Structural and magnetic properties of GdCo$_{5-x}$Ni$_x$
Amy L. Tedstone Christopher E. Patrick Santosh Kumar Rachel S. Edwards Martin R. Lees Geetha Balakrishnan Julie B. Staunton












J.B.Staunton@warwick.ac.uk
Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom




GdCo_5 may be considered as two sublattices—one of Gd and one of Co—whose 
magnetizations are in antiparallel alignment, forming a ferrimagnet. 

Substitution of nickel in the cobalt sublattice of GdCo_5 has been 
investigated to gain insight into how the magnetic properties of this 
prototype rare-earth/transition-metal magnet are affected by changes in 
the transition metal sublattice.

Polycrystalline samples of GdCo_5-xNi_x for 0 ≤ x ≤ 5 
were synthesized by arc melting. 

Structural characterization was carried out by powder x-ray diffraction 
and optical and scanning electron microscope imaging of metallographic slides, 
the latter revealing a low concentration of Gd_2(Co, Ni)_7 lamellae for x ≤ 2.5. 

Compensation—i.e. the cancellation of the opposing Gd and transition metal moments— 
is observed for 1 < x < 3 at a temperature which increases with Ni content;
for larger x, no compensation is observed below 360 K.

A peak in the coercivity is seen at x ≈ 1 at 10 K 
coinciding with a minimum in the saturation magnetization.

Density-functional theory calculations within the disordered local 
moment picture reproduce the dependence of the magnetization on 
Ni content and temperature.

The calculations also show a peak in the magnetocrystalline anisotropy 
at similar Ni concentrations to the experimentally-observed coercivity maximum.




Structural and magnetic properties of GdCo_5-xNi_x
    Julie B. Staunton
    December 30, 2023
==================================================





§ INTRODUCTION 


The RETM_5 [(RE = rare earth; TM = transition metal)] family of materials have widely 
ranging magnetic properties owing to the differing number of 4f electrons found 
in the RE elements.

These materials crystallize into a hexagonal lattice (the CaCu_5 type structure, 
space group P6/mmm, Fig. <ref>) with a unit cell consisting of layers with a central RE atom 
surrounded by TM atoms in 2c positions, alternating with layers of TM atoms 
in the 3g positions <cit.>. 

One pertinent example is SmCo_5, a permanent magnet which can be favored over 
Nd-Fe-B magnets for its superior high-temperature performance (Curie temperature 
of around 1020 K <cit.>, as opposed to approximately 580 K for 
Nd-Fe-B magnets <cit.>). 

Another member of this family is GdCo_5, where the symmetry of the Gd 4f 
shell causes crystal-field effects to vanish <cit.>.

The absence of crystal-field effects make GdCo_5 a particularly useful system 
to study the rare-earth/transition-metal interaction via both theory and experiment. 



GdCo_5 is ferrimagnetic.

Starting from T=0 K its magnetization increases with increasing temperature 
reaching a maximum at around 800 K <cit.>.

With a further increase in temperature, the spontaneous magnetization decreases 
to zero at the Curie temperature (1014 K) <cit.>.

This unusual temperature dependence is a consequence of the Gd moments disordering 
more rapidly with temperature than the Co moments  <cit.>.

Doping a RETM_5 material can change its magnetic properties in a controlled 
manner <cit.>. 

Here, only doping of the TM sublattice is considered. 

The effects of doping on coercive field and saturation magnetization 
have been studied for single crystals of GdCo_5-xCu_x by 
Grechishkin et al. <cit.> and later 
by de Oliveira et al. <cit.>.

The Cu reduces the TM sublattice magnetization.

Both papers report a peak in coercivity at a composition of x ≈ 1.5.

This is found to be the compensation composition of this intermetallic 
at room temperature, where the (Co,Cu) sublattice magnetization 
exactly cancels (fully compensates) the Gd sublattice magnetization.

A peak in coercivity was also found in YCo_5-xNi_x <cit.> 
and for RECo_5-xNi_x (RE = Sm, La, Y, Th and Ce) <cit.> 
for certain compositions.

It is interesting that RECo_5 compounds containing nonmagnetic REs 
such as Y and La still exhibit a peak in coercivity, despite not having a compensation composition.

Buschow and Brouha (Ref. ) suggested that the presence of narrow 
Bloch walls in YCo_5-xNi_x is primarily responsible for the high 
coercivity observed for certain compositions.

In a previous work <cit.> we prepared polycrystalline samples 
of GdCo_5-xTM_x and YCo_5-xTM_x (TM = Ni and Fe) with x ≤ 1 
and single crystal GdCo_5 and YCo_5, and compared the experimentally 
determined magnetic properties of these samples with theoretical 
calculations made using density-functional theory.

An increase (decrease) in magnetization was observed for Fe (Ni) doping.

The calculations showed that substituting Ni onto the Co lattice led to 
Ni preferentially occupying the 2c site,
although experimentally this may depend on the method of sample preparation.

The doping site was not found to have a large effect on magnetization, 
but did affect the Curie temperature, with a larger change for the 2c site doping.

However, possible effects on the coercivity and magnetocrystalline anisotropy 
were not explored in the paper, nor were concentrations with x > 1.

The magnitude of the Ni moment in GdCo_5-xNi_x is very small <cit.> 
compared to that of Co and Gd (in GdCo_5, the Co moment 
is ≈ 1.6μ_B/atom at both the 2c and the 3g sites 
and the Gd moment is ≈ 7μ_B <cit.>), 
hence the (Co, Ni) sublattice magnetization is expected to decrease 
with increasing Ni content.

The fully substituted material GdNi_5 is ferrimagnetic, but the main 
contribution to the magnetization comes from the ferromagnetic Gd 
sublattice, giving a Curie temperature of 32 K <cit.>.

At absolute zero at a particular composition for GdCo_5-xNi_x the 
(Co, Ni) sublattice magnetization will fully compensate the Gd 
sublattice magnetization.

The compensation composition at absolute zero will fulfill the 
condition μ_Gd - μ_Co(5-x)-μ_Nix = 0.

Taking approximate zero temperature values for the moments of Co, Ni, and 
Gd (1.6, 0.6, 7μ_B/f.u. [formula unit]), respectively, 
the compensation composition is x∼1.

At other compositions there may exist a finite compensation temperature 
where the different disordering of the Gd and (Co, Ni)
sublattice magnetizations again leads to compensation.

Chuang et al. <cit.> replaced Co with Ni in 
GdCo_5-xNi_x for 0≤ x≤ 5 measuring magnetization 
versus temperature at 12 kOe for several compositions, 
focusing primarily on temperatures from 300 to 1015 K, with the 
exception of GdCo_2Ni_3 and GdCoNi_4 for which measurements 
were taken over the ranges of 77–1015 K and 77–300 K, respectively.

Therefore, for compositions with x<3, any compensation point 
at temperatures lower than 300 K would not have been observed.

GdCo_5-xNi_x has been investigated by Liu et al. <cit.> 
for x ≤ 1.05 in order to determine the intersublattice RE/TM coupling constant.

Magnetization compensation has also been studied in Gd(Co_4-xNi_x)Al <cit.>, 
where increased Ni content was observed to increase the compensation 
temperature and in RE(Co_4-xFe_xB) (RE = Gd and Dy) <cit.>, 
where the compensation temperature was reduced for increased Fe content.

