# On the magnetic nanostructure of a Co-Cu alloy processed by high-pressure
torsion

Martin Stückler
Erich Schmid Institute of Materials Science, Austrian Academy of Sciences
Jahnstraße 12, 8700 Leoben, Austria
<EMAIL_ADDRESS>&Christian Teichert
Institute of Physics, Montanuniversität Leoben
Franz-Josef-Straße 18, 8700 Leoben, Austria &Aleksandar Matković
Institute of Physics, Montanuniversität Leoben
Franz-Josef-Straße 18, 8700 Leoben, Austria &Heinz Krenn
Institute of Physics, University of Graz
Universitätsplatz 5, 8010 Graz, Austria &Lukas Weissitsch
Erich Schmid Institute of Materials Science, Austrian Academy of Sciences
Jahnstraße 12, 8700 Leoben, Austria &Stefan Wurster
Erich Schmid Institute of Materials Science, Austrian Academy of Sciences
Jahnstraße 12, 8700 Leoben, Austria &Reinhard Pippan
Erich Schmid Institute of Materials Science, Austrian Academy of Sciences
Jahnstraße 12, 8700 Leoben, Austria &Andrea Bachmaier
Erich Schmid Institute of Materials Science, Austrian Academy of Sciences
Jahnstraße 12, 8700 Leoben, Austria

###### Abstract

In this study, a preparation route of Co-Cu alloys with soft magnetic
properties by high-pressure torsion deformation is introduced.
Nanocrystalline, supersaturated single-phase microstructures are obtained
after deformation of Co-Cu alloys, which are prepared from an initial powder
mixture with Co-contents above 70 wt.%. Isochronal annealing treatments up to
400°C further reveal a remarkable microstructural stability. Only at 600°C,
the supersaturated phase decomposes into two fcc-phases. The coercivity,
measured by SQUID as a function of annealing temperature, remains
significantly below the value for bulk-Co in all states investigated. In order
to understand the measured magnetic properties in detail, a quantitative
analysis of the magnetic microstructure is carried out by magnetic force
microscopy and correlated to the observed changes in coercivity. Our results
show that the rising coercivity can be explained by a magnetic hardening
effect occurring in context with spinodal decomposition.

_Keywords_ severe plastic deformation (SPD) $\cdot$ high-pressure torsion
$\cdot$ supersaturation $\cdot$ magnetic force microscopy (MFM) $\cdot$
nanocrystalline

##  1 Introduction

Desirable magnetic properties have frequently been attributed to the
nanocrystalline regime [1, 2]. Nanocrystalline soft magnetic materials are
already commercially produced, in particular by melt spinning, yielding
amorphous sheets. In additional processing steps, these sheets are stacked and
exposed to annealing treatments to adjust the grain size, further tuning the
magnetic properties such as saturation magnetization, coercivity, and
permeability [3, 4]. In contrast to this type of material synthesis, also
known as bottom-up approach, the production of such nanocrystalline magnetic
materials starting with coarse grained materials (top-down approach) has
gained attraction recently [5, 6]. The advantage is obvious: additional
processing steps, such as stacking of sheets can be omitted. Furthermore,
(expensive) rare-earth elements, necessary for metallic glass formation, can
be neglected. For the top-down approach, high-pressure torsion (HPT) is an
attractive technique, as the prepared samples are already present in bulk
form. Moreover, with this technique the microstructure can be tuned while the
sample retains its shape during preparation. Being a technique of severe
plastic deformation (SPD), HPT exhibits the advantage that the applied shear
deformation can act continuously, i.e., any desireable amount of deformation
can be applied [7]. This deformation can cause grain refinement with the
possibility of attaining the regime of nanocrystallinity [8]. Metastable
phases can form during HPT-deformation, and may be retained even after
pressure release [9]. Starting with conventional powders, any chemical
composition can be investigated by HPT. In particular, Co-based materials have
raised interest due to their low magnetostriction, favoring soft magnetic
properties [1, 10]. Studies dealing with the immiscible Co-Cu system have
demonstrated that single phase supersaturated solid solutions can be prepared
by HPT [11], whereas higher Co-contents yield better soft magnetic properties
[12]. As recent studies reported on failing synthesis by HPT for Co-contents
above 67 wt.% [12], the scope of the current study is to establish a promising
sample preparation route for high Co-contents yielding a single phase
supersaturated solid solution. The magnetic properties of supersaturated solid
solutions are highly sensitive to temperature [13]. Therefore, in this study
an in-depth characterization of the temperature stability and its influence on
the magnetic properties is carried out.

