- Email: [email protected]
Anomalous field dependence of the inverse magnetocaloric effect in Ce(Fe0.93Ru0.07)2
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 320 (2008) 2144–2148 www.elsevier.com/locate/jmmm
Anomalous field dependence of the inverse magnetocaloric effect in Ce(Fe0.93Ru0.07)2 Wanjun Jiang, Xuezhi Zhou, Henry Kunkel, Gwyn Williams Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2 Received 23 December 2007; received in revised form 19 February 2008 Available online 1 April 2008
Abstract A summary of detailed isothermal magnetization along with the ac susceptibility measurements on Ce(Fe0.93Ru0.07)2 is presented. Near the first-order transition, i.e. near 110 K, Ce(Fe0.93Ru0.07)2 displays a large positive magnetic entropy change, DSm, of 7.8 J/kg K in fields of only 2 T, i.e. it displays a strong inverse magnetocaloric (MCE) effect, as expected, on entering an antiferromagnetic (AF) state. However, the variation of the magnitude and width of this entropy change with field are anomalous when compared with model predictions, the former increasing with applied field below 2 T, while the latter exceeds 60 K in a field of 8 T. Crown Copyright r 2008 Published by Elsevier B.V. All rights reserved. Keywords: Magnetocaloric effect; Magnetic entropy; Phase transition; ac susceptibility; Magnetization
It is well established that the magnetocaloric effect (MCE) accompanying magnetic ordering is related to the nature of the underlying phase transition. Following the discovery of an enhanced MCE near room temperature in Gd [1], the search for other materials displaying a large room temperature MCE progressed rapidly, driven by the large energy saving and reduced environmental impact of magnetic refrigeration compared with traditional gas/ liquid refrigeration; such materials currently include Gd5(SiGe)4 [2], FeMn P1xAsx [3], Ni2MnGa [4] and La(FeSi)13[5]. All of the listed materials have an MCE— resulting from a first-order phase transition—greater than that of metallic Gd, with the accompanying magnetic entropy change being negative. Consequently, they are all promising candidates for room temperature magnetic refrigeration. Materials that exhibit a so-called ‘‘reverse’’ MCE, first observed in PrNi5 [6], have also been the subject of recent study. As their name implies, they display a positive magnetic entropy change (a negative temperature change) in an applied field, and are typified by the MnTSb (T ¼ Cr, V) [7,8] and the NiMnM (M=Sn, In, Sb) [9–11] series, along with NiMnSn [12]. Despite displaying several Corresponding author. Tel.: +1 204 474 9366; fax: +1 204 474 7622.
E-mail address: [email protected] (X. Zhou).
features commensurate with a large MCE—in particular, sequential magnetic transitions, the temperatures of which can be tuned by compositional variations—information on the MCE in CeFe2 and its pseudobinaries is relatively sparse. Here, detailed analysis of data on one such pseudobinary alloy, Ce(Fe0.93Ru0.07)2, is presented. Such data are of considerable interest in this context since they show that near its first-order transition at 110 K, Ce (Fe0.93Ru0.07)2 exhibits not only a large magnetic entropy change of 7.8 J/ kg K in fields of only 2 T ( fields that, incidentally, can be produced by available NdFeB permanent magnets), but this entropy change is also positive, i.e. an enhanced reverse MCE. Second, and equally important in assessing the effectiveness of potential magnetic refrigerants, the width in temperature of the peak in DSm (frequently characterized by the full-width at half-maximum) approaches 40 K in a field of 5 T. This peak structure exhibits an unusual variation with field; its height and width change significantly—indeed anomalously—with increasing field. Specifically, while both the height and width of the DSm peak increase with increasing field (increments) below 2 T, with the width approaching 15 K in that field, the height subsequently saturates while the width increases to some 40 K in 5 T and exceeds 60 K in 8 T. In comparative terms, the latter is much wider than in many other systems
0304-8853/$ - see front matter Crown Copyright r 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.03.038
ARTICLE IN PRESS W. Jiang et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2144–2148
exhibiting a first-order phase transition, far exceeding both the 17 K width at 5 T for Mn1.82Cr0.18Sb [7], and the 3 K width in 2 T (increasing marginally to some 4 K at 5 T) for Ni50Mn37+xSb13x [11]. It is slightly larger than that reported at 5 T for both 8% Ru doping in the same system [13] and Mn3GaC [14], as discussed in more detail below. The sample used in the present study was taken from a section of a specimen used in a previous investigation of the detailed field- and temperature-dependent ac susceptibility and transport behavior of this system [15]. It had been prepared originally by Roy and Coles. Details of the preparation technique and materials used, along with the annealing procedure, have been given previously [16]. The present specimen was in the form of a rectangular bar of approximate dimension 3.6 1.5 1.5 mm3, weighing 0.0703 g. The temperature dependence of ac susceptibility (measured at 2.4 kHz with an ac driving field amplitude of 10 mT) over the temperature range 70–200 K in applied fields between 0 and 0.35 T, and the dependence of the isothermal magnetization on field up to 8 T at a range of temperatures, particularly in the vicinity of both transition temperatures, were measured in a Quantum Design Model 6000 PPMS magnetometer/susceptometer. All fields were applied along the largest sample dimension to minimize demagnetization effects. From the ac susceptibility, w(H, T) versus temperature T curves shown in Fig. 1, the presence of two phase transitions at temperatures near 110 and 165 K is clear, in good agreement with previous estimates [15,17]. The detailed field-dependent magnetic and transport properties of CeFe2 and its pseudobinaries display numerous subtleties, as discussed, for example, by Chattopadhyay et al. [18], and references listed therein. Here the focus is on the MCE accompanying the magnetization process at various temperatures.
