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Spin-glass behavior of Zr(FexCr1−x)2 compounds
Journal of Magnetism and Magnetic Materials 226}230 (2001) 1306}1308
Spin-glass behavior of Zr(Fe Cr ) compounds V \V J.A.H. Coaquira*, H.R. Rechenberg Instituto de Fn& sica, Universidade de SaJ o Paulo, C.P. 66318, 05315-970 Sao Paulo, Brazil
Abstract The magnetic properties of C14 Laves-phase Zr(Fe Cr ) (0.7)x)0.85) alloys have been investigated. Arrott V \V plots showed evidence of ferromagnetic ordering for alloys with x'0.7 but not for x"0.7. Zero "eld cooling/"eld cooling magnetization and MoK ssbauer spectroscopy data indicated spin-glass-like freezing for the sample with x"0.7 and a reentrant spin-glass behavior for samples with x'0.7. Dynamical behavior of the spin-glass sample (x"0.7) was studied by means of AC susceptibility. Two critical lines described by ¹ (H)!¹(0)&H B were obtained with "4.4 and 2.5, respectively. 2001 Elsevier Science B.V. All rights reserved. Keywords: Laves-phase compounds; Magnetization; Susceptibility; MoK ssbauer spectroscopy; Spin glass; Reentrant spin glass
The structural and magnetic properties of transition metal-based Laves-phase compounds AB have aroused long-standing interest. Although various Zr(Fe M ) V \V alloy systems have been investigated in detail (e.g. with M"Mn, Co, Al [1]), magnetic data are rather scarce for the M"Cr [2,3]. In this paper, we report on magnetic properties of Zr(Fe Cr ) alloys at low temperatures V \V in 0.7)x)0.85 range. Details of the experimental procedure are reported elsewhere [4]. X-ray di!raction revealed that all samples are single-phased with the hexagonal MgZn structure. Vibrating-sample mag netometer (in "eld up to 9 T), SQUID magnetometer and Fe MoK ssbauer spectroscopy measurements were carried out on powdered samples at temperatures 4.2}300 K. M vs. H curves obtained at ¹"4.2 K showed no ferromagnetic behavior for the x"0.7 sample. These curves present a slowly increasing magnetization when the "eld is increased, with no tendency towards saturation. When the iron concentration is greater than x"0.7, the behavior of M vs. H curves changes towards more saturated curves. Arrott plots of M vs. H/M are presented in Fig. 1. At high "elds, it can be observed that samples
* Corresponding author. Fax: #011-818-6984. E-mail address: [email protected] (J.A.H. Coaquira).
with x)0.75 do not extrapolate towards the positive side of M-axis, thus con"rming the absence of longrange ferromagnetic order, although these samples present a bit of hysteresis and remanent magnetization at low temperatures. On the other hand, samples with x'0.75 extrapolate to "nite value of M-axis, indicating a longrange ferromagnetic ordering, consistent with the saturation observed at M vs. H curves. These Arrott plots present a curvature at low "elds and this is more evident when x is increased. It was also observed in the pseudobinary Y(Fe,Al) by Hilscher [1] and it was inter preted using the model of cluster freezing proposed by Coles et al. [5]. Fig. 2a shows M vs. ¹ curves obtained by cooling with and without a magnetic "eld of H"100 Oe (FC and ZFC). For the sample with x"0.7, zero "eld cooling (ZFC)-curve grows until a peak around 44 K, above which a Curie}Weiss behavior is followed. Irreversibilities in M vs. ¹ curve are observed only at temperatures below the peak. This tendency is also observed for the sample with x"0.8 at temperatures below its broad peak. This broadening suggests the presence of another peak at high temperatures. That second peak is better observed in the M vs. ¹ curve for the sample with x"0.85. In this case, the irreversibilities are observed to start at higher temperatures. MoK ssbauer spectra were obtained in a wide range of temperatures. At 4.2 K the spectrum showed a broad mixture of sextets and this pattern collapses to a doublet
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 8 3 6 - 2
J.A.H. Coaquira, H.R. Rechenberg / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1306}1308
Fig. 1. Arrott plots obtained at ¹"4.2 K for the indicated samples.
Fig. 2. (a) M vs. ¹ curves obtained in H"100 Oe for the indicated samples. (b) Average hyper"ne "elds as a function of the temperature for the samples as in (a). The arrows indicate the transition temperature.
as the temperature is increased. The "tting of the spectra was done with a histogram distribution of hyper"ne "elds. Fig. 2b shows the mean value of the hyper"ne magnetic "elds (B ) as a function of temperature. For a sample with x"0.7, it can be observed that the collapse happens at a higher temperature than the susceptibility peak, and it is interpreted as due to the di!erent time window of the experimental techniques [3]. For samples with x'0.7, the behavior of the B vs. ¹ curve is rather di!erent. In addition to the magnetic collapse another jump occurs at a lower temperature.
1307
Fig. 3. AC susceptibility vs. ¹ curves obtained in several magnetic "elds. The inset shows the behavior of the two critical lines. The continuous lines are the "tting of the experimental points and the dashed one corresponds to the theoretical AT-line.