In this paper the magnetic behavior of polycrystalline powders and buttons of 
GdCo_5-xNi_x is reported for temperatures from 5 to 360 K for 
x=0, 0.5, 1, 1.25, 1.28, 1.3, 1.5, 2, 2.5, 3, 3.5, 4, and 5. 

The compensation temperature, coercivity and magnetization at 70 kOe are 
presented as a function of x.

This extends the previous work of Chuang et al. <cit.> 
to a temperature range in which the compensation point can be observed for x<3.

The behavior is then analyzed with the help of density functional theory 
calculations within the disordered local moment picture <cit.>, 
calculating the composition-dependent magnetization, coercivity, and 
magnetocrystalline anisotropy.

The calculations provide microscopic insight into the macroscopic quantities 
observed experimentally, demonstrating the utility of the joint 
computational/experimental approach in understanding the 
behavior of RE/TM permanent magnets.

The rest of this paper is organized as follows.
Section <ref> describes the experimental and theoretical
techniques used.
Sections <ref> and <ref> describes the results
of the experiments and calculations, respectively.
The conclusions and summary are presented in Section <ref>.





§ METHODOLOGY





 §.§ Experimental approach


Polycrystalline samples of the series GdCo_5-xNi_x were synthesized by arc 
melting the constituent elements on a water cooled copper hearth under an argon atmosphere. 

The starting elements (99% purity) were taken in the stoichiometric ratios with 1% 
excess of Gd to compensate for losses during melting.

To ensure homogeneity, the ingots were flipped and remelted at least three times.

Annealing for 10 days at 950 ^∘C was tried to improve phase homogeneity, 
as discussed by Buschow and den Broeder <cit.>.

However, analysis of the annealed samples (via the same methods described below) 
showed no convincing evidence that annealing promotes the 1:5 [Gd:(Co, Ni)] 
phase formation over the neighboring phases of 2:17 and 2:7, and so as-cast 
samples were used (provided they were found to be sufficiently phase pure, 
as described in the remainder of this section). 

The structures were characterized by powder x-ray diffraction using a 
Panalytical Empryean diffractometer with CoK_α radiation.

To confirm the phase content, metallographic slides were prepared from 
slices of ingots mounted in Epomet-F plastic and polished using 
progressively finer diamond suspensions.

Optical microscopy and scanning electron microscopy (SEM) 
imaging of the slides were used to further examine the structure.

Magnetization measurements were made as a function of temperature and 
applied field using a Quantum Design Magnetic Property Measurement 
System (MPMS) superconducting quantum interference device (SQUID) magnetometer.

Free to rotate powders were used to obtain the best estimate of saturation 
magnetization. 

The magnetization vs temperature, M(T), data were taken in a 
10 kOe field with the temperature decreasing from 360 to 10 K at a 
rate of 3 K/min.

The magnetization versus field [(M(H))] data 
were taken at 10 K (5 K for x = 0, 0.5, and 1) by first 
applying a 70 kOe field then collecting the magnetization data at 
incrementally decreasing fields (until 0 kOe).

Polycrystalline buttons were fixed to a sample holder using GE 
varnish to measure coercivity in an Oxford Instruments vibrating 
sample magnetometer.

The buttons were fixed in this manner to prevent sample rotation, 
and thus get a more accurate measurement of coercivity.

The coercivities were determined from four quadrant hysteresis loops 
starting at 70 kOe, as the coercivity is known to depend on the 
initial applied field <cit.>.




 §.§ Theoretical approach


The magnetic properties of Ni-doped GdCo_5 were calculated at 
zero and finite temperature using density-functional theory 
within the disordered local moment (DFT-DLM) picture <cit.>.

In this approach, both the temperature-induced local moment 
disorder and the compositional disorder from the Ni doping are modeled
using the coherent potential approximation (CPA) within the Korringa-Kohn-Rostocker
(KKR) multiple-scattering formulation of DFT <cit.>.

A detailed description of this approach applied to Ni-doped GdCo_5 
is given in Ref. ; here the computational 
details specific to this work are given.

The calculations were performed on the CaCu_5 structure with 
lattice parameters fixed at a= 4.979 Å, c=3.972 Å, which 
were measured for pristine GdCo_5 at 300 K <cit.>.

As discussed in Section <ref> the Ni dopants were set 
to either occupy the 2c and 3g crystal sites with equal 
probability, or to preferentially sit at the 2c crystal sites.

The KKR multiple-scattering equations were solved within the 
atomic sphere approximation (ASA) with Wigner-Seitz radii 
of (1.58, 1.39, 1.42) Å at the (Gd, 2c, 3g) sites.

The KKR-CPA code  <cit.> was used 
to generate scalar-relativistic potentials for the 
magnetically-ordered (ferrimagnetic) state,
expanding the key quantities in an angular momentum basis up 
to a maximum quantum number l=3. 

Exchange and correlation were treated within the local spin-density 
approximation <cit.>, with the local self-interaction 
correction <cit.> also applied to the Gd-4f electrons.

The scalar-relativistic potentials were then fed into our own code which solves
the fully-relativistic scattering problem in the presence of magnetic 
disorder <cit.>.

For selected Ni concentrations an orbital polarization correction 
(OPC) <cit.> was included on 
the d scattering channels <cit.>.

The DFT-DLM Weiss fields, which govern the temperature dependence 
of the calculated quantities, were calculated self-consistently 
using an iterative procedure <cit.>.

The magnetocrystalline anisotropy constants were calculated using 
the torque formalism described in Ref. , using an 
adaptive reciprocal-space sampling scheme to ensure numerical accuracy <cit.>.

To calculate magnetization versus field curves the first-principles approach 
to calculate temperature-dependent magnetization vs field (FPMVB) curves introduced
in Ref.  was used.

A set of 28 DFT-DLM calculations are used to fit the parameters contained 
in F_2, which quantify exchange and magnetic anisotropy.

The magnetization for a given field and sample orientation is then determined 
by minimizing the free energy with respect to the angles between the Gd 
and the transition metal magnetizations and the crystal axes.

The approach does not account for any canting between moments within the 
transition metal sublattices, since this was previously calculated to 
be less than 0.1^∘ for GdCo_5 <cit.>.





§ RESULTS




 §.§ Structural characterization


Figure <ref> shows the powder x-ray diffraction 
pattern obtained from GdCo_3Ni_2 (x=2, black data). 

The red line is the fit obtained when a Rietveld refinement 
is carried out using the TOPAS software <cit.>.

The goodness of fit parameter is 2.03 (a similar value was 
found from fitting the diffraction patterns of all samples). 

The blue line is the difference plot between the observed data 
and the fit.

The green ticks represent indexed peaks.

All the peaks in each diffraction pattern have been indexed 
using the GdCo_5 structure—space group P6/mmm—as demonstrated here, 
suggesting the samples form as single phase materials to 
within the detection limits of the technique.

The lattice parameters for all x are given in Table <ref>, along 
with the lattice parameters found in the literature.

As expected from previous research, there is a contraction in 
the ab plane with increasing Ni content, 
and a less pronounced general contraction along the c axis.
 







The x-ray diffraction measurements show that the samples are single phase, 
but this technique may miss small percentages of impurity phases.

For this reason, optical microscopy and SEM images were taken of 
metallographic slides; some example SEM images are shown in 
Fig. <ref>.

A decreasing quantity of lamellae of a secondary phase were 
observed with increasing x, until x = 2.5, beyond which 
no lamellae were observed.

Energy-dispersive x-ray spectroscopy showed that the majority 
phase is the 1:5 [Gd:(Co, Ni)] phase and the small lamellae 
are a 2:7 phase.

