On the origin of giant magnetocaloric effect and thermal hysteresis in multifunctional α-FeRh thin films

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On the origin of giant magnetocaloric effect and thermal hysteresis in multifunctional α -FeRh thin films Tiejun Zhou

a,∗

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, M.K. Cher , L. Shen , J.F. Hu , Z.M. Yuan

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Data Storage Institute, A*STAR (Agency for Science Technology and Research), 5 Engineering Drive 1, Singapore 117608, Singapore b Department of Physics, 2 Science Drive 3, National University of Singapore, Singapore 117542, Singapore

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Article history: Received 8 May 2013 Received in revised form 5 September 2013 Accepted 17 September 2013 Available online xxxx Communicated by R. Wu

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a b s t r a c t

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We report temperature and field dependent lattice structure, magnetic properties and magnetocaloric effect in epitaxial Fe50 Rh50 thin films with (001) texture. Temperature-dependent XRD measurements reveal an irreversible first-order phase transition with 0.66% lattice change upon heating/cooling. Firstprinciple calculation shows a state change of Rh from non-magnetic (0 μB ) for antiferromagnetic phase to magnetic (0.93 μB ) state for ferromagnetic phase. A jump of magnetization at temperature of 305 K and field more than 5 T indicates a field-assisted magnetic state change of Ru that contributes to the jump. Giant positive magnetic entropy change was confirmed by isothermal magnetization measurements and an in-situ temperature rise of 15 K. The magnetic state change of Rh between antiferromagnetic and ferromagnetic states is the main origin of giant magnetic entropy change and large thermal hysteresis observed. © 2013 Published by Elsevier B.V.

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1. Introduction

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Magnetic refrigeration based on magneto-caloric effect (MCE) are environmentally friendly and economically beneficial [1,2]. Recent progress on magnetic refrigeration with achieved cooling efficiency of 60% of the theoretical limit has demonstrated that magnetic refrigeration is a promising alternative to conventional vapor-cycle refrigeration [3]. To achieve high efficiency, large magnetic entropy change near room temperature is required. Gd is the first material which was found to have a large magnetic entropy change of 8–10 J kg−1 K−1 at 293 K for a field change of 0–5 T [4]. Recently, followed the discovery of giant magnetic entropy change of 18 J kg−1 K−1 around 278 K for Gd5 Si2 Ge2 for a field change of 0–5 T [5], other materials with giant magnetocaloric effect, including LaFe13−x Six [6–8], MnAs1−x Sbx [9], and MnFeP0.45 As0.55 [10] were found to have entropy changes between 18 and 30 J kg−1 K−1 under the similar conditions. Large magnetic entropy change was also discovered in La0.8 Ca0.2 MnO3 [11,12]. A common feature of the giant MCE is that it is usually accompanied by a first-order magnetic transition from ferromagnetic (F) to paramagnetic (PM) state, which results in a giant negative magnetic entropy change [13]. With those materials, alignment of randomly oriented magnetic moments causes a decrease in entropy, resulting in heating, while, randomization of magnetic moments makes an increase of entropy, leading to cooling [1,2,10].

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*

Corresponding author. Tel.: +65 68748778, fax: +65 65160900. E-mail address: [email protected] (T. Zhou).

0375-9601/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.physleta.2013.09.027

Other than those materials with giant negative (normal) magnetic entropy change, materials with giant positive (inverse) magnetic entropy change were also discovered [14–19]. Of which, FeRh has been found, very recently, to have very large effective refrigerant capacity of 492.8 J/kg at room temperature for a field change of 0–5 T in spite of its large thermal hysteresis [20,21], which is one of the largest achieved so far at room temperature and is higher than the two well-known systems with giant negative MCE, namely MnFeP0.45 As0.55 having a value of 355 J/kg [10] and Gd5 Ge1.9 Si2 Fe0.1 having a value of 390 to 400 J/kg under the similar conditions [22]. The finding makes it possible to use FeRh as a practical working medium for room-temperature magnetic refrigeration. Chemically ordered FeRh is structurally bcc (α -FeRh), which undergoes a first-order phase transition from antiferromagnetic (AF) to F state upon heating to the transition temperature (Tc ) which is tunable over a wide range by changing the relative ratio of Fe to Rh or by small addition of Pt, Pd, or Ni [23–27]. Further study showed that this transition is accompanied by an isotropic volume increase of 1% and an increase in entropy [28,29]. Beyond the interests in the fundamental physics of the magnetism of these materials and being used as a working medium for magnetic refrigeration, FeRh has the great potential to be used in ultrahigh density magnetic recording. It was recently proposed to utilize exchange coupled FeRh/FePt bilayers for thermally assisted magnetic recording media with significant reduction of switching field and enhanced effective field gradient [30–33]. It is believed that the bilayer films have the potential to support recording density up to a few Tbit per square inch given optimized microstructure and magnetics.

