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Magnetic properties of metastable Gd–Cr alloys
Journal of Magnetism and Magnetic Materials 323 (2011) 2005–2011
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Magnetic properties of metastable Gd–Cr alloys F.P. Rouxinol a,n, G.Z. Gadioli a, R.V. Gelamo c, A.O. dos Santos a,b, L.P. Cardoso a, S. Gama a, M.A. Bica de Moraes a a
Instituto de Fı´sica Gleb Wataghin, Universidade Estadual de Campinas—UNICAMP, 13083-970 Campinas, SP, Brazil ~ 65900-410 Imperatriz, MA, Brazil CCSST, Universidade Federal do Maranhao, c ´gicas e Exatas, Universidade Federal do Triˆ Instituto de Ciˆencias Tecnolo angulo Mineiro, 38025-180 Uberaba, MG, Brazil b
a r t i c l e i n f o
abstract
Article history: Received 1 September 2010 Received in revised form 10 December 2010 Available online 5 March 2011
We report on the magnetization, magnetocaloric effect, magnetic ordering temperatures, saturation magnetic moments and anisotropy of sputter-deposited GdxCr1 x alloys with Gd atomic concentrations, x, ranging from 0.13 to 0.52. The complex magnetic nature of the Gd–Cr films was revealed from the M H isotherms, which do not show saturation even at an applied field of 70 kOe and a temperature of 2 K and do not exhibit a linear behavior at higher temperatures. For some of the samples, the isotherms were used to determine the isothermal entropy variation as a function of temperature, for a change of 50 kOe in the applied magnetic field. The saturation magnetic moment varies with x and follows the dilution law, implying that the Cr atoms do not contribute to the total moment of the Gd–Cr alloys. Both static magnetization and dynamic susceptibility measurements reveal the existence of a magnetic glassy behavior in the alloys, which occurs below a freezing temperature. The existence of anisotropy at low temperatures for all samples was revealed by their M H hysteresis loops from which the in-plane coercive fields, Hc, were determined. A monotonical increase in Hc with increasing Gd concentration was observed. & 2011 Elsevier B.V. All rights reserved.
Keywords: ac susceptibility Spin glass-like Amorphous alloys Coercive field
1. Introduction Owing to their interesting and often unexpected properties magnetic nanostructured materials have been intensively investigated. A possible and frequently studied configuration of these materials is that of a nanocomposite, i.e., a system in which nanosized magnetic particles, or clusters, are embedded in a nonmagnetic medium. Such a configuration enables unusual transport properties such as giant magnetoresistance [1], extraordinary Hall effect [2] and may exhibit high coercivity, a most important property in materials for magnetic recording [3]. Gadolinium-based nanocomposites [4,5] have received a great deal of attention mainly due to the high magnetic moment of Gd, capable of imparting a high magnetization to these materials. The purpose of this work is to investigate the magnetic properties of GdxCr1 x alloys as a function of the Gd atomic concentration, x, for x in the range 0.13–0.52. The investigations include magnetization, magnetocaloric effect, magnetic ordering temperatures, magnetic moments of saturation, and anisotropy. Since Gd and Cr are mutually insoluble under equilibrium conditions, conventional metallurgical techniques could not be used for the preparation of the alloys and a
n
Corresponding author E-mail address: rouxinol@ifi.unicamp.br (F.P. Rouxinol).
0304-8853/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2011.02.040
vapor condensation technique – sputtering – was employed. The alloys are thus thin films that were deposited onto silicon substrates. Owing to the Gd and Cr insolubility the metals segregate during the deposition process and, as no thermal treatment was performed macroscopic segregation was prevented. Consequently, the films are nanocomposites. Only samples possessing Gd in a low crystalline or amorphous phase, which implies that Gd atomic concentrations not higher than 52%, are investigated. Samples with Gd concentration higher than 52%, for which the Gd phase are crystalline will be considered in a future paper. Despite the interest in the magnetic properties of Gd-containing alloys, only a few investigations have been carried out on the Gd–Cr system. Hsu and Fu [6] have investigated the electrical resistivity and the Ne´el temperature of the alloys, while Huang et al. [7] studied their entropy changes at the Curie temperature. In both investigations, the alloys were deposited by dc sputtering, but the Gd atomic concentrations were not higher than 7%. Also using dc sputtering, Hsu et al. [8] and Gavrin et al. [9] deposited Gd–Cr alloy films with Gd concentrations ranging from 0 to 100%, in which the magnetic ordering temperatures were investigated and the existence of a spin glass state was proposed. Although a magnetic glassy behavior is observed in our work, our results in general differ from those of Refs. [8,9]. The latter two investigations are concerned with films having thicknesses of a few micrometers deposited onto liquid nitrogen-cooled substrates, in contrast to our deposition procedure in which films with
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thicknesses of at most 500 nm were deposited onto substrates kept at room temperature. Distinct film structures resulted from these different procedures, implying the differences in magnetic properties. Furthermore, to our knowledge, this is the first report regarding the GdxCr1 x system in which the magnetocaloric effect is investigated for Gd concentrations exceeding 7%, the anisotropy is studied, and ac susceptibility measurements are used to investigate the magnetic glassy behavior of the alloys.
2. Experimental The alloys were deposited by magnetron sputtering from separate Gd and Cr targets at an argon pressure of 5 10 3 mbar in a stainless steel vacuum chamber. The chamber base pressure was about 1 10 7 mbar. Silicon (001) slabs were used as substrates. The substrate holder was kept at room temperature. The purities of the Gd and the Cr targets were of 99.9% and 99.95%, respectively. Film thicknesses were in the range of 200–500 nm, measured using a high resolution profilometer. To determine the atomic composition of the films, Rutherford Backscattering Spectroscopy (RBS) analyses were performed at the Laboratory for Analysis of Materials by Ion Beams at the Institute of Physics, University of Sa~ o Paulo. Only Gd, Cr and traces of O were revealed by the RBS spectra. The SIMNRA computational program [10] was used to fit the RBS data yielding the area density ni (number of atoms per unit area), of each element in the films. Knowing ni and the area of the films, the masses of the elements were calculated. For the samples in which oxygen was observed, the atomic concentration was not higher than 3%. Grazing incidence X-ray diffraction (GIXRD) (y E51) patterns of the Gd–Cr alloys were collected using a diffractometer with Cu Ka radiation (l ¼0.15418 nm), operating at 40 kV/50 mA, in a geometry with a flat graphite diffracted beam monochromator crystal and a parallel plate collimator. Superconducting quantum interference device (SQUID) magnetometer was used to measure the magnetic moments of the films as a function of temperature (2–350 K) and applied field (0–70 kOe). Alternating-field susceptibility measurements were performed using physical properties measurement system (PPMS) to determine the real part of the ac susceptibility as a function of temperature (2–350 K) and frequency of the alternating driving field (10 104 Hz). For the SQUID and PPMS measurements, the applied magnetic fields were parallel to the film surface, thus avoiding demagnetizing corrections. The data were corrected for the magnetic moments of the substrate and sample holders. From M H isotherm sets for some of the samples, the isothermal entropy change, DSM, for the removal of a 50 kOe field was calculated according to a procedure outlined by Pecharsky and Gschneidner [11].