0.007
0
Ce(Fe0.93R0.07)2
0.006 Susceptibility (emu/g)
100
0.005 300
0.004 0.003
400
0.002
500
0.001
700
0.000 60
80
100
120
140 T (K)
160
180
200
220
Fig. 1. Temperature dependence of ac susceptibility at various applied fields in Oe as indicated in the figure in the range between 70 and 200 K for the sample of Ce (Fe0.93Ru0.07)2.
2145
The MCE can be measured directly from the adiabatic temperature change resulting from the removal of an applied magnetic field. It can also be estimated indirectly from the change in magnetization or heat capacity with temperature and applied field. In view of our current magnetometer capabilities and to facilitate comparisons with literature data, the indirect approach is adopted here, with magnetic entropy change, DSm, estimated from isothermal magnetization data through use of the wellknown Maxwell relation [19] Z
H
DS M ðT; HÞ ¼ S M ðT; HÞ S M ðT; 0Þ ¼ 0
qM qT
dH H
(1) a relationship used extensively near both ferromagnetic (FM) and antiferromagnetic (AF) transitions [2–7]. Correspondingly, the isothermal magnetization was measured in applied fields up to 8 T at various temperatures from 60 to 190 K. Prior to each measurement, the sample was heated to 250 K, i.e. well above Tc165 K, to ensure a demagnetized state, and then cooled to the selected measuring temperature in zero field. The resulting data are presented in two figures. Fig. 2a displays data acquired in the vicinity of the lower transition temperature TN ¼ 110 K (specifically from 60 to 120 K), in steps of 5 K from 60 to 95 K and in steps of 2 K from 98 to 120 K. Fig. 2b shows magnetization data measured in the vicinity of upper transition Tc ¼ 165 K, actually from 125 to 190 K in steps of 5 K. These latter data in Fig. 2b are typical of a soft ferromagnet; the magnetization increases rapidly towards a high field (saturation) value, which itself decreases with increasing temperature. The behavior of the magnetization at lower temperatures, shown in Fig. 2a, is quite different. Near 60 K, at the lower range of the temperatures shown, the magnetization increases slowly with increasing applied field, reaching a plateau value far below that achieved at significantly higher temperature (Fig. 2b); this plateau extends up to 6 T. Beyond this critical field—the metamagnetic field [17], Hm(T),—the magnetization increases abruptly, achieving values in excess of those shown in Fig. 2b. With increases in temperature above 60 K, this metamagnetic field decreases, approaching zero as the temperature reaches that of the lower transition. As reported previously, the metamagnetic field transforms the low-temperature AF state into its intermediate temperature (110–165 K) FM counterpart. Above 110 K, the magnetization-field behavior becomes similar to that shown in Fig. 2b, that of a conventional ferromagnet. Such behavior is detailed here since it contrasts markedly with the corresponding critical/metamagnetic field in the other giant MCE materials such as Gd5Si1.7Ge2.3 [8], where, in contrast, this critical field induces a paramagnetic (PM) to FM transition, and increases in magnitude as the temperature increases. This distinction underlies both the differing signs of the accompanying entropy changes and its evolution with field in the two systems.
ARTICLE IN PRESS W. Jiang et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2144–2148
2146
2000
50
Ce(Fe0.93Ru0.07)2
Ce (Fe0.93Ru0.07)2
190
1500 180
30
170
20
120
100
110
90
80
70
H/M
Magnetization (emu/g)
40
60K
1000 160 150
500
140
10
130 125
0 0 200
0 0.0
2.0
4.0 Applied field (T)
6.0
400
8.0
600 800 M2 (emu2/g2)
1000
1200
3000 50 Ce (Fe0.93Ru0.07)2
Ce(Fe0.93Ru0.07)2
2500
125
40
190
102
H/M
Magnetization emu/g)
30
100K
2000
160
1500
104 106
1000
20
108 110
500
10
112
0 0
0 0
2
4 Applied Field (T)
6
8
Fig. 2. (a) Isothermal magnetization versus applied field at various temperatures in the lower temperature range between 60 and 120 K in steps of 5 K from 60 to 95 K and in steps of 2 K from 98 to 120 K for the sample of Ce (Fe0.93Ru0.07)2. (b) Isothermal magnetization versus applied field at various temperatures in the higher temperature range from 125 to 190 K in steps of 5 K for the sample of Ce (Fe0.93Ru0.07)2.
