Making the most of the magnetic and lattice entropy changes

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Journal of Magnetism and Magnetic Materials 321 (2009) 3541–3547 www.elsevier.com/locate/jmmm

Current perspectives

Making the most of the magnetic and lattice entropy changes V.K. Pecharskya,b,, K.A. Gschneidner Jr.a,b, Ya. Mudryka, Durga Paudyala a

b

Ames Laboratory, Iowa State University, Ames, IA 50011-3020, USA Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011-2300, USA Available online 7 March 2008

Abstract Recent discoveries of novel materials exhibiting a magnetocaloric effect that is strongly enhanced by the magnetoelastic coupling—the so-called giant magnetocaloric effect materials—stimulated an unprecedented expansion of research related both to the fundamentals of the phenomenon and potential future applications of these materials in continuous magnetic cooling near room temperature. The subject of this work is twofold. On one hand, systems exhibiting the giant magnetocaloric effect may be prone to hysteresis, and may exist in nonequilibrium, phase-separated states, thus requiring a special care when their intrinsic physical properties are of interest. On the other hand, in order to harvest most of the magnetocaloric potential of a specific compound, both the magnetic and lattice degrees of freedom of the material must be precisely controlled. r 2008 Elsevier B.V. All rights reserved. PACS: 73.50.Sg; 77.80.Bh; 65.40.Gr Keywords: Magnetocaloric effect; Giant magnetocaloric effect; Magnetic cooling; Isothermal magnetic entropy change; Adiabatic temperature change; Magnetostructural transformation; Phase-separated state; Magnetic hysteresis

1. Introduction The magnetocaloric effect (MCE) is among the most fundamental physical properties of magnetic solids. The MCE describes thermal behavior of a material when the latter is exposed to a varying magnetic field: its temperature may be appreciably increased or decreased, with both the sign and the extent of the temperature difference between the final and the initial states of the material dependent on numerous intrinsic and extrinsic factors. The chemical composition, the crystal structure and the magnetic state of a compound are among the most important intrinsic material parameters that determine its MCE. The extrinsic factors include the temperature, the surrounding pressure, and the sign of the magnetic field change, i.e. whether the magnitude of the magnetic field has been raised or lowered. Any of these variables may and will affect the magnetic field-induced temperature and/or Corresponding author at: Ames Laboratory, Iowa State University, Ames, IA 50011-3020, USA. Tel.: +1 515 294 8220; fax: +1 515 294 9579. E-mail address: [email protected] (V.K. Pecharsky).

0304-8853/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.03.013

entropy changes of a material, and therefore, play a role in defining the MCE. The MCE is inherent to every magnetic solid, and the phenomenon has extraordinary fundamental importance because it spans many orders of magnitude over length, energy, and time scales: from quantum mechanics to micromagnetics, from statistical to macroscopic thermodynamics, and from spin dynamics to bulk heat flow and thermal conductivity. Understanding and, ultimately, controlling this many-body, many-parameter landscape is a challenging task, yet even partial successes along the way facilitate greater precision and better control over the design of novel MCE solids. In other words, knowing how changes in the chemical composition, the crystal structure and the microstructure affect the physical behavior of solids helps to create an environment in which a material may be tailored to exhibit a specific combination of magnetic and thermal properties. In addition to its basic scientific significance, the MCE is the cornerstone of near-room temperature magnetic cooling (and also for cooling anywhere between a few mK and 300 K, and heating above 300 K), which is poised for

