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Journal of Alloys and Compounds 767 (2018) 1094e1101
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
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Spin glass re-entrant s-phase FeCr and CoCr alloys: Heat capacity
b, S.M. Dubiel c
A. Arauzo a, b, *, J. Bartolome
Servicio de Medidas Físicas, Universidad de Zaragoza, Pedro Cerbuna 12, 50009, Zaragoza, Spain
n, CSIC-Universidad de Zaragoza and Departamento de Física de la Materia Condensada, 50009, Zaragoza,
Instituto de Ciencia de Materiales de Arago
w, Poland
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, PL-30-059, Krako
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 1 April 2018
Received in revised form
11 July 2018
Accepted 14 July 2018
Available online 17 July 2018
Experiments of heat capacity on the s-phase archetypal magnetic FeCr alloy, Fe0.54Cr0.46, and the
reportedly non-magnetic s-phase CoCr alloy, Co0.342Cr0.658, indicate the presence of a spin-glass state in
€ ssbauer experiments are
both systems at zero magnetic field. Magnetic measurements and 119Sn Mo
rendering very different behavior for each compound. FeCr compound undergoes a ferromagnetic-like
transition, with Tc ¼ 30 K and average magnetic moment per Fe-atom, <m> ¼ 0.24 mB. Conversely, the
CoCr complex, shows almost non-magnetic behavior, exhibiting a very small average magnetic moment
per Co-atom, <m > ¼ 0.15 103 mB. The observed contribution to the heat capacity at zero magnetic field is
associated to magnetic degrees of freedom of the spin-glass ground state in both systems. The application of a magnetic field induces a transition to a polarized state which takes place at 6.0 K for FeCr alloy
and at 5.6 K for CoCr alloy. In FeCr the spin-glass state coexists with the ferromagnetic order of the
longitudinal spin component.
© 2018 Elsevier B.V. All rights reserved.
Spin glass
Heat capacity
€ssbauer spectroscopy
1. Introduction
The s-phase has a tetragonal unit cell (space group D144h-P42/
mnm) and is known to exist in numerous alloy systems. From the
many members of the s-phase family in binary alloys, we have
focused this study on Fe-Cr and Co-Cr alloys. The s-FeCr seems to
be the best known example of the family not only as the archetype,
but also for technological reasons. In fact, the precipitation of the s
phase is one of the main reasons for the deterioration of important
materials based on Fe-Cr alloys e. g. loss of corrosion resistance and
reduction of ductility and toughness [1].
On the other hand, sigma phase has a complex crystallographic
structure, hosting 30 atoms distributed randomly over five
different crystallographic sites with high coordination numbers. It
is a member of the Frank-Kasper family of phases. The combination
of the lack of stoichiometry and the complex crystallographic
structure makes the interpretation of experimental results challenging. Theoretical studies, based on electronic structure
* Corresponding author. Servicio de Medidas Físicas, Universidad de Zaragoza,
Pedro Cerbuna 12, 50009, Zaragoza, Spain.
E-mail address: (A. Arauzo).
0925-8388/© 2018 Elsevier B.V. All rights reserved.
calculations using charge and spin self-consistent Korringa KohnRostoker (KKR) methods [2,3], are often used in the interpretation of experimental results, especially those obtained with
€ssbauer spectroscopy [4e7].
microscopic methods like Mo
Although the s-FeCr and s-CoCr alloys have been known for
many years, their physical properties, and, in particular, magnetic
properties, are not known satisfactorily. Specifically, the magnetism
of s-FeCr was regarded as ferromagnetic [8], however recent
studies gave evidence that it is more complex, viz., it has a reentrant character, where behavior of both, spin glass and ferromagnetic states, have been observed [9]. The Debye temperature
(qD ¼ 437(7) K for Fe0.54Cr0.46) was determined for the first time
only relatively recently [10]. Much less is known about the physical
properties of s-phase in the Co-Cr alloy system. According to a heat
capacity study the s-CoCr has a magnetic ordering of Tc z 80 K [11].