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Table 1 In-plane and out-of-plane lattice constants, strain parameters and cell unit volume of 100-nm FeRh thin films on MgO measured at room temperature. Bulk values of FeRh are shown for comparison.

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FeRh thin film

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Lattice parameter

c /a

Cell unit volume, Å3

Lattice parameter

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a, Å c, Å

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It is believed that the giant MCE found in FeRh parent materials is associated with the first-order phase change and the large moment of Fe (3.3 μB per Fe atom [34], compared to 2.2 μB per Fe atom for pure Fe). However the mechanism of the metamagnetic phase transition, which is also the origin of the giant MCE, is not well understood. Furthermore, for technological applications for both magnetic refrigeration and magnetic recording, the thermal hysteresis is a big concern. In this Letter, detailed study on temperature and field dependent structure, magnetic properties and magnetocaloric effect in epitaxial Fe50 Rh50 thin films with (001) texture was carried out. The (001) textured FeRh films undergo an irreversible first-order phase transition with 0.66% lattice change upon heating/cooling. Although the phase transition involves in the change of lattice strain, it is reversible, implying that the strain change is not the main origin of thermal hysteresis. Giant positive magnetic entropy change, confirmed by isothermal magnetization measurements and indicated by an in-situ temperature rise of 15 K, is attributed to magnetic state change of Rh between AF and F phases. The magnetic state change of Rh is also the origin of large thermal hysteresis found in FeRh. 2. Experimental details

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Cell unit volume, Å3

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FeRh bulk (Ref. [36]) Strain (%)

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Fe50 Rh50 thin films of 100 nm thick were deposited on MgO (001) single crystal substrates from a FeRh alloy target by means of DC magnetron sputtering with a base pressure of 2 × 10−8 Torr. The substrate was subjected to in-situ heating to 400 ◦ C prior to deposition. Argon with purity of 99.999% was used as the working gas with a working pressure of 3 mT. FeRh films of thickness of 5, 10, 20 and 50 nm were also prepared under the same conditions to check thickness-dependent lattice structure. It is found that the lattice constants change sharply at thickness thinner than 10 nm, while almost keep constant if thickness is more than 50 nm. To minimize the substrate effect, the thickness in this study is therefore fixed at 100 nm. Pd doped FeRh thin films, (FeRh)97 Pd3 (FeRhPd3) and (FeRh)95 Pd5 (FeRhPd5), of thickness of 100 nm were also prepared by co-sputtering FeRh and Pd under the same conditions for magneto-caloric study in order to have a comparison among parent FeRh alloys with different phase transition temperature. Composition of the thin films was confirmed using Rutherford backscattering spectrometry (RBS). The temperature-dependent lattice structure and lattice strain without the presence of magnetic field were characterized by X-Ray Diffraction (XRD) using Cu Kα radiation measured at different temperatures upon heating up and cooling down. The measurements started at room temperature (298 K) and the run consisted of heating the sample at a constant rate of 2 K per minute to a targeted temperature, waiting there for 10 min, and then collecting XRD data. After reaching 403 K, the sample was cooled down to room temperature at a controlled rate of 2 K per minute and XRD spectra were collected during the cooling process. The magnetic properties of non-ambient temperature were measured by a Superconducting Quantum Interference Device (SQUID, from Quantum Design) for both increased and decreased temperature with magnetic field up to 7 T. In order to correctly probe the phase transition and eliminate the memory effect, the isothermal mea-

surements were performed in the following way (loop measurement proposed by Brück et al. [35]): the sample was firstly cooled down to 200 K, which was much lower than the transition temperature (310–350 K). The field was then increased until 7 T and magnetization was measured in discrete steps followed by bringing the field back to zero. Next, the sample was heated to a higher temperature of T1 and magnetization was recorded as a function of field in discrete steps. After that, remove the magnetic field. The sample was then cooled all the way to 200 K without the presence of magnetic field to make sure the sample was completely AF. Only then the sample was heated to the next measurement temperature, T1 + T, followed by recording the magnetization as a function of field in discrete steps. The loop in temperature was performed before every isotherm, without the presence of magnetic field.