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commercialization in the foreseeable future and may soon become an energy-efficient and environmentally friendly alternative to vapor-compression refrigeration technology [1–7]. Practical applications of the MCE, therefore, have the potential to reduce the global energy consumption, and eliminate or minimize the use of ozone-depleting compounds, greenhouse gases, and hazardous chemicals. Among the many components that need to come together in order to make a successful operating magnetic refrigerator, the magnetocaloric compound (the magnetic refrigerant material) is of utmost importance. First, its MCE must be large for a given, usually relatively small (1–2 T) magnetic field change, and it should occur in the temperature range between that of the hot and cold heat exchangers of a device. Second, the magnetocaloric material must be chemically stable, noncorrosive, nonflammable, and nontoxic. Third, the compound or alloy must be composed from readily available, inexpensive components. Fourth, the manufacturing of the material should be economical without adding too much to the cost of the final product, which is a regenerator bed. Finally, in addition to chemical stability, the magnetocaloric material should exhibit sufficient mechanical stability to ensure that the life span of a magnetic refrigerator is comparable to the life span of a modern conventional refrigeration device. Over the past decade, basic research on the magnetocaloric materials enjoyed a nearly explosive growth [5,7]. As a result, a variety of advanced magnetocaloric materials have been discovered, and without a doubt, more exciting breakthroughs lie ahead. After the discovery of the giant magnetocaloric effect (GMCE) in Gd5Si2Ge2 [8] and related Gd5SixGe4x compounds [9], the list of systems exhibiting strong magnetocaloric responses near room temperature has been extended far beyond the prototypical elemental Gd to include binary and ternary rare earthbased alloys, oxide perovskite materials, complex intermetallics, chalcogenides, and pnictides. In addition to Gd5SixGe4x and other R5T4 systems (R ¼ rare-earth metal and T ¼ Si, Ge, Sn, and Ga), the most promising materials for near-ambient magnetic cooling include MnAs [10] and closely related MnAs1xSbx [11] and Mn1xFexAs [12] systems; MnFeP0.45As0.55 [13] and closely related MnFe(P, Si, Ge) compounds [14,15], in which arsenic has been replaced by Si and Ge; LaFe13xSix and their hydrides LaFe13xSixHy [16]; and some of the ferromagnetic shape memory alloys such as Ni–Mn–Ga [17,18] and Ni–Mn–Sn [19]. Besides the fact that all of these materials are intermetallic compounds, which means that they are all dense spin systems and are reasonable conductors of heat, the real unifying theme is that all of them undergo coupled magnetostructural transformations, which thermodynamically are first-order phase transitions. 2. Hysteresis: a scarecrow or a problem It is commonly assumed that hysteresis (measurable thermal and/or magnetic irreversibility) is a signature of a

true first-order phase transition. Yet, hysteresis is not mandated by thermodynamics since the fundamental (and only) requirement for a first-order phase transformation to be such is discontinuous behavior of first-order derivatives of the Gibbs free energy with respect to temperature, pressure, magnetic field, or any other free thermodynamic variable [20]. As a result, a system that undergoes a firstorder phase transition will exhibit discontinuities of easily measured physical properties, such as entropy, phase volume, or magnetization. Thermal or magnetic irreversibilities may and do occur because at equilibrium (i.e. when the Gibbs free energies of the two coexisting phases are equal), the driving force is 0, while in a solid the driving force may need to be substantial when phase transformation involves overcoming a considerable strain. In reality, however, thermal fluctuations, which are always present at any finite temperature and are quite strong near ambient conditions, may be sufficient to render a first-order phase transition fast, practically reversible and nonhysteretic. In fact, real microstructural features rather than idealized periodic lattice features are keys that normally define the extent of thermal and magnetic hystereses. Generally, the more pure the solid and the more refined is its microstructure, the less hysteretic and faster a firstorder phase transition would be. Although not much research has been carried out specifically in this direction, two such examples have been described in the past. Thus, Refs. [21] and [22] report that hysteresis in solid-state electrolysis purified polycrystalline Dy and Er metals is smaller than the same in less pure, polycrystalline metals. Since the majority of potentially important MCE materials are multicomponent compounds, and because it is easier to produce a clean elemental metal than a clean two- or three-component alloy, it is interesting to examine whether or not hysteresis is inevitable in complex magnetic solids undergoing first-order phase transformations. Consider a well-known family of RCo2 alloys [23]. Three of its members, i.e. DyCo2, HoCo2, and ErCo2 exhibit first-order itinerant electron metamagnetic phase transformations. The first-order nature of the phase transition in DyCo2 is confirmed by the behavior of heat capacity (Fig. 1a) and by lattice distortion accompanied by the discontinuities of unit-cell dimensions and phase volume observed at the phase transition temperature (Fig. 2) in zero magnetic fields. Yet, regardless of this, no obvious thermal (not shown) or magnetic (Fig. 1b) hysteresis can be detected in this material. The MCE in DyCo2 (Fig. 3) is substantial, and it also exhibits a behavior typically expected for first-order phase transformation materials [24]. In the example described above, no special effort was made to develop a peculiar microstructure of DyCo2 in order to minimize hysteresis, except for using high-purity Dy metal, which was prepared by the Materials Preparation Center (MPC) of the Ames Laboratory [25]. Elemental Co is readily available from commercial sources in a 99.99 wt% pure form. The MPC routinely produces