3. Results and discussion Fig. 1 shows X-ray diffraction patterns of the GdxCr1 x alloys with x in the range 0.13–0.52. For comparisons in the forthcoming discussion, the peak positions for hcp Gd and bcc Cr structures, calculated for isotropic distributions are also represented in the figure by vertical bars. It can be seen that all peaks are broad, indicating the absence of long range periodicity. For the Gd hcp structure, the three reflections calculated for the isotropic distribution at 2y ¼28.331, 30.961, and 33.421 are very intense and this has been experimentally verified for sputter-deposited Gd thin films [5,12], Gd alloys [5,8,13], and Gd/Cr layers [14]. Thus, the broad peak in the range 27–351 for
Fig. 1. X-ray diffraction patterns for the Gdx–Cr1 x alloys. 2y reflections for bcc Cr and for hcp Gd, calculated for isotropic distributions, are indicated by vertical bars.
samples with x¼0.17 through 0.52 is assigned to Gd. There are no contributions of Cr to this peak, as no significant Cr reflections are predicted in the latter range. For the 13% Gd sample, the absence of any feature in the interval 27–351 indicates a completely amorphous Gd phase. Therefore, as the Gd concentration increases from 13 to 52%, the Gd phase evolves from amorphous to a low crystalline state. Peaks at 2y ¼441, 571, and 641, for the x¼ 0.13 sample are relatively well defined, are assigned to Cr. They show, however, some small displacements from their predicted positions (44.161, 57.131 and 64.631), probably because of stress-induced distortions in the Cr lattice parameter, as usually observed in vacuum-deposited thin films. To these peaks, the Gd phase may also contribute, as Gd reflections are predicted at 2y-values close to 42.51, 56.01 and 64.51. Nevertheless, this contribution is not expected to be significant. In fact, as the Gd concentration increases, there is a concomitant intensity decrease of the latter peaks while that of Gd, at the interval 27–351, shows an overall increase. Our X-ray diffraction results are different from those of Hsu et al. [8] for Gd–Cr alloys deposited by sputtering on glass substrates cooled by liquid nitrogen, and investigated over the entire composition range as their diffraction patterns show that crystalline phases of either Gd or Cr, or both, are present at any composition. Such a difference is, in a first examination, unexpected, as the higher substrate temperature (room temperature) used in our depositions should result in more crystalline specimens than those of Ref. [8]. However, besides substrate temperature, the film crystalline structure depends on the rate of deposition, R, and film thickness, t. Usually, high deposition rates favor less crystalline and, in many cases, amorphous film structures [15]. Regarding film thickness, a typical behavior [16] in film deposition is the small grain size in the early stages of film formation and the fast increase in grain size as the film thickness approaches one or more micrometers [11,12]. For the films of this work, R¼1.5 mm/h and t is at most 0.5 mm, while for the films
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of Ref. [8] R¼1 mm/h and t is in the range of several micrometers. Thus, the tendency to form a less crystalline state than that reported in Ref. [8] is favored in the films of this work. It seems that their structural dependence on R and t at room temperature overcomes the effect of temperature-induced crystallite formation. Fig. 2 shows representative M H isotherms of the Gd–Cr alloys at fields up to 50 kOe. The sharp increase of M with increasing H for low fields in the lower temperature isotherms is typical of all samples. Furthermore, saturation is not observed even at a field of 70 kOe and at temperatures as low as 2 K. From the M H isotherms, the magnetic entropy change as a function of T for the removal of a 50 kOe field was calculated for various alloys using the previously outlined procedure. The results are plotted in Fig. 3. Since the calculated DSM values are negative, they are represented by their absolute values, 9DSM9. For the samples with x¼0.13 and 0.17, 9DSM9 monotonically decrease with T, while for the other samples, broad peaks can be observed. As a general behavior, the highest entropy change 9DSmax M 9, and its corresponding temperature Tmax, for each specimen, change with Gd concentration. The relatively high 9DSM9 values (7.0 and 8.3 J kg 1 K 1 at about 7 K for samples with x¼0.13 and 0.17, respectively, and in the range 2.4–5.0 J kg 1 K 1, at higher temperatures, for the 29%, 38% and 52%
Gd samples), suggest that the alloys can be useful in magnetic refrigeration as their 9DSmax M 9 or Tmax values can be tailored according to the alloy composition. The 9DSM9 T plots for the alloys with x ¼0.29, 0.38 and 0.52 clearly reveal ferromagnetic transition temperatures as it is well known that for a ferromagnet, these plots show a peak at T¼TC [17,18]. The transitions, particularly for the x¼0.29 sample, occur in a large temperature interval, indicating highly inhomogeneous materials. Nevertheless, we will take the values of 33, 57 and 61 K as Curie temperatures for our alloys with x¼0.29, 0.38 and 0.52, respectively, corresponding to the maxima of the DSM peaks of Fig. 3b, even if these temperatures do not correspond to sharp transitions. The inhomogeneity indicated by the 9DSM9 T curves was already expected from the diffraction patterns as they indicate regions of Gd and Cr only, arising from the immiscibility of the two metals. The TC values determined from Fig. 3b are well below that for bulk polycrystalline Gd (TC E290 K [19]) as a consequence of finite-size effects in the Gd clusters. In fact, according to theoretical predictions for a ferromagnetic cluster with dimensions in the nanometer range, TC is significantly reduced as the cluster size approaches the magnetic correlation length [20,21]. In thin films of Gd deposited onto W substrates, a TC of nearly 120 K was observed for a five monolayer film [22] while for Gd/W multilayer films an even lower TC (15 K) has been reported for a Gd layer thickness of 0.8 nm [23]. As for the DSM T plots for the x ¼0.13 and 0.17 alloys (Fig. 3a) the monotonical decrease of DSM with increasing T implies that a ferromagnetic ordering temperature cannot be assigned to them. It is, however, interesting to compare the latter plots with those theoretically predicted for a SPM system, i.e., a collection of single-domain non-interacting magnetic particles. If all particles in such a system have the same magnetic moment mp, the entropy variation for the removal of a magnetic field H is given by the equation [24]
sinh ðaÞ
DSM ¼ NkB 1 þ cothðaÞln
Fig. 2. M H isotherms for Gd–Cr alloys for Gd atomic concentrations of 0.13 and 0.52.
