,{\rm K})$ as recorded at $T=4.3$ K (blue line). Applying the
convolution

$\frac{dI}{dV}_{\rm sim}(V,T=22\,{\rm
K}):=\int_{-\infty}^{\infty}\frac{dI}{dV}\left(\frac{E}{e},T=4.3\,{\rm
K}\right)\cdot\frac{df(eV-E,T=22\,{\rm K})}{dE}\hskip 5.69054ptdE$ (1)

with Fermi-Dirac distribution $f(E,T)=(e^{E/k_{\rm B}T}+1)^{-1}$ ($e$:
electron charge, $k_{\rm B}$: Boltzmann constant, $E$: energy) returns the
expected appearance of $dI/dV(V)$ at 22 K resulting from the same LDOS (red
line). Evidently, the broadening due to the Fermi-Dirac distribution reduces
the apparent $\Delta$ for identical LDOS. To account for this error, we
employed a set of 7500 $dI/dV(V,T=4.3\,{\rm K})$ curves to determine the band
gaps $\Delta(4.3{\rm K})$ and applied eq. 1 to determine the apparent band
gaps at 22 K, denoted $\Delta_{\rm sim}(22{\rm K})$. The resulting scatter
plot for the 7500 curves is shown in Fig. 4b with a linear fit (black line) of
all data points exhibiting $\Delta_{\rm sim}(22{\rm K})\neq 0$ meV. The fit is
then used to relate measured $\Delta(22{\rm K})$ to the expected $\Delta_{\rm
exp}(4.3{\rm K})$ of the same LDOS that we regard as the true gap of the LDOS
at 22 K: $\Delta_{\rm LDOS,22\,{\rm K}}:=\Delta_{\rm exp}(4.3{\rm K})$. The
method does not work for $\Delta(22{\rm K})=0$ meV, where we instead use
$R=dI/dV(0\,{\rm mV})/dI/dV(-50\,{\rm mV})$ to estimate $\Delta_{\rm
LDOS,22\,\rm K}$ (Fig. 4c). This more complex method has been established
previously Wimmer2021  (Supplementary Section S2) and is relevant for 38 % of
the curves leading to Fig. 4d–i. For $R>0.1$, one reliably gets $\Delta_{\rm
LDOS,22\,\rm K}=0$ meV (Fig. 4c).

Figure 4d–i show the resulting $\Delta_{\rm LDOS,22\,\rm K}(x,y)$ maps in a
time series. Here, $25-40$ % of the surface area exhibits $\Delta_{\rm
LDOS,22\,\rm K}=0$ meV interrupted by irregularly shaped patches with
$\Delta_{\rm LDOS,22\,\rm K}>0$ meV. The average gap size within the six
images amounts to $\overline{\Delta}_{\rm LDOS,22\,\rm K}=5-8$ meV, while
within the patches it is $\overline{\Delta}_{\rm
LDOS,22\,K,\Delta>0}=8.5-10.5$ meV. Both values are significantly smaller than
the average gap size at $6$ K (13 meV) as expected from the fact that the
magnetization decreases with increasing temperature Wimmer2021 . The
correlation length amounts to $\xi_{22{\rm K}}=1.2-2.0$ nm, i.e. slightly
smaller than $\xi_{6{\rm K}}=2.1$ nm, but still close to $d_{\rm Mn-Mn}\simeq
2$ nm (Supplementary Section S3). Most intriguingly, the patches change quasi-
continuously in size and shape as a function of time. This is revealed by the
dashed circles in Fig. 4e–h that identifies a similar structure that only
slightly changes its shape. Since subsequent images differ by 4 hours, the
fluctuations are extremely slow. The same experiment performed at $T\simeq 25$
K exhibits $\Delta(x,y)$ fluctuations as well, but due to the larger changes
it was not possible to identify similar patches in subsequent images
(Supplementary Section S3). All in all, spatiotemporal fluctuations of the gap
size start at $T\simeq T_{\rm C}/2$, i.e. when the magnetization starts to
decay. This important observation perfectly corroborates the magnetic origin
of the gap. We note that $T=22$ K is very close to the Neel temperature
$T_{\rm N}=21$ K of antiferromagnetic MnSb2Te4 McQueeneyPRB19 ; ChenPRM20 .
Hence, we conjecture that the competition between ferromagnetic and
antiferromagnetic interlayer coupling driven by the local distribution of Mn
atoms in the Sb layer liu2021 ; Riberolles2021 ; li2021 ; HuarXiv2020 ;
Wimmer2021  is responsible for the magnetic fluctuations at this temperature
well below $T_{\rm C}$. Recently, large $\bf{M}$ fluctuations well below
$T_{\rm C}$ have also been found for Mn(Bi,Sb)2nTe3n+1 by ac magnetic
susceptibility measurements Hu2021b  as well as for Cr-doped Sb2Te3 by spin
resonance relaxation Figueroa2020 . This establishes $\bf{M}$ fluctuations as
a general phenomenon in (Bi,Sb)2Te3 based magnetic topological insulators. We
tried to quantify the spatiotemporal fluctuation at $T\simeq 22$ K in more
detail by various correlation functions, but could not establish a clear trend
probably due to the limited data set and the remaining lateral drift during
the measurements.

In summary, we have shown that the band gap of Mn-rich MnSb2Te4 is controlled
by the perpendicular magnetization of the surface. Thus, it is strongly
reduced in size by about 1/3 when an in-plane magnetic field of
$B_{\parallel}=3$ T is applied, which nicely agrees to the in-plane
magnetization at this field being 1/3 of the saturation magnetization Lai2021
. At temperatures approaching $T_{\rm C}$, the magnetic gap starts to
fluctuate spatiotemporarily as measured for $T_{\rm C}/2$, in line with the
starting reduction of remanent magnetization. Both results corroborate our
assignment of the gap to a magnetic gap of the topological surface state.
Moreover, our results establish MnSb2Te4 as a highly promising material for
direct spatiotemporal investigation of magnetization changes close to a
quantum critical point. The criticality is likely induced by the competition
between ferromagnetic and antiferromagnetic interlayer coupling that can be
tuned, in principle, by $B$ field.

Acknowledgements

We gratefully acknowledge insightful discussion with G. Bauer and funding by
the Deutsche Forschungsgemeinschaft via Germany’s Excellence Strategy —
Cluster of Excellence: Matter and Light for Quantum Computing (ML4Q) EXC
2004/1 — 390534769, and by Mo 858/19-1, by the Graphene Flagship Core 3, and
by the Austrian Science Funds (Projects No. P30960-N27 and I3938-N27).

## Supplementary Sections

The Supplementary Sections describe the experimental and theoretical methods
as well as additional data supporting the conclusions from the main text.

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