Arrott plots confirm the nature of the two transitions, and these are reproduced in Figs. 3a and 4b, respectively. Those displayed near 160 K ( Fig. 3a), in the vicinity of the upper transition, all exhibit a positive slope, confirming by alternate means that the transition at 165 K is second order, as reported previously [15,17,20]. In contrast, the situation near the lower transition at 110 K is quite different; the Arrott plot data in Fig. 3b exhibit clearly a negative slope in the temperature range from 100 to 110 K. The transition at lower temperature, designated TN, is thus unequivocally discontinuous/first order. The applicability of the Arrott plot criterion to this lower transition—despite the magnetization M not being the order parameter for
100
200
300
400
M2 (emu2/g2) Fig. 3. (a) Arrott plot, i.e. H/M versus M2 of sample Ce (Fe0.93Ru0.07)2 in the vicinity of higher transition temperature of 165 K. (b) Arrott plot, i.e. H/M versus M2 of sample Ce (Fe0.93Ru0.07)2 in the vicinity of lower transition temperature of 110 K.
the AF state—have been demonstrated by previous studies at such transitions [21], and likely reflects in part the low value of the magnetization /order parameter in its vicinity [22]. Figs. 4a and 4b reproduces the magnetic entropy changes, DSm(H,T), estimated using Eq. (1), as a function of temperature in various fields in the vicinity of the lower and upper transition temperature, respectively. Fig. 4b demonstrates that the peaks in DSm in the vicinity of 160 K are both negative and small (1.2 J/kg K in 5 T), and very broad (the peak width at half maximum is about 45 K at 2 T, increasing to around 60 K at 5 T). This is typical of the behavior near a continuous/second-order transition. By contrast, the entropy change estimates presented in Fig. 4a are far more interesting for a number of reasons. First, DSm is positive here, thus confirming [13] that doped
ARTICLE IN PRESS W. Jiang et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2144–2148
12 Ce(Fe0.93Ru0.07)2
10
ΔSm (J/kg K)
8 6 4T
5T
6T
3T
2T
4
1T
2 0 -2 50
60
70
80
90 T (K)
100
110
120
130
190
200
0.0 1T
-0.2
ΔSm (J/kg K)
-0.4
2T
-0.6 3T
-0.8 4T
-1.0 5T
-1.2
Ce(Fe0.93Ru0.07)2
-1.4 120
130
140
150
160 T (K)
170
180
Fig. 4. (a) Magnetic entropy change, DSm, as a function of temperature in various applied fields for the sample of Ce (Fe0.93Ru0.07)2 in the vicinity of lower transition temperature of 110 K. (b) Magnetic entropy change, DSm, as a function of temperature in various applied fields for the sample of Ce (Fe0.93Ru0.07)2 in the vicinity of higher transition temperature of 165 K.
CeFe2 exhibits a reverse magnetocaloric effect, a result that has been reported previously in a limited number of cases that include the MnTSb (T ¼ Cr, V) [7,8] and NiMnM (M=Sn, In, Sb) [9–11] series, amongst others [14]. Second, the principal result of the present study, the peak value for DSm increases rapidly with increasing applied field, reaching 7.8 J/kg K in 2 T. Beyond 2 T, however, the peak value increases marginally to 8.8 J/kg K at 5 T, which is nevertheless some 19% larger than the 7.4 J/kg K reported for Ce(Fe0.96Ru0.04)2, the highest value found previously in the Ru-doped CeFe2 alloys series [13]. Third, an important result when assessing the effectiveness of potential magnetic refrigerants, the width in temperature of the peak in DSm (measured by the full-width at half-maximum) increases significantly with increasing field, approaching
2147
15 K in a field of 2 T, increasing to about 40 K in 5 T and exceeding 60 K in 8 T. These values are far larger than those for both Mn1.82Cr0.18Sb [7] and Ni50Mn37+xSb13x [11] mentioned earlier. Fourth, in the present system the peak width increases as a result of a field-induced enhancement of the entropy change on the low-temperature side of the initial peak. In contrast, in Gd5Si1.7Ge 2.3 and DyMn2Ge2, where DSm is negative, the width increases due to a corresponding enhancement at temperatures above the original peak [8,22]. Percharsky et al. [23] have analyzed in detail the characteristic features of the MCE in terms of a general thermodynamic approach, including the sign of DSm and the variation of its magnitude and width with field As is evident from Eq. (1), the sign of DSm reflects that for (qM/ qT)H. Briefly, in the present system DSm is negative near the continuous FM–PM transition at Tc since (qM/qT)H is negative there, which is a result of the thermal randomization of moments with increasing temperature. The variation in magnitude and width evident in Fig. 4b is typical of the behavior of the MCE near such a transition, as has been modeled in DyAl2, likely reflecting the field dependence of the heat capacity. In contrast, (qM/qT)H is positive through the first-order/discontinuous AFM–FM transition at TN, as it is in Mn3GaC [14] and RhFe [24], leading to a positive DSm. In terms of the model approach of Perchasky et al., at such transitions the MCE is controlled principally by the accompanying enthalpy change, leading to an entropy change of essentially constant