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3. Temperature-dependent lattice structure and magnetic properties

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At room temperature, the as-deposited FeRh thin films with thickness of 100 nm show only (001) superlattice and (002) fundamental peaks, suggesting that chemically ordered phase with ordering parameter of 0.93 is obtained. XRD phi scan measurements of the FeRh (110) peaks reveal four-fold symmetry and confirm the epitaxial growth of FeRh on the MgO (001) single crystal substrates. Table 1 summarizes the in-plane and out-of-plane lattice constants, strain parameters and cell unit volume of 100-nm FeRh thin films on MgO measured at room temperature (bulk values are shown for comparison). The strain values are derived from the experimental lattice constant of 2.987 Å for bulk FeRh in AF phase [36]. It can be seen that the FeRh films are slightly expanded in c direction and compressed in a–b plane (tetragonal distortion) with a c /a of 1.008. Compared to bulk FeRh, the cell unit volume of thin film is also a little smaller (about 1% contraction). The lattice constant √ of MgO (4.212 Å) is a little smaller than that of FeRh (2.987 × 2 = 4.224 Å), that could result in shorter a axis and longer c axis in epitaxial FeRh thin films as observed. Fig. 1 shows temperature-dependent XRD patterns (θ –2θ scan) upon heating up and cooling down. As temperature increases/decreases, both (001) and (002) peaks shift to lower/higher angle side. The shifting is not continuous, indicating possible first-order phase change. Furthermore, the peak positions between heating and cooling process do not coincide with each other in the temperature range of 310 K to 350 K, suggesting thermal hysteresis behavior corresponding to the first-order phase transition. The Rietveld standard program was used to obtain the peak position and the full widths at half maximum (FWHM) of the Bragg peaks [37], with which the lattice constant and the mean-square-root lattice strain, e2 1/2 , can be determined [38–40]. Fig. 2(a) reveals how the lattice constant changes with temperature upon heating/cooling. The lattice constants change sharply at temperature range of 323 K to 353 K and 333 K to 308 K upon heating up and cooling down, respectively, which confirms the irreversible first-order phase change. The change of lattice parameter is 0.66%, which is almost two times of that reported for the bulk samples [41–43]. As shown before, films are slightly tetragonal distorted due to epitax-

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Fig. 3. Transition temperature, Tc , versus applied magnetic field upon temperature increase (solid circle dots, Tc (AF-F)) and decrease (open circle dots, Tc (F-AF)). The lines are the linear fits to the data points. The solid and open stars are the Tc (AF-F) and Tc (F-AF) without the presence of magnetic field based on XRD measurements, respectively.

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Fig. 1. Temperature-dependent XRD patterns measured upon temperature increase and decrease.

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Hc = H0 1 −

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Fig. 2. Lattice parameter and magnetic moment, measured under a constant magnetic field of 0.5 T, versus temperature upon heating up and cooling down.

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temperatures of Tc (AF-F) and Tc (F-AF) without the presence of magnetic field can be determined using XRD data. They are 334.3 K and 323.5 K, respectively, which are about 3.0 K higher than those obtained from the M–T curve under 0.5 T field. The intrinsic thermal hysteresis, Tc , which is defined as the difference between Tc (AF-F) and Tc (F-AF) without the presence of magnetic field, is about 10.8 K, and is almost same as that obtained from M–T curves (11 K). A phase diagram of Tc versus magnetic field can be constructed by extracting the values of Tc (AF-F) and Tc (F-AF) from temperature hysteresis loop measurements at fixed field and is shown in Fig. 3. Both Tc (AF-F) and Tc (F-AF) versus field collapse onto two parallel lines, indicating that the thermal hysteresis does not change with external field. A linear function with slope of dT /dH = 8.75 K/T, which is a little higher than the reported data in the same alloy [44], gives a very good fit to all the data points. The intrinsic Tc (AF-F) and Tc (F-AF) are also shown in Fig. 3 as solid and open star, respectively, which are about 3.5 K lower than the linear fitting data. McKinnon et al. [41], using a much wider range of magnetic field, found that the AF-F phase transition can be described by the empirical field-temperature relationship