However, this result should be taken with precaution. For example,
in a similar study on the s-FeCr alloy, analysis of heat capacity
measurements yielded a Tc z 90 K [12], whereas the actual mag€ ssbauer
netic transition, according to magnetization and 57Fe Mo
spectroscopic studies, takes place at Tc ~39 K [13,14]. Therefore,
the reported heat capacity continuous anomalies in both compounds seems to be related to short range ordering where no
A. Arauzo et al. / Journal of Alloys and Compounds 767 (2018) 1094e1101
definitive Tc can be drawn.
Also theoretical calculations predict magnetism in the s-CoCr
alloys [15,16], yet the calculations were performed at 0 K and the
obtained values of magnetic moments seem to be highly overestimated, a feature also known for other weak and itinerant systems [17,18].
There appears to be some contradictions between experimental
and theoretical studies about the origin and kind of magnetism in
binary sigma phases. It has been reported in the literature that all
Fe-containing systems (s-FeCr, s-FeV, s-FeRe, s-FeMo) have well
evidenced magnetic properties, exhibiting spin glass behavior at
low temperatures [14,19e21]. In a recent study, the reason for the
experimental disappearance of magnetic properties in the s-phase
FeCrX (X ¼ Ni, Co) when replacing Fe by Co is analyzed theoretically
with electronic structure calculations using KKR and KKR with
coherent potential approximation (CPA) methods [22]. Experimental magnetic moments are compared with calculated average
magnetic moment assuming different models for chemical disorder
in electronic structure calculations. The sigma phase CoCr was
established as non-magnetic from experimental results, however
theoretical calculations found it either weakly magnetic or almost
non-magnetic, depending on models of disorder used in
Theoretical calculations of sigma phase energy of formation in
FeCr and CoCr systems show that these compounds should be spin
polarized at T ¼ 0 K [15]. In CoCr, Co atoms account for the
magnetization, and the calculated value for individual Co magnetic
moment depends on the specific position in the lattice. Cr plays a
secondary role a priori, with a magnetic moment close to zero and
antiparallel to Fe or Co. Furthermore, electronic structure calculations in sigma-FeCr alloys has shown that the Stoner criterion for
the existence of itinerant ferromagnetism (Id$nd(EF) > 1, Id is the
Stoner parameter and nd(EF) the density of states at the Fermi level)
is satisfied for Fe atoms located on the five crystallographic sites,
while it is not fulfilled for all Cr atoms [5]. Based on above results, Cr
atoms have not been taken into consideration in the present study.
Within this context, we have performed a detailed heat capacity
study to further investigate the complex magnetic behavior of
€ ssbauer experiments on the
these compounds. Complementary Mo
s-CoCr alloy and magnetization measurements on both compounds have been additionally carried out.
2. Experimental
The temperature dependence of the heat capacity C(T), between
1.8 K and 300 K under different applied fields, was measured on
polycrystalline samples whose preparation and characterization
was described elsewhere [10,23]. The samples were measured using the commercial Heat Capacity option (HC) of a Quantum Design
Physical Properties Measurement System (PPMS). This option
measures the heat capacity at constant pressure (CP). Equipment
was calibrated using a copper calibration sample supplied by NIST
(US National Institute of Standards and Technology). This equipment uses a semiadiabatic method based on thermal relaxation
[24] and presents the advantage of using small samples with high
accuracy [25]. Sample mass was 1.23 mg and 14.56 mg for FeCr and
CoCr alloy respectively. Uncertainty in the measurement has been
observed to be less than 3% for FeCr sample and less than 0.6% in
the CoCr sample in the whole temperature range.
€ ssbauer spectra were recorded in a transmission geSn Mo
ometry at three different temperatures using a Ca119SnO3 as emitter
of the 23.9 keV g-rays. The s-phase Co0.342Cr0.658(119Sn) sample
was prepared by melting an appropriate amount of the 119Sn
isotope (~0.1 at%) with the master a-Co0.342Cr0.658 alloy. The obtained ingot was subsequently transformed into s as described
elsewhere [23]. The low temperature spectra were recorded on the
sample in form of powder that was placed in a closed-cycle
The magnetization of polycrystalline samples was measured
from 1.8 K to 300 K, at different magnetic fields (0.1 kOe, 1 kOe and
5 kOe), using a Quantum Design superconducting quantum interference device (SQUID) magnetometer. Isothermal magnetization
measurements were carried out at 1.8 K varying magnetic field up
to 50 kOe.