magnitude but of increasing width as the field increases. Near first-order PM–FM transitions, where the influence of the applied field is to elevate the transition temperature, the entropy change is field enhanced on the high-temperature side, whereas near AFM–FM transitions, the uniform applied field being the conjugate field for ferromagnetism, the transition temperature and the accompanying entropy change are modified on the lowtemperature side of the initial peak. Such predictions are consistent with the behavior observed in a variety of systems including Mn3GaC, Gd5(Si1xGex)4 and RhFe, mentioned above. In the present system, the behavior is different—indeed anomalous— as Fig. 4a demonstrates. While the entropy change is essentially constant in magnitude but increases in width with increasing field beyond 2 T, the magnitude of this change is strongly field dependent in lower applied fields. As such, it appears to represent a combination of the entropy changes observed at both continuous and firstorder/discontinuous transitions. This occurs despite the fact that the temperature of the metamagnetic boundary between the AFM and FM phases decreases monotonically with increasing field over the regime of interest, viz. [15], H m ðTÞ ¼ aðT N TÞ;
TpT N
(2)
with a ¼ 0.13–0.17 T/K and no anomaly evident near 2 T. Whether this results from a heat capacity initially displaying a strong field dependence or more complicated
ARTICLE IN PRESS 2148
W. Jiang et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2144–2148
enthalpy changes than those envisaged by Percharsky et al. remains to be resolved (heat capacity measurements cannot be carried out currently in our laboratory). In summary then, detailed measurements on a novel inverse MCE material, Ce(Fe0.93Ru0.07)2, are presented. Near its first-order transition, Ce(Fe0.93Ru0.07)2 displays an enhanced positive magnetic entropy change, which initially increases rapidly with field, reaching a value of DSm ¼ 7.8 J/kg K in a field of only 2 T (comparable to that of Gd), climbing subsequently by only some 13% to 8.8 J/kg K as the field is increased to 5 T. The width of this entropy change DSm is broad, 15 K in 2 T, 40 K in 5 T and exceeding 60 K at 8 T, values slightly larger than those reported at lower Ru doping in the same system and in Ni3GaC but well in excess of those observed in many other materials displaying first-order transitions, the recently reported NiMnM (M ¼ Sn, In, Sb) [9–11] series, for example. Thus, from an applied perspective, Ce(Fe0.93Ru0.07)2 not only displays several generally soughtafter features of a magnetic refrigerant, but it has also emerged as a potential magnetic refrigerant specifically for the liquefaction of gases such as H2, He2 and possibly natural gas. This work was supported by Grants from the Natural Science and Engineering Research Council (NSERC) of Canada. References [1] G.V. Brown, J. Appl. Phys. 47 (1976) 3673. [2] V.K. Pecharsky, K.A. Gschneidner Jr., Phys. Rev. Lett. 78 (1997) 4494. [3] O. Tegus, E. Bruck, K.H.J. Buschow, F.R. de Boer, Nature 415 (2002) 150.
[4] Xuezhi Zhou, Wei Li, H.P. Kunkel, Gwyn Williams, J. Phys. Condens. Matter 16 (2004) L39. [5] A. Fujita, S. Fujieda, Y. Hasegawa, K. Fukamichi, Phys. Rev. B 67 (2003) 104416. [6] P.J. von Ranke, V.K. Pecharsky, K.A. Gschneider Jr., B.J. Korte, Phys. Rev. B 58 (1998) 14437. [7] Y.Q. Zhang, Z.D. Zhang, J. Alloys Compd. 365 (2004) 35. [8] O. Tegus, E. Bruck, L. Zhang, Dagula, K.H.J. Buschow, F.R. de Boer, Physica B 319 (2002) 174. [9] A.K. Pathak, M. Khan, I. Dubenko, S. Stadler, N. Ali, Appl. Phys. Lett. 90 (2007) 262504. [10] Z.D. Han, D.H. Wang, C.L. Zhang, H.C. Xuan, B.X. Gu, Y.W. Du, Appl. Phys. Lett. 90 (2007) 042507. [11] M. Khan, N. Ali, S. Stadler, J. Appl. Phys. 101 (2007) 053919. [12] A. Krenke, E. Duman, M. Acet, E.F. Wassermann, X. Moya, L. Manosa, A. Planes, Nat. Mater. 4 (2005) 450. [13] M.K. Chattopadhyay, M.A. Manekar, S.B. Roy, J. Phys.D: Appl. Phys. 39 (2006) 1006. [14] T. Tohel, H. Wada, T. Kanomata, J. Appl. Phys. 94 (2003) 1800. [15] H.P. Kunkel, X.Z. Zhou, P.A. Stampe, J.A. Cowen, Gwyn Williams, Phys. Rev. B 54 (1996) 16039. [16] S.B. Roy, B.R. Coles, Phys. Rev. B 39 (1989) 9360. [17] D. Wang, H.P. Kunkel, Gwyn Williams, Phys. Rev. B 51 (1995) 2872. [18] M.K. Chattopadhyay, S.B. Roy, J. Phys.: Condens. Matter 20 (2008) 025209; M.K. Chattopadhyay et al., Phys. Rev. B 68 (2003), 174404 and references listed therein, including [13,15–17,19] of the present paper. [19] A.H. Morrish, The Physical Principles of Magnetism, IEEE Press, New York, 2001, p. 83. [20] H.P. Kunkel, X.Z. Zhou, P.A. Stampe, J.A. Cowen, Gwyn Williams, Phys. Rev. B 53 (1996) 15099. [21] P. Chen, Y.W. Du, Chin. J. Phys.(Taipei) 39 (2001) 357; J. Phys. Soc. Jnp. 70 1080 (2001). [22] Xuezhi Zhou, Wei Li, H.P. Kunkel, Gwyn Williams, Phys. Rev. B 73 (2006) 012412. [23] V.K. Pecharsky, K.A. Gschneidner Jr., A.O. Pecharsky, A.M. Tishin, Phys. Rev. B 64 (2001) 144406. [24] M.P. Annaorazov, S.A. Nikitin, A.L. Tyurin, K.A. Asatryan, A.Kh. Dovletov, J. Appl. Phys. 79 (1996) 1689.