##  2 Experimental

Conventional powders (Co: Alfa Aesar, -22 mesh,
Puratronic${}^{\text{\textregistered}}$, 99.998%; Cu: Alfa Aesar, -170+400
mesh, 99.9%) were mixed to a desired composition and hydrostatically
consolidated in Ar-atmosphere. The resulting coin-shaped specimen (diameter: 8
mm; thickness: 1 mm) was exposed to SPD by HPT at temperatures between ambient
conditions and 500°C (facilitated by inductive heating of the anvils) [8].
During HPT, a pressure of 5 GPa was applied, while using a rotational speed of
1.28 min-1. To ensure a microstructural steady state, 50-150 numbers of turns
were chosen, corresponding to a shear strain of about 1000-3000 at a radius of
3 mm. Subsequently, isochronal annealing treatments were performed in a
conventional furnace for 1 h each, followed by a quick cooling in air. Vickers
microhardness was measured with a used load of 500 g (HV0.5; Buehler Micromet
5100). The microstructure was investigated using scanning electron microscopy
(SEM; Zeiss LEO1525). An attached energy dispersive X-ray spectrometer (EDS;
Bruker e--Flash) was used to measure the samples’ chemical compositions, which
are given in weight percent (wt.%) herein. The crystallographic states were
characterized using X-ray diffraction (Bruker D2 Phaser) using Co-Kα
radiation. DC-hysteresis measurements were performed with a SQUID-magnetometer
(Quantum Design MPMS-XL 7) at 300 K and 8 K. Magnetic force microscopy (MFM)
measurements were carried out using a Horiba France SmartSPM in two-pass mode
at lift-heights between 10 nm and 20 nm using hard magnetically coated tips
(coercivity 15 Oe) exhibiting tip radii of $\leq$15 nm
(NANOSENSORS${}^{\text{{TM}}}$ SSS-MFMR). For MFM measurements, sample and tip
were put on the same potential, eliminating electrostatic interaction.
Topographic as well as MFM scans are visualized and processed with the
software Gwyddion 2.53. Topographic scans are corrected by mean plane
subtraction as well as by aligning rows. In case of MFM scans, data are
analyzed as measured.

##  3 Results and Discussion

###  3.1 Sample synthesis with high Co-content

Figure 1: SEM micrographs: (a) and (b) show the initial Cu and Co powders,
respectively. (c) shows a HPT-sample deformed at RT (100 turns) consisting of
Co78-Cu22 (wt.%). (d) and (e) show Co78-Cu22 deformed at 300°C (100 turns) and
Co93-Cu7 deformed at 500°C (50 turns) respectively. (f) shows a sample
consisting of Co88-Cu12, which was exposed to a two-step deformation process
at 500°C (50 turns) and RT (50 turns). Micrographs of HPT samples are taken in
tangential direction at a radius of 3 mm. Please note the different scale
bars.

As has recently been reported in [12], single-phase Co-Cu samples can be
prepared for intermediate Co-contents (28 wt.% - 67 wt.%) by HPT at room
temperature, yielding bulk samples with grain sizes in the nanocrystalline
regime (77 nm-100 nm [12]). Using the same processing parameters, sample
preparation with higher Co-contents ($>$ 67 wt.%) fails due to crack
formation. To obtain the desired single phase nanocrystalline microstructure
at higher Co-contents, the sample synthesis is improved as presented in the
following method.
The initial powders used in this study are shown in Fig. 1(a),(b). The
morphology of the Cu-powder (Fig. 1(a)) appears globular, whereas the Co-
powder (Fig. 1(b)) shows many tiny particles agglomerating to structures with
large surfaces. Room temperature deformation of Cu mixed with Co-powder shows
abrasion of the harder (dark) Co particles (Fig. 1(c)) which is considered as
an intermediate stage in the formation of supersaturated solid solutions [14],
but the formation of cracks impedes further deformation. To overcome the crack
formation limiting the development of a homogeneous microstructure, the idea
is to generate the desired microstructure by two consecutive steps of HPT
deformation: in the first step, HPT deformation is performed at elevated
temperatures, avoiding crack formation, and generating an ultra-fine grained
structure at enhanced homogeneity. In the second step, the same sample is
exposed to HPT-deformation at room temperature, yielding the desired,
nanocrystalline microstructure.
Fig. 1(d) shows an SEM micrograph of Co78-Cu22 deformed at 300°C for 100 turns
yielding a homogeneous deformation with a complete absence of cracks.
Homogeneous deformation is also reached for even higher Co-concentrations:
Fig. 1(e) shows Co93-Cu7 deformed at 500°C (50 turns). Although the
deformation at elevated temperatures yields homogenization of strain
distribution darker and brighter regions in the sub-µm regime are observed in
the micrographs fig. 1(d) and (e). Therefore, a homogeneous supersaturation is
not yet reached. As the scope of this study is to reach nanocrystalline grain
sizes while maintaining a high chemical homogeneity, a subsequent HPT-
deformation step at lower temperatures (e.g., room temperature) is expected to
yield the desired microstructure. Fig. 1(f) shows a micrograph of a sample
consisting of Co88-Cu12 deformed at 500°C (50 turns), which was subsequently
exposed to an additional deformation step at room temperature (50 turns). The
resulting microstructure exhibits enhanced chemical homogeneity and
furthermore a smaller grain size, in comparison to Fig. 1(e). As has been
reported in the literature, the steady state grain size is a function of
temperature [15], which has been recently attributed to the deformation
temperature dependent mobility of triple junctions [16].