Table <ref> shows the percentage of the 2:7 phase 
found in the as-cast samples.

Buschow and den Broeder noted that a slight excess of Co 
during the arc-melting promotes the formation of the 
2:7 phase within the 1:5 matrix <cit.>.

GdNi_5 forms congruently from the melt, and is stable down 
to, at least, room temperatures.

On the other hand, GdCo_5 undergoes eutectic decomposition 
at 775 ^∘C into Gd_2Co_7 (2:7 Gd:Co) and 
Gd_2Co_17 (2:17 Gd:Co) <cit.> and so 
increasing Ni content improves the stability of the 1:5 phase.






The relative unimportance of the secondary 2:7 phase in 
these quantities (2–7%) to the measurement of intrinsic 
quantities such as the magnetization can be demonstrated 
for the case of no Ni doping.

The moment per formula unit of GdCo_5 is 1.37μ_B/f.u. <cit.> 
and of Gd_2Co_7 is 2.5μ_B/f.u. <cit.>.

Assuming no other impurities or other phases, taking 93% of the total 
powder to be GdCo_5 and 7% to be Gd_2Co_7 (i.e. the maximum 
amount of the impurity phase estimated) the total moment becomes 
1.45μ_B/f.u.

This is an ∼6% increase to pure GdCo_5; which is 
insignificant compared to the almost 300% increase in moment 
from GdCo_5 to GdNi_5.

On the other hand, it is possible that the presence of a 
secondary phase affects extrinsic properties such as the 
coercivity, as in Sm-Co or Nd-Fe-B magnets <cit.>.

As no 2:7 phase was observed in as-cast samples of 
x ≥ 3, these can be used as a comparison when 
studying trends in the measurements.





 §.§ Compensation temperature


M versus T curves are shown in Fig. <ref> for x=1.5, 
2, and 3 measured in an applied magnetic field of 10 kOe.

A clear minimum occurs at progressively lower temperatures 
as Ni content is decreased.

At this minimum the net total magnetization aligns with 
the bias field of 10 kOe.

In contrast, when the sample is warmed in the (small, negative) 
trapped field of the magnetometer magnet, after cooling 
in 10 kOe, the magnetization changes sign at the compensation 
temperature, as shown in Fig. <ref> for x=2. 


As shown in Fig. <ref>, the magnetization of the powders
subject  to the 10 kOe applied field does not go to zero, even
at the compensation temperature.

An explanation for this behavior in terms of a change in the internal
magnetic structure of the powder particles (from antiparallel to canted RE/TM moments)
is given in Sec. <ref>.








Fig. <ref> shows the dependence of the compensation 
temperature with composition.

A small hysteresis in compensation temperature with increasing/decreasing 
temperature was noted in a 10 kOe field for x ≤ 2.

No hysteresis was found for these compositions in the trapped 
field of the magnet.

The compensation temperature increases for increasing nickel content, 
as expected.

Compensation is not observed for x ≥ 3.5 and x ≤ 1 in this 
temperature range.

In the case of low Ni doping, the Co sublattice magnetization, 
whilst reduced by the addition of Ni, remains dominant over 
the Gd sublattice for all measured temperatures.

At high Ni doping, the Co sublattice magnetization is reduced 
so much that the Gd sublattice magnetization dominates 
for all measured temperatures.

Chuang et al. (Ref. ) reported a 
compensation temperature for x=3 of 380 K in a 12 kOe field, 
however here it is 323 K in a 10 kOe field.

Earlier results used a large temperature step size, and 
hence some disagreement is to be expected.

Measurements here were obtained on as-cast powder 
samples, whereas Ref.  reports on annealed samples. 




 §.§ Magnetization and coercivity


Four-quadrant M versus H loops for buttons of composition 
x=0.5, 1.3, 2.5, and 5 are shown in Fig. <ref>, 
with the inset showing the low-field region.

It is clear that the samples do not reach full saturation at 
70 kOe, which is the experimental limit.

This is to be expected, since the samples consist of a 
number of grains with randomly oriented c axes, such that both 
easy and hard axes are being probed.






The magnetization at 70 kOe and the coercive field obtained from the 
M versus H loops on powders/buttons as discussed above are 
shown in Fig. <ref> as a function of composition.

The magnetization has a minimum at x ∼ 1, which is the 
composition for which the sublattice magnetizations 
cancel maximally in the presence of a 70 kOe applied field at 10 K.

This is consistent with the value predicted in section <ref> 
and with the values obtained via the theoretical approach, 
section <ref>.

The coercive field has a broad peak that corresponds with 
the minimum in magnetization.

This behavior is consistent with that observed for single 
crystals of Cu-doped GdCo_5, <cit.> 
and other RECo_5-xNi_x materials <cit.>.

A corresponding peak in magnetocrystalline anisotropy is found 
in the theoretical calculations  discussed in <ref>. 



§ THEORY





 §.§ Zero temperature magnetization




Figure <ref> shows zero temperature DFT-DLM calculations 
of the magnetization of GdCo_5-xNi_x as a function of 
nickel content x.

The antiferromagnetic coupling of the RE and TM moments means 
that the total moment is obtained as the difference between 
these two contributions.

For GdCo_5, without the orbital polarisation correction a total moment of 0.62μ_B/f.u. is calculated, 
which consists of a contribution from the Co sublattices 
of (2×1.65 + 3×1.61 = 8.13μ_B) and 
from the Gd atom of 7.49μ_B.

The main effect of the OPC is to increase the orbital 
moments on each Co atom by ≈ 0.1μ_B, 
giving an increased Co contribution to the moment 
of (2×1.79 + 3× 1.73 = 8.77μ_B) 
and total moment of 1.30μ_B/f.u. 

The theoretical justification for including the OPC is that it 
approximates the contribution to the exchange-correlation 
energy from the orbital current, which is missing in the local 
spin-density approximation <cit.>.

Practically, previous work both on YCo_5 and GdCo_5 
found that including the OPC improved the agreement of 
magnetic moments and magnetocrystalline anisotropy with 
experiment <cit.>.

Considering the other limit of GdNi_5, the Ni sublattices 
give a much weaker contribution of 
(2×0.22 + 3×0.35 = 1.49μ_B) (no OPC). 

The weaker TM magnetism leads to a smaller induced contribution 
to the Gd moment, whose total value is reduced to 7.27μ_B.

The total GdNi_5 moment is therefore 5.78μ_B/f.u. 

The OPC has a much smaller effect on the Ni orbital moments 
compared to Co, so that the OPC-calculated total moment is 
reduced only slightly, to 5.73μ_B/f.u.

The absolute value of the moment of GdNi_5 exceeds that of GdCo_5.

The difference is that, in GdCo_5 the total moment points in 
the same direction as the transition metal moments (TM dominated), 
whereas in GdNi_5 the total moment points in the same direction as 
the Gd moment (Gd dominated).

In Fig. <ref> the sign convention is adopted that Gd (TM) 
dominated systems have positive (negative) moments.

The gradual addition of Ni weakens the TM contribution, causing
a compositionally-induced transition from TM to Gd dominated magnetism 
with increasing x.

At the concentration when the TM and Gd contributions to the magnetization are 
equal, the moments are fully compensated and the total magnetic moment 
of GdCo_5-xNi_x is zero.

Since the OPC increases the TM moment whilst leaving the Gd moment 
largely unaffected, this compensation concentration is different 
for calculations with and without the OPC.