Journal of Magnetism and Magnetic Materials 320 (2008) 2144–2148 www.elsevier.com/locate/jmmm
Anomalous field dependence of the inverse magnetocaloric effect in Ce(Fe0.93Ru0.07)2 Wanjun Jiang, Xuezhi Zhou, Henry Kunkel, Gwyn Williams Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2 Received 23 December 2007; received in revised form 19 February 2008 Available online 1 April 2008
Abstract A summary of detailed isothermal magnetization along with the ac susceptibility measurements on Ce(Fe0.93Ru0.07)2 is presented. Near the first-order transition, i.e. near 110 K, Ce(Fe0.93Ru0.07)2 displays a large positive magnetic entropy change, DSm, of 7.8 J/kg K in fields of only 2 T, i.e. it displays a strong inverse magnetocaloric (MCE) effect, as expected, on entering an antiferromagnetic (AF) state. However, the variation of the magnitude and width of this entropy change with field are anomalous when compared with model predictions, the former increasing with applied field below 2 T, while the latter exceeds 60 K in a field of 8 T. Crown Copyright r 2008 Published by Elsevier B.V. All rights reserved. Keywords: Magnetocaloric effect; Magnetic entropy; Phase transition; ac susceptibility; Magnetization
It is well established that the magnetocaloric effect (MCE) accompanying magnetic ordering is related to the nature of the underlying phase transition. Following the discovery of an enhanced MCE near room temperature in Gd [1], the search for other materials displaying a large room temperature MCE progressed rapidly, driven by the large energy saving and reduced environmental impact of magnetic refrigeration compared with traditional gas/ liquid refrigeration; such materials currently include Gd5(SiGe)4 [2], FeMn P1xAsx [3], Ni2MnGa [4] and La(FeSi)13[5]. All of the listed materials have an MCE— resulting from a first-order phase transition—greater than that of metallic Gd, with the accompanying magnetic entropy change being negative. Consequently, they are all promising candidates for room temperature magnetic refrigeration. Materials that exhibit a so-called ‘‘reverse’’ MCE, first observed in PrNi5 [6], have also been the subject of recent study. As their name implies, they display a positive magnetic entropy change (a negative temperature change) in an applied field, and are typified by the MnTSb (T ¼ Cr, V) [7,8] and the NiMnM (M=Sn, In, Sb) [9–11] series, along with NiMnSn [12]. Despite displaying several Corresponding author. Tel.: +1 204 474 9366; fax: +1 204 474 7622.
E-mail address: [email protected] (X. Zhou).
features commensurate with a large MCE—in particular, sequential magnetic transitions, the temperatures of which can be tuned by compositional variations—information on the MCE in CeFe2 and its pseudobinaries is relatively sparse. Here, detailed analysis of data on one such pseudobinary alloy, Ce(Fe0.93Ru0.07)2, is presented. Such data are of considerable interest in this context since they show that near its first-order transition at 110 K, Ce (Fe0.93Ru0.07)2 exhibits not only a large magnetic entropy change of 7.8 J/ kg K in fields of only 2 T ( fields that, incidentally, can be produced by available NdFeB permanent magnets), but this entropy change is also positive, i.e. an enhanced reverse MCE. Second, and equally important in assessing the effectiveness of potential magnetic refrigerants, the width in temperature of the peak in DSm (frequently characterized by the full-width at half-maximum) approaches 40 K in a field of 5 T. This peak structure exhibits an unusual variation with field; its height and width change significantly—indeed anomalously—with increasing field. Specifically, while both the height and width of the DSm peak increase with increasing field (increments) below 2 T, with the width approaching 15 K in that field, the height subsequently saturates while the width increases to some 40 K in 5 T and exceeds 60 K in 8 T. In comparative terms, the latter is much wider than in many other systems
0304-8853/$ - see front matter Crown Copyright r 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.03.038
ARTICLE IN PRESS W. Jiang et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2144–2148
exhibiting a first-order phase transition, far exceeding both the 17 K width at 5 T for Mn1.82Cr0.18Sb [7], and the 3 K width in 2 T (increasing marginally to some 4 K at 5 T) for Ni50Mn37+xSb13x [11]. It is slightly larger than that reported at 5 T for both 8% Ru doping in the same system [13] and Mn3GaC [14], as discussed in more detail below. The sample used in the present study was taken from a section of a specimen used in a previous investigation of the detailed field- and temperature-dependent ac susceptibility and transport behavior of this system [15]. It had been prepared originally by Roy and Coles. Details of the preparation technique and materials used, along with the annealing procedure, have been given previously [16]. The present specimen was in the form of a rectangular bar of approximate dimension 3.6 1.5 1.5 mm3, weighing 0.0703 g. The temperature dependence of ac susceptibility (measured at 2.4 kHz with an ac driving field amplitude of 10 mT) over the temperature range 70–200 K in applied fields between 0 and 0.35 T, and the dependence of the isothermal magnetization on field up to 8 T at a range of temperatures, particularly in the vicinity of both transition temperatures, were measured in a Quantum Design Model 6000 PPMS magnetometer/susceptometer. All fields were applied along the largest sample dimension to minimize demagnetization effects. From the ac susceptibility, w(H, T) versus temperature T curves shown in Fig. 1, the presence of two phase transitions at temperatures near 110 and 165 K is clear, in good agreement with previous estimates [15,17]. The detailed field-dependent magnetic and transport properties of CeFe2 and its pseudobinaries display numerous subtleties, as discussed, for example, by Chattopadhyay et al. [18], and references listed therein. Here the focus is on the MCE accompanying the magnetization process at various temperatures.