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Fig. 1. (Color online) The heat capacity (a) and isothermal magnetization (b) in the vicinity of the first-order phase transformation of polycrystalline DyCo2. In (b), large open symbols represent field increasing and small filled symbols represent field decreasing measurements.

a√ 2tetragonal

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Fig. 2. (Color online) Unit-cell dimensions (a) and phase volume (b) of DyCo2 as functions of temperature determined from X-ray powder diffraction data collected in 0 kOe (open symbols) and 40 kOe magnetic (filled symbols) fields.

rare-earth metals that are 99.8–99.9 at% pure with respect to all other elements, including light-weight interstitial impurities, such as H, C, O, and N. The alloy was prepared by arc melting of stoichiometric amounts of elemental Dy and Co and it was examined in the as cast condition. The absence of measurable magnetic hysteresis, may therefore, be related to the effect of the magnetic field on the nature of the phase transformation in DyCo2. As seen in Fig. 1a, increasing magnetic field not only shifts the heat-capacity anomaly toward high temperatures, but it progressively broadens the peak. Supported by the change in the behaviors of the unit-cell dimensions and phase volume when the magnetic field increases from 0 to 40 kOe (Fig. 2), this indicates that in the presence of magnetic field, the

transformation in this compound loses its first-order nature and becomes a second-order phase transition. While both the magnetic ordering and cubic to tetragonal distortion are preserved in high magnetic fields, the discontinuity of the phase volume has disappeared. An example of how the microstructure affects thermal and magnetic hysteresis is found in Gd5Si2Ge2. According to different reports, thermal hysteresis in polycrystalline samples of Gd5Si2Ge2 may vary from 2 K [8] to 14–15 K [26] depending on the preparation and processing history of the sample. Single crystalline samples, on the other hand, exhibit thermal hysteresis ranging from 2 to 5 K [27,28] depending on which physical property has been measured. This occurs due to different sizes and shapes of

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Fig. 3. (Color online) The magnetocaloric effect of DyCo2 [DSM left panel (a) and DTad right panel (b)] calculated from heat capacity data measured as function of temperature in magnetic fields 0, 20, 50, 75, and 100 kOe.

single crystals used in different measurements because of highly anisotropic change of the unit-cell dimensions across the magnetostructural phase transition in this material [29,30]. Even though only preliminary data are available on the effects of particle size, it has been observed that in small fragments of R5T4 materials, the magnetostructural transformation is sharper, and the widths of thermal and magnetic hystereses are reduced [31]. Obviously, excessive hysteresis is detrimental to the possible use of GMCE materials in magnetic cooling. Yet, considering all of the above this does not mean that the GMCE materials will only have a basic scientific interest and that hysteresis losses are bound to negate most of the benefits of strong MCEs originating from both the magnetic and crystallographic phase changes. The extent of hysteresis should be minimized by appropriate processing to develop a material-specific microstructure that will reduce losses due to hysteresis to an acceptable level. We believe that microstructural modifications are preferred over chemical modifications (alloying) because substituting elements may change thermodynamics and destroy the first-order nature of the transitions of interest, thus resulting in a considerable reduction of the MCE [32]. In some extreme cases, alloying may reduce the giant MCE by as much as a factor of 3 [33]. 3. Metastability: what are we really measuring and reporting? With first-order phase transition materials drawing more and more interest among the condensed matter commu-

nity, it may be tempting to report the largest ‘‘observed’’ (in reality, the calculated values using the Maxwell equations) MCE after a series of simple measurements of the isothermal magnetization, thus claiming a new victorious material. One problem, which may easily be overlooked, is that many of the giant magnetocaloric materials exist in a phase-separated state in the immediate vicinity of the magnetostructural transition, which combined with a measurable hysteresis may result in spuriously large computed values of the MCE. By using the La0.7Pr0.3Fe11.5Si1.5 compound as an example, a team of Chinese scientists recently showed that a straightforward numerical integration using Maxwell equation is not applicable in the phase-separated state [34]. In other words, when a material exists as a mixture of paramagnetic and ferromagnetic phases, only a fraction of its volume occupied by the paramagnetic phase when it is transformed by the magnetic field into the ferromagnetic phase contributes to the GMCE. A large part of the normalized area between two adjacent M(H) isotherms (one or both must correspond to the phase-separated state), however, is present and is included in the summation because of the remaining volume fraction of the ferromagnetic phase. The latter does not contribute much to the MCE but its presence is carried over through the integration process yielding unreasonably large and spurious values of the isothermal magnetic entropy change. As Ref. [34] suggests, in order to properly calculate the MCE in a phase-separated system one needs to account for a fraction of each component (paramagnetic and ferromagnetic) that exists at each measurement temperature.

