Journal of Alloys and Compounds 767 (2018) 1094e1101 Contents lists available at ScienceDirect Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom Spin glass re-entrant s-phase FeCr and CoCr alloys: Heat capacity study b, S.M. Dubiel c A. Arauzo a, b, *, J. Bartolome a 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 Spain c w, Poland AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, PL-30-059, Krako b 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. Keywords: Magnetism Spin glass Heat capacity €ssbauer spectroscopy Mo 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 . 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: email@example.com (A. Arauzo). https://doi.org/10.1016/j.jallcom.2018.07.171 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 , 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 . The Debye temperature (qD ¼ 437(7) K for Fe0.54Cr0.46) was determined for the ﬁrst time only relatively recently . 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 . 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 , 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 . 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 calculations. 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 . 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 . 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  and presents the advantage of using small samples with high accuracy . 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. 119 € 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 1095 elsewhere . The low temperature spectra were recorded on the sample in form of powder that was placed in a closed-cycle refrigerator. 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  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 . 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 . 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, Clat: CP ¼ Cm þ Ce þ Clat ¼ Cm þ gT þ AT 3 (1) 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 . 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 . 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 , 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 1096 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 . 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 . 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 1097 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 . 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 . 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 temperature. €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 57 €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. . 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 . € 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 . € 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. 1098 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 . Conversely, no signs of magnetic behavior have been observed in the sigma phase CoCr system . 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] singlet IS G doublet IS G QS 24.3 198 300 1.018 1.138 1.029 1.094 1.063 1.068 1.019 0.934 0.414 1.029 0.810 0.408 1.063 0.828 0.400 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 curve. 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 . 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 . 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. 1099 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 . 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 . 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 . 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. , 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 1100 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 . 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 . 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 . 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. Acknowledgments This work has been ﬁnanced by Spanish MINECO Projects MAT2014-53921-R and MAT2017-83468-R. 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