0.007
0
Ce(Fe0.93R0.07)2
0.006 Susceptibility (emu/g)
100
0.005 300
0.004 0.003
400
0.002
500
0.001
700
0.000 60
80
100
120
140 T (K)
160
180
200
220
Fig. 1. Temperature dependence of ac susceptibility at various applied fields in Oe as indicated in the figure in the range between 70 and 200 K for the sample of Ce (Fe0.93Ru0.07)2.
2145
The MCE can be measured directly from the adiabatic temperature change resulting from the removal of an applied magnetic field. It can also be estimated indirectly from the change in magnetization or heat capacity with temperature and applied field. In view of our current magnetometer capabilities and to facilitate comparisons with literature data, the indirect approach is adopted here, with magnetic entropy change, DSm, estimated from isothermal magnetization data through use of the wellknown Maxwell relation [19] Z
H
DS M ðT; HÞ ¼ S M ðT; HÞ S M ðT; 0Þ ¼ 0
qM qT
dH H
(1) a relationship used extensively near both ferromagnetic (FM) and antiferromagnetic (AF) transitions [2–7]. Correspondingly, the isothermal magnetization was measured in applied fields up to 8 T at various temperatures from 60 to 190 K. Prior to each measurement, the sample was heated to 250 K, i.e. well above Tc165 K, to ensure a demagnetized state, and then cooled to the selected measuring temperature in zero field. The resulting data are presented in two figures. Fig. 2a displays data acquired in the vicinity of the lower transition temperature TN ¼ 110 K (specifically from 60 to 120 K), in steps of 5 K from 60 to 95 K and in steps of 2 K from 98 to 120 K. Fig. 2b shows magnetization data measured in the vicinity of upper transition Tc ¼ 165 K, actually from 125 to 190 K in steps of 5 K. These latter data in Fig. 2b are typical of a soft ferromagnet; the magnetization increases rapidly towards a high field (saturation) value, which itself decreases with increasing temperature. The behavior of the magnetization at lower temperatures, shown in Fig. 2a, is quite different. Near 60 K, at the lower range of the temperatures shown, the magnetization increases slowly with increasing applied field, reaching a plateau value far below that achieved at significantly higher temperature (Fig. 2b); this plateau extends up to 6 T. Beyond this critical field—the metamagnetic field [17], Hm(T),—the magnetization increases abruptly, achieving values in excess of those shown in Fig. 2b. With increases in temperature above 60 K, this metamagnetic field decreases, approaching zero as the temperature reaches that of the lower transition. As reported previously, the metamagnetic field transforms the low-temperature AF state into its intermediate temperature (110–165 K) FM counterpart. Above 110 K, the magnetization-field behavior becomes similar to that shown in Fig. 2b, that of a conventional ferromagnet. Such behavior is detailed here since it contrasts markedly with the corresponding critical/metamagnetic field in the other giant MCE materials such as Gd5Si1.7Ge2.3 [8], where, in contrast, this critical field induces a paramagnetic (PM) to FM transition, and increases in magnitude as the temperature increases. This distinction underlies both the differing signs of the accompanying entropy changes and its evolution with field in the two systems.
ARTICLE IN PRESS W. Jiang et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2144–2148
2146
2000
50
Ce(Fe0.93Ru0.07)2
Ce (Fe0.93Ru0.07)2
190
1500 180
30
170
20
120
100
110
90
80
70
H/M
Magnetization (emu/g)
40
60K
1000 160 150
500
140
10
130 125
0 0 200
0 0.0
2.0
4.0 Applied field (T)
6.0
400
8.0
600 800 M2 (emu2/g2)
1000
1200
3000 50 Ce (Fe0.93Ru0.07)2
Ce(Fe0.93Ru0.07)2
2500
125
40
190
102
H/M
Magnetization emu/g)
30
100K
2000
160
1500
104 106
1000
20
108 110
500
10
112
0 0
0 0
2
4 Applied Field (T)
6
8
Fig. 2. (a) Isothermal magnetization versus applied field at various temperatures in the lower temperature range between 60 and 120 K in steps of 5 K from 60 to 95 K and in steps of 2 K from 98 to 120 K for the sample of Ce (Fe0.93Ru0.07)2. (b) Isothermal magnetization versus applied field at various temperatures in the higher temperature range from 125 to 190 K in steps of 5 K for the sample of Ce (Fe0.93Ru0.07)2.