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4. Making the most of the magnetic and lattice entropy changes As was shown in Refs. [35–37], the GMCE consists of two fundamentally different contributions. The first one is purely magnetic and it occurs due to change(s) occurring in the magnetic sublattice. Consider what has become a classic example of the giant magnetocaloric system—the Gd5Si2Ge2 compound. It is well known that this intermetallic material exists in one of the two polymorphic modifications: the orthorhombic, Gd5Si4-type structure and the monoclinic, Gd5Si2Ge2-type structure [29,30]. We refer to them as the O(I)- and M-types, respectively. According to density functional theory-based calculations, each of the two polymorphs orders magnetically via a conventional second-order phase transformation at its own and T M Curie temperature, T OðIÞ C , respectively, as illuC strated in Fig. 4 [38]. It is important to note that the Curie temperature of the O(I)–Gd5Si2Ge2 is greater than the same of the M–Gd5Si2Ge2. The Helmholtz-free energies of the two polymorphic modifications of Gd5Si2Ge2 are also illustrated in Fig. 4, and according to this, they become OðIÞ equal at a critical temperature T M C oT C oT C . Thus, at high temperatures, the compound is in the monoclinic, paramagnetic state with zero spontaneous magnetization. As the temperature is lowered below OðIÞ , the free energy of M–Gd5Si2Ge2 remains lower than TC that of O(I)–Gd5Si2Ge2 down to TC, and the spontaneous magnetization remains 0. Below TC, the O(I)–Gd5Si2Ge2 becomes the equilibrium phase. Since T C oT OðIÞ C , spontaneous magnetization changes discontinuously from 0 in the paramagnetic monoclinic state to a value characteristic for the ferromagnetic orthorhombic state of the compound at TC. The predicted behavior of the spontaneous magnetization of Gd5Si2Ge2 is shown in Fig. 4 together with the experimentally determined values. We note that the two sets of the magnetization data are in a nearly quantitative agreement.

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Another source of errors, which may be large in the phase-separated state, arises from an imperfect temperature control during the isothermal magnetization measurements. A typical automated temperature controller approaches the target temperature Tt via decaying oscillations. Due to hysteresis, the system does not return to a state corresponding to Tt after temperature is stable at Tt, but it will always remain in the state corresponding to Tt+DT. Here, DT is the largest overshot of Tt. Since the absolute value of DT is usually lower than the extent of thermal hysteresis, this results in an incorrect normalization of the areas enclosed between adjacent magnetization isotherms where at least one of the M(H) curves represents the phase-separated state. Obviously the severity of this error increases greatly as M(H) data are collected with smaller and smaller temperature intervals, and/or when the phase-separated region is narrow.

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Temperature, T (K) Fig. 4. (Color online) Magnetization (lower part of the plot, dashed and dotted lines) and Helmholtz-free energies (upper part of the plot, solid and dash-dotted lines) of two polymorphic modifications of Gd5Si2Ge2 calculated from first principles. The thick solid line in the lower part of the plot illustrates predicted behavior of the magnetization when the monoclinic paramagnetic polymorph of Gd5Si2Ge2 transforms into the orthorhombic ferromagnetic polymorph at TC when the free energies of the two phases become equal. The symbols represent measured values of the spontaneous magnetization of Gd5Si2Ge2 as a function of temperature.