With or without the OPC, compensation occurs at x=1.04 or x=0.54 respectively.

Comparing the calculations with the experimentally-estimated compensation 
concentration of x≈1 also supports the use of the OPC for GdCo_5-xNi_x.

The calculations discussed above were performed assuming that the Ni atoms 
substitute onto the 2c and 3g sites with equal probability, and 
are shown as the blue triangles and black squares in Fig. <ref> 
(with and without OPC, respectively).

However, previous calculations found it to be more energetically 
favorable for Ni to substitute at the 2c sites <cit.>.

Neutron diffraction experiments on Ni-doped YCo_5 also found this 
preferential 2c occupation <cit.>.

To investigate how this site preference affects the magnetic properties, 
calculations were also performed where the Ni atoms fill the 2c sites first, 
with the 3g sites only becoming occupied with Ni atoms for x>2. 

The moments calculated in this way (without the OPC) are shown as the red 
circles in Fig. <ref>.

The location of the Ni dopants does not have a large effect on the calculated 
moment, yielding a maximum difference of 0.16μ_B/f.u. at x=2.

The compensation concentration is also unaffected.

However, as discussed below, there is a more pronounced effect on the 
magnetocrystalline anisotropy from site-preferential doping.




 §.§ Temperature dependent magnetization




We now consider the magnetization at finite temperature, focusing 
on two cases: pristine GdCo_5 and GdCo_3.74Ni_1.26.

The latter Ni concentration was selected due to the interesting coercivity 
behavior observed experimentally for samples around this composition, 
as shown in Fig. <ref>.

In these calculations the OPC was included, and the Ni dopants occupied the 2c sites only.

Figure <ref> shows the DFT-DLM magnetizations calculated for 
the temperature range 0–300 K. As in Fig. <ref>, positive 
values correspond to the Gd moment having a larger moment than 
the TM contribution.

The magnetization of both GdCo_5 and GdCo_3.74Ni_1.26 becomes 
more negative (TM-dominated) in this temperature range.

The change is effectively linear with temperature, with a difference 
of 1.0μ_B/f.u. for GdCo_5 and 0.8μ_B/f.u. 
for GdCo_3.74Ni_1.26 between 0 and 300 K.

The origin of the change in magnetization is a faster disordering of 
Gd moments compared to the TM as the temperature is 
increased <cit.>.

This disordering is quantified by the order parameters 
(m_Gd,m_TM), which vary between 1 at 0 K and 
zero at the Curie temperature.

At 300 K, (m_Gd,m_TM) = (0.75,0.91) 
in GdCo_5 and (0.75,0.83) in GdCo_3.74Ni_1.26.

Therefore in both cases the relative strength of the TM contribution 
compared to Gd has increased with increasing temperature, 
producing a shift towards TM dominated magnetization.

The fact that m_Gd = 0.75 for both cases at 300 K 
shows that the introduction of Ni at the 2c sites has not affected 
the rate of Gd disordering, consistent with results obtained 
previously <cit.>.

However, the presence of Ni does lead to a faster disordering of 
TM moments (m_TM = 0.83 compared to 0.91), which is 
why the change in magnetization between 0–300 K is smaller 
for GdCo_3.74Ni_1.26 than GdCo_5.

Overall, this faster disordering reduces the Curie temperature, 
which is calculated to be 915 K for GdCo_5 and 713 K for 
GdCo_3.74Ni_1.26.

These values are consistent with the experiments of Chuang et al. <cit.>, 
who observed a Curie temperature of 1000 K for GdCo_5 and 
730 K for GdCo_3.75Ni_1.25.

As shown in Fig. <ref>, at 140 K GdCo_3.74Ni_1.26 
switches from Gd to TM dominated magnetization.

This temperature, where the antiparallel Gd and TM moments 
cancel each other, is the calculated compensation point 
of this composition, and agrees well with the experimental 
data shown in Fig. <ref>.

In passing, we note that not including the OPC shifts the 
magnetization to a more negative value by 0.55μ_B/f.u. 
at 0 K, and raises the compensation temperature to ∼300 K (not shown).



 §.§ Zero temperature magnetocrystalline anisotropy





We next consider the experimentally-observed variation in coercive 
field with composition (Fig. <ref>).

Arguably the simplest model of coercivity is based on magnetization 
rotation (the Stoner-Wohlfarth [SW] model) <cit.> 
which gives a coercive field of 2K/M for a ferromagnet 
of anisotropy K and magnetization M.

The same expression is obtained for the nucleation of 
reverse domains within micromagnetic theory <cit.>.

Postponing a discussion of M to Sec. <ref>, we first
consider the magnetocrystalline anisotropy of GdCo_5-xNi_x.

At zero temperature, the angular variation of the free energy was 
calculated, when the Gd and TM moments are held antiparallel to each 
other and rotated from being parallel to perpendicular to the 
crystallographic c axis.

This variation is well described by 
E_an (θ) = K_1 sin^2θ + K_2 sin^4θ, 
with K_2 ≪ K_1. Fig. <ref> shows K_1 as a function of Ni composition x.

The dominant contribution to this anisotropy energy is the TM sublattice, with
a minor 5d contribution from Gd <cit.>.


As for the zero temperature magnetization in Fig. <ref>, 
both preferentially substituting the Ni at 2c sites 
(circles in Fig. <ref>) and equally distributing the Ni over 
the 2c and 3g sites (squares) was investigated.

In both cases, adding Ni increases K_1 compared to pristine 
GdCo_5.

Furthermore, both cases show a peak in K_1 with Ni content.

For preferential 2c substitution this peak occurs for x between 
1.5–2.0, while for equal 2c/3g substitution the peak for x 
is between 2.5–3.0.

The enhanced K_1 is much more pronounced for preferential 2c 
substitution, becoming 3.5 times larger compared to 
pristine GdCo_5 at x=1.5.

In these calculations, the Ni doping has been modeled using the CPA. 

In a simpler rigid-band calculation, the effects of Ni-doping are simulated 
by shifting the Fermi level of pristine GdCo_5 so that the integrated 
density of states equals the number of electrons in the Ni-doped system.

The rigid band calculations of K_1 are shown as the blue triangles 
in Fig. <ref>.

Here, the enhancement in K_1 with x is even greater than 
that found with the CPA.

The rigid band model does not provide a fully consistent picture
of doping, e.g. with the value of K_1 
at x=5 not coinciding with K_1 calculated for GdNi_5.

Nonetheless, the rigid band data emphasizes how, as has 
been previously discussed for YCo_5 <cit.>, 
changing the occupations of the bands located close to the 
Fermi level can have large effects on the anisotropy.

The calculations in Fig. <ref> were performed without the OPC. 

Calculations including the OPC show the same variation with band 
filling, but the values of K_1 are strongly enhanced, as observed 
previously for YCo_5 <cit.>.

For instance, for x=1.26 with preferential 2c Ni doping, 
values of 2.0 and 6.5 meV/f.u. for K_1 without and with 
the OPC, respectively, are found.



 §.§ Zero temperature coercivity




The previous section showed that increasing the Ni content
causes a boost to the anisotropy energy of the transition metal
sublattice.

Assuming Ni substitutes preferentially at 2c sites,
the calculated peak in anisotropy and the experimentally measured peak
in coercivity are located at similar concentrations.

This observation may explain the increased coercivity with Ni doping 
of RECo_5 compounds with nonmagnetic REs <cit.>.