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ial growth relationship between substrate and film. Such epitaxial growth relationship restricts the expansion/contraction of a axis upon heating/cooling, while restriction on c axis is much less due to lack of epitaxial growth relationship. That could be the possible reasons that cause a larger c-axis change in thin films. The magnetic moment versus temperature (M–T curves) measured under a constant magnetic field of 0.5 T is also shown in Fig. 2. It is clearly confirmed that the first-order phase change is accompanied by a magnetic phase change between AF and F states. The phase transition temperatures from AF to F, Tc (AF-F), and that from F to AF, Tc (F-AF), are defined as the temperatures where half of maximum moment for fixed-field measurement, or half of the lattice change (0.33%) for XRD measurement, upon heating and cooling, is reached, respectively. The intrinsic phase transition



T T0

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(1)

where H 0 and T 0 are composition dependent quantities describing the transition field at T = 0 K and the transition temperature at H = 0 T, respectively. With such empirical fieldtemperature relationship, it is expected that at very low field (close to 0), the Tc versus field will deviate from linear relationship as observed. T 0 can be determined, based on XRD data, to be [Tc (AF-F) + Tc (F-AF)]/2 = 326.05 K, which is the mid-point of the transition temperatures without the presence of magnetic field. With the measured T 0 and the slope of dT /dH = 8.75 K/T, we obtained H 0 = 21.2 T, which is very close to the reported data [41,44]. It is believed that the thermal hysteresis is, at least partially, related to the change in lattice strain caused by the lattice expansion/shrink during the phase transition process. Fig. 4 depicts how the mean-square-root lattice strain, e2 1/2 , changes with temperature upon heating up (solid diamonds) and cooling down (solid circles). It decreases/increases sharply at transition temperature

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Fig. 4. Root-Mean-Square strain, e  , as a function of temperature upon heating up and cooling down (error bar indicates the experimental uncertainty). 2 1/2

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Fig. 5. Isothermal magnetization curves of FeRh at increased temperature.

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upon heating/cooling, respectively, indicating that the phase transition does involve in the change of lattice strain. The lattice strain is reduced by about 15% upon heating up, resulting from heatinginduced expansion of a-axis. However, the change of lattice strain is almost reversible within the experimental errors, indicating that the strain change is nearly elastic. The reversible change of lattice strain implies that lattice strain is not the main origin of large thermal hysteresis observed. Fig. 5 illustrates the isothermal magnetization curves of FeRh measured at increased temperature (using loop method). Measurements of isothermal magnetization were done in the following way: set a targeting field, wait there for 5 min after reaching the target, and then measure the moment thrice. From the isothermal magnetization curves at temperature lower than 300 K, there is a magnetically soft layer of thickness around 5 nm that does not undergo phase change upon heating/cooling. Previous theoretical studies predicated that if the film thickness is too thin, the AF phase becomes ferromagnetic due to surface/interface effects [45,46], which agrees well with the current findings. Fieldinduced phase transition from AF to F states can be clearly seen from the shape of the magnetization curves at different temperature. The field required to induce the phase transition decreases with increase of temperature. A nearly constant jump of magnetization of ∼300 emu/cc for fields between 5 and 6 T has been observed as temperature is increased from 300 K to 305 K. Furthermore, at field higher than 6 T and temperature higher than