A similar two-transition behavior, characteristic of reentrant spin glass (RSG), has been observed in other systems like Fe Zr or Au Fe [4]. This behavior is V \V \V V interpreted as follows: at equilibrium, bulk magnetization and B are proportional to M and M, respectively. Upon cooling the sample through the paramagnetic to ferromagnetic transition (longitudinal ordering, ¹ ) where M O0 and M "M "0, both ! X V W measurements show increased signal. With additional temperature decrease the transverse components of magnetization become non-zero (transversal freezing state, ¹ ) and one observes a strong increase in B without 67 signi"cant variation in bulk magnetic measurement [6]. This was observed in our experimental results, although the magnetic signal of the FC-curve decreases somewhat instead of remaining constant below the peak observed at ZFC curve. In order to study the dynamic behavior of the spin freezing state, AC susceptibility was measured as a function of temperature at di!erent magnetic DC "elds for the sample with spin-glass behavior (x"0.7). The peak observed at zero magnetic "eld splits into a plateau when the "eld is increased as is shown in Fig. 3. The kinks on either end of the plateau de"ne two temperatures ¹ , ¹YY. We analyzed the behavior of these temperatures as a function of the magnetic "eld strength. The inset of Fig. 3 shows the observed trends. The lower temperature is described well by the function ¹ (0)!¹ (H)&H B with &4.4, although the predicted Almeida}Thouless line [7] in the mean "eld model of Ising spin glass ("3) is well satis"ed for H(1.2 kOe. The second characteristic temperature increases with applied "eld following a similar power law with &2.5. This work was "nancially supported by FAPESP and CNPq.
1308
J.A.H. Coaquira, H.R. Rechenberg / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1306}1308
References [1] G. Hilscher, J. Magn. Magn. Mater 27 (1982) 1. [2] K. Kanematsu, Y. Fujita, J. Phys. Soc. Jpn. 29 (1970) 864. [3] W.E. Wallace, F. Pourarian, A.T. Pedziwiatr, E.B. Boltich, J. Less-Common Met. 130 (1987) 33.
[4] J.A.H. Coaquira, H.R. Rechenberg, C.H.Westphal, Mater. Sci. Forum 302, 303 (1999) 384. [5] B.R. Coles, B.V.B. Sarkissian, R.H. Taylor, Phil. Mag. 37 (1978) 489. [6] D.H. Ryan, in: D.H. Ryan (Ed.), Recent Progress in Random Magnets, World Scienti"c, Singapore, 1992, p. 1. [7] J.R.L. de Ameida, D.J. Thouless, J. Phys. A 11 (1978) 983.
Spin-glass behavior of Zr(Fe Cr ) compounds V \V J.A.H. Coaquira*, H.R. Rechenberg Instituto de Fn& sica, Universidade de SaJ o Paulo, C.P. 66318, 05315-970 Sao Paulo, Brazil
Abstract The magnetic properties of C14 Laves-phase Zr(Fe Cr ) (0.7)x)0.85) alloys have been investigated. Arrott V \V plots showed evidence of ferromagnetic ordering for alloys with x'0.7 but not for x"0.7. Zero "eld cooling/"eld cooling magnetization and MoK ssbauer spectroscopy data indicated spin-glass-like freezing for the sample with x"0.7 and a reentrant spin-glass behavior for samples with x'0.7. Dynamical behavior of the spin-glass sample (x"0.7) was studied by means of AC susceptibility. Two critical lines described by ¹ (H)!¹(0)&H B were obtained with "4.4 and 2.5, respectively. 2001 Elsevier Science B.V. All rights reserved. Keywords: Laves-phase compounds; Magnetization; Susceptibility; MoK ssbauer spectroscopy; Spin glass; Reentrant spin glass
The structural and magnetic properties of transition metal-based Laves-phase compounds AB have aroused long-standing interest. Although various Zr(Fe M ) V \V alloy systems have been investigated in detail (e.g. with M"Mn, Co, Al [1]), magnetic data are rather scarce for the M"Cr [2,3]. In this paper, we report on magnetic properties of Zr(Fe Cr ) alloys at low temperatures V \V in 0.7)x)0.85 range. Details of the experimental procedure are reported elsewhere [4]. X-ray di!raction revealed that all samples are single-phased with the hexagonal MgZn structure. Vibrating-sample mag netometer (in "eld up to 9 T), SQUID magnetometer and Fe MoK ssbauer spectroscopy measurements were carried out on powdered samples at temperatures 4.2}300 K. M vs. H curves obtained at ¹"4.2 K showed no ferromagnetic behavior for the x"0.7 sample. These curves present a slowly increasing magnetization when the "eld is increased, with no tendency towards saturation. When the iron concentration is greater than x"0.7, the behavior of M vs. H curves changes towards more saturated curves. Arrott plots of M vs. H/M are presented in Fig. 1. At high "elds, it can be observed that samples
* Corresponding author. Fax: #011-818-6984. E-mail address: [email protected] (J.A.H. Coaquira).