However, as shown in Fig. <ref>, the maximum in the coercive field for
GdCo_5-xNi_x
coincides with a minimum in magnetization.

Referring again to the micromagnetic expression for
the coercive field of a ferromagnet of 2K/M, we note that 
naively setting M to zero 
at finite K should yield a divergent coercive field at the 
compensation point.

This divergence remains even when
Kronmüller's prefactor α <cit.>
is introduced in order to account for microstructural variation in K.

Therefore the boost in coercivity in GdCo_5 may simply result from compensation
of the Gd and TM magnetic moments.

However, GdCo_5-xNi_x is a ferrimagnet, so it is by no 
means obvious that models based on the rotation of a single 
magnetization vector should apply.

Extending the SW model for a ferrimagnet produces a two-sublattice model, 
which was investigated for positive applied fields in 
Ref. .

Crucially, the competition between the external field, the antiparallel 
exchange interaction and the magnetocrystalline anisotropy can lead to 
canting between the Gd and the TM sublattices when a magnetic field is applied.


We recently introduced a method of calculating magnetization versus field curves
including this effect from first principles, which we applied to 
GdCo_5 (x = 0) at low <cit.> and 
high <cit.> magnetic fields.

In this approach,  DFT-DLM calculations are used to 
parameterize the following expression for the free energy F_2.



    F_2(θ_Gd,θ_TM)    =     K_1,TMsin^2θ_TM
    - μ_0𝐌·𝐇
           + K_2,TMsin^4θ_TM + K_1,Gdsin^2θ_Gd
           + S(θ_TM,θ_Gd) + A  𝐌̂_𝐆𝐝·𝐌̂_𝐓𝐌


with 𝐌 = 𝐌_𝐆𝐝 + 𝐌_𝐓𝐌.

The first line of Eq. <ref> resembles the free energy
found in the Stoner-Wohlfarth model.

θ_i denotes the angle that the magnetization of sublattice i makes with the
c axis, K_j,i represents the various anisotropy constants, and S represents the anisotropy
energy due to dipolar interactions.

A quantifies the  exchange interaction, which with a positive
value favors antiferromagnetic alignment of the Gd and TM moments.


For a compensated magnet, M_Gd = M_TM 
and in the absence of an external field the magnetic moments are antiparallel.

Naively we might therefore set 𝐌 = 0 and, from inspection of 
equation <ref>, argue that the external field can have no effect on 
the free energy or magnetization, corresponding  to infinite coercivity.

However, 𝐌 = 0 is only true as long as the moments remain
antiparallel.

If the antiparallel alignment breaks, the magnetic sublattices couple
individually to the external field.

For instance, in the limit of extremely strong external fields both sublattices
align to the field, giving a resultant magnetization of 
M_Gd + M_TM.

We note that this model provides an explanation for the magnetization measurements of
the powder in a 10 kOe field as a function of temperature (Fig. <ref>).

On free-to-rotate samples, the critical field required to trigger the
transition from antiparallel to canted moments essentially scales as
|M_Gd - M_TM| <cit.>.

Therefore, as one approaches the compensation point in the (free-to-rotate) powder,
the antiparallel alignment can be broken with a small field, and a nonzero
magnetic moment measured.





Now, considering fixed samples,
in Fig. <ref>, the results of minimizing F_2 
along the full multi-quadrant magnetization curve are shown, 
sweeping the field along the sequence
0→ H_max→ -H_max→ H_max,
for GdCo_5 and GdCo_3.74Ni_1.26.

Here the OPC is included, preferential Ni doping at the 2c 
sites is assumed (cf. Fig. <ref>), and the calculations 
performed at zero temperature.

The field is applied along the crystallographic c axis.

The size of the field is not intended to match experimental
results, as described below, but the relative changes between 
different compositions can be extracted.

Focusing first on GdCo_5 (blue line) for |H| < 820 kOe,
the boxlike curve resembles that of a SW ferromagnet.

At 820 kOe, there is a transition from the rigid antiparallel alignment 
of Gd and Co moments to a canted configuration, with the energy gain 
of the Gd moments aligning with the magnetic field competing with 
the exchange and anisotropy terms.

This transition is reversible, such that there is no hysteresis in 
the first quadrant.

In the second quadrant, at H = -473 kOe 
(blue arrow in Fig. <ref>) there is a discontinuous jump 
in the magnetization corresponding to a simultaneous 180^∘ 
rotation of the Gd and Co moments.

This jump is irreversible, so returning the field to zero now gives 
a negative magnetization, with the majority of the Co moments 
now pointing opposite to the field until the symmetric jump at 
H = 473 kOe occurs.

GdCo_3.74Ni_1.26 (x = 1.26, pink line) shows broadly the same 
behavior, but the nature of the transitions themselves are 
slightly different.

At the high-field transition from antiparallel to canted moments 
at |μ_0H| = 1060 kOe, the moments rotate rapidly 
with field such that there is a very sudden, but reversible, 
increase in magnetization.

However, the demagnetizing curve in the second quadrant shows 
a new feature, which is a continuous and reversible decrease of 
magnetization in the region -835 kOe < μ_0H < -785 kOe.

The magnetization passes through zero at -792 kOe, and becomes 
increasingly negative, exceeding its zero-field magnitude at -800 kOe.

This new feature is a result of the system getting trapped in a 
metastable energy minimum corresponding to canted Gd and TM moments.

For |H|> 835 kOe this minimum disappears, and 
the system undergoes an irreversible transition back to antiparallel moments.

Equating the coercive fields with the magnitudes of the applied 
fields which produce zero magnetization in the second quadrant, 
we extract values of 473 kOe for x = 0 and 792 kOe for x = 1.26.

For now ignoring the fact that these numbers are huge compared 
to experiment, in terms of relative magnitudes an increase in 
coercivity by a factor of 1.7 is observed at a Ni doping 
of x=1.26.

We note that this increase is relatively modest compared to a 
naive prediction based on assuming that the coercivity was 
proportional to K_1/M; since K_1 and M increase/decrease 
by a factor of 3 respectively, we might have expected a 
coercivity enhancement by a factor of 9.

The calculations in Fig. <ref> are illustrative, but 
cannot be considered a realistic picture of macroscopic magnetization 
reversal.

In reality, the nucleation of reverse domains, e.g. at the edge 
of the sample, will facilitate magnetization reversal at far 
lower fields than found here <cit.>.

The coercivity will then depend on how the domain walls propagate 
through the sample, which is likely to be affected by the 
presence of the secondary phase <cit.>.

We also note that the peak in coercivity observed experimentally 
here was found for polycrystalline samples.

However, it is interesting that the small single crystals of 
Cu-doped GdCo_5 reported in Ref.  
do show box-like demagnetization curves such as the calculated
ones shown in Fig. <ref>.




§ SUMMARY & CONCLUSIONS 


Polycrystalline samples of GdCo_5-xNi_x for x=0 to 5 have 
been synthesized using an arc furnace. 

The predominant formation  of a  single phase was confirmed by comparing powder 
x-ray diffraction patterns to the pattern measured for pure GdCo_5.

Optical and SEM imaging showed small (<7%) amounts of a 2:7 phase in 
the 1:5 matrix for x ≤ 2.5, and no 2:7 phase at higher concentrations. 

No evidence was found to say with confidence that the annealing improves 
(or indeed, affects at all) the microstructure and phase purity of the samples.

The magnetization of the samples measured at 70 kOe and 10 K initially decreases as the
nickel content is increased.

