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The magnetocaloric effect in Er2Fe17 near the magnetic phase transition

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2013 J. Phys.: Condens. Matter 25 496010 (http://iopscience.iop.org/0953-8984/25/49/496010) View the table of contents for this issue, or go to the journal homepage for more

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IOP PUBLISHING

JOURNAL OF PHYSICS: CONDENSED MATTER

J. Phys.: Condens. Matter 25 (2013) 496010 (6pp)

doi:10.1088/0953-8984/25/49/496010

The magnetocaloric effect in Er2Fe17 near the magnetic phase transition 1 , Pedro Gorria2 , Jorge S´ ´ Pablo Alvarez-Alonso anchez Marcos3 , 4 ´ A Blanco5 Jos´e L S´anchez Llamazares and Jesus 1

Departamento de Electricidad y Electr´onica, UPV/EHU, Bo Sarriena, s/n, E-48940 Leioa, Spain Departamento de F´ısica, EPI, Universidad de Oviedo, E-33203 Gij´on, Spain 3 Departamento de Qu´ımica F´ısica Aplicada, Universidad Aut´onoma de Madrid, Cantoblanco, E-28049 Madrid, Spain 4 Divisi´on de Materiales Avanzados, IPCyT, 78216, San Luis Potos´ı, Mexico 5 Departamento de F´ısica, Universidad de Oviedo, Calvo Sotelo, s/n, E-33007 Oviedo, Spain 2

E-mail: [email protected]

Received 16 August 2013, in final form 2 October 2013 Published 8 November 2013 Online at stacks.iop.org/JPhysCM/25/496010 Abstract Recent investigations in R2 Fe17 intermetallic compounds have evidenced that these materials present a moderate magnetocaloric effect (MCE) near room temperature. A series of accurate magnetization measurements was carried out to show that the value of the demagnetizing factor has a significant influence on the absolute MCE value of Er2 Fe17 . In addition, the critical exponents determined from heat capacity and magnetization measurements allow us to describe the field dependence of the observed MCE around the Curie temperature. (Some figures may appear in colour only in the online journal)

1. Introduction

others [12–16]. However, material processing with high R-content will be somewhat more expensive than for M-based alloys, so activity in searching for materials with low rare earth content exhibiting MCE has dominated research in this field during recent years. In particular, the Fe-rich R2 Fe17 compounds have recently attracted moderate interest due to the MCE shown around room temperature, especially those with collinear ferromagnetic alignment of both Fe and R magnetic sublattices, such as Pr2 Fe17 and Nd2 Fe17 , with values of the magnetic entropy change of 1SM ≈ −6 J kg−1 K−1 [17–19]. In order to magnetically characterize a material, we must inevitably pay attention to the demagnetizing field, which reduces the applied field H to Hint = H − NM, where Hint represents the inner magnetic field, N the demagnetizing factor, and M the magnetization of the material. Recently, some studies on the effect of the demagnetizing field on the adiabatic temperature change and magnetic entropy change [20, 21] have been reported; however, the effect on the magnetic entropy change still remains unclear. Neglecting the demagnetization field could lead to erroneous results in some cases, such as a reduction of the value of 1SM and a shift of

The magnetocaloric effect (MCE) offers around 30% better energy efficiency for room temperature refrigeration than conventional techniques based on the Peltier effect, and avoids the use of environmentally detrimental gases [1, 2]. For this reason this effect is important for its potential applications in domestic and industrial refrigeration markets, the prospects of a breakthrough into commercial use being closer than ever [3–5]. The MCE is a magneto-thermodynamical property characterized by isothermal entropy change (1SM ) and adiabatic temperature change as a result of variation of the applied magnetic field on the sample [6]. This property has been extensively and intensively investigated over recent decades [1–3, 7]. The seminal work of Pecharsky and Gschneidner in this field achieved a very large entropy change (−1SM ≈ 18 J K−1 kg−1 under a magnetic field variation from 0 to 5 T at 273 K) in Gd5 Si2 Ge2 [8]. This finding boosted a great deal of activity that still remains cutting-edge research into what have been called giant magnetocaloric materials. Since then, the MCE has been studied in many other systems, such as rare earth (R)-transition metal (M) compounds [1, 2, 9, 10], metallic glasses [7, 11], and 0953-8984/13/496010+06$33.00