Arrott plots confirm the nature of the two transitions, and these are reproduced in Figs. 3a and 4b, respectively. Those displayed near 160 K ( Fig. 3a), in the vicinity of the upper transition, all exhibit a positive slope, confirming by alternate means that the transition at 165 K is second order, as reported previously [15,17,20]. In contrast, the situation near the lower transition at 110 K is quite different; the Arrott plot data in Fig. 3b exhibit clearly a negative slope in the temperature range from 100 to 110 K. The transition at lower temperature, designated TN, is thus unequivocally discontinuous/first order. The applicability of the Arrott plot criterion to this lower transition—despite the magnetization M not being the order parameter for
100
200
300
400
M2 (emu2/g2) Fig. 3. (a) Arrott plot, i.e. H/M versus M2 of sample Ce (Fe0.93Ru0.07)2 in the vicinity of higher transition temperature of 165 K. (b) Arrott plot, i.e. H/M versus M2 of sample Ce (Fe0.93Ru0.07)2 in the vicinity of lower transition temperature of 110 K.
the AF state—have been demonstrated by previous studies at such transitions [21], and likely reflects in part the low value of the magnetization /order parameter in its vicinity [22]. Figs. 4a and 4b reproduces the magnetic entropy changes, DSm(H,T), estimated using Eq. (1), as a function of temperature in various fields in the vicinity of the lower and upper transition temperature, respectively. Fig. 4b demonstrates that the peaks in DSm in the vicinity of 160 K are both negative and small (1.2 J/kg K in 5 T), and very broad (the peak width at half maximum is about 45 K at 2 T, increasing to around 60 K at 5 T). This is typical of the behavior near a continuous/second-order transition. By contrast, the entropy change estimates presented in Fig. 4a are far more interesting for a number of reasons. First, DSm is positive here, thus confirming [13] that doped
ARTICLE IN PRESS W. Jiang et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2144–2148
12 Ce(Fe0.93Ru0.07)2
10
ΔSm (J/kg K)
8 6 4T
5T
6T
3T
2T
4
1T
2 0 -2 50
60
70
80
90 T (K)
100
110
120
130
190
200
0.0 1T
-0.2
ΔSm (J/kg K)
-0.4
2T
-0.6 3T
-0.8 4T
-1.0 5T
-1.2
Ce(Fe0.93Ru0.07)2
-1.4 120
130
140
150
160 T (K)
170
180
Fig. 4. (a) Magnetic entropy change, DSm, as a function of temperature in various applied fields for the sample of Ce (Fe0.93Ru0.07)2 in the vicinity of lower transition temperature of 110 K. (b) Magnetic entropy change, DSm, as a function of temperature in various applied fields for the sample of Ce (Fe0.93Ru0.07)2 in the vicinity of higher transition temperature of 165 K.
CeFe2 exhibits a reverse magnetocaloric effect, a result that has been reported previously in a limited number of cases that include the MnTSb (T ¼ Cr, V) [7,8] and NiMnM (M=Sn, In, Sb) [9–11] series, amongst others [14]. Second, the principal result of the present study, the peak value for DSm increases rapidly with increasing applied field, reaching 7.8 J/kg K in 2 T. Beyond 2 T, however, the peak value increases marginally to 8.8 J/kg K at 5 T, which is nevertheless some 19% larger than the 7.4 J/kg K reported for Ce(Fe0.96Ru0.04)2, the highest value found previously in the Ru-doped CeFe2 alloys series [13]. Third, an important result when assessing the effectiveness of potential magnetic refrigerants, the width in temperature of the peak in DSm (measured by the full-width at half-maximum) increases significantly with increasing field, approaching
2147
15 K in a field of 2 T, increasing to about 40 K in 5 T and exceeding 60 K in 8 T. These values are far larger than those for both Mn1.82Cr0.18Sb [7] and Ni50Mn37+xSb13x [11] mentioned earlier. Fourth, in the present system the peak width increases as a result of a field-induced enhancement of the entropy change on the low-temperature side of the initial peak. In contrast, in Gd5Si1.7Ge 2.3 and DyMn2Ge2, where DSm is negative, the width increases due to a corresponding enhancement at temperatures above the original peak [8,22]. Percharsky et al. [23] have analyzed in detail the characteristic features of the MCE in terms of a general thermodynamic approach, including the sign of DSm and the variation of its magnitude and width with field As is evident from Eq. (1), the sign of DSm reflects that for (qM/ qT)H. Briefly, in the present system DSm is negative near the continuous FM–PM transition at Tc since (qM/qT)H is negative there, which is a result of the thermal randomization of moments with increasing temperature. The variation in magnitude and width evident in Fig. 4b is typical of the behavior of the MCE near such a transition, as has been modeled in DyAl2, likely reflecting the field dependence of the heat capacity. In contrast, (qM/qT)H is positive through the first-order/discontinuous AFM–FM transition at TN, as it is in Mn3GaC [14] and RhFe [24], leading to a positive DSm. In terms of the model approach of Perchasky et al., at such transitions the MCE is controlled principally by the accompanying enthalpy change, leading to an entropy change of essentially constant