3. Heat capacity measurement results
3.1. s-phase Fe0.54Cr0.46
When measuring the heat capacity from 1.8 K to 300 K there is
no sign of any sharp peak singularity due to a phase transition in
the whole temperature range, thus the expected PM-FM transition
at ~34 K [14] is not apparent. Instead, apart from the lattice
contribution to the heat capacity (T3 law), a smooth broad contribution below T ~ 20 K appears (see Fig. 1a). Interestingly, although
no singularity is evident in the CP curve, the analysis of the CP error
reveals an anomaly. This subtle effect can be visualized in the inset
of Fig. 1a, where the percentage of the relative error in CP is
depicted, exhibiting a peak at about 30 K. CP error value is obtained
as the fit deviation from the exponential behavior of the measured
relaxation curve, within the relaxation method model [25].
Therefore, the observed peak is indicating the presence of a thermodynamic process which affects the thermal relaxation of the
sample. Large deviations from conventional PPMS fitting procedure
are known to exists for the analysis of first order transitions, where
relaxation data do not follow an exponential relaxation model [25].
Visual inspection of relaxation data and fit curves near 30 K reveal a
slight increased deviation of experimental data from the fit. Hence,
the presence of this anomaly in the CP error may be tentatively
attributed to the PM-FM transition in this compound.
On the other hand, as s-phase FeCr and CoCr compounds can be
considered as itinerant ferromagnets, we may expect to have an
electronic contribution to the heat capacity, which may dominate
over the lattice term in the low T range. The CP/T vs T2 representation (see Fig. 1b) can help to distinguish the different contributions to the heat capacity in the low temperature range (2e50 K),
the magnetic, Cm, the electronic, Ce and the lattice contributions,
CP ¼ Cm þ Ce þ Clat ¼ Cm þ gT þ AT 3
The fit of the observed linear dependence in the 20e50 K range
for CP/T vs T2 allows the experimental determination of the electronic and lattice contribution. The obtained lattice term, A/
R ¼ 3.8 ± 0.1 106 K3 gives a value of the Debye temperature of
qD ¼ 393 ± 2 K, slightly lower than reported values in the literature,
qD ¼ 437 ± 7 K obtained by Cieslak et al. by MS measurements [10].
These values for the Debye temperature are in agreement with
reported values, qD ¼ 455 K, determined by heat capacity studies in
Fe0.525Cr0.475 and Fe0.566Cr0.434 compounds [12]. The obtained
electronic contribution is small but not negligible, g ¼ 7 ± 1 104
RK1 ¼ 6.1 ± 0.8 mJ/molK2. The electronic contribution to the low
temperature heat capacity is the simplest experimental method to
account for the density of states at the Fermi surface d(EF); Ce ¼ gT,
with g ¼ (p2k2B/3)d(EF) for non-interacting electrons. From theoretical calculations of the density of states for Fe0.54Cr0.46,
d(EF) z 2.2 states/eV [5], we can estimate a value for the electronic
contribution of heat capacity gthe z 5.1 mJ/molK2, in quite good
agreement with obtained experimental value. Above values are
both in agreement with estimated values, g ¼ 5.6 mJ/molK2
A. Arauzo et al. / Journal of Alloys and Compounds 767 (2018) 1094e1101
Fig. 1. a) Specific heat of Fe0.54Cr0.46 as a function of temperature, T, at H ¼ 0 kOe in logarithmic scale. Inset: Relative error in CP as a function of temperature. b) CP/T vs T2 representation in the low temperature region. Fit is done to a lattice and an electronic contribution to the heat capacity.
deduced from heat capacity analysis at high temperatures
(470e800 K) of similar compounds [12].
The observed low temperature extra contribution, which can be
assigned to magnetic degrees of freedom, depends on the applied
magnetic field. This magnetic contribution, obtained after removal
of the lattice and electronic part, exhibits a peculiar dependence
with magnetic field, the low temperature part, which shows a Tn
with n ¼ 1 slope (see Fig. 2a), decreases as magnetic field increases.