###  3.2 Investigations on the thermal stability

Nanocrystalline materials are often prone to grain growth at low homologous
temperatures [1], causing the loss of the initial superior magnetic properties
[3, 4]. The thermal stability can be reduced further by a positive heat of
mixing, as it is the case for the presented Co-Cu samples [11]. Therefore, a
detailed investigation of the thermal stability of a Co72-Cu28 (wt.%) alloy is
carried out in the following, serving as an example of the Co-Cu alloys
described above. The presented sample was prepared by a two-step HPT
deformation process, where the first step is performed at 300°C (100 turns)
and the second step is performed at room temperature (50 turns).

Figure 2: SEM micrographs of (a) Co72-Cu28 (wt.%) processed by a two-step
deformation process at 300°C (100 turns) and subsequently at RT (50 turns).
The sample in (a) has been exposed to subsequent annealing treatments at 150°C
(b), 300°C (c), 400°C (d) and 600°C (e). The scale bar in (a) applies to all
micrographs. Images are taken in BSE-mode in the tangential direction. (f)
shows the hardness as a function of annealing temperature.

####  3.2.1 Microstructural characterization

Figure 2(a) shows the micrograph of a sample consisting of Co72-Cu28 in the
as-deformed state. In comparison to the sample, which has been exposed only to
deformation at 300°C (c.f. Fig. 1(d)), the microstructure reveals an enhanced
chemical homogeneity, as well as reduced grain size. The micrographs in Fig.
2(b)-(e) show the sample annealed at temperatures of 150°C, 300°C, 400°C and
600°, for 1 h each. From these images, no grain growth can be observed, but
chemical contrast forms slightly, indicating separation of the chemical phases
for annealing treatments up to 400°C (Fig. 2(b)-(d)). A considerable phase
contrast as well as significant larger grain sizes can be observed for an
annealing treatment at 600°C (Fig. 2(e)). Mechanical properties are very
sensitive to the microstructure. Therefore, Vickers-hardness is measured as a
function of annealing temperature. The mean values of several measurements
between radii ,$r$, of 2 mm and 3.5 mm (according to an average of the HPT
strain status) are plotted in Fig. 2(f). Due to the nanocrystalline grain size
as well as solid solution hardening, the hardness in the as-deformed state is
enhanced with respect to the coarse grained and pure phase materials. An
increasing hardness is observed for annealing treatments up to 400°C, which is
a common behavior for nanocrystalline materials, for details see [17]. The
600°C-annealed state shows the lowest hardness among all measured values,
which can be explained by the largest grain size as well as by the reduction
or absence of solid solution hardening.

Figure 3: XRD-pattern (Co-Kα radiation) of Co72-Cu28 (wt.%) exposed to
different subsequent annealing treatments (c.f. Fig. 2). Peak positions of
fcc-Cu, fcc-Co and hcp-Co are indicated below the spectra.

XRD-measurements are presented in Fig. 3. In the as-deformed state, only one
set of fcc-peaks is visible, showing a single-phase solid solution. Apart from
slightly diminishing FWHM, no significant change in the XRD spectra can be
observed for annealing treatments up to 400°C. A splitting into two sets of
fcc-peaks is found for annealing at 600°C coinciding with the microstructure
obtained by SEM (c.f. Fig. 2(e)). From the XRD-pattern, the lattice constants
are evaluated. To compensate for experimental errors, the Nelson-Riley
function is used for a precise evaluation of the lattice constants [18].

$\frac{\Delta
a}{a}\propto\frac{cos^{2}\theta}{sin\theta}+\frac{cos^{2}\theta}{\theta}$ (1)

[Eq. (1)] is used for evaluating the lattice constant $a$, with $\theta$ being
the diffraction angle of the maxima. The y-intercept of a linear regression
represents $\Delta a\>=\>0$ and leads to a precise determination in $a$. The
resulting lattice constants are displayed in Fig. 4, showing slight changes
for annealing treatments up to 400°C, arising most likely from compositional
fluctuations in powder metallurgical sample preparation. At 600°C, two
different fcc-phases are identified, with the lattice constants being very
close to the pure elements. However, it can not be concluded that both phases
are chemically pure, i.e, some small amounts of Co might persist in the Cu-
phase and vice versa. Furthermore, the Co-contents $x_{Co}$ (at.%) are
calculated for each $a$ according to Vegard’s law [19].