This model is the key to understanding the GMCE, and especially the purely magnetic part of the phenomenon. In order to maximize the contribution from a spin system to the MCE, one needs to maximize the magnitude of the discontinuity of the magnetization. One way to achieve this is to ensure that at TC, the ferromagnetic phase has the highest possible magnetization. Theoretically, it is easy to achieve by lifting the free energy of the O(I) polymorph, OðIÞ as illustrated in Fig. 5. thus shifting TC further below T C The resulting MCE, which is the difference between the magnetic entropies of the two spin systems at the transition temperature, will also increase as shown schematically in Fig. 6. Although specific details of how to achieve this in practice will be different from one material to another, the most common approach facilitating adjustments of the free energy is via chemical substitutions. Another interesting method that is suitable in manipulation of the magnetostructural phase transition temperature may be once again derived from the known behavior of the Gd5Si2Ge2 system. It has been reported that heat treatment significantly increases the MCE of the compound [39]. While most of the enhancement has been appropriately assigned to a sharper transition as a result of homogenization, the observed reduction of the magnetostructural transition temperature from 277 to 272 K definitely played a role in the observed increase of the isothermal magnetic entropy change, which is consistent with the discussion found in the previous paragraph. It is worthwhile to note that in another representative of the Gd5SixGe4x family

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Magnetic moment, m (μB/Gd atom)

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Fig. 5. (Color online) Effect of shifting of the magnetostructural transition temperature on the magnitude of the discontinuity of the OðIÞ is further away from T C than TC in Fig. 4. This is magnetization. T New C equivalent to lifting the free energy of the O(I) phase and results in the increased magnitude of the discontinuity of the spontaneous magnetization. The free energy of the O(I) phase and the predicted behavior of the spontaneous magnetization from Fig. 4 are shown as thin dashed lines. Refer to Fig. 4 for explanations of the symbols.

TCNew

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e i2 G 5S

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I)-G

induced structural changes are well documented for many of the GMCE materials [29,30,35,40–42], the contribution from the lattice to the MCE presents an interesting basic science question. Ab initio calculations of the entropies of phases involved in the magnetostructural phase changes are difficult, to say the least, even though the underlying fundamental definition of the entropy is very simple, i.e. ðqG=qTÞP ¼ S, where G is the Gibbs free energy. However, an insight into this question may be provided using some of the available experimental data. Once again, we use the classic example of the Gd5Si2Ge2 compound. At this composition, the material may be retained at room temperature (i.e. in the paramagnetic state) in either of the two crystallographic modifications: the monoclinic Gd5Si2Ge2-type, or the orthorhombic Gd5Si4-type structures [43,44]. The monoclinic paramagnetic polymorph undergoes a magnetostructural phase transformation and exhibits the GMCE, while the orthorhombic paramagnetic polymorph orders magnetically via a conventional second-order phase transition exhibiting a conventional MCE. Considering the difference in the nature of the phase transitions of the two polymorphic modifications of the compound and similar phase transition temperatures (270 and 301 K, respectively) it is easy to show that the difference in the MCEs (isothermal magnetic entropy changes), if any, is due to the contribution from the lattice, i.e. DSlat, between the M-Gd5Si2Ge2 and O(I)-Gd5Si2Ge2 [35,37]. Furthermore, since DSlat is independent of the magnetic field, the difference between the MCEs of the two allotropic modifications of Gd5Si2Ge2 should also be magnetic field independent. By using this approach, DSlat was shown to contribute between 60% and 40% of the total measured MCE, depending on the magnitude of the magnetic field change [36,37,45].

O(

Temperature Fig. 6. (Color online) Schematic representation of the magnetic entropies as functions of temperature of M–Gd5Si2Ge2 (thick dashed line) and O(I)–Gd5Si2Ge2 (thick solid line). At the corresponding Curie temperatures, each function reaches the theoretical maximum of R ln(2J+1), which is shown as the dash-dotted line. Thick vertical lines indicate the magnetocaloric effects corresponding to two different magnetostructural in Fig. 5). phase transition temperatures (TC in Fig. 4 and T New C

(with x ¼ 0.5), the temperature of the magnetostructural phase transition has been reduced by as much as 12 K by a short-term anneal [40], and the MCE also rises as the result of the heat treatment. The second major contribution to the GMCE is the difference between the lattice entropies of the low- and high-field phases [12,35–37], in other words, the (nonmagnetic) entropy of a structural phase transition. Although crystallographic details of the magnetic field-