Additionally, the application of an external magnetic field is promoting the emergence of a cusp at about 6 K whose intensity increases as the magnetic field increases up to 10 kOe (see Fig. 2b). At
temperatures above the peak, the broad signal shows a weak
variation with the magnetic field. The high temperature slope has a
T 2 dependence for T > 20 K.
From these results, it can be inferred that we have in this
compound a field-induced magnetic transition at ~ 6 K. In Fig. 3 we
have plotted the DCm/Cm as a function of temperature to enhance
the effect.
The smooth and broad magnetic contribution for H ¼ 0 and the
Tn with n ¼ 1 power low temperature dependence at low temperatures, is entirely consistent with the presence of a spin-glass state,
which is known to constitute the magnetic ground state of the
investigated sample [10]. Furthermore, when calculating the corresponding entropy contribution, a very low value is obtained, viz.,
DSm(2e30 K) < 0.03 R, that decreases with increasing applied
magnetic field.
Therefore, it can be concluded that in the FeCr s-phase alloy no
FM transition is directly observed at zero magnetic field, although
the subtle discontinuity in the fit error is pointing to the onset of a
magnetic transition at T ~30 K. Besides, the sample shows a spinglass like behavior at T < 20 K with a broad magnetic contribution
to the heat capacity, centered at about 10 K. Furthermore, a field-
Fig. 3. Relative increase in the magnetic contribution to the heat capacity, DCm/Cm, for
the Fe0.54Cr0.46 as a function of temperature, T, at different magnetic fields.
induced magnetic transition takes place at T ¼ 6.0 ± 0.5 K. It may
be inferred that a polarization of the spins along the applied field
similar to an ordered ferromagnet takes place at this temperature.
3.2. s-phase Co0.342Cr0.658
In the case of the Co-Cr alloy, the heat capacity study displays
similar results to those revealed for the Fe-Cr alloy. The heat capacity curve from 2 K to 300 K does not exhibit any sharp anomaly
Fig. 2. a) Magnetic contribution to the heat capacity, Cm, for the Fe0.54Cr0.46 as a function of temperature, T, at different magnetic fields ranging between 0 and 30 kOe b) Same curves
in a stacked mode to show the emergence of the peak at 6 K.
A. Arauzo et al. / Journal of Alloys and Compounds 767 (2018) 1094e1101
that would indicate a magnetic phase transition. It has a T3 lattice
contribution between 20 and 50 K and a broad contribution at low
temperatures (see Fig. 4a). Nevertheless, CP error analysis reveals a
peak at about 20 K (see inset Fig. 4a) associated with the presence
of a behavior affecting thermal relaxation of the sample. We may
assign this feature to the fingerprint of a hidden magnetic transition
in the s-CoCr alloy at about 20 K.
The fit of the observed linear dependence in the 20e50 K range
for CP/T vs T2 allows the experimental determination of the electronic and lattice contribution. The obtained lattice term, A/
R ¼ 4.01 ± 0.04 106 K3 gives a value of the Debye temperature of
qD ¼ 387 ± 2 K. Higher values for the Debye temperature have been
reported in the literature for a member of the family, the s-phase
Co0.435Cr0.565, qD ¼ 436 K [11]. Determined electronic contribution,
is rather low, g ¼ 3.0 ± 0.5 104 RK1 ¼ 2.5 ± 0.4 mJ/molK2. This
value is smaller than the reported value for Co0.435Cr0.565, g ¼ 8.02
mJ/molK2, deduced from heat capacity measurements at high
temperatures [11].
Removing the lattice and electronic contribution, we obtain the
magnetic contribution to the heat capacity at low temperatures,
which has the shape of a smooth broad band centered around 10 K
with a n ¼ 1 Tn power law dependence for T < 10 K, typical of a spinglass state, and a high temperature T2 slope (see Fig. 5a). The
application of a magnetic field higher than 10 kOe decreases the
low T contribution and a cusp at T ¼ 5.6 ± 0.5 K is observed.