with x)0.75 do not extrapolate towards the positive side of M-axis, thus con"rming the absence of longrange ferromagnetic order, although these samples present a bit of hysteresis and remanent magnetization at low temperatures. On the other hand, samples with x'0.75 extrapolate to "nite value of M-axis, indicating a longrange ferromagnetic ordering, consistent with the saturation observed at M vs. H curves. These Arrott plots present a curvature at low "elds and this is more evident when x is increased. It was also observed in the pseudobinary Y(Fe,Al) by Hilscher [1] and it was inter preted using the model of cluster freezing proposed by Coles et al. [5]. Fig. 2a shows M vs. ¹ curves obtained by cooling with and without a magnetic "eld of H"100 Oe (FC and ZFC). For the sample with x"0.7, zero "eld cooling (ZFC)-curve grows until a peak around 44 K, above which a Curie}Weiss behavior is followed. Irreversibilities in M vs. ¹ curve are observed only at temperatures below the peak. This tendency is also observed for the sample with x"0.8 at temperatures below its broad peak. This broadening suggests the presence of another peak at high temperatures. That second peak is better observed in the M vs. ¹ curve for the sample with x"0.85. In this case, the irreversibilities are observed to start at higher temperatures. MoK ssbauer spectra were obtained in a wide range of temperatures. At 4.2 K the spectrum showed a broad mixture of sextets and this pattern collapses to a doublet
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 8 3 6 - 2
J.A.H. Coaquira, H.R. Rechenberg / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1306}1308
Fig. 1. Arrott plots obtained at ¹"4.2 K for the indicated samples.
Fig. 2. (a) M vs. ¹ curves obtained in H"100 Oe for the indicated samples. (b) Average hyper"ne "elds as a function of the temperature for the samples as in (a). The arrows indicate the transition temperature.
as the temperature is increased. The "tting of the spectra was done with a histogram distribution of hyper"ne "elds. Fig. 2b shows the mean value of the hyper"ne magnetic "elds (B ) as a function of temperature. For a sample with x"0.7, it can be observed that the collapse happens at a higher temperature than the susceptibility peak, and it is interpreted as due to the di!erent time window of the experimental techniques [3]. For samples with x'0.7, the behavior of the B vs. ¹ curve is rather di!erent. In addition to the magnetic collapse another jump occurs at a lower temperature.
1307
Fig. 3. AC susceptibility vs. ¹ curves obtained in several magnetic "elds. The inset shows the behavior of the two critical lines. The continuous lines are the "tting of the experimental points and the dashed one corresponds to the theoretical AT-line.
A similar two-transition behavior, characteristic of reentrant spin glass (RSG), has been observed in other systems like Fe Zr or Au Fe [4]. This behavior is V \V \V V interpreted as follows: at equilibrium, bulk magnetization and B are proportional to M and M, respectively. Upon cooling the sample through the paramagnetic to ferromagnetic transition (longitudinal ordering, ¹ ) where M O0 and M "M "0, both ! X V W measurements show increased signal. With additional temperature decrease the transverse components of magnetization become non-zero (transversal freezing state, ¹ ) and one observes a strong increase in B without 67 signi"cant variation in bulk magnetic measurement [6]. This was observed in our experimental results, although the magnetic signal of the FC-curve decreases somewhat instead of remaining constant below the peak observed at ZFC curve. In order to study the dynamic behavior of the spin freezing state, AC susceptibility was measured as a function of temperature at di!erent magnetic DC "elds for the sample with spin-glass behavior (x"0.7). The peak observed at zero magnetic "eld splits into a plateau when the "eld is increased as is shown in Fig. 3. The kinks on either end of the plateau de"ne two temperatures ¹ , ¹YY. We analyzed the behavior of these temperatures as a function of the magnetic "eld strength. The inset of Fig. 3 shows the observed trends. The lower temperature is described well by the function ¹ (0)!¹ (H)&H B with &4.4, although the predicted Almeida}Thouless line [7] in the mean "eld model of Ising spin glass ("3) is well satis"ed for H(1.2 kOe. The second characteristic temperature increases with applied "eld following a similar power law with &2.5. This work was "nancially supported by FAPESP and CNPq.
1308
J.A.H. Coaquira, H.R. Rechenberg / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1306}1308
References [1] G. Hilscher, J. Magn. Magn. Mater 27 (1982) 1. [2] K. Kanematsu, Y. Fujita, J. Phys. Soc. Jpn. 29 (1970) 864. [3] W.E. Wallace, F. Pourarian, A.T. Pedziwiatr, E.B. Boltich, J. Less-Common Met. 130 (1987) 33.
[4] J.A.H. Coaquira, H.R. Rechenberg, C.H.Westphal, Mater. Sci. Forum 302, 303 (1999) 384. [5] B.R. Coles, B.V.B. Sarkissian, R.H. Taylor, Phil. Mag. 37 (1978) 489. [6] D.H. Ryan, in: D.H. Ryan (Ed.), Recent Progress in Random Magnets, World Scienti"c, Singapore, 1992, p. 1. [7] J.R.L. de Ameida, D.J. Thouless, J. Phys. A 11 (1978) 983.