In summary, the GMCE materials present a fertile ground for both basic and applied science. Much remains to be learned about how to control and make the best use of the GMCE in particular and first-order phase transition materials in general in future energy-related applications, including magnetic cooling, magnetomechanical devices, sensors, and others. We need to discover ways and develop tools to maximize the contributions from both the lattice and the magnetic entropy changes while simultaneously maintaining low hysteresis. Obviously, first principles theory is becoming and will remain a major player, especially when it has been validated and refined by carefully designed experiments. Both theory and experiment will remain keys for future breakthroughs in this rapidly expanding field. Acknowledgments This work was supported by the Office of Basic Energy Sciences of the Office of Sciences of the US Department of

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Energy under Contract no. DE-AC02-07CH11358 with Iowa State University of Science and Technology. References [1] V.K. Pecharsky, K.A. Gschneidner Jr., J. Magn. Magn. Mater. 200 (1999) 44. [2] C. Zimm, A. Jastrab, A. Sternberg, V.K. Pecharsky, K.A. Gschneidner Jr., M. Osborne, I.E. Anderson, Adv. Cryo. Eng. 43 (1998) 1759. [3] A.M. Tishin, Y.I. Spichkin, The Magnetocaloric Effect and its Applications, IOP Publishing, Bristol, 2003. [4] E. Bru¨ck, O. Tegus, X.W. Li, F.R. de Boer, K.H.J. Buschow, Physica B: Condens. Matter 327 (2003) 431. [5] K.A. Gschneidner Jr., V.K. Pecharsky, A.O. Tsokol, Rep. Progr. Phys. 68 (2005) 1479. [6] S.L. Russek, C. Zimm, Intern. J. Refriger. 29 (2006) 1366. [7] K.A. Gschneidner Jr., V.K. Pecharsky, in: A. Poredosˇ , A. Sˇarlah (Eds.), Proceedings of the Second International Conference on Magnetic Refrigeration at Room Temperature, Portoroz, Slovenia, 11–13 April 2007 (International Institute of Refrigeration, Paris, France, 2007), p. 9. [8] V.K. Pecharsky, K.A. Gschneidenr Jr., Phys. Rev. Lett. 78 (1997) 4494. [9] V.K. Pecharsky, K.A. Gschneidenr Jr., Appl. Phys. Lett. 70 (1997) 3299. [10] H. Wada, Y. Tanabe, Appl. Phys. Lett. 79 (2001) 3302. [11] H. Wada, K. Taniguchi, Y. Tanabe, Mater. Trans. 43 (2002) 73. [12] A. de Campos, D.L. Rocco, A.M.G. Carvalho, L. Caron, A.A. Coelho, S. Gama, L.M. DaSilva, F.C.G. Gandra, A.O. dos Santos, L.P. Cardoso, P.J. von Ranke, N.A. de Oliveira, Nat. Mater. 5 (2006) 802. [13] O. Tegus, E. Bru¨ck, K.H.J. Buschow, F.R. de Boer, Nature 415 (2002) 150. [14] D.T. Cam Thanh, E. Bru¨ck, O. Tegus, J.C.P. Klaasse, T.J. Gortenmulder, K.H.J. Buschow, J. Appl. Phys. 99 (2006) 08Q107. [15] Z.Q. Ou, G.F. Wang, Song Lin, O. Tegus, E. Bru¨ck, K.H.J. Buschow, J. Phys.: Condens. Matter 18 (2006) 11577. [16] A. Fujita, S. Fujieda, Y. Hasegagwa, K. Fukamichi, Phys. Rev. B 67 (2004) 104416. [17] F. Albertini, F. Canepa, S. Cirafici, E.A. Franceschi, M. Napoletano, A. Paoluzi, L. Pareti, M. Solzi, J. Magn. Magn. Mater. 272–276 (2004) 2111. [18] M. Pasquale, C.P. Sasso, L.H. Lewis, J. Appl. Phys. 95 (2004) 6918. [19] T. Krenke, E. Duman, M. Acet, E.F. Wassermann, X. Moya, L. Man˜osa, A. Planes, Nat. Mater. 4 (2005) 450. [20] D.V. Ragone, Thermodynamics of Materials, vol. 1, Wiley, New York, 1995. [21] V.K. Pecharsky, K.A. Gschneidner Jr., D. Fort, Scr. Mater. 35 (1996) 843. [22] K.A. Gschneidner Jr., V.K. Pecharsky, D. Fort, Phys. Rev. Lett. 78 (1997) 4281.