Therefore, similarly to the Fe-Cr s-phase alloy, we obtain the
signature of a spin-glass state at low temperature and a fieldinduced magnetic transition. The associated change of entropy is
very low, DSm(2e30 K) < 0.01 R, which is about a factor 3e4 lower
than in the Fe-Cr compound. This effect is clearly observed in Fig. 6
where Cm(T) for both compounds is compared. The contribution is
similar in shape, but three times lower in the case of the Co-Cr alloy
which may be, at least partially, related with the lower concentration of the magnetic atoms, considering that only the iron or
cobalt atoms carry the magnetization in these compounds. Interestingly CP fit error exhibits a subtle anomaly at about 20 K,
tentatively assigned to the onset of a magnetic transition at this
€ssbauer spectra
NPD experiments are considered in order to fit Mo
for these complex systems [4e7,14]
The archetype sigma phase FeCr has been the object of different
€ssbauer studies in order to describe its magnetic properties
Fe Mo
€ssbauer study of the sigma phase
[4,13,14]. A systematic Mo
Fe0.54Cr0.46 as a function of temperature and magnetic field has
been done in Ref. [14]. The spectra at the lowest temperature, 4.2 K
is not well resolved which is explained by the existence of five
different crystallographic sites and the tetragonal structure. In order to increase the resolution, the application of a high magnetic
field, 135 kOe at the lowest temperature, 4.2 K has allowed to obtain
a distribution of the hyperfine field with a five peak structure. The
fitting of the spectra in terms of five single-line subspectra with
Lorentzian shape, has allowed the determination of the critical
temperature, Tc from the variation of the line width as a function of
temperature. The average magnetic hyperfine field of this composition is 〈Bhf〉 ¼ 3.35 T at Tc ¼ 34.1 K [14].
€ ssbauer spectra for a
In this work, we have recorded the 119Sn Mo
s-CoCr alloy which was doped with ~0.1 at% 119Sn isotope. Measurements on 119Sn are advantageous relative to those on 57Fe in
that the former do not have own magnetic moment so they can see
the magnetism of the investigated sample, if any, via a transferred
hyperfine field. The three obtained spectra are shown in Fig. 7
where no visible sign of splitting is found, and they were fitted
either to a singlet or to a doublet. The latter analysis, being more
relevant due to the tetragonal symmetry of the s-phase, resulted in
a better quality of the fits. The best-fit spectral parameters obtained
with the two procedures are displayed in Table 1.
It can be seen that the G-value derived from the spectrum
measured at 23.4 K is by ~10% broadened relative to the corresponding values at higher temperatures. This effect can be either
due to an instrumental broadening (via vibrations that may occur in
closed-cycle refrigerators) or it may be indicative of a weak
magnetism. Assuming the latter, the broadening corresponds to the
hyperfine magnetic field of ~1.3 kOe. In a previous study on 119Sndoped s-Fe0.545Cr0.445 alloy performed at room temperature, ISvalues were similar to those found for 119Sn-doped s-Co0.342Cr0.658
while no average hyperfine field was detected [26].
€ ssbauer-effect measurements
4. Mo
5. Magnetization measurements
The interpretation of the experimental results obtained for sphase samples is challenging, given the complex structure and a
lack of stoichiometry. Microscopic techniques such as Mossbauer
spectroscopy makes it possible to access to sublattice magnetic
properties. However, low resolution in the measured spectra prevents the distinction between nonequivalent sites. Theoretical
studies based on KKR methods and additional results from XRD and
Recent reports about the magnetic properties of sigma phase
FeCr compounds show experimental evidence of a re-entrant state
at low temperature, where transverse spin degrees of freedom are
frozen. In general, in reentrant spin glass systems, the phase diagram consists of a transition from the high temperature paramagnetic phase into a ferromagnetic-like phase indicated by the
rapid rise to very large magnetization. The onset of this
Fig. 4. a) Specific heat of Co0.342Cr0.658 as a function of temperature, T, at H ¼ 0 kOe in logarithmic scale. Inset: Relative error in CP as a function of temperature. b) CP/T vs T2
representation in the low temperature region. Fit is done to a lattice and an electronic contribution to the heat capacity.