Fig. 3. Magnetic entropy change per kg of the alloy for the removal of 50 kOe field as a function of temperature for Gd–Cr specimens with (a) x ¼0.13 and 0.17, and (b) x¼ 0.29, 0.38 and 0.52.
2007
a
ð1Þ
where a ¼ mpH/kBT, kB is the Boltzman constant, and N is the number of magnetic clusters per unit mass. Plots of 9DSM9 T for SPM systems of Gd clusters of different numbers of atoms, calculated using Eq. (1), are shown in Fig. 4a. A comparison of the 9DSM9 T curves for the alloys with x¼0.13 and 0.17 with those of Fig. 4a indicates a SPM behavior in the former samples. It should be, however, remembered that Eq. (1) holds for a set of clusters of uniform magnetic moment while in our samples a cluster moment distribution is expected due to the non-uniform cluster sizes. Nevertheless, if only single-domain particles are considered, regardless their moment distribution, DSM is still a monotonically decreasing function of T. In principle, single-domain particles can magnetically interact with the other particles of the set. In this case, and for a uniform magnetic moment distribution, DSM can still be calculated by Eq. (1) but with T replaced by T–TI where TI is the interaction temperature [25]. Plots DSM T would thus show a cusp at T¼TI as can be seen in Fig. 4b, simulated for TI ¼25 K and for clusters of different numbers of Gd atoms. The DSM T plots for the alloys with x¼0.13 and 0.17 (Fig. 3a) do not show a cusp at any T and thus magnetic interaction between the particles is not suggested. If interaction exists, TI would be below 3 K, which is the lowest temperature for which DSM could be determined for these specimens. From the M H isotherms at 2 K for fields in the range 0–70 kOe, the saturation magnetization, Ms, was determined from plots of M as a function of 1/H (Fig. 5) by extrapolation of the lines to 1/H¼0
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Fig. 6. Saturation magnetic moment in units of mB per alloy atom as a function of the Gd concentration. Dashed line is the function ms ¼7.0x. Fig. 4. Magnetic entropy change for the removal of a 50 kOe field as a function of temperature for systems of Gd clusters with 15 and 30 atoms. 9DSM9 calculated using (a) Eq. (1) and (b) Eq. (1) with T replaced by T–TI for TI ¼ 25 K .
Table 1 ms, Tmax and Tf for Gd–Cr alloys as functions of Gd atomic concentration. x
ms (mB/Gd atom)
Tmax ðKÞ
Tf (K)
0.13 0.17 0.20 0.29 0.38 0.52
7.87 0.4 7.27 0.3 – 6.97 0.3 6.97 0.3 6.97 0.3
– – o2 10 21 28
14 – 19 24 36 44
Fig. 5. Magnetization at 2 K as a function of the inverse field for specimens with various Gd concentrations.
according to the approximation law [26] a M ¼ Ms 1 H
ð2Þ
where a is a constant. The saturation magnetic moments, ms, calculated from the Ms values, in units of Bohr magnetons, mB, per atom of the alloy, are plotted in Fig. 6, as a function of the Gd concentration. It can be seen that the data points can be fitted by a straight line. Thus the dilution law is followed in the Gd–Cr system, as the equation for the straight line can be written as ms ¼ mGd(1 y)¼xmGd, where mGd is the saturation moment per atom in pure amorphous Gd, and y is the atomic Cr concentration. The slope of the straight line in Fig. 6, determined using linear regression, is (7.370.3)mB, which is in good agreement with the saturation moment of amorphous Gd (7.0 70.3)mB [27]. This result is a strong indication that the Cr atoms do not contribute to the total magnetic moment of the samples. The saturation magnetic moments in units of mB per Gd atom are listed in Table 1 for various Gd–Cr specimens. Within experimental error, the values of ms per Gd atom are in fairly good agreement with that of the saturation moment of amorphous Gd. The closeness of the ms values to 7.0mB is not unexpected despite the sizable content
Fig. 7. ZFC and FC magnetizations as a function of temperature for Gd–Cr alloys with various Gd concentrations.
of the solvent atoms in the alloys. In Gd, the 4f shell, which contains the electrons of unpaired spins is so well shielded by outer electrons that direct interaction with the Cr atoms must be negligible. Field-cooled (FC) and zero field-cooled (ZFC) M T curves in the range 2–200 K are shown in Fig. 7 for various alloys. To obtain the FC curves, the magnetic moment was measured under a field of 200 Oe during the cooling process from ambient temperature to 2 K. For the ZFC curves, the sample temperature was lowered without applied magnetic field down to the lowest temperature of the measurement (2 K). Subsequently, the magnetic field (200 Oe) was applied and the temperature raised while the magnetic moment was measured. The Gd–Cr alloys of this work can be regarded as an array of giant spin clusters in a nonmagnetic medium. In these disordered magnetic systems, the existence of a low temperature ground state with glassy characteristics is possible [28] in which the magnetic moments are immobilized or frozen in random directions in their own field. In the
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M T ZFC curves for cluster glasses (as for spin glasses) the appearance of the magnetic ground state is characterized by a peak at the freezing temperature Tf [29]. In each ZFC curves of Fig. 7, for x¼0.29, 0.38 and 0.52, a prominent peak is seen at a temperature T¼Tmax whose values are listed in Table 1. In the ZFC curves for x¼0.13 and 0.17, a peak is not seen, probably because it would occur around or below 2 K, which is the lowest temperature of our measurements. All the FC and ZFC curves coincide at the high temperature region, but as the sample is cooled, they separate at a temperature Ts 4Tmax. For ToTs, the FC and ZFC magnetization difference, DM¼ DMFC DMZFC, at any given temperature, monotonically increases with decreasing temperature. The FC and ZFC plots strongly suggest a glassy magnetic nature for the Gd–Cr alloys, as the peak in the ZFC curve, the existence of a separation temperature for the FC and ZFC curves, and the monotonical increase of DM for decreasing temperatures are typical of spin glass or cluster glass materials [30]. For these, the decrease of M in the ZFC curves is caused by the random freezing of the cluster moments into different metastable states. In a classical spin glass, in the ZFC process, the spins freeze within a very short temperature interval around Tf and a sharp peak or cusp appears in the ZFC susceptibility T curve at T¼Tf [31]. Furthermore, ZFC and FC curves for a spin glass depart at T¼Tf and the susceptibility of the FC branch for ToTf is nearly constant. A different behavior is observed for the Gd–Cr alloys of this work (Fig. 7). For ToTf the magnetization and, as a consequence, the susceptibility increase with decrease in temperature, providing an evidence of a cluster glass behavior. Unlike a spin glass, in a cluster glass a distribution of dipole moments due to cluster size distribution often exists. Because exchange interaction between spins depend on the spin magnitudes, spin freezing does not occur at once but in a range of temperatures during the cooling process, producing a broad freezing peak, as