$a=x_{Co}\cdot a_{Co}+(1-x_{Co})\cdot a_{Cu}$ (2)

For the above estimation of Co-contents, the lattice constant are taken as in
the following: $a_{Cu}=3.615\>\mathring{\text{A}}$,
$a_{Co}=3.544\>\mathring{\text{A}}$. In Fig. 4, the Co-contents according to
Vegard’s law are indicated.
Although the single-phase nanocrystalline microstructure was determined to be
stable up to 400°C, it should be stated, that this value might not be achieved
for different Co-Cu ratios. Actually, in several studies dealing with SPD-
processed materials the temperature limit for single phase supersaturated
microstructures was reported to be extremely sensitive to the particular
composition investigated [9, 20].

Figure 4: Lattice constants as evaluated with the Nelson-Riley function [eq.
(1)] from XRD-patterns. The Co-content (at.%) is calculated using Vegard’s law
for each lattice constant (orange dashed line:
$a_{Cu}=3.615\>\mathring{\text{A}}$, green dashed line:
$a_{Co}=3.544\>\mathring{\text{A}}$).

####  3.2.2 DC-magnetic properties

In [12], it has been proposed that an increasing Co-content yields higher
saturation magnetization as well as lower coercivity. To examine this
presumption, hysteresis measurements using SQUID are performed at $300$ K and
$8$ K between $-7$ T and $+7$ T. DC-hysteresis curves are shown in Fig. S.2.
The approach to saturation magnetization is monitored by plotting the mass
magnetization $\sigma$ versus the inverse external field $H^{-1}$ between $2$
T and $7$ T, whereas the y-intercept of a linear regression yields
$\sigma_{SAT}$ at $H\>=\>\infty$, i.e., the saturation mass magnetization,
which is plotted in Fig. 5. The positive as well as the negative saturation
magnetization is evaluated. Fig. 5 shows changes in $\sigma_{SAT}$ upon
annealing. It is known that the magnetic moment of fcc-Co ($166.1$
emu$\cdot$g-1) deviates from the magnetic moment of hcp-Co ($162.5$
emu$\cdot$g-1). As revealed in the XRD-pattern (c.f. Fig. 3), Co is present in
an fcc configuration in all investigated states. It is therefore more likely
that the observed changes in $\sigma_{SAT}$ up to an annealing temperature of
400 °C arise from compositional fluctuations, which can be also seen in the
XRD-pattern to some extent and are a common problem in powder metallurgy. A
change in $\sigma_{SAT}$ between 400°C and 600°C can be attributed to chemical
demixing, as the supersaturated Co-Cu phase exhibits a suppressed magnetic
moment [21]. Assuming the magnetic moment for fcc-Co to be $166.1$
emu$\cdot$g-1 an evaluation of the mean Co-content from $\sigma_{SAT}$ yields
$71\>\pm\>1$ wt.%. This is in good accordance with the results from XRD-
measurements, taking into account the completely different approaches for
these quantification methods.
For an enhanced resolution in the determination of the coercivity $H_{C}$,
hysteresis loops are measured at $8$ K. It should be stated that errors in the
applied $H$-field lead to a deviation in the determination of $H_{C}$. But as
this is a reversible artifact [22], the relative evolution of $H_{C}$ is
unaffected. $H_{C}$ as determined from hysteresis measurements is also plotted
in Fig. 5 for all measured states. $H_{C}$ increases with increasing annealing
temperature, in contrast to the classical assumption that large grain sizes
(possessing multidomain structure) favor soft magnetic properties. The
observed behavior of $H_{C}$ corresponds rather to random anisotropy [4, 23].
However, it should be noted that a prerequisite for random anisotropy is for
the magnetic exchange length to exceed the grain size, which seems not to be
the case when referring to micromagnetic constants of bulk-Co. Another
important aspect is the huge change in coercivity between the initial powder
and the as-deformed state. $H_{C}$ of the initial powder is also not reached
for annealing treatments at 600°C, revealing the strong influence of the
microstructure on the coercivity. Furthermore, a reduced magnetocrystalline
anisotropy is assumed for fcc-Co in comparison to hcp-Co, which is present in
the initial powder [24]. Yet the mentioned points do not suffice to
quantitatively describe the observed changes in $H_{C}$. A similar temperature
behavior of the coercivity has also been reported for SPD-processed Co26-Cu74
(at.%) [13], but in contrast, in the present study a significantly smaller
coercivity is measured and no indications of dilute ferromagnetic phase nor
superparamagnetism were found. This is most likely due to the enhanced Co-
content in our study forming percolating ferromagnetic structures rather than
isolated clusters.

Figure 5: Saturation mass magnetization $\sigma_{SAT}$ (at $300$ K) and
coercivity $H_{C}$ (at $8$ K) evaluated as a function of annealing
temperature. The data are slightly shifted in $x$ for better visibility. The
saturation magnetization of fcc-Co is $166.1$ emu $\cdot$ g-1. The coercivity
of the initial Co-powder is also indicated. Note the break in the right
y-axis.