A. Arauzo et al. / Journal of Alloys and Compounds 767 (2018) 1094e1101
Fig. 5. a) Magnetic contribution, Cm, to the heat capacity for the Co0.342Cr0.658 as a function of temperature, T, at different magnetic fields ranging between 0 and 30 kOe. B)
Corresponding DCm/Cm as a function of temperature.
Fig. 6. Comparison of the magnetic contribution to the heat capacity, Cm, for the
Fe0.54Cr0.46 and Co0.342Cr0.658 as a function of temperature, T, at H ¼ 0 and 10 kOe.
spontaneous magnetization is considered the Curie temperature,
Tc. Further cooling reveals irreversible behavior and frustration
effects characteristic of spin glasses, below a freezing temperature,
Tf [27,28]. In the particular case of s-FeCr alloy, near the zero field
limit in the H-T phase diagram, the transition tends to proceed
directly from the paramagnetic state to the spin glass state [9].
Conversely, no signs of magnetic behavior have been observed in
the sigma phase CoCr system [22].
In order to assess the observed heat capacity contribution, the
magnetic properties of both alloys have been revisited and
compared under the same experimental conditions.
Zero-Field-Cooled (ZFC) and Field-Cooled (FC) experiments have
been carried out at different magnetic fields, 0.1 kOe, 1 kOe and
5 kOe between 1.8 K and 300 K for both alloys. Isothermal magnetization up to 50 kOe has been measured at the lowest reached
temperature, T ¼ 1.8 K.
5.1. s-phase Fe0.54Cr0.46
Curves for ZFC/FC at the lowest field, 0.1 kOe, exhibit the clear
signature of a paramagnetic to a ferromagnetic transition at
Tc ¼ 30 ± 2 K (see Fig. 8). At low temperatures, the onset of an
irreversibility zone occurs at Tf ¼ 10 K. This freezing temperature is
considered to be the temperature at which the re-entrant spin glass
phase takes place. The maximum in the ZFC curve denotes the
crossing point to the temperature range of stronger irreversibilities.
€ssbauer spectra recorded on the 119Sn-doped s-Co0.342Cr0.658 at
Fig. 7. 119Sn Mo
different temperatures. The solid lines represent the best-fit to the data in terms of a
singlet (upper panel) and doublet (lower panel).
Table 1
The best-fit spectral parameters obtained from the analysis of the spectra using two
different procedures. IS stays for the isomer shift (relative to b-Sn at room temperature); G is the full width of the line at half maximum, and QS represents the
quadrupole splitting. The values of the spectral parameters are in mm/s.
T [K]
A. Arauzo et al. / Journal of Alloys and Compounds 767 (2018) 1094e1101
Fig. 8. Magnetization versus temperature ZFC and FC curves for the s-Fe0.54Cr0.46 alloy
for H ¼ 0.1 kOe. Inset: susceptibility-temperature product, cdc$T, calculated from ZFC
ZFC/FC experiment at 1 kOe shows much lower irreversibility,
which vanishes completely for the 5 kOe curves (not shown).
Isothermal magnetization at 1.8 K has a dominant ferromagnetic
component with a non-saturating behavior at high fields, which is
expected, given the itinerant character of the magnetism in these
compounds [14]. Extrapolation of magnetization to H ¼ 0 Oe, gives
a mean value of the magnetic moment per Fe atom of <m
> ¼ 0.24 ± 0.02 mB, similar to reported values in the literature [13].
At very low fields (H < 0.3 kOe), a small hysteresis can be observed,
with a remanence of the order of 0.015 mB (see Fig. 9).
5.2. s-phase Co0.342Cr0.658
For the CoCr alloy, the magnetic signal is extremely low; even at
300 K magnetization is two orders of magnitude lower than that of
FeCr compound. However, it is evident that a small magnetic
moment is provided by the Co sublattice.
Even though some irreversibility is observed in the ZFC FC
curves, these results have to be taken with caution, as the signal is
very low and some instrument and temperature artifacts may be
present in the curves at 0.1 kOe. To highlight upon decreasing
temperature, there is a broad bump at 35 K, from which the ZFC and
FC curves split further apart, followed by an upturn of the
magnetization at temperatures below 10 K, with no evident sign of
Fig. 9. Magnetization versus magnetic field curve at T ¼ 1.8 K. Inset: zoom of the low
field region showing the remanence.