seen in Fig. 7. Regarding the peak temperature Tmax, in the M T curves of Fig. 7, it should be pointed out that the magnetic signatures of spin freezing in a magnetic glass and of spin blocking in a superparamagnetic (SPM) system are very similar. Both are characterized by the low temperature peak in the M T ZFC curves. From ac susceptibility measurements, however, it is possible to distinguish blocking from freezing, as discussed below. The real part of the ac susceptibility, w0 , as a function of temperature for various alloys and frequencies of the driving field is illustrated in Fig. 8. The amplitude of the driving field was 10 Oe and no static field was applied. The w0 T curves for various samples for the frequency of 10 kHz are shown in Fig. 8a, while the curves for a single sample (x¼0.31) for various frequencies are represented in Fig. 8b. As can be seen in the latter figure, the frequency of the ac field affects the position and intensity of the w0 peak. The inset clearly shows that as the frequency is increased from 10 to 104 Hz, the peak monotonically shifts to higher temperatures, while its intensity is reduced. The other specimens investigated (x ¼0.13, 0.20, 0.29, 0.38 and 0.52) show identical behaviors. To distinguish the freezing process from that of blocking, a criterion outlined by Mydosh [30] was used. It relies on the application of the parameter F, defined as F¼
DTp Tp Dðlog nÞ
ð3Þ
where DTp is the peak temperature shift for an increase in frequency from ni to nf and Dðlog nÞ ¼ log nf log ni . For spin glass or spin glass-like freezing, F varies, typically, from 5 10 3 to 8 10 2, while for SPM blocking the F is about one order of magnitude higher than the latter value [30]. For all Gd–Cr alloys of Fig. 8, F varies from 5 10 3 to 1 10 2. Thus, the temperature of the susceptibility peak of the curves of Fig. 8 is the freezing
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Fig. 8. Real part of the ac susceptibility as a function of temperature: (a) for various Gd–Cr samples at the frequency of 10 kHz and (b) for the sample with x¼ 0.31 for various frequencies.
temperature, Tf. Values of Tf for 10 kHz for various samples are listed in Table 1. It is noted that Tf increases with increasing atomic Gd concentration. A comparison between Tf and Tmax shows that Tmax oTf for all alloys. Since an applied field of 200 Oe was used to obtain the static M T data and the w0 T data was obtained without a static applied field, this result is consistent with the often reported observation that a static applied field depresses the freezing temperature of a spin glass [32] or cluster glass [33] system as predicted by the Almeida–Thouless theory [34]. The existence of anisotropy in the Gd–Cr alloys was investigated from hysteresis loops for which the field was cycled between þ70 and 70 kOe after cooling the samples to 2 K under the field of þ70 kOe. Representative hysteresis curves are shown in Fig. 9. As can be seen, the hysteresis loops open up with increasing Gd concentration. The coercive field, Hc, determined from the hysteresis curves, is plotted in Fig. 10, as a function of x. It can be seen that as x increases, Hc rises from a few Oe to E530 Oe, revealing a strong increase in the anisotropy energy with x for x 40.17. Because of the amorphous or nearly amorphous nature of the Gd phase of the alloys, the contribution of crystal anisotropy to the total anisotropy is ruled out. For the same reason, Bloch wall hindrances due to occlusion and stress are not likely to occur in the Gd clusters. Shape anisotropy, however, must be considered. It is well known [35] that in nanocomposites, the size of the clusters increases with increase in concentration of the cluster material. Furthermore, the shape of the clusters evolve, typically, from spherical (or nearly spherical), at low concentrations, to irregular, at higher concentrations. As we expect the Gd clusters in our samples to follow this behavior,
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Fig. 9. Hysteresis M H loops for various Gd–Cr samples at 2 K.
The magnetocaloric effect was studied in terms of the magnetic entropy change for the removal of a 50 kOe field. The higher 9DSM9 value observed for each sample was seen to vary in the range 4.5–8.4 J kg 1 K 1. For the specimens with x Z0.29, Curie temperatures were assigned from the DSM T curves, while for the low Gd concentration samples (x ¼0.13 and 0.17) these curves indicated a superparamagnetic behavior. The alloys are cluster glasses whose freezing temperatures increase with increasing Gd concentration. The saturation magnetic moment per alloy atom was found to obey the dilution law, implying that the Cr atoms do not contribute to the magnetic moment of the alloys. The saturation magnetic moment per Gd atom, on the other hand, did not significantly vary with x, according to the principle that the spin-carrying Gd atomic shell (4f) is magnetically shielded by the Gd outer electrons and thus not affected by the Cr atoms in its neighborhood. Finally, the existence of anisotropy of the Gd–Cr alloys was revealed by the hysteresis loops at 2 K. The coercive field is almost negligible for the x¼0.13 alloy but steadily increases with increasing x to nearly 530 Oe for the alloy with the highest Gd content (x ¼0.52).
Acknowledgments We thank FAPESP, CAPES and CNPq of Brazil for financial support. The help of Dr. A.A. Coelho and Dr. A.M.G. Carvalho in the acquisition of magnetic data is greatly acknowledged. References
Fig. 10. Coercive field as a function of Gd concentration determined from hysteresis loops at 2 K.
and as shape anisotropy tends to be higher in irregular particles, this is a possible explanation for the increase of the coercive field with increasing Gd concentration. Since the hysteresis loops were obtained at a temperature of 2 K, which is well below the freezing temperature of all samples, another contribution to the coercive field may arise from an effective anisotropy field [36] due to the random freezing of the Gd clusters. Examination of the hysteresis loops for all alloys of this work reveal that the intercepts of these curves with the H axis are symmetrical with respect to the vertical axis, i.e., there is no exchange bias [37] (shift of hysteresis loops along the H axis). This implies that mechanisms leading to exchange anisotropy [30,38] are not operative even in the alloys of higher Gd concentration, despite the fact that antiferromagnetic (Cr) and ferromagnetic (Gd) phases are present in these alloys and antiferro–ferromagnetic interfaces necessarily exist. However, for a pronounced exchange bias, a high anisotropy energy of the antiferromagnetic phase is necessary. Thus, a possible explanation for the observed absence of exchange bias in our alloys is the low anisotropy of the Cr phase as the latter is either in the amorphous or quasi-amorphous state.
4. Conclusions Metastable Gd–Cr alloys with Gd concentrations in the interval 13–52% were investigated. The Gd phase was either amorphous or very low crystalline, as revealed by grazing incidence X-ray diffraction.