####  3.2.3 Magnetic force microscopy

For an in-depth understanding of the observed DC-magnetic properties, a
quantitative analysis of the magnetic microstructure is carried out. MFM
measurements are performed in two-pass intermittant-contact (tapping) mode,
i.e., in the first pass the topography is measured, whereas in the second pass
the magnetic stray field is measured by keeping the tip-to-sample distance
constant at an increased lift-height to minimize short-range interactions
contribution in the phase lag of the cantilever oscillations in the second
pass, i.e., to measure mainly magnetic force contribution to the phase lag of
the cantilever in the second pass. The magnetic microstructure is measured in
axial sample direction. Fig. 6 shows representative topography and MFM
measurements of the as-deformed and the 300°C annealed state. The topography
(Fig. 6(a),(c)) appears very smooth in both states and does not show any
correlation to its respective MFM scan (Fig. 6(b),(d)). An irregular
appearance of the domains is visible in both MFM measurements, most likely
arising from sample synthesis by SPD causing residual stresses [25]. The
domain sizes are in the range of 100 nm corresponding to the grain size in the
as-deformed state [12], indicating single-domain behavior.

|
---|---
|
Figure 6: 2µm x 2µm AFM scans of (a) as-deformed state and (c) 300°C annealed
state. The corresponding MFM scans of the as-deformed and 300°C annealed state
are shown in (b) and (d) respectively. The axial direction of the HPT specimen
points out of the plane, the shear direction is in horizontal direction. The
lateral scale bar in (a) applies to all scans. The minimum height and phase
signal values are shifted to zero for visualization purposes.

To qualitatively characterize the morphology and magnetic domain sizes for
each annealing temperature, we employ the following procedure which has been
introduced for a comprehensive surface roughness characterization [26, 27] but
can also be applied to the MFM signal [28]. This procedure considers so-called
auto-correlation and height-height correlation functions [26]. For isotropic
samples as in our case it is sufficient to perform a one-dimensional analysis.
The auto-correlation function $C(x)$ is calculated for each scan line of the
image [26].

$\centering C(x)=<[z(x_{0}+x)\>-<z>][z(x_{0})\>-<z>]>\@add@centering$ (3)

where $z$ stands either for the height in nm or the phase signal of the MFM
image in degrees. For a self-affine surface with a cut-off [26, 27] $C(x)$ can
be described by

$\centering C(x)=\sigma^{2}\cdot exp[-(|x|/\xi)^{2\alpha}]\@add@centering$ (4)

with $\sigma$ being the root mean square roughness (for MFM $\sigma$
represents the standard deviation of the average magnetic signal which is
related to the out-of-plane magnetization contrast). $\xi$ represents the
lateral correlation length, i.e., the length scale within the height or the
MFM signal of two points correlate. The Hurst parameter $\alpha$ represents
the “jaggedness” of the surface or the magnetic signal and ranges from 0 to 1,
where small values in $\alpha$ represent sudden fluctuations in height.
Another function describing surface statistics is the height-height
correlation function $H(x)$ [26].

$\centering H(x)=<[z(x_{0}+x)-z(x_{0})]^{2}>\@add@centering$ (5)

with the asymptotic behavior

$H(x)=x^{2\alpha}\>\text{for}\>x\ll\xi$ (6)

|
---|---
|
Figure 7: Quantitative analysis of AFM and MFM-scans. (a) and (b) shows auto-
correlation functions $C(x)$ [eq. 3] of topographic scans and MFM scans
respectively. (c) and (d) shows height-height correlation functions $H(x)$
[eq. 5] of topographic scans and MFM scans respectively.

In the following, both the auto-correlation function and the height-height
correlation function are calculated for the MFM scans [28]. To disentangle the
magnetic information from topography, these functions are also evaluated for
the topographic (first-pass) scans. At least 6 individual scans are evaluated
for each state to enhance statistical significance. Fig. 7 shows
representative $C(x)$ and the $H(x)$ curves evaluated for the the topographic
signal and MFM signal. Note that the data are plotted in the statistically
significant range for small values in $x$. Different shapes can be identified
in the presented $C(x)$. In contrast to the topographic $H(x)$ (Fig. 7(c)),
two slopes can be identified in magnetic $H(x)$ (Fig. 7(d)), representing a
multi-fractal behavior [28]. Therefore, a superposition of two self-affine
fits [29] yields a better description of the magnetic $C(x)$:

$\centering C(x)=\sigma^{2}(c\cdot
exp[-(|x|/\xi_{1})^{2\alpha_{1}}]+(1-c)\cdot
exp[-(|x|/\xi_{2})^{2\alpha_{2}}])\@add@centering$ (7)

with $c$ being a proportionality constant (0 $\leq\>c\>\leq$ 1). In tab. S.1,
the mean values of the fit parameters of $C(x)$ and $H(x)$ are listed. The
proportionality constant $c$ weights the second term ($\xi_{2}$ and
$\alpha_{2}$) in [eq. 7] stronger. The analysis of the magnetic microstructure
focuses therefore on the second term in [eq. 7]. Fig. 8(a) presents the
magnetic correlation lengths ($\xi_{1}$, $\xi_{2}$) and the topographic
correlation length ($\xi_{TOPO}$) as a function of annealing temperature.
Magnetic $\xi_{2}$ shows a correlation with annealing temperature, whereas for
the topographic lateral correlation length $\xi_{TOPO}$ such a correlation
cannot be observed. We can therefore conclude that $\xi_{2}$ is uniquely
attributed to the magnetic microstructure. In particular $\xi_{2}$ is (75
$\pm$ 34) nm in the as-deformed state, corresponding to the grain size, as
obtained for similar materials [12] and therefore showing single-domain
behavior. $\xi_{2}$ decreases as a function of annealing temperature, i.e.,
upon annealing the domain size decreases causing a magnetic hardening.
In the following, the coercivity measured by SQUID-magnetometry is put into
relation with $\xi_{2}$. It is important to keep in mind that the magnetic
$\xi_{2}$ decreases with increasing annealing temperature, meaning that in
Fig. 8(b) rising annealing temperature shifts from the right to the left. When
referring to annealing treatments it seems unreasonable that higher annealing
temperatures cause smaller magnetic feature sizes, but as it was shown in Fig.
2 the microstructure does not show any change in grain size up to 400°C. As
the as-deformed state is very far from thermodynamical equilibrium, it is more
likely that the change in $\xi_{2}$ arises from a demixing process causing the
magnetic Co-phase to agglomerate. Similar phase separation processes have
already been observed in the Co-Cu system and have been attributed to spinodal
decomposition [30]. The same seperation process could be responsible for the
improved magnetoresistive behavior of annealed Cu-Co HPT-materials [31]. In
the 600°C annealed sample, a demixed state is present with the highest
coercivity and the smallest magnetic $\xi_{2}$.
It is important to mention that, although the magnetic hardening can be
attributed to single-domain behavior, the critical diameter for single-domain
particle size is in the range of 50 nm [23]. However, this value refers to
bulk hcp-Co and one has to keep in mind that Co neither is present in its hcp-
phase nor chemically pure, i.e., further investigations on the micromagnetic
properties of such supersaturated fcc-Co phases need to be carried out.

Figure 8: (a) Magnetic lateral correlation lengths $\xi_{1}$, $\xi_{2}$ in
comparison to topographic $\xi_{TOPO}$ as a function of annealing temperature
(c.f. tab. S.1). The data are slightly shifted in x for better visibility. (b)
Coercivity $H_{C}$ determined by SQUID-magnetometry versus magnetic $\xi_{2}$
obtained from correlating analysis of the MFM images. Note the log-axes.

##  4 Conclusion

In this study, Co-Cu samples with high Co-fractions are prepared using SPD by
HPT. The thermal stability of Co72-Cu28 (wt.%) is investigated in detail, with
the main focus being on microstructural and magnetic properties. By using a
two-step HPT deformation at different temperatures a homogenization of strain
distribution, and as a consequence an improved chemical homogeneity, is
obtained. The resulting sample is nanocrystalline and exhibits a
supersaturated, fcc single-phase microstructure. The microstructure exhibits a
remarkeable thermal stability, since no changes can be observed in SEM and XRD
for annealing treatments up to 400°C. For annealing at 600°C, a demixed state,
consisting of two fcc-phases, is present. Magnetometric measurements showed an
increasing coercivity as a function of annealing temperature, meaning the
observed changes in coercivity cannot be explained by formation of multidomain
structures. Correlating MFM measurements with DC-SQUID magnetometry reveals
domain sizes close to single-domain, whereas the demixed phases (with a
magnetic correlation length smaller than the grain size) yield a magnetic
hardening effect, which is able to explain the observed increase in coercivity
– an indicator of demixing of the phases in context with spinodal
decomposition.

## Acknowledgments

This project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(Grant No. 757333). A. M. acknowledges the support from the Lise Meitner
fellowship by Austrian Science Fund (FWF): M 2323-N36.