At a composition of x ≈ 1, the (absolute) magnetization reaches a minimum
and then increases with further Ni addition.

This behavior is due to the Ni weakening the magnetization of the transition
metal sublattice, such that at low temperature, for x < 1 the net magnetization
points along the direction of the transition metal moments, while for x > 1
the net magnetization points along the direction of the Gd moments.

Zero temperature DFT-DLM calculations find the compensation composition, i.e.the point at which the transition metal and Gd sublattice magnetizations cancel each
other to be x = 1.04, in good agreement with the experimentally-observed
minimum.

The calculations found the magnetization to be rather insensitive to the 
location of the Ni dopants, which can occupy either 2c or 3g crystallographic 
sites. 

For a Ni content of 1 ≤ x ≤ 3, compensation temperatures in the range 10–360 K
were observed.

The compensation temperatures increase with increasing Ni doping, and occur due to
the faster disordering of the Gd moments compared to the transition metal.

Finite temperature DFT-DLM calculations on pristine GdCo_5 and GdCo_3.74Ni_1.26
demonstrate this behavior explicitly, finding a compensation temperature of 140 K for
the latter compound which corresponds well to the experimental measurements shown
in Fig. <ref>.

The coercivity of polycrystalline buttons measured below 10 K 
is found to have a maximum value at a composition x ≈ 1, 
coinciding with the minimum in magnetization. 

One might argue that such behavior is consistent with the Stoner-Wohlfarth model
and micromagnetics, where the coercive field is inversely proportional to the magnetization
(H_c=2K/M).

However, such a picture is based on the rotation of a single magnetic sublattice and
neglects the possibility that magnetization reversal might proceed via a canted arrangement
of Gd and transition metal moments.

Magnetization versus field loops calculated allowing for such canting
do show an increase in coercivity from x=0 to x=1.26, but not by as 
great an amount as predicted by the Stoner-Wohlfarth
model given the reduction in M.

Apart from the reduction in magnetization, the DFT-DLM calculations also found 
an increase in the magnetocrystalline anisotropy of the transition-metal 
sublattice with Ni doping.

Indeed, assuming preferential substitution at the 2c sites 
the peak in anisotropy was
found for a concentration of x=1.5,
reasonably close to the experimentally observed
coercivity maximum.

Such an explanation for increased coercivity, independent of phenomena related to 
compensation, would be consistent with measurements on doped RECo_5 compounds
with nonmagnetic RE, which also undergo peaks in coercivity despite having no
compensation points.

However, apart from these intrinsic factors, it should also be noted that the peak
in coercivity also coincides with the largest amount of secondary 
2:7 phase (Table <ref>).

Although the amount of secondary phase we observe is small in terms of measuring
intrinsic quantities, interfaces between the 1:5 and 2:7 phases could 
inhibit the motion of domain walls through the sample, increasing 
the coercivity.

Being able to better control the formation of the 2:7 
phase would allow the magnitude of this extrinsic effect to be tested.

The current study emphasizes the complementary roles played by experiments and theory.

On one hand, the experiments provide valuable input for developing the calculations,
particularly in terms of validating the methodology.

On the other hand, the calculations provide microscopic insight into macroscropic
measurements.

Here we have shown that quantitative comparisons are possible between intrinsic
quantities such as magnetizations and compensation temperatures.

However, whilst the calculations can give hints about extrinsic quantities such as
the coercivity, in reality a multiscale approach capable of describing e.g. microstructure
and long range demagnetizing fields is required.

Nonetheless, the first-principles calculations (as validated by experimental measurements
of intrinsic quantities) can still play a fundamental role by providing the 
microscopic parameters required as input for such simulations.



§ ACKNOWLEDGEMENTS

This work forms part of the PRETAMAG project, funded by the UK Engineering 
and Physical Sciences Research Council (EPSRC) Grant No. EP/M028941/1.

Crystal growth work at Warwick was also supported by EPSRC Grant No. EP/M028771/1.

We thank the Warwick Research Technology Platform (X-ray Diffraction and Electron Microscopy) 
for their assistance.

We acknowledge the Warwick Manufacturing Group and Buehler for assistance with 
slide production.

We thank E. Mendive-Tapia and G. Marchant for useful discussions.











52
fxundefined [1]
 ifx#1

fnum [1]
 #1firstoftwo
 secondoftwo
 
fx [1]
 #1firstoftwo
 secondoftwo
 





noop [0]secondoftwo

ref[1]@startlink#1@href
href[1]#1@endlink
anitize@url [0]`
12`$12`&12`#12`1̂2`_12`%12
startlink[1]
endlink[0]