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Magnetic properties of metastable Gd–Cr alloys F.P. Rouxinol a,n, G.Z. Gadioli a, R.V. Gelamo c, A.O. dos Santos a,b, L.P. Cardoso a, S. Gama a, M.A. Bica de Moraes a a
Instituto de Fı´sica Gleb Wataghin, Universidade Estadual de Campinas—UNICAMP, 13083-970 Campinas, SP, Brazil ~ 65900-410 Imperatriz, MA, Brazil CCSST, Universidade Federal do Maranhao, c ´gicas e Exatas, Universidade Federal do Triˆ Instituto de Ciˆencias Tecnolo angulo Mineiro, 38025-180 Uberaba, MG, Brazil b
a r t i c l e i n f o
abstract
Article history: Received 1 September 2010 Received in revised form 10 December 2010 Available online 5 March 2011
We report on the magnetization, magnetocaloric effect, magnetic ordering temperatures, saturation magnetic moments and anisotropy of sputter-deposited GdxCr1 x alloys with Gd atomic concentrations, x, ranging from 0.13 to 0.52. The complex magnetic nature of the Gd–Cr films was revealed from the M H isotherms, which do not show saturation even at an applied field of 70 kOe and a temperature of 2 K and do not exhibit a linear behavior at higher temperatures. For some of the samples, the isotherms were used to determine the isothermal entropy variation as a function of temperature, for a change of 50 kOe in the applied magnetic field. The saturation magnetic moment varies with x and follows the dilution law, implying that the Cr atoms do not contribute to the total moment of the Gd–Cr alloys. Both static magnetization and dynamic susceptibility measurements reveal the existence of a magnetic glassy behavior in the alloys, which occurs below a freezing temperature. The existence of anisotropy at low temperatures for all samples was revealed by their M H hysteresis loops from which the in-plane coercive fields, Hc, were determined. A monotonical increase in Hc with increasing Gd concentration was observed. & 2011 Elsevier B.V. All rights reserved.
Keywords: ac susceptibility Spin glass-like Amorphous alloys Coercive field
1. Introduction Owing to their interesting and often unexpected properties magnetic nanostructured materials have been intensively investigated. A possible and frequently studied configuration of these materials is that of a nanocomposite, i.e., a system in which nanosized magnetic particles, or clusters, are embedded in a nonmagnetic medium. Such a configuration enables unusual transport properties such as giant magnetoresistance [1], extraordinary Hall effect [2] and may exhibit high coercivity, a most important property in materials for magnetic recording [3]. Gadolinium-based nanocomposites [4,5] have received a great deal of attention mainly due to the high magnetic moment of Gd, capable of imparting a high magnetization to these materials. The purpose of this work is to investigate the magnetic properties of GdxCr1 x alloys as a function of the Gd atomic concentration, x, for x in the range 0.13–0.52. The investigations include magnetization, magnetocaloric effect, magnetic ordering temperatures, magnetic moments of saturation, and anisotropy. Since Gd and Cr are mutually insoluble under equilibrium conditions, conventional metallurgical techniques could not be used for the preparation of the alloys and a
n
Corresponding author E-mail address: rouxinol@ifi.unicamp.br (F.P. Rouxinol).
0304-8853/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2011.02.040
vapor condensation technique – sputtering – was employed. The alloys are thus thin films that were deposited onto silicon substrates. Owing to the Gd and Cr insolubility the metals segregate during the deposition process and, as no thermal treatment was performed macroscopic segregation was prevented. Consequently, the films are nanocomposites. Only samples possessing Gd in a low crystalline or amorphous phase, which implies that Gd atomic concentrations not higher than 52%, are investigated. Samples with Gd concentration higher than 52%, for which the Gd phase are crystalline will be considered in a future paper. Despite the interest in the magnetic properties of Gd-containing alloys, only a few investigations have been carried out on the Gd–Cr system. Hsu and Fu [6] have investigated the electrical resistivity and the Ne´el temperature of the alloys, while Huang et al. [7] studied their entropy changes at the Curie temperature. In both investigations, the alloys were deposited by dc sputtering, but the Gd atomic concentrations were not higher than 7%. Also using dc sputtering, Hsu et al. [8] and Gavrin et al. [9] deposited Gd–Cr alloy films with Gd concentrations ranging from 0 to 100%, in which the magnetic ordering temperatures were investigated and the existence of a spin glass state was proposed. Although a magnetic glassy behavior is observed in our work, our results in general differ from those of Refs. [8,9]. The latter two investigations are concerned with films having thicknesses of a few micrometers deposited onto liquid nitrogen-cooled substrates, in contrast to our deposition procedure in which films with
2006
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thicknesses of at most 500 nm were deposited onto substrates kept at room temperature. Distinct film structures resulted from these different procedures, implying the differences in magnetic properties. Furthermore, to our knowledge, this is the first report regarding the GdxCr1 x system in which the magnetocaloric effect is investigated for Gd concentrations exceeding 7%, the anisotropy is studied, and ac susceptibility measurements are used to investigate the magnetic glassy behavior of the alloys.
2. Experimental The alloys were deposited by magnetron sputtering from separate Gd and Cr targets at an argon pressure of 5 10 3 mbar in a stainless steel vacuum chamber. The chamber base pressure was about 1 10 7 mbar. Silicon (001) slabs were used as substrates. The substrate holder was kept at room temperature. The purities of the Gd and the Cr targets were of 99.9% and 99.95%, respectively. Film thicknesses were in the range of 200–500 nm, measured using a high resolution profilometer. To determine the atomic composition of the films, Rutherford Backscattering Spectroscopy (RBS) analyses were performed at the Laboratory for Analysis of Materials by Ion Beams at the Institute of Physics, University of Sa~ o Paulo. Only Gd, Cr and traces of O were revealed by the RBS spectra. The SIMNRA computational program [10] was used to fit the RBS data yielding the area density ni (number of atoms per unit area), of each element in the films. Knowing ni and the area of the films, the masses of the elements were calculated. For the samples in which oxygen was observed, the atomic concentration was not higher than 3%. Grazing incidence X-ray diffraction (GIXRD) (y E51) patterns of the Gd–Cr alloys were collected using a diffractometer with Cu Ka radiation (l ¼0.15418 nm), operating at 40 kV/50 mA, in a geometry with a flat graphite diffracted beam monochromator crystal and a parallel plate collimator. Superconducting quantum interference device (SQUID) magnetometer was used to measure the magnetic moments of the films as a function of temperature (2–350 K) and applied field (0–70 kOe). Alternating-field susceptibility measurements were performed using physical properties measurement system (PPMS) to determine the real part of the ac susceptibility as a function of temperature (2–350 K) and frequency of the alternating driving field (10 104 Hz). For the SQUID and PPMS measurements, the applied magnetic fields were parallel to the film surface, thus avoiding demagnetizing corrections. The data were corrected for the magnetic moments of the substrate and sample holders. From M H isotherm sets for some of the samples, the isothermal entropy change, DSM, for the removal of a 50 kOe field was calculated according to a procedure outlined by Pecharsky and Gschneidner [11].