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J. Phys.: Condens. Matter 25 (2013) 496010

the temperature corresponding to the peak value of 1SM to higher temperatures [20–24]. On the other hand, the role of critical phenomena has been stressed in materials showing the MCE [25, 26]. In fact, the critical exponents related to a magnetic phase transition correspond to the exponents in the power laws of the deviations of the thermodynamic quantities from their values at the Curie temperature, TC . Thus, they characterize a magnetic transition from an ordered magnetic configuration to a disordered one: α indicates the temperature dependence of the heat capacity around TC , β describes how the ordered moment grows when the temperature decreases below TC , δ describes the curvature of the M(H) curve at TC , and γ describes the divergence of the magnetic susceptibility at TC [27]. This investigation is focused on two main issues: first, we have studied the influence of the demagnetization factor on the determination of the magnitude of the MCE in Er2 Fe17 ; second, the magnetic field dependence of the magnetic entropy change around TC has been determined from the critical exponents of the ferri-to-paramagnetic transition for the Er2 Fe17 compound.

Figure 1. Observed (dots) and calculated (solid line) x-ray powder diffraction patterns collected at room temperature for Er2 Fe17 with Mo-radiation (Cu-radiation in the inset). The vertical bars indicate the positions of the Bragg diffraction reflections belonging to the hexagonal Th2 Ni17 crystal structure. The observed–calculated difference is depicted at the bottom.

The magnetic entropy change, 1SM (T, H), due to a variation of the applied magnetic field from an initial value H = 0 to a final value H under isothermal conditions was calculated using the Maxwell relation Z H ∂M(t, h) 1SM (T, H) = dh. (1) ∂t 0 t=T

2. Experimental methods and theory As starting materials for the preparation of Er2 Fe17 as-cast pellets, pieces of commercial (Goodfellow) 99.9% pure elements were mixed in the nominal molar ratio 2:17. The ingots (4 g each) were prepared by the common arc melting technique under controlled Ar atmosphere, being re-melted at least three times to ensure their homogeneity. An excess of 5% Er was added to compensate for the evaporation losses during melting. Each specimen was wrapped in tantalum foil and sealed under vacuum in a quartz ampoule and annealed for one week at 1373 K. The annealing was followed by water quenching of the quartz ampoules directly from the furnace. An irregular-shaped piece was used for magnetic measurements. The lattice parameters were determined using a highresolution powder diffractometer (Seifert model XRD3000) operating in Bragg–Brentano geometry using both Cu (λ = ˚ and Mo (λ = 0.7071 A) ˚ Kα radiation. The scans 1.5418 A) ◦ in 2θ were collected between 2 and 50◦ (Mo) and 10◦ and 160◦ (Cu) with steps of 12θ = 0.025◦ and counting times of 2 s per point. Analysis of the diffraction patterns was carried out with the Fullprof suite package [28]. Magnetic measurements were performed using the vibrating sample magnetometer (VSM) option of a Quantum Design PPMS-9 T platform. The temperature dependence of the magnetization, M(T), curves were measured under different values of the applied magnetic field, µ0 H = 5 mT, 100 mT and 1 T. The isothermal magnetization, M(H), curves were measured up to µ0 H = 5 T, and in the temperature range 2–350 K with T-steps of 10 K or 5 K for temperatures far from or near TC , respectively. In addition, M(H) loops between µ0 H = ±5 T were measured at six selected temperatures between 10 and 310 K in order to evaluate the evolution of the coercive field with temperature.

The refrigerant capacity (RC) is usually estimated in three complementary ways [29]: (a) RC-1 = |1SM |Peak δTFWHM , with δTFWHM = Thot − Tcold corresponding to the temperatures of the full width at half maximum of the |1SM | (T) curve; R Thot (b) RC-2 = Tcold |1SM |(T) dT; (c) RC-3 = max{|1SM |(Tb )(Tb − Ta )} for Ta and Tb satisfying 1SM (Ta ) = 1SM (Tb ) and Tb > Ta .