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[23] N.H. Duc, T. Goto, in: K.A. Gschneidner Jr., L.R. Eyring (Eds.), Handbook on the Physics and Chemsitry of Rare Earths, vol. 26, Elsevier, Amsterdam, 1999, p. 177 (Chapter 171). [24] V.K. Pecharsky, K.A. Gschneidner Jr., A.O. Pecharsky, A.M. Tishin, Phys. Rev. B 64 (2001) 144406. [25] Materials Preparation Center, Ames Laboratory US-DOE, Ames, IA, USA, /www.mpc.ameslab.govS. [26] E.M. Levin, V.K. Pecharsky, K.A. Gschneidner Jr., Phys. Rev. B 60 (1999) 7993. [27] J.E. Leib, J.E. Snyder, C.C.H. Lo, J.A. Paulsen, P. Xi, D.C. Jiles, J. Appl. Phys. 91 (2002) 8852. [28] C. Magen, L. Morellon, P.A. Algarabel, M.R. Ibarra, Z. Arnold, J. Kamarad, T.A. Lograsso, D.L. Schlagel, V.K. Pecharsky, A.O. Tsokol, K.A. Gschneidner Jr., Phys. Rev. B 72 (2005) 024416. [29] L. Morellon, P.A. Algarabel, M.R. Ibarra, J. Blasco, B. GarciaLanda, Z. Arnold, F. Albertini, Phys. Rev. B 58 (1998) R14721. [30] W. Choe, V.K. Pecharsky, A.O. Pecharsky, K.A. Gschneidner Jr., V.G. Young Jr., G.J. Miller, Phys. Rev. Lett. 84 (2000) 4617. [31] J.D. Moore, G.K. Perkins, Y. Bugoslavsky, M.K. Chattopadhyay, S.B. Roy, P. Chaddah, V.K. Pecharsky, K.A. Gschneidner Jr., L.F. Cohen, Appl. Phys. Lett. 88 (2006) 072501. [32] V.K. Pecharsky, K.A. Gschneidner Jr., J. Magn. Magn. Mater. 167 (1997) L179. [33] V. Provenzano, A.J. Shapiro, R.D. Shull, Nature (London) 429 (2004) 853. [34] G.J. Liu, J.R. Sun, J. Shen, B. Gao, H.W. Zhang, F.X. Hu, B.G. Shen, Appl. Phys. Lett. 90 (2007) 032507. [35] V.K. Pecharsky, A.P. Holm, K.A. Gschneidner Jr., R. Rink, Phys. Rev. Lett. 91 (2003) 197204. [36] L. Morellon, Z. Arnold, C. Magen, C. Ritter, O. Prokhnenko, Y. Skorokhod, P.A. Algarabel, M.R. Ibarra, J. Kamarad, Phys. Rev. Lett. 93 (2004) 137201. [37] V.K. Pecharsky, K.A. Gschneidner Jr., in: A. Planes, L. Man˜osa, A. Saxena (Eds.), Magnetism and Structure in Functional Materials, Springer, Berlin, 2005, p. 199. [38] D. Paudyal, V.K. Pecharsky, K.A. Gschneidner Jr., B.N. Harmon, Phys. Rev. B 73 (2006) 144406. [39] A.O. Pecharsky, K.A. Gschneidner Jr., V.K. Pecharsky, J. Appl. Phys. 93 (2003) 4722. [40] Ya. Mudryk, D. Paudyal, V.K. Pecharsky, K.A. Gschneidner Jr., Phys. Rev. 77 (2008) 024408. [41] A. Fujita, K. Fukamichi, K. Koyama, K. Watanabe, J. Appl. Phys. 95 (2004) 6687. [42] O. Tegus, E. Bru¨ck, W. Dagula, X.W. Li, L. Zhang, K.H.J. Buschow, F.R. de Boer, J. Appl. Phys. 93 (2003) 7655. [43] V.K. Pecharsky, G.D. Samolyuk, V.P. Antropov, A.O. Pecharsky, K.A. Gschneidner Jr., J. Solid State Chem. 171 (2003) 57. [44] Y. Mozharivskyj, A.O. Pecharsky, V.K. Pecharsky, G.J. Miller, J. Am. Chem. Soc. 127 (2005) 317. [45] V.K. Pecharsky, K.A. Gschneidner Jr., in: H. Kronmuller, S. Parkin (Eds.), Handbook of Magnetism and Advanced Magnetic Materials, vol. 4, Wiley, New York, 2007 (part 7).