3. Results and discussion Fig. 1 shows X-ray diffraction patterns of the GdxCr1 x alloys with x in the range 0.13–0.52. For comparisons in the forthcoming discussion, the peak positions for hcp Gd and bcc Cr structures, calculated for isotropic distributions are also represented in the figure by vertical bars. It can be seen that all peaks are broad, indicating the absence of long range periodicity. For the Gd hcp structure, the three reflections calculated for the isotropic distribution at 2y ¼28.331, 30.961, and 33.421 are very intense and this has been experimentally verified for sputter-deposited Gd thin films [5,12], Gd alloys [5,8,13], and Gd/Cr layers [14]. Thus, the broad peak in the range 27–351 for
Fig. 1. X-ray diffraction patterns for the Gdx–Cr1 x alloys. 2y reflections for bcc Cr and for hcp Gd, calculated for isotropic distributions, are indicated by vertical bars.
samples with x¼0.17 through 0.52 is assigned to Gd. There are no contributions of Cr to this peak, as no significant Cr reflections are predicted in the latter range. For the 13% Gd sample, the absence of any feature in the interval 27–351 indicates a completely amorphous Gd phase. Therefore, as the Gd concentration increases from 13 to 52%, the Gd phase evolves from amorphous to a low crystalline state. Peaks at 2y ¼441, 571, and 641, for the x¼ 0.13 sample are relatively well defined, are assigned to Cr. They show, however, some small displacements from their predicted positions (44.161, 57.131 and 64.631), probably because of stress-induced distortions in the Cr lattice parameter, as usually observed in vacuum-deposited thin films. To these peaks, the Gd phase may also contribute, as Gd reflections are predicted at 2y-values close to 42.51, 56.01 and 64.51. Nevertheless, this contribution is not expected to be significant. In fact, as the Gd concentration increases, there is a concomitant intensity decrease of the latter peaks while that of Gd, at the interval 27–351, shows an overall increase. Our X-ray diffraction results are different from those of Hsu et al. [8] for Gd–Cr alloys deposited by sputtering on glass substrates cooled by liquid nitrogen, and investigated over the entire composition range as their diffraction patterns show that crystalline phases of either Gd or Cr, or both, are present at any composition. Such a difference is, in a first examination, unexpected, as the higher substrate temperature (room temperature) used in our depositions should result in more crystalline specimens than those of Ref. [8]. However, besides substrate temperature, the film crystalline structure depends on the rate of deposition, R, and film thickness, t. Usually, high deposition rates favor less crystalline and, in many cases, amorphous film structures [15]. Regarding film thickness, a typical behavior [16] in film deposition is the small grain size in the early stages of film formation and the fast increase in grain size as the film thickness approaches one or more micrometers [11,12]. For the films of this work, R¼1.5 mm/h and t is at most 0.5 mm, while for the films
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of Ref. [8] R¼1 mm/h and t is in the range of several micrometers. Thus, the tendency to form a less crystalline state than that reported in Ref. [8] is favored in the films of this work. It seems that their structural dependence on R and t at room temperature overcomes the effect of temperature-induced crystallite formation. Fig. 2 shows representative M H isotherms of the Gd–Cr alloys at fields up to 50 kOe. The sharp increase of M with increasing H for low fields in the lower temperature isotherms is typical of all samples. Furthermore, saturation is not observed even at a field of 70 kOe and at temperatures as low as 2 K. From the M H isotherms, the magnetic entropy change as a function of T for the removal of a 50 kOe field was calculated for various alloys using the previously outlined procedure. The results are plotted in Fig. 3. Since the calculated DSM values are negative, they are represented by their absolute values, 9DSM9. For the samples with x¼0.13 and 0.17, 9DSM9 monotonically decrease with T, while for the other samples, broad peaks can be observed. As a general behavior, the highest entropy change 9DSmax M 9, and its corresponding temperature Tmax, for each specimen, change with Gd concentration. The relatively high 9DSM9 values (7.0 and 8.3 J kg 1 K 1 at about 7 K for samples with x¼0.13 and 0.17, respectively, and in the range 2.4–5.0 J kg 1 K 1, at higher temperatures, for the 29%, 38% and 52%
Gd samples), suggest that the alloys can be useful in magnetic refrigeration as their 9DSmax M 9 or Tmax values can be tailored according to the alloy composition. The 9DSM9 T plots for the alloys with x ¼0.29, 0.38 and 0.52 clearly reveal ferromagnetic transition temperatures as it is well known that for a ferromagnet, these plots show a peak at T¼TC [17,18]. The transitions, particularly for the x¼0.29 sample, occur in a large temperature interval, indicating highly inhomogeneous materials. Nevertheless, we will take the values of 33, 57 and 61 K as Curie temperatures for our alloys with x¼0.29, 0.38 and 0.52, respectively, corresponding to the maxima of the DSM peaks of Fig. 3b, even if these temperatures do not correspond to sharp transitions. The inhomogeneity indicated by the 9DSM9 T curves was already expected from the diffraction patterns as they indicate regions of Gd and Cr only, arising from the immiscibility of the two metals. The TC values determined from Fig. 3b are well below that for bulk polycrystalline Gd (TC E290 K [19]) as a consequence of finite-size effects in the Gd clusters. In fact, according to theoretical predictions for a ferromagnetic cluster with dimensions in the nanometer range, TC is significantly reduced as the cluster size approaches the magnetic correlation length [20,21]. In thin films of Gd deposited onto W substrates, a TC of nearly 120 K was observed for a five monolayer film [22] while for Gd/W multilayer films an even lower TC (15 K) has been reported for a Gd layer thickness of 0.8 nm [23]. As for the DSM T plots for the x ¼0.13 and 0.17 alloys (Fig. 3a) the monotonical decrease of DSM with increasing T implies that a ferromagnetic ordering temperature cannot be assigned to them. It is, however, interesting to compare the latter plots with those theoretically predicted for a SPM system, i.e., a collection of single-domain non-interacting magnetic particles. If all particles in such a system have the same magnetic moment mp, the entropy variation for the removal of a magnetic field H is given by the equation [24]
sinh ðaÞ
DSM ¼ NkB 1 þ cothðaÞln
Fig. 2. M H isotherms for Gd–Cr alloys for Gd atomic concentrations of 0.13 and 0.52.