## References

  * [1] H Gleiter.  Nanocrystalline materials.  Prog. Mater. Sci., 33(4):223 – 315, 1989.
  * [2] G Herzer, M Vazquez, M Knobel, A Zhukov, T Reininger, HA Davies, Roland Grössinger, and JL Sanchez Ll.  Round table discussion: Present and future applications of nanocrystalline magnetic materials.  J. Magn. Magn. Mater., 294(2):252–266, 2005.
  * [3] K Suzuki, A Makino, A Inoue, and T Masumoto.  Soft magnetic properties of nanocrystalline bcc Fe-Zr-B and Fe-M-B-Cu (M= transition metal) alloys with high saturation magnetization.  J. Appl. Phys., 70(10):6232–6237, 1991.
  * [4] G Herzer.  Modern soft magnets: Amorphous and nanocrystalline materials.  Acta Mater., 61(3):718–734, 2013.
  * [5] T Ambrose, A Gavrin, and CL Chien.  Magnetic properties of metastable fcc Fe-Cu alloys prepared by high energy ball milling.  J. Magn. Magn. Mater., 124(1-2):15–19, 1993.
  * [6] T D Shen, R B Schwarz, and J D Thompson.  Soft magnetism in mechanically alloyed nanocrystalline materials.  Phys. Rev. B, 72(1):014431, 2005.
  * [7] R Z Valiev, R K Islamgaliev, and I V Alexandrov.  Bulk nanostructured materials from severe plastic deformation.  Prog. Mater. Sci., 45(2):103–189, 2000.
  * [8] R Pippan, F Wetscher, M Hafok, A Vorhauer, and I Sabirov.  The limits of refinement by severe plastic deformation.  Adv. Eng. Mater., 8(11):1046–1056, 2006.
  * [9] A R Kilmametov, Y Ivanisenko, A A Mazilkin, B B Straumal, A S Gornakova, O B Fabrichnaya, M J Kriegel, D Rafaja, and H Hahn.  The $\alpha\rightarrow\omega$ and $\beta\rightarrow\omega$ phase transformations in Ti–Fe alloys under high-pressure torsion.  Acta Mater., 144:337 – 351, 2018.
  * [10] R C O’Handley.  Opportunities in magnetic anisotropy and magnetostriction.  Mater. Sci. Eng. B, 3(4):365–369, 1989.
  * [11] K S Kormout, R Pippan, and A Bachmaier.  Deformation-induced supersaturation in immiscible material systems during high-pressure torsion.  Adv. Eng. Mater., 19(4):1600675, 2017.
  * [12] M Stückler, H Krenn, R Pippan, L Weissitsch, S Wurster, and A Bachmaier.  Magnetic binary supersaturated solid solutions processed by severe plastic deformation.  Nanomaterials, 9(1):6, 2019.
  * [13] A Bachmaier, H Krenn, P Knoll, H Aboulfadl, and R Pippan.  Tailoring the magnetic properties of nanocrystalline cu-co alloys prepared by high-pressure torsion and isothermal annealing.  J. Alloys Compd, 725:744 – 749, 2017.
  * [14] A Bachmaier, J Schmauch, H Aboulfadl, A Verch, and C Motz.  On the process of co-deformation and phase dissolution in a hard-soft immiscible CuCo alloy system during high-pressure torsion deformation.  Acta Mater., 115:333–346, 2016.
  * [15] R Pippan, S Scheriau, A Taylor, M Hafok, A Hohenwarter, and A Bachmaier.  Saturation of fragmentation during severe plastic deformation.  Annu. Rev. Mater. Sci., 40:319–343, 2010.
  * [16] O Renk and R Pippan.  Saturation of grain refinement during severe plastic deformation of single phase materials: reconsiderations, current status and open questions.  Mater. Trans., 60(7):1270–1282, 2019.
  * [17] O Renk, A Hohenwarter, K Eder, K S Kormout, J M Cairney, and R Pippan.  Increasing the strength of nanocrystalline steels by annealing: Is segregation necessary?  Scr. Mater., 95:27–30, 2015.
  * [18] J B Nelson and D P Riley.  An experimental investigation of extrapolation methods in the derivation of accurate unit-cell dimensions of crystals.  Proc. Phys. Soc., 57(3):160, 1945.
  * [19] L Vegard.  Die Konstitution der Mischkristalle und die Raumfüllung der Atome.  Z. Phys., 5(1):17–26, 1921.
  * [20] M J Kriegel, A Kilmametov, V Klemm, C Schimpf, B B Straumal, A S Gornakova, Y Ivanisenko, O Fabrichnaya, H Hahn, and D Rafaja.  Thermal stability of athermal $\omega$-ti (fe) produced upon quenching of $\beta$-ti (fe).  Adv. Eng. Mater., 21(1):1800158, 2019.
  * [21] J R Childress and C L Chien.  Reentrant magnetic behavior in fcc Co-Cu alloys.  Phys. Rev. B, 43(10):8089, 1991.
  * [22] Quantum Design, San Diego, California.  Application Note 1500-011, 5 2010.  Rev. A0.
  * [23] H Kronmüller and M Fähnle.  Micromagnetism and the microstructure of ferromagnetic solids.  Cambridge university press, 2003.
  * [24] M Jamet, W Wernsdorfer, C Thirion, D Mailly, V Dupuis, P Mélinon, and A Pérez.  Magnetic anisotropy of a single cobalt nanocluster.  Phys. Rev. Lett., 86(20):4676, 2001.
  * [25] N V Andreeva, A V Filimonov, A I Rudskoi, G S Burkhanov, I S Tereshina, G A Politova, and I A Pelevin.  A study of nanostructure magnetosolid Nd-Ho-Fe-Co-B materials via atomic force microscopy and magnetic force microscopy.  Phys. Solid State, 58(9):1862–1869, 2016.
  * [26] Y Zhao, G-C Wang, and T-M Lu.  Characterization of Amorphous and Crystalline Rough Surface–Principles and Applications.  Elsevier, 2000.
  * [27] C Teichert.  Self-organization of nanostructures in semiconductor heteroepitaxy.  Phys. Rep., 365(5-6):335–432, 2002.
  * [28] C Teichert, J J De Miguel, and T Bobek.  Ion beam sputtered nanostructured semiconductor surfaces as templates for nanomagnet arrays.  J. Phys. Condens. Matter, 21(22):224025, 2009.
  * [29] M Tolan, O H Seeck, J-P Schlomka, W Press, J Wang, S K Sinha, Z Li, M H Rafailovich, and J Sokolov.  Evidence for capillary waves on dewetted polymer film surfaces: A combined X-ray and atomic force microscopy study.  Phys. Rev. Lett., 81(13):2731, 1998.
  * [30] A Bachmaier, M Pfaff, M Stolpe, H Aboulfadl, and C Motz.  Phase separation of a supersaturated nanocrystalline Cu-Co alloy and its influence on thermal stability.  Acta Mater., 96:269–283, 2015.
  * [31] S Wurster, M Stückler, L Weissitsch, T Müller, and A Bachmaier.  Microstructural changes influencing the magnetoresistive behavior of bulk nanocrystalline materials.  Appl. Sci., 10(15):5094, Jul 2020.