305 K, the magnetization oscillates between 1050–1100 emu/cc and 1350–1400 emu/cc. To check the experimental repeatability, similar measurements were carried out on other samples with thickness of 50 or 100 nm. Similar results were obtained. To understand the observed phenomena, first-principles DFT calculation was performed to study element-specific change of magnetic state (individual state change of Fe and Rh) from AF to F using the pseudopotential plane wave method as implemented in the Vienna ab initio Simulation Package [47]. We adopted the generalized gradient approximation (GGA) proposed by Perdew–Burke–Ernzerhof (PBE) [48] for the exchange correlation energy functional. A planewave basis set was used to expand the Kohn–Sham orbitals with a 350 eV kinetic energy cut-off. We optimized the lattice parameters and atom positions using a conjugated-gradient algorithm based on Hellmann–Feynman forces. In the structural optimization, a 15 × 15 × 15 k-mesh based on the Monkhorst and Pack scheme was used for integration over the first Brillouin zone. To consider the magnetic configuration, either A-type ferromagnetism or G-type antiferromagnetism, a supercell of sixteen atoms (eight Fe and eight Rh atoms) was used. All atoms and the cell shape and volume were allowed to relax in the optimization process until the Hellmann–Feynman forces acting on them becomes less than 5 meV/Å. The calculated results are shown in Table 2. Some benchmark results from literatures [49–51] are also listed for comparison. The lattice parameters from theoretical calculation are very close to the experimental values and similar with the previous publications, indicating the validity of the calculations. Theoretical calculation clearly indicates a magnetic state change of Rh from non-magnetic (0 μB ) to magnetic (∼0.93 μB ) upon transition from AF to F, while the change of Fe moment is negligible. Experimental measurements on both the AF and F phases using Mössbauer and neutron diffraction also revealed that the F phase has collinear magnetic moments of 3.2 μB per Fe atom and 0.9 μB per Rh atom [52], while at low temperatures an AF-II spin structure is found with Fe moments of 3.3 μB and vanished Rh moments [53,54]. The magnetic state change of Rh from 0 to 0.9 μB contributes a magnetization increase of 305 emu/cc, which is very close to the observed magnetization jump of 300 emu/cc at temperature of 305 K. It is, thus, suggested that a field-assisted magnetic state change of Rh is in favor of the phase transition from AF to F state. The oscillation of magnetization at temperature higher than 305 K and field larger than 6 T falls in the magnetization difference of FeRh with 0 and 0.9 μB Rh moment. This might indicate an instability of Rh moment under high field at temperature around and above transition temperature. A similar behavior showing field-assisted magnetic state change of Rh was observed at lower temperature upon cooling down, indicating thermal hysteresis of field-assisted magnetic state change of Rh. In order to probe temperature-dependent reversibility of field induced magnetic phase change between AF and F, isothermal magnetization loops of 0 T → 7 T → 0 T → −7 T → 0 T were measured at different temperature upon heating. Symmetric loops represent reversible phase change (no memory effect), while nonsymmetric loops indicate irreversible phase change (memory effect) induced by magnetic field. Selected loops for temperature around phase transition region are shown in Fig. 6(a). At 305 K or below, symmetric loops were observed. At 310 K, visible nonsymmetric feature was seen. At 315 K and above, clear nonsymmetric loops were obtained and the loop difference between the first and third quadrants becomes larger as temperature increases, indicating heating-enhanced irreversibility of field-induced phase change. Moreover, at 320 K, magnetization drops sharply as field is reduced to about 1 T. The drop is ∼300 emu/cc, suggesting possible magnetic state change of Rh. The non-symmetric loops appear when the remnant magnetization starts increase.

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Table 2 The lattice parameters, magnetic moment of Fe and Rh in AF and F phases from first-principles DFT calculation, together with some benchmark results from literatures for comparison.

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tion isotherms only if the phase transition is correctly probed [35]. Using the Maxwell relation

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Fig. 6. (a) Isothermal magnetization loops of 0 T → 7 T → 0 T → −7 T → 0 T measured at different temperature and (b) remnant magnetization as a function of temperature.

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Therefore, the remnant magnetization can be an indicator for the field-induced irreversibility. Fig. 6(b) shows the remnant magnetization (under a maximum field of 7 T) as a function of temperature. Clearly, the irreversibility starts at 305–310 K. The Tc (AF-F) is about 320 K from the remnant magnetization curve.