magnitude but of increasing width as the field increases. Near first-order PM–FM transitions, where the influence of the applied field is to elevate the transition temperature, the entropy change is field enhanced on the high-temperature side, whereas near AFM–FM transitions, the uniform applied field being the conjugate field for ferromagnetism, the transition temperature and the accompanying entropy change are modified on the lowtemperature side of the initial peak. Such predictions are consistent with the behavior observed in a variety of systems including Mn3GaC, Gd5(Si1xGex)4 and RhFe, mentioned above. In the present system, the behavior is different—indeed anomalous— as Fig. 4a demonstrates. While the entropy change is essentially constant in magnitude but increases in width with increasing field beyond 2 T, the magnitude of this change is strongly field dependent in lower applied fields. As such, it appears to represent a combination of the entropy changes observed at both continuous and firstorder/discontinuous transitions. This occurs despite the fact that the temperature of the metamagnetic boundary between the AFM and FM phases decreases monotonically with increasing field over the regime of interest, viz. [15], H m ðTÞ ¼ aðT N TÞ;
TpT N
(2)
with a ¼ 0.13–0.17 T/K and no anomaly evident near 2 T. Whether this results from a heat capacity initially displaying a strong field dependence or more complicated
ARTICLE IN PRESS 2148
W. Jiang et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2144–2148
enthalpy changes than those envisaged by Percharsky et al. remains to be resolved (heat capacity measurements cannot be carried out currently in our laboratory). In summary then, detailed measurements on a novel inverse MCE material, Ce(Fe0.93Ru0.07)2, are presented. Near its first-order transition, Ce(Fe0.93Ru0.07)2 displays an enhanced positive magnetic entropy change, which initially increases rapidly with field, reaching a value of DSm ¼ 7.8 J/kg K in a field of only 2 T (comparable to that of Gd), climbing subsequently by only some 13% to 8.8 J/kg K as the field is increased to 5 T. The width of this entropy change DSm is broad, 15 K in 2 T, 40 K in 5 T and exceeding 60 K at 8 T, values slightly larger than those reported at lower Ru doping in the same system and in Ni3GaC but well in excess of those observed in many other materials displaying first-order transitions, the recently reported NiMnM (M ¼ Sn, In, Sb) [9–11] series, for example. Thus, from an applied perspective, Ce(Fe0.93Ru0.07)2 not only displays several generally soughtafter features of a magnetic refrigerant, but it has also emerged as a potential magnetic refrigerant specifically for the liquefaction of gases such as H2, He2 and possibly natural gas. This work was supported by Grants from the Natural Science and Engineering Research Council (NSERC) of Canada. References [1] G.V. Brown, J. Appl. Phys. 47 (1976) 3673. [2] V.K. Pecharsky, K.A. Gschneidner Jr., Phys. Rev. Lett. 78 (1997) 4494. [3] O. Tegus, E. Bruck, K.H.J. Buschow, F.R. de Boer, Nature 415 (2002) 150.
[4] Xuezhi Zhou, Wei Li, H.P. Kunkel, Gwyn Williams, J. Phys. Condens. Matter 16 (2004) L39. [5] A. Fujita, S. Fujieda, Y. Hasegawa, K. Fukamichi, Phys. Rev. B 67 (2003) 104416. [6] P.J. von Ranke, V.K. Pecharsky, K.A. Gschneider Jr., B.J. Korte, Phys. Rev. B 58 (1998) 14437. [7] Y.Q. Zhang, Z.D. Zhang, J. Alloys Compd. 365 (2004) 35. [8] O. Tegus, E. Bruck, L. Zhang, Dagula, K.H.J. Buschow, F.R. de Boer, Physica B 319 (2002) 174. [9] A.K. Pathak, M. Khan, I. Dubenko, S. Stadler, N. Ali, Appl. Phys. Lett. 90 (2007) 262504. [10] Z.D. Han, D.H. Wang, C.L. Zhang, H.C. Xuan, B.X. Gu, Y.W. Du, Appl. Phys. Lett. 90 (2007) 042507. [11] M. Khan, N. Ali, S. Stadler, J. Appl. Phys. 101 (2007) 053919. [12] A. Krenke, E. Duman, M. Acet, E.F. Wassermann, X. Moya, L. Manosa, A. Planes, Nat. Mater. 4 (2005) 450. [13] M.K. Chattopadhyay, M.A. Manekar, S.B. Roy, J. Phys.D: Appl. Phys. 39 (2006) 1006. [14] T. Tohel, H. Wada, T. Kanomata, J. Appl. Phys. 94 (2003) 1800. [15] H.P. Kunkel, X.Z. Zhou, P.A. Stampe, J.A. Cowen, Gwyn Williams, Phys. Rev. B 54 (1996) 16039. [16] S.B. Roy, B.R. Coles, Phys. Rev. B 39 (1989) 9360. [17] D. Wang, H.P. Kunkel, Gwyn Williams, Phys. Rev. B 51 (1995) 2872. [18] M.K. Chattopadhyay, S.B. Roy, J. Phys.: Condens. Matter 20 (2008) 025209; M.K. Chattopadhyay et al., Phys. Rev. B 68 (2003), 174404 and references listed therein, including [13,15–17,19] of the present paper. [19] A.H. Morrish, The Physical Principles of Magnetism, IEEE Press, New York, 2001, p. 83. [20] H.P. Kunkel, X.Z. Zhou, P.A. Stampe, J.A. Cowen, Gwyn Williams, Phys. Rev. B 53 (1996) 15099. [21] P. Chen, Y.W. Du, Chin. J. Phys.(Taipei) 39 (2001) 357; J. Phys. Soc. Jnp. 70 1080 (2001). [22] Xuezhi Zhou, Wei Li, H.P. Kunkel, Gwyn Williams, Phys. Rev. B 73 (2006) 012412. [23] V.K. Pecharsky, K.A. Gschneidner Jr., A.O. Pecharsky, A.M. Tishin, Phys. Rev. B 64 (2001) 144406. [24] M.P. Annaorazov, S.A. Nikitin, A.L. Tyurin, K.A. Asatryan, A.Kh. Dovletov, J. Appl. Phys. 79 (1996) 1689.