3. Results and discussion 3.1. Crystal structure Figure 1 depicts the x-ray powder diffraction pattern of Er2 Fe17 collected at room temperature using Mo-radiation, and the inset that corresponding to Cu-radiation. We have used as x-axis representation the interplanar distance, d, in order to facilitate the comparison of both patterns measured with different wavelengths. The observed intensity peaks correspond to the Bragg reflections of a hexagonal Th2 Ni17 -type crystal structure. The estimated cell parameters ˚ and c = 8.267 ± 0.001 A ˚ for the are a = 8.454 ± 0.001 A ˚ and c = 8.263 ± Mo-radiation, and a = 8.453 ± 0.001 A ˚ for the Cu-radiation. These values are in excellent 0.001 A agreement with those obtained from previous neutron powder diffraction experiments [30]. 2

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J. Phys.: Condens. Matter 25 (2013) 496010

Figure 3. The magnetic hysteresis loop measured at T = 10 K. The inset at the bottom right shows a zoom of the low magnetic field region, and that at the upper left the temperature evolution of HC . Lines connecting points are guides for the eyes.

Figure 2. Temperature dependence of the magnetization, M(T), under different values of the applied magnetic field. Data were obtained from isothermally measured M(H) curves. The inset shows the linear fit of the temperature at which the kink point of the magnetization is observed for low applied magnetic field values.

calculated the value of N through two different procedures: (i) the kink point method [34] which derives from Wojtowicz and Rayl’s one for obtaining the value of TC ; and (ii) by estimating the angle between an experimental and an ideal hysteresis curve for low magnetization values [35]. The calculated values are N = 0.28 and 0.25, respectively. Note that these values are lower than the theoretical value for a sphere (N = 1/3), but similar to those for a magnetized cylinder along its axis with m ≈ 1, a prolate ellipsoid with m ≈ 1.3 or an oblate ellipsoid with m ≈ 1.8 (m is the ratio of length to diameter in cylinders, and the major axis is m times the minor axis for ellipsoids) [36–38]. Anyway, we are not able to distinguish between a cylindrical- and an ellipsoidal-type shape from the determination of the demagnetizing factor. In addition, the temperature dependence of the coercive field was obtained from the M(H) loops in order to discard any effect of the magnetic hysteresis on the evaluation of the magnetocaloric effect different from that of the demagnetizing field. We show in figure 3 the hysteresis loop measured at T = 10 K. The maximum value for HC ≈ 15 mT (see the inset at the bottom right in figure 3) corresponds to the lowest measuring temperature; it decreases rapidly for higher temperatures (see the inset at the upper left in figure 3), being lower than 1 mT within the temperature range in which the magnetocaloric effect has been studied (see section 3.3).

3.2. Temperature and applied magnetic field dependences of the magnetization The temperature dependence of the magnetization shows remarkable differences as the value (constant) of the applied magnetic field is varied. In the low magnetic field range, the magnetization increases almost linearly on heating from the low-temperature region (see figure 2), and then falls to almost zero value at TC ≈ 300 K. However, for applied magnetic field values over 0.2 T a broad maximum between 100 and 250 K appears, and the decrease of the magnetization is much less abrupt around TC . The ferrimagnetic character of the Er2 Fe17 compound explains the existence of these features: the magnetic field and temperature dependences of the magnetic moments of the Fe and Er sublattices follow a different trend [30]. We estimated the Curie temperature using the method proposed by Wojtowicz and Rayl [31]: at a certain value of the applied magnetic field, the change from the long-range to short-range ordered magnetic states occurs at the transition temperature Tt (note that this temperature, Tt , depends on the applied magnetic field, and should not be mixed up with TC ); the magnetization equals H/N at this temperature and N represents the demagnetizing factor. Thus, Wojtowicz and Rayl deduced that Tt (H) = 1 − 1/3[H/MT=0 K N]2 .

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3.3. The magnetocaloric effect

Extrapolating Tt (H) to H = 0 (see the inset in figure 2), we found that TC = 300 ± 0.1 K, which closely agrees with the values obtained by other methods [