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4. Determination of entropy change and its temperature dependence

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For materials with first-order phase transition (having large thermal hysteresis), the magnetic entropy change, S, as function of temperature and field, can be determined from the magnetiza-

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where T is the absolute temperature and H is the applied field, the magnetic entropy change  S can be obtained as,

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It has been criticized that the use of Eq. (3) may result in artificial colossal peaks for materials with first-order phase transition [55,56]. Therefore it is not suitable for evaluating the entropy change in materials with first-order phase transition. Giguere et al. [57] proposed that the Clausius–Clapeyron relation, rather than the Maxwell relation, should be used. However, Sun et al. [58] commented that the Clausius–Clapeyron relation is just a special case of the integrated Maxwell relations and thus the latter should be applicable. Recently, de Oliveira et al. [59] showed that the so-called magnetic Clausius–Clapeyron relation does not hold for magnetic systems since it assumes there is no work done to take the system from the ferromagnetic to the paramagnetic state. The same work states that in the temperature region around the first-order phase transition, the determination of  S, using magnetization data through the Maxwell relation, should be done very carefully, and the result should be confirmed by specific-heat measurements. More recently, Brück et al. reconsidered the Maxwell relations and argued that the “colossal” peaks in the entropy change arise not from the application of the Maxwell relations but from the incorrect probing of the phase transition [35]. They showed that it is possible to obtain the isothermal magnetic entropy change just by employing the Maxwell relations if the phase transition can be correctly probed. The loop method was, therefore, proposed to replace the conventional method in order to correctly probe the phase transition in materials with first-order phase transition [35]. They further studied typical materials with first-order phase transition using loop method and Maxwell relations, and confirmed the validation of the method. Due to the difficulties in measuring the specific-heat of thin films, the loop method, as detailed in the Experimental Part of this study, was applied to obtain the isothermal magnetization curves and then Maxwell relations were used to determine the entropy change. Accordingly, the magnetic entropy changes  S ( T , H ) are obtained. The magnetic entropy change,  S, of FeRh, together with Pd doped FeRh thin films, (FeRh)97 Pd3 (FeRhPd3) and (FeRh)95 Pd5 (FeRhPd5) for comparison, as a function of temperature are shown in Fig. 7 for a field change of 0–5 T.  S of FeRh reaches 20 J kg−1 K−1 at 320 K which is a little higher than that of the LaFeSiH having a typical value of 18 J kg−1 K−1 around room temperature for a field change of 0–5 T [13,60]. A small addition of 3% and 5% Pd shifts the  S peaks from 319 K to 281 K and 238 K, respectively, indicating an effective tuning of the Tc by Pd doping. FeRhPd3 and FeRhPd5 have lower entropy change of about 16 J kg−1 K−1 but have broader  S peaks under similar conditions. Previous reports

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Fig. 7. Magnetic entropy change, S, of FeRh, FeRhPd3 and FeRhPd5, versus temperature under external magnetic field change of 0 to 5 T.

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[24] and our results showed that the Tc of FeRhPd is very sensitive to the concentration of Pd. The broad  S peaks indicate that the Pd may not be homogeneously distributed in the films. To achieve a homogeneous Pd distribution, a long-time post-annealing process may be needed. The refrigerant capacity, which is a more useful factor for accessing a magnetic refrigerant, can be calculated by taking the full width at half maximum of the  S ( T ) curve following the method by Pecharsky and Gscheindner [61]. Such estimated refrigerant capacity under a field change of 0–5 T, are 431 J kg−1 , 453 J kg−1 and 420 J kg−1 for FeRh, FeRhPd3 and FeRhPd5, respectively. The hysteresis losses estimated based on the magnetic measurements are about 62 J kg−1 , 73 J kg−1 , and 57 J kg−1 , giving out effective refrigerant capacity of 369 J kg−1 , 380 J kg−1 , and 363 J kg−1 for FeRh, FeRhPd3 and FeRhPd5 for a field change of 0–5 T, respectively. As can been seen, the average hysteresis losses are quite large due to considerable thermal and field hysteresis observed in those alloys. The magnetocaloric effect of bulk FeRh [62] and Ni doped FeRh [21] was investigated in detail by Manekar and Roy. A lower magnetic entropy change of about 10 J kg−1 K−1 was observed in bulk FeRh for a field change of 0–5 T [62]. However the  S peak is much broader [62]. Using the same method, they calculated the refrigerant capacity and average hysteresis loss in bulk FeRh. The refrigerant capacity is about 379 J kg−1 with an average hysteresis loss of 54 J kg−1 , giving out an effective refrigerant capacity of 325 J kg−1 in bulk FeRh for a field change of 0–5 T. Compared to bulk, thin films have slight higher refrigerant capacity and hysteresis loss. It is noted that in our study, the film composition is equiatomic (Fe50 Rh50 ), while in Manekar and Roy’s investigation, the composition is slightly away from equiatomic (Fe48 Rh52 ). It was reported that the phase and phase transition in FeRh alloy are very sensitive to the relative composition of Fe and Rh [63]. Therefore, the difference in composition might be one of the possible reasons that cause the difference observed. Other than that, the slight distortion of lattice in thin films may also play a partial role. Selected isothermal magnetization curves of FeRh between 285 K and 310 K measured during the heating process upon field increase and decrease (demagnetization process) are shown in Fig. 8. For field increase, same measurement procedure was followed as what described previously. However, upon field decrease, moment was measured immediately after targeted field was reached in order to observe any field-induced effects during fast demagnetization process. It is found that the magnetization