Fig. 10. Magnetization versus temperature ZFC and FC curves for the s-Co0.34Cr0.66
alloy for H ¼ 0.1 kOe. Inset: Magnetization versus magnetic field curve at T ¼ 1.8 K.
a magnetic transition (see Fig. 10). The observed irreversibility,
which is completely suppressed with an applied field of 5.0 kOe,
could be the indication of a spin-glass state at low temperatures in
this compound.
The isothermal magnetization increases almost linearly with
magnetic field. Extrapolation of values at high fields to H ¼ 0 gives
an estimation of the average moment per Co atom of <m
> ¼ 1.54 ± 0.05 104 mB, similar to the 104 mB value obtained in the
literature [22]. This value stems from the initial magnetization of
the curve which is saturated at about 5 kOe. The value is small but
measurable well above noise level, which is four orders of magnitude lower.
6. Discussion and conclusions
One of the most striking results of the present study is that the
FeCr alloy paramagnetic to ferromagnetic transition, which is
evident in magnetic measurements, could not be observed directly
in the heat capacity experiments. As shown in section 3.1, the
fingerprint of the PM-FM transition is only indirectly detected as a
side-effect in the measurement fit error. To explain this feature we
may argue the following; according to the Stoner theory, the
magnetic contribution to the specific heat in itinerant ferromagnets
is clearly predicted, where spin-split bands are defined below Tc,
and the splitting vanishes exactly at Tc, where specific heat drops to
zero. The magnetic contribution to the discontinuity at the transition temperature is given by, DCm ¼ M20/c0Tc, where M0 is the
spontaneous magnetization, and c0 is the initial ferromagnetic
susceptibility. However, most of the systems present large deviations from the Stoner model, due to the influence of spin fluctuations on the specific heat of itinerant ferromagnets. These
fluctuations may decrease the magnetic contribution to the
discontinuity at Tc, DCm, by a factor up to 4 [29]. Typical values for
the calculated DCm of weak itinerant magnets range between 100
mJ/molK to 1 J/molK which are overestimated compared to experimental values due to spin fluctuations effects [29]. Experimental
observation is not possible when the estimated value is smaller
than experimental resolution of the measurement. Additionally,
the observation of the transition is not achieved by a well-defined
lambda anomaly due to spin fluctuations. For instance, only a
kink in Cp at Tc is observed in Ref. [30], where the calculated
contribution for pure Stoner type excitations is 1.2 J/mol.K, which
would give a maximum contribution of about 10% of the heat
A. Arauzo et al. / Journal of Alloys and Compounds 767 (2018) 1094e1101
capacity value at Tc.
From magnetic measurements of s-FeCr we have obtained the
values M0 ¼ 15.3 emu/g and c0 ¼ 6.5 105 emu/gOe from high field
susceptibility at 1.8 K. The calculated discontinuity in Cm at Tc
without taking into account fluctuations (Stoner case) is DCm ¼ 570
mJ/molK ¼ 0.068 R. Even if reduced due to spin fluctuations, we
would expect that this value could be observed at Tc because it
amounts to more than 30% of the observed Cp value around
30e40 K. Even if the small contribution could prevent the observation of an obvious lambda anomaly at Tc, a change of slope or a
kink in Cp/T should be seen, while no such feature is observed.
The reason for this absence could be argued in terms of a
possible overestimation of the calculation given the high uncertainty in the determination of M0 and c0 combined with a highly
reduced anomaly height and broadening caused by the spin fluctuations. The magnetic contribution would be therefore hidden
within the lattice contribution to the heat capacity in this temperature range.
However, in a different approach, the absence of a l-type singularity in the heat capacity can be considered as an indication that
no 3D long-range order takes place in these alloys. This assertion is
in agreement with a study of extended scaling in the magnetic
critical phenomenology near the para-ferromagnetic transition of
the sigma phase Fe0.53Cr0.47 alloy [9]. The authors found that the
obtained values for the magnetic susceptibility critical exponent,
g ¼ 1.5, is intermediate between the prediction of the 3D Heisenberg universality class for ordered ferromagnets (g ¼ 1.4) and the
values observed in spin glasses (g ¼ 2.2). It is suggested that the
ferromagnetic-like phase in s-FeCr alloy is at the edge of destabilization to become a pure spin glass state.