Fig. 3. Magnetic entropy change per kg of the alloy for the removal of 50 kOe field as a function of temperature for Gd–Cr specimens with (a) x ¼0.13 and 0.17, and (b) x¼ 0.29, 0.38 and 0.52.
2007
a
ð1Þ
where a ¼ mpH/kBT, kB is the Boltzman constant, and N is the number of magnetic clusters per unit mass. Plots of 9DSM9 T for SPM systems of Gd clusters of different numbers of atoms, calculated using Eq. (1), are shown in Fig. 4a. A comparison of the 9DSM9 T curves for the alloys with x¼0.13 and 0.17 with those of Fig. 4a indicates a SPM behavior in the former samples. It should be, however, remembered that Eq. (1) holds for a set of clusters of uniform magnetic moment while in our samples a cluster moment distribution is expected due to the non-uniform cluster sizes. Nevertheless, if only single-domain particles are considered, regardless their moment distribution, DSM is still a monotonically decreasing function of T. In principle, single-domain particles can magnetically interact with the other particles of the set. In this case, and for a uniform magnetic moment distribution, DSM can still be calculated by Eq. (1) but with T replaced by T–TI where TI is the interaction temperature [25]. Plots DSM T would thus show a cusp at T¼TI as can be seen in Fig. 4b, simulated for TI ¼25 K and for clusters of different numbers of Gd atoms. The DSM T plots for the alloys with x¼0.13 and 0.17 (Fig. 3a) do not show a cusp at any T and thus magnetic interaction between the particles is not suggested. If interaction exists, TI would be below 3 K, which is the lowest temperature for which DSM could be determined for these specimens. From the M H isotherms at 2 K for fields in the range 0–70 kOe, the saturation magnetization, Ms, was determined from plots of M as a function of 1/H (Fig. 5) by extrapolation of the lines to 1/H¼0
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Fig. 6. Saturation magnetic moment in units of mB per alloy atom as a function of the Gd concentration. Dashed line is the function ms ¼7.0x. Fig. 4. Magnetic entropy change for the removal of a 50 kOe field as a function of temperature for systems of Gd clusters with 15 and 30 atoms. 9DSM9 calculated using (a) Eq. (1) and (b) Eq. (1) with T replaced by T–TI for TI ¼ 25 K .
Table 1 ms, Tmax and Tf for Gd–Cr alloys as functions of Gd atomic concentration. x
ms (mB/Gd atom)
Tmax ðKÞ
Tf (K)
0.13 0.17 0.20 0.29 0.38 0.52
7.87 0.4 7.27 0.3 – 6.97 0.3 6.97 0.3 6.97 0.3
– – o2 10 21 28
14 – 19 24 36 44
Fig. 5. Magnetization at 2 K as a function of the inverse field for specimens with various Gd concentrations.
according to the approximation law [26] a M ¼ Ms 1 H
ð2Þ
where a is a constant. The saturation magnetic moments, ms, calculated from the Ms values, in units of Bohr magnetons, mB, per atom of the alloy, are plotted in Fig. 6, as a function of the Gd concentration. It can be seen that the data points can be fitted by a straight line. Thus the dilution law is followed in the Gd–Cr system, as the equation for the straight line can be written as ms ¼ mGd(1 y)¼xmGd, where mGd is the saturation moment per atom in pure amorphous Gd, and y is the atomic Cr concentration. The slope of the straight line in Fig. 6, determined using linear regression, is (7.370.3)mB, which is in good agreement with the saturation moment of amorphous Gd (7.0 70.3)mB [27]. This result is a strong indication that the Cr atoms do not contribute to the total magnetic moment of the samples. The saturation magnetic moments in units of mB per Gd atom are listed in Table 1 for various Gd–Cr specimens. Within experimental error, the values of ms per Gd atom are in fairly good agreement with that of the saturation moment of amorphous Gd. The closeness of the ms values to 7.0mB is not unexpected despite the sizable content
Fig. 7. ZFC and FC magnetizations as a function of temperature for Gd–Cr alloys with various Gd concentrations.
of the solvent atoms in the alloys. In Gd, the 4f shell, which contains the electrons of unpaired spins is so well shielded by outer electrons that direct interaction with the Cr atoms must be negligible. Field-cooled (FC) and zero field-cooled (ZFC) M T curves in the range 2–200 K are shown in Fig. 7 for various alloys. To obtain the FC curves, the magnetic moment was measured under a field of 200 Oe during the cooling process from ambient temperature to 2 K. For the ZFC curves, the sample temperature was lowered without applied magnetic field down to the lowest temperature of the measurement (2 K). Subsequently, the magnetic field (200 Oe) was applied and the temperature raised while the magnetic moment was measured. The Gd–Cr alloys of this work can be regarded as an array of giant spin clusters in a nonmagnetic medium. In these disordered magnetic systems, the existence of a low temperature ground state with glassy characteristics is possible [28] in which the magnetic moments are immobilized or frozen in random directions in their own field. In the
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M T ZFC curves for cluster glasses (as for spin glasses) the appearance of the magnetic ground state is characterized by a peak at the freezing temperature Tf [29]. In each ZFC curves of Fig. 7, for x¼0.29, 0.38 and 0.52, a prominent peak is seen at a temperature T¼Tmax whose values are listed in Table 1. In the ZFC curves for x¼0.13 and 0.17, a peak is not seen, probably because it would occur around or below 2 K, which is the lowest temperature of our measurements. All the FC and ZFC curves coincide at the high temperature region, but as the sample is cooled, they separate at a temperature Ts 4Tmax. For ToTs, the FC and ZFC magnetization difference, DM¼ DMFC DMZFC, at any given temperature, monotonically increases with decreasing temperature. The FC and ZFC plots strongly suggest a glassy magnetic nature for the Gd–Cr alloys, as the peak in the ZFC curve, the existence of a separation temperature for the FC and ZFC curves, and the monotonical increase of DM for decreasing temperatures are typical of spin glass or cluster glass materials [30]. For these, the decrease of M in the ZFC curves is caused by the random freezing of the cluster moments into different metastable states. In a classical spin glass, in the ZFC process, the spins freeze within a very short temperature interval around Tf and a sharp peak or cusp appears in the ZFC susceptibility T curve at T¼Tf [31]. Furthermore, ZFC and FC curves for a spin glass depart at T¼Tf and the susceptibility of the FC branch for ToTf is nearly constant. A different behavior is observed for the Gd–Cr alloys of this work (Fig. 7). For ToTf the magnetization and, as a consequence, the susceptibility increase with decrease in temperature, providing an evidence of a cluster glass behavior. Unlike a spin glass, in a cluster glass a distribution of dipole moments due to cluster size distribution often exists. Because exchange interaction between spins depend on the spin magnitudes, spin freezing does not occur at once but in a range of temperatures during the cooling process, producing a broad freezing peak, as seen