86

Fig. 8. Isothermal magnetization curves of FeRh between 285 K and 310 K measured during heating process upon field increase (solid lines and points) and field decrease (dashed lines and open points).

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oscillation at temperature above 305 K is reversible upon field increase and decrease. The reversible oscillation of magnetization excludes the effect of magnetic-field induced cooling (magnetization process) or heating (demagnetization process) due to self-GMC effect. Most interestingly, the magnetization shows jump/oscillation upon field decrease at temperature above 290 K but below 305 K, while magnetization steadily increases with field upon field increase. Such field irreversibility of magnetization jump/oscillation upon field decrease is different from the reversible oscillation of magnetization for temperature above 305 K and field more than 6 T. At 290 K, the magnetization jumps from 870 emu/cc to 1080 emu/cc when field is reduced from 5.6 T to 4.6 T. After that, magnetization decreases steadily with field. At 295 K, the magnetization jumps from 1010 emu/cc to 1310 emu/cc when field is reduced from 6.2 T to 5.9 T. Further reducing filed to 5.65 T, magnetization drops to 900 emu/cc. After that, magnetization jumps back to 1120 emu/cc via an intermediate value of 1050 emu/cc and steadily decreases with field. Similar behavior was observed for temperature at 300 K. The fields at which magnetization jumps increase with temperature from 5.6 T (at 290 K) to 6.6 T (at 300 K). The magnetization jump/oscillation is about 250–310 emu/cc, which is close to the contribution of magnetic Rh, indicating possible change of magnetic state of Rh. During a fast demagnetization process, randomization of moments reduces material’s entropy leading to heating. Such heating combined with high field (5.6 T and above) may change the magnetic states of Rh from 0 to 0.9 μB , which contributes a magnetization increase of about 305 emu/cc. However once Rh become magnetic, FeRh’s entropy will increase, leading to cooling. Such cooling may be enough to change the Rh moment back to 0, causing the drop of magnetization. Further reducing field will continuously heat the sample and make Rh jump back to magnetic state, resulting in a steady decrease of magnetization with field. It is that the giant MCE combined with high field makes the magnetization jump/oscillation during the fast demagnetization process. As discussed above, magnetic state change of Rh happens at field higher than 5 T and such change occurs at a certain temperature of 305 K. As such, a temperature rise of 15 K can be inferred during the fast demagnetization process at 290 K. The fast demagnetization can be roughly treated as an adiabatic process. Under adiabatic condition, the temperature change of giant MCE materials upon field change can be estimated using  T ad = −Tc ·  S /C p , where C p is the heat

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capacity. Given a C p of 450 J/kg/K for FeRh [29,53] and a  S of 26.5 at 7 T,  T ad is estimated to be 19.1 K, which is very close to the inferred temperature rise of 15 K. The unnormal magnetic curves at field higher than 6 T in Figs. 5 and 8 show magnetization oscillation and the oscillation falls in the magnetization difference of 300–310 emu/cc, which is very close to the contribution from magnetic state change of Rh. This might indicate an unstable magnetic moment of Rh under high field at temperature around and above transition temperature. We have shown that FeRh shows giant positive entropy change as phase change occurs and the phase change involves in the magnetic state change of Rh, that is its entropy increases as Rh becomes magnetic (resulting in cooling), while it decreases as Rh turns back to non-magnetic state (bringing about heating). Such change may induce a temperature variation up to 19 K. As field is higher than 6 T, the entropy change is very large (more than 24.3 J kg−1 K−1 ). As Rh changes from non-magnetic to magnetic states under high field, cooling happens. Such cooling may be enough to change the Rh moment back to 0, causing the drop of magnetization. However as the Rh changes from magnetic to nonmagnetic state, heating happens. Such heating combined with high field may change Rh back to magnetic states, resulting in magnetization increase. It is thus suggested that the giant self-magnetocaloric effect under high field makes an unstable magnetic state of Rh, which accounts for the magnetization oscillating observed in Figs. 5 and 8