rl [1]href #1












@bib@innerbibempty

[Kumar(1988)]Kumar1988
  author author K. Kumar, 10.1063/1.341084 journal journal J. Appl. Phys. volume 63, pages R13 (year 1988)NoStop
[Strnat et al.(1967)Strnat,
  Hoffer, Olson, Ostertag,  and Becker]Strnat1967
  author author K. Strnat, author G. Hoffer,
  author J. Olson, author W. Ostertag,  and author J. J. Becker, 10.1063/1.1709459 journal journal J. Appl.
  Phys. volume 38, pages 1001 (year 1967)NoStop
[Sagawa et al.(1984)Sagawa,
  Fujimura, Togawa, Yamamoto,  and Matsuura]Sagawa1984
  author author M. Sagawa, author S. Fujimura,
  author N. Togawa, author H. Yamamoto,  and author Y. Matsuura, 10.1063/1.333572 journal journal J. Appl.
  Phys. volume 55, pages 2083 (year 1984)NoStop
[Croat et al.(1984)Croat,
  Herbst, Lee, and Pinkerton]Croat1984
  author author J. J. Croat, author J. F. Herbst,
  author R. W. Lee,  and  author F. E. Pinkerton, 10.1063/1.333571 journal journal J.
  Appl. Phys. volume 55, pages 2078
  (year 1984)NoStop
[Kuz'min and Tishin(2008)]Kuzmin2008
  author author M. D. Kuz'min and author A. M. Tishin, in @noop  booktitle Handbook of
  Magnetic Materials, editor
  edited by editor K. H. J. Buschow (publisher Elsevier B.V., address
  Amsterdam, year 2008), Vol. volume 17, Chap. chapter 3, p.  pages 149NoStop
[Nesbitt et al.(1959)Nesbitt, Wernick, and Corenzwit]Nesbitt1959
  author author E. A. Nesbitt, author J. H. Wernick,  and author E. Corenzwit, @noop  journal journal J.
  Appl. Phys. volume 30, pages 365
  (year 1959)NoStop
[Nassau et al.(1960)Nassau,
  Cherry, and Wallace]Nassau1960
  author author K. Nassau, author L. V. Cherry,   and author W. E. Wallace,  @noop  journal journal J. Phys. Chem.
  Solids. volume 16, pages 131
  (year 1960)NoStop
[Buschow(1977)]Buschow1977
  author author K. H. J.  Buschow, 10.1088/0034-4885/40/10/002
  journal journal Rep. Prog. Phys. volume 40, pages 1179 (year
  1977)NoStop
[Yermolenko(1980)]Yermolenko1980
  author author A. S. Yermolenko, @noop  journal journal
  Fiz. Metal. Metalloved. volume 50, pages 741 (year 1980)NoStop
[Patrick et al.(2017)Patrick, Kumar, Balakrishnan, Edwards, Lees, Mendive-Tapia, Petit, and Staunton]Patrick2017
  author author C. E. Patrick, author S. Kumar,
  author G. Balakrishnan, author R. S. Edwards, author
  M. R. Lees, author
  E. Mendive-Tapia, author
  L. Petit,  and author
  J. B. Staunton, @noop  journal journal Phys. Rev. Mater. volume 1, pages 024411 (year
  2017)NoStop
[Bajorek et al.(2011)Bajorek, Chełkowska, and Andrzejewski]Bajorek2011
  author author A. Bajorek, author G. Chełkowska,  and author B. Andrzejewski, @noop  journal journal
  J. Alloy. Compd. volume 509, pages
  578 (year 2011)NoStop
[Grechishkin et al.(2006)Grechishkin, Kustov, Cugat, Delamare, Poulin, Mavrudieva, and  Dempsey]Grechishkin2006
  author author R. M. Grechishkin, author M. S. Kustov, author O. Cugat,
  author J. Delamare, author G. Poulin, author
  D. Mavrudieva,  and author
  N. M. Dempsey, @noop  journal journal Appl. Phys. Lett. volume 89, pages 122505 (year
  2006)NoStop
[de Oliveira et al.(2011)de Oliveira, Sinnecker, Grössinger,
  Pentón-Madrigal, and Estévez-Rams]deOliveira2011
  author author L. A. S.  de Oliveira, author J. P.  Sinnecker, author R. Grössinger, author A. Pentón-Madrigal,  and author E. Estévez-Rams, @noop  journal
  journal J. Magn. Magn. Mater. volume
  323, pages 1890 (year 2011)NoStop
[Buschow and Brouha(1976)]Buschow1976
  author author K. H. J.  Buschow and author M. Brouha, @noop  journal journal J. Appl. Phys. volume 47, pages 1653 (year 1976)NoStop
[Chuang et al.(1982)Chuang,
  Wu, and Chang]Chuang1982
  author author Y. C. Chuang, author C. H. Wu,   and author Y. C. Chang,  @noop  journal journal J. Less-Common
  Met. volume 84, pages 201 (year 1982)NoStop
[Chuang et al.(1981)Chuang,
  Wu, Li, Chang, and  Wang]Chuang1981
  author author Y. C. Chuang, author C. H. Wu,
  author T. C. Li, author S. C. Chang,  and author M. S. Wang, @noop 
  journal journal J. Less-Common Met. volume 78, pages 219 (year
  1981)NoStop
[Liu et al.(1991)Liu,
  Zhong, de Boer, and Buschow]Liu1991
  author author J. P. Liu, author X. P. Zhong,
  author F. R. de Boer,  and  author K. H. J. Buschow,  @noop  journal journal J. Appl. Phys.  volume 69, pages 5536 (year
  1991)NoStop
[Burzo and Pop(1999)]Burzo1999
  author author E. Burzo and author V. Pop,  @noop  journal journal J. Magn. Magn.
  Mater. volume 196–197, pages 768
  (year 1999)NoStop
[Drzazga et al.(1989)Drzazga, Winiarska, and Stein]Drzazga1989
  author author Z. Drzazga, author A. Winiarska,
   and author F. Stein,  @noop  journal journal J. Less-Common
  Met. volume 153, pages L21 (year 1989)NoStop
[Gignoux et al.(1976)Gignoux, Givord, and del
  Moral]Gignoux1976
  author author D. Gignoux, author D. Givord,   and author A. del Moral,  @noop  journal journal Solid State
  Commun. volume 19, pages 891
  (year 1976)NoStop
[Gyorffy et al.(1985)Gyorffy, Pindor, Staunton, Stocks, and Winter]Gyorffy1985
  author author B. L. Gyorffy, author A. J. Pindor,
  author J. Staunton, author G. M. Stocks,  and author H. Winter, 10.1088/0305-4608/15/6/018 journal journal J.
  Phys. F Met. Phys. volume 15, pages
  1337 (year 1985)NoStop
[Staunton et al.(2006)Staunton, Szunyogh, Buruzs, Gyorffy, Ostanin, and Udvardi]Staunton2006
  author author J. B. Staunton, author L. Szunyogh,
  author A. Buruzs, author B. L. Gyorffy, author
  S. Ostanin,  and author
  L. Udvardi, 10.1103/PhysRevB.74.144411 journal journal Phys.
  Rev. B volume 74, pages 144411
  (year 2006)NoStop
[Buschow and den
  Broeder(1973)]Buschow1973
  author author K. H. J.  Buschow and author F. J. A.  den Broeder, @noop  journal journal J. Less-Common Met. volume 33, pages 191 (year 1973)NoStop
[Katayama et al.(1976)Katayama, Ohkoshi, Koizumi, Shibata, and Tsushima]Katayama1976
  author author T. Katayama, author M. Ohkoshi,
  author Y. Koizumi, author T. Shibata,  and author T. Tsushima, @noop 
  journal journal Appl. Phys. Lett. volume 28, pages 635 (year
  1976)NoStop
[Ebert et al.()Ebert,
  Ködderitzsch, and Minár]Ebert2011
  author author H. Ebert, author D. Ködderitzsch,  and author J. Minár, @noop  journal journal Rep. Prog. Phys volume 74, pages 096501 (year
  2011)NoStop
[Andreev and Zadvorkin(1991)]Andreev1991
  journal   author author A. V. Andreev and author S. M. Zadvorkin, http://dx.doi.org/10.1016/0921-4526(91)90011-3 journal
  journal Physica B. volume 172,  pages 517  (year 1991)NoStop
[Däne et al.(2009)Däne,
  Lüders, Ernst, Ködderitzsch, Temmerman, Szotek, and  Hergert]Daene2009
  author author M. Däne, author M. Lüders,
  author A. Ernst, author D. Ködderitzsch, author W. M. Temmerman, author
  Z. Szotek,  and author
  W. Hergert, 10.1088/0953-8984/21/4/045604 journal journal J.
  Phys.: Condens. Matter volume 21, pages
  045604 (year 2009)NoStop
[Vosko et al.(1980)Vosko,