in Fig. 7. Regarding the peak temperature Tmax, in the M T curves of Fig. 7, it should be pointed out that the magnetic signatures of spin freezing in a magnetic glass and of spin blocking in a superparamagnetic (SPM) system are very similar. Both are characterized by the low temperature peak in the M T ZFC curves. From ac susceptibility measurements, however, it is possible to distinguish blocking from freezing, as discussed below. The real part of the ac susceptibility, w0 , as a function of temperature for various alloys and frequencies of the driving field is illustrated in Fig. 8. The amplitude of the driving field was 10 Oe and no static field was applied. The w0 T curves for various samples for the frequency of 10 kHz are shown in Fig. 8a, while the curves for a single sample (x¼0.31) for various frequencies are represented in Fig. 8b. As can be seen in the latter figure, the frequency of the ac field affects the position and intensity of the w0 peak. The inset clearly shows that as the frequency is increased from 10 to 104 Hz, the peak monotonically shifts to higher temperatures, while its intensity is reduced. The other specimens investigated (x ¼0.13, 0.20, 0.29, 0.38 and 0.52) show identical behaviors. To distinguish the freezing process from that of blocking, a criterion outlined by Mydosh [30] was used. It relies on the application of the parameter F, defined as F¼
DTp Tp Dðlog nÞ
ð3Þ
where DTp is the peak temperature shift for an increase in frequency from ni to nf and Dðlog nÞ ¼ log nf log ni . For spin glass or spin glass-like freezing, F varies, typically, from 5 10 3 to 8 10 2, while for SPM blocking the F is about one order of magnitude higher than the latter value [30]. For all Gd–Cr alloys of Fig. 8, F varies from 5 10 3 to 1 10 2. Thus, the temperature of the susceptibility peak of the curves of Fig. 8 is the freezing
2009
Fig. 8. Real part of the ac susceptibility as a function of temperature: (a) for various Gd–Cr samples at the frequency of 10 kHz and (b) for the sample with x¼ 0.31 for various frequencies.
temperature, Tf. Values of Tf for 10 kHz for various samples are listed in Table 1. It is noted that Tf increases with increasing atomic Gd concentration. A comparison between Tf and Tmax shows that Tmax oTf for all alloys. Since an applied field of 200 Oe was used to obtain the static M T data and the w0 T data was obtained without a static applied field, this result is consistent with the often reported observation that a static applied field depresses the freezing temperature of a spin glass [32] or cluster glass [33] system as predicted by the Almeida–Thouless theory [34]. The existence of anisotropy in the Gd–Cr alloys was investigated from hysteresis loops for which the field was cycled between þ70 and 70 kOe after cooling the samples to 2 K under the field of þ70 kOe. Representative hysteresis curves are shown in Fig. 9. As can be seen, the hysteresis loops open up with increasing Gd concentration. The coercive field, Hc, determined from the hysteresis curves, is plotted in Fig. 10, as a function of x. It can be seen that as x increases, Hc rises from a few Oe to E530 Oe, revealing a strong increase in the anisotropy energy with x for x 40.17. Because of the amorphous or nearly amorphous nature of the Gd phase of the alloys, the contribution of crystal anisotropy to the total anisotropy is ruled out. For the same reason, Bloch wall hindrances due to occlusion and stress are not likely to occur in the Gd clusters. Shape anisotropy, however, must be considered. It is well known [35] that in nanocomposites, the size of the clusters increases with increase in concentration of the cluster material. Furthermore, the shape of the clusters evolve, typically, from spherical (or nearly spherical), at low concentrations, to irregular, at higher concentrations. As we expect the Gd clusters in our samples to follow this behavior,
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Fig. 9. Hysteresis M H loops for various Gd–Cr samples at 2 K.
The magnetocaloric effect was studied in terms of the magnetic entropy change for the removal of a 50 kOe field. The higher 9DSM9 value observed for each sample was seen to vary in the range 4.5–8.4 J kg 1 K 1. For the specimens with x Z0.29, Curie temperatures were assigned from the DSM T curves, while for the low Gd concentration samples (x ¼0.13 and 0.17) these curves indicated a superparamagnetic behavior. The alloys are cluster glasses whose freezing temperatures increase with increasing Gd concentration. The saturation magnetic moment per alloy atom was found to obey the dilution law, implying that the Cr atoms do not contribute to the magnetic moment of the alloys. The saturation magnetic moment per Gd atom, on the other hand, did not significantly vary with x, according to the principle that the spin-carrying Gd atomic shell (4f) is magnetically shielded by the Gd outer electrons and thus not affected by the Cr atoms in its neighborhood. Finally, the existence of anisotropy of the Gd–Cr alloys was revealed by the hysteresis loops at 2 K. The coercive field is almost negligible for the x¼0.13 alloy but steadily increases with increasing x to nearly 530 Oe for the alloy with the highest Gd content (x ¼0.52).
Acknowledgments We thank FAPESP, CAPES and CNPq of Brazil for financial support. The help of Dr. A.A. Coelho and Dr. A.M.G. Carvalho in the acquisition of magnetic data is greatly acknowledged. References
Fig. 10. Coercive field as a function of Gd concentration determined from hysteresis loops at 2 K.
and as shape anisotropy tends to be higher in irregular particles, this is a possible explanation for the increase of the coercive field with increasing Gd concentration. Since the hysteresis loops were obtained at a temperature of 2 K, which is well below the freezing temperature of all samples, another contribution to the coercive field may arise from an effective anisotropy field [36] due to the random freezing of the Gd clusters. Examination of the hysteresis loops for all alloys of this work reveal that the intercepts of these curves with the H axis are symmetrical with respect to the vertical axis, i.e., there is no exchange bias [37] (shift of hysteresis loops along the H axis). This implies that mechanisms leading to exchange anisotropy [30,38] are not operative even in the alloys of higher Gd concentration, despite the fact that antiferromagnetic (Cr) and ferromagnetic (Gd) phases are present in these alloys and antiferro–ferromagnetic interfaces necessarily exist. However, for a pronounced exchange bias, a high anisotropy energy of the antiferromagnetic phase is necessary. Thus, a possible explanation for the observed absence of exchange bias in our alloys is the low anisotropy of the Cr phase as the latter is either in the amorphous or quasi-amorphous state.
4. Conclusions Metastable Gd–Cr alloys with Gd concentrations in the interval 13–52% were investigated. The Gd phase was either amorphous or very low crystalline, as revealed by grazing incidence X-ray diffraction.
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