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5. The origin of thermal hysteresis

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Theoretical study showed that the AF and F phases are metastable, i.e., they are separated by an energy barrier [54]. Therefore, one phase has to be over-heated or under-cooled before transforming to another phase, resulting in a large thermal hysteresis or irreversible behavior. The thermal hysteresis can be either intrinsic caused by the energy barrier between the two phases or extrinsic induced by the lattice strain change involved in the phase transition. The reversible change in lattice strain involved in the phase transition indicates that lattice strain is not the dominating origin of thermal hysteresis. It has been shown that the phase transition from AF to F involves the change of magnetic state of Rh from 0 to 0.9 μB. Such change needs to overcome an energy barrier. Suppose the moment of Rh is m( Rh) and the internal molecular field is H i , the energy barrier can be roughly estimated as the internal Zeeman energy:

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−m( Rh) · H i

(4)

For the phase transition from AF to F, the internal Zeeman energy, which is −0.9 μB · H i , contributes positively to the phase transition and therefore promotes the phase transition. However, when F phase is transited back to AF phase with vanished Rh moment, the F phase has to be super-cooled to overcome the loss of internal Zeeman energy (energy increase by 0–(−0.9 μB · H i ) = 0.9 μB · H i ). Suppose a super-cooled temperature,  T , is needed to induce the phase transition from F to AF, one have

k B ·  T  0.9 μB · H i

(5)

where k B is Boltzmann constant. While, H i can be replaced by H 0 , which is the field required to induce phase transition from AF to F at 0 K. Based on the H 0 value obtained in this study,  T is estimated to be about 12.8 K, which is very close to the observed thermal hysteresis of 11 K. It was previously reported that transition from AF to F involves in the slight change of Fe moment from 3.3 μB to 3.2 μB [52–54]. Furthermore, upon phase transition from AF to F, the magnetic Rh can benefit from the exchange with ferromagnetic iron neighbors by lowering down the system free energy

7

that promote the phase transition from AF to F. As such, the Tc (AF-F) can be reduced, resulting in a little smaller thermal hysteresis compared with the estimated value. Under an external magnetic field, H a , the phase transition from AF to F can be promoted due to Zeeman energy of external field acting on magnetic Rh, which is m( Rh) · H a . On the other hand, the external field stabilizes the F phase due to the same Zeeman energy which retards the phase transition from F to AF. As a results of it, the thermal hysteresis, Tc = Tc (AF-F) − Tc (F-AF), will not be affected by the external field as observed although it does alter the phase transition temperature. It is, therefore, plausible to conclude that the change of magnetic state of Rh is the dominating origin of thermal hysteresis found in FeRh thin films.

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6. Summary and outlook

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We firstly propose and experimentally demonstrate the change of magnetic state of Rh is the origin of giant MCE and thermal hysteresis in FeRh epitaxial thin films. The findings help to improve the performance of FeRh as a working medium for magnetic refrigeration and as a recording medium for magnetic recording. Other than the conventional applications in magnetic recording and room temperature magnetic refrigeration, FeRh can also be used as a working medium for hyperthermia due to its chemical stability, non-toxic nature, giant MCE and having a tunable Tc close to human body temperature. FeRh nanoparticles can be prepared by various ways [64–68]. Such nanoparticles will have a magnetically soft shell due to surface effect discovered in this study and an antiferromagnetic core. If the FeRh nanoparticles are bonded with tumor-targeting ligands, they can be attached to tumor cells under the direction of a gradient field because of the magnetically soft shell. With giant magnetic entropy change, during a fast demagnetization process, the tumor cells can be heated considerably above their living temperature of 315–317 K [69], resulting the direct killing of tumor cells without side effects. This may open a new field for further development.

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