  Wilk, and Nusair]Vosko1980
  author author S. H. Vosko, author L. Wilk,  and  author M. Nusair, 10.1139/p80-159 journal journal Can.
  J. Phys. volume 58, pages 1200
  (year 1980)NoStop
[Lüders et al.(2005)Lüders, Ernst, Däne, Szotek, Svane, Ködderitzsch,
  Hergert, Györffy, and Temmerman]Lueders2005
  author author M. Lüders, author A. Ernst,
  author M. Däne, author Z. Szotek, author
  A. Svane, author D. Ködderitzsch, author W. Hergert, author B. L.  Györffy,  and author W. M.  Temmerman, 10.1103/PhysRevB.71.205109
  journal journal Phys. Rev. B volume 71, pages 205109 (year
  2005)NoStop
[Eriksson et al.(1990)Eriksson, Johansson, Albers, Boring, and Brooks]Eriksson19901
  author author O. Eriksson, author B. Johansson,
  author R. C. Albers, author A. M. Boring,  and author M. S. S. Brooks, 10.1103/PhysRevB.42.2707 journal journal Phys.
  Rev. B volume 42, pages 2707
  (year 1990)NoStop
[Steinbeck et al.(2001)Steinbeck, Richter, and Eschrig]Steinbeck2001
  author author L. Steinbeck, author M. Richter,
   and author H. Eschrig, http://dx.doi.org/10.1016/S0304-8853(00)01189-6 journal journal J. Magn. Magn. Mater. volume 226–230, pages 1011  (year
  2001), note proceedings of the International Conference on
  Magnetism (ICM 2000)NoStop
[Ebert and Battocletti(1996)]Ebert1996
  author author H. Ebert and author M. Battocletti, http://dx.doi.org/10.1016/0038-1098(96)00202-5 journal
  journal Solid State Commun. volume
  98, pages 785  (year 1996)NoStop
[Patrick and Staunton(2018)]PatrickStaunton2018
  author author C. E. Patrick and author J. B. Staunton, 10.1103/PhysRevB.97.224415 journal journal Phys. Rev. B volume
  97, pages 224415 (year 2018)NoStop
[Matsumoto et al.(2014)Matsumoto, Banerjee, and Staunton]Matsumoto2014
  author author M. Matsumoto, author R. Banerjee,
   and author J. B. Staunton,  10.1103/PhysRevB.90.054421 journal journal Phys. Rev. B volume 90, pages 054421 (year 2014)NoStop
[Bruno and Ginatempo(1997)]Bruno1997
  author author E. Bruno and author B. Ginatempo, 10.1103/PhysRevB.55.12946 journal journal Phys. Rev. B volume
  55, pages 12946 (year 1997)NoStop
[Patrick et al.(2018a)Patrick, Kumar,
  Balakrishnan, Edwards, Lees,
  Petit, and Staunton]Patrick2018
  author author C. E. Patrick, author S. Kumar,
  author G. Balakrishnan, author R. S. Edwards, author
  M. R. Lees, author
  L. Petit,  and author
  J. B. Staunton, 10.1103/PhysRevLett.120.097202 journal journal
  Phys. Rev. Lett. volume 120, pages
  097202 (year 2018a)NoStop
[Top()]Topas
  @noop  note A. A. Coelho, TOPAS-Academic, Ver.6,
  Bruker-AXS, Karlsruhe, Germany, 2016.Stop
[Lihl et al.(1969)Lihl,
  Ehold, Kirchmayr, and Wolf]Lihl1969
  author author F. Lihl, author J. R. Ehold,
  author H. R. Kirchmayr,  and  author H. D. Wolf, @noop
   journal journal Acta Phys. Austriaca  volume 30, pages 164 (year
  1969)NoStop
[Wernick and Geller(1959)]Wernick1959
  author author J. H. Wernick and author S. Geller, @noop  journal journal Acta
  Crystallogr. volume 12, pages 662
  (year 1959)NoStop
[Sorgic et al.(1995)Sorgic,
  Drasner, and Blazina]sorgic1995
  author author B. S̆orgić, author A. Dras̆ner,   and author Ẑ. Blaẑina,  @noop  journal journal J. Alloy. Compd.  volume 221, pages 169 (year
  1995)NoStop
[Lemaire and Paccard(1969)]lemaire1969
  author author R. Lemaire and author D. Paccard, @noop  journal journal Bull.
  Soc. Fr. Mineral. Cristallogr. volume 92, pages 9 (year 1969)NoStop
[Sepehri-Amin et al.(2017)Sepehri-Amin, Thielsch, Fischbacher,
  Ohkubo, Schrefl, Gutfleisch,  and Hono]SepehriAmin2017
  author author H. Sepehri-Amin, author J. Thielsch, author J. Fischbacher, author T. Ohkubo,
  author T. Schrefl, author O. Gutfleisch,  and author K. Hono, https://doi.org/10.1016/j.actamat.2016.12.050 journal
  journal Acta Mater. volume 126,  pages 1  (year 2017)NoStop
[Eschrig et al.(2005)Eschrig, Sargolzaei, Koepernik, and  Richter]Eschrig2005
  author author H. Eschrig, author M. Sargolzaei,
  author K. Koepernik,  and  author M. Richter, 10.1209/epl/i2005-10285-9 journal journal Europhys. Lett. volume 72, pages 611 (year 2005)NoStop
[Daalderop et al.(1996)Daalderop, Kelly, and Schuurmans]Daalderop1996
  author author G. H. O.  Daalderop, author P. J.  Kelly,  and author M. F. H.  Schuurmans, 10.1103/PhysRevB.53.14415
  journal journal Phys. Rev. B volume 53, pages 14415 (year
  1996)NoStop
[Deportes et al.(1976)Deportes, Givord, Schweizer, and  Tasset]Deportes1976
  author author J. Deportes, author D. Givord,
  author J. Schweizer,  and  author F. Tasset, 10.1109/TMAG.1976.1059185 journal journal IEEE Trans. Magn. volume 12, pages 1000 (year 1976)NoStop
[Chikazumi(1997)]Chikazumi1997
  author author S. Chikazumi, @noop  title Physics of
  Ferromagnetism, edition 2nd ed. (publisher
  Oxford University Press, address Oxford, year
  1997) p. pages 495NoStop
[Brown(1957)]Brown1957
  author author W. F. Brown, 10.1103/PhysRev.105.1479 journal
  journal Phys. Rev. volume 105,  pages 1479 (year 1957)NoStop
[Kronmüller(1987)]Kronmuller1987
  author author H. Kronmüller, 10.1002/pssb.2221440134 journal journal Phys. Status Solidi (b) volume 144, pages 385 (year
  1987)NoStop
[Radwański(1986)]Radwanski1986
  author author R. J. Radwański, http://dx.doi.org/10.1016/0378-4363(86)90225-1 journal
  journal Physica B+C volume 142,  pages 57  (year 1986)NoStop
[Patrick et al.(2018b)Patrick, Kumar,
  Götze, Pearce, Singleton,
  Rowlands, Balakrishnan, Lees,
  Goddard, and Staunton]PatrickKumar2018
  author author C. E. Patrick, author S. Kumar,
  author K. Götze, author M. J. Pearce, author
  J. Singleton, author
  G. Rowlands, author
  G. Balakrishnan, author
  M. R. Lees, author
  P. A. Goddard,  and author
  J. B. Staunton, 10.1088/1361-648X/aad029 journal journal J.
  Phys.: Condens. Matter volume 30, pages
  32LT01 (year 2018b)NoStop
[Isnard et al.(2012)Isnard,
  Skourski, Diop, Arnold,
  Andreev, Wosnitza, Iwasa,
  Kondo, Matsuo, and Kindo]Isnard2012
  author author O. Isnard, author Y. Skourski,
  author L. V. B. Diop, author Z. Arnold, author
  A. V. Andreev, author
  J. Wosnitza, author
  A. Iwasa, author A. Kondo, author A. Matsuo,  and author K. Kindo, 10.1063/1.4710995 journal journal J. Appl. Phys. volume 111, pages 093916 (year
  2012)NoStop
[Fischbacher et al.(2017)Fischbacher, Kovacs, Oezelt, Gusenbauer, Schrefl, Exl, Givord, Dempsey, Zimanyi, Winklhofer, Hrkac, Chantrell, Sakuma, Yano, Kato, Shoji,  and Manabe]Fischbacher2017
  author author J. Fischbacher, author A. Kovacs,
  author H. Oezelt, author M. Gusenbauer, author
  T. Schrefl, author L. Exl, author D. Givord, author N. M. Dempsey,
  author G. Zimanyi, author M. Winklhofer, author
  G. Hrkac, author R. Chantrell, author N. Sakuma, author M. Yano, author A. Kato, author T. Shoji,  and  author A. Manabe, 10.1063/1.4999315 journal journal
  Appl. Phys. Lett. volume 111, pages
  072404 (year 2017)NoStop