Interestingly, in the case of the so called ‘non-magnetic’ CoCr
alloy, it is observed a non-negligible contribution to the heat capacity. The obtained contribution at low temperatures from magnetic degrees of freedom is only 3 times lower for the CoCr than for
the FeCr alloy and shows similar features to the latter, with a
magnetic field induced transition at about the same temperature
while the experimentally observed magnetic moment in CoCr is
about 3 orders of magnitude lower than in FeCr. A plausible
explanation would be as follows. The values obtained with spin
polarized calculations in KKR and KKR CPA models consider
collinear ordering of Fe, Co and Cr moments in the different sublattices. The calculated magnetic moment per atom is the average of
the magnetic moment over different sites. Values calculated for Co
atoms are about twice smaller for Co than for Fe [22]. Therefore, a
possible interpretation would be that the observation of a much
lower magnetic moment is the result of predominant AF interactions in the CoCr system, non-collinearity effects and magnetic
frustration. The transition to a spin glass state, where transverse
spin degrees of freedom are frozen, is manifested at low temperature in the irreversibility of the ZFC FC curves at low fields and the
magnetic contribution to the heat capacity.
These combined results are consistent with a spin-glass ground
state in both systems. In FeCr the glass-state is coexistent with a
ferromagnetic-like phase. Moreover, in the case of CoCr alloy,
electronic structure calculations indicate that the ground state of
this alloy seems to be strongly dependent on magnitude and
character of the chemical disorder between Co and Cr atoms on the
five sublattices [15,22]. Additionally, some discrepancies appear
between calculated values of average magnetic moment, ~0.04 mB
per atom and estimated magnetic moment from experiments, 104
mB. Further theoretical investigations are proposed in order to
elucidate this difference, which would be an effect of noncollinearity together with a magnetic structure of the spin-glass
type which is not taken into account in the KKR calculations [22].
From the analysis of the heat capacity of the s-phase Fe0.54Cr0.46
and Co0.342Cr0.658 alloys measured between 2 K and 300 K and at
different magnetic fields, H ¼ 0e30 kOe, we can conclude that no
PM-FM transition is directly observed in the whole temperature
range, although a discontinuity in the heat capacity relaxation
model fit error is observed at T ~ 30 K for FeCr alloy, in coincidence
with observed FM transition, and at T ~ 20 K for CoCr system, that
would indicate the onset of a magnetic transition in this compound.
In both compounds a smooth broad magnetic contribution appears
below ~20 K which can be associated with a spin-glass-like state at
low temperatures. This broad contribution is centered at ~10 K for
both alloys. Additionally, a field-induced cusp is observed at ~6 K
for the Fe-Cr alloy and ~5.6 K for the Co-Cr alloy. The main difference between the two alloys exists in the magnitude of the magnetic contribution which is three times larger for the Fe-Cr alloy.
The presence of a field-induced peak at ~6 K in the heat capacity
may be the result of an alignment of spins by the applied magnetic
field. This result is compatible with the suppression of irreversibility in the ZFC/FC curves by application of a high enough mag€ ssbauer-effect measurements performed on a119Snnetic field. Mo
doped sample give evidence on absence of magnetism down to
~24 K.
The presence of a spin-glass like state at low temperatures in
these compounds can be explained as due to an intrinsic disorder of
the s-phase hosting 30 atoms per unit cell which are randomly
distributed over 5 different crystallographic sites. Each atom has a
high coordination number (from 12 to 15), belonging to various
sites and with substantially different interatomic distances,
providing a complex magnetic interaction landscape prone to
frustration effects leading to the spin-glass state.
This work has been financed by Spanish MINECO Projects
MAT2014-53921-R and MAT2017-83468-R. Authors would like to
acknowledge the use of Servicio General de Apoyo a la Invesn-SAI, Universidad de Zaragoza. This work was partially
supported by the Faculty of Physics and Applied Computer Science
AGH UST statutory tasks within subsidy of Ministry of Science and
Higher Education of Poland.
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