## Supplementary

Table S.1: Roughness $\sigma$, lateral correlation length $\xi$, and Hurst parameter $\alpha$ as evaluated from auto-correlation function $C(x)$ and height-height correlation function $H(x)$ for the topographic (top) and magnetic signal (bottom). The data represent the mean values from at least 6 individual scans. As the magnetic signal exhibits two different Hurst parameters, the magnetic $C(x)$ is fitted by [eq. 7] with $c$ being a proportionality constant. fit-parameters | as-deformed | 150°C | 300°C | 600°C
---|---|---|---|---
topographic |  $\sigma_{TOPO}$ (nm) | $3.2$ | $\pm$ | $0.7$ | $3.0$ | $\pm$ | $0.2$ | $2.6$ | $\pm$ | $0.5$ | $2.8$ | $\pm$ | $0.2$
|  $\xi_{TOPO}$ (nm) | $75$ | $\pm$ | $30$ | $55$ | $\pm$ | $10$ | $55$ | $\pm$ | $15$ | $70$ | $\pm$ | $20$
| $\alpha_{TOPO}$ | $0.55$ | $\pm$ | $0.05$ | $0.35$ | $\pm$ | $0.05$ | $0.60$ | $\pm$ | $0.05$ | $0.65$ | $\pm$ | $0.10$
magnetic |  $\sigma$ (deg) | $0.15$ | $\pm$ | $0.03$ | $0.12$ | $\pm$ | $0.02$ | $0.11$ | $\pm$ | $0.01$ | $0.17$ | $\pm$ | $0.01$
|  $\xi_{1}$ (nm) | $110$ | $\pm$ | $50$ | $110$ | $\pm$ | $70$ | $20$ | $\pm$ | $15$ | $20$ | $\pm$ | $10$
|  $\xi_{2}$ (nm) | $80$ | $\pm$ | $30$ | $70$ | $\pm$ | $20$ | $50$ | $\pm$ | $10$ | $40$ | $\pm$ | $10$
| $\alpha_{1}$ | $0.40$ | $\pm$ | $0.10$ | $0.30$ | $\pm$ | $0.10$ | $0.15$ | $\pm$ | $0.05$ | $0.25$ | $\pm$ | $0.05$
| $\alpha_{2}$ | $0.25$ | $\pm$ | $0.10$ | $0.30$ | $\pm$ | $0.10$ | $0.35$ | $\pm$ | $0.10$ | $0.60$ | $\pm$ | $0.05$
| $c$ | $0.2$ | $\pm$ | $0.1$ | $0.2$ | $\pm$ | $0.2$ | $0.1$ | $\pm$ | $0.2$ | $0.2$ | $\pm$ | $0.1$

### M-H curves

Figure. S.2 shows the hysteresis of the as-deformed and the annealed states in
comparison to the pure Co-powder, measured at 8 K. The as-deformed and the
annealed samples are measured in hard axis configuration and exhibit therefore
a smaller susceptibility than the powder, which morphological shape appears
more uniform. The evolution of coercivity and saturation magnetization have
already been discussed in detail in fig. 5.

Figure S.2: Hysteresis loops measured by SQUID-magnetometry at 8 K. The inset
shows parts of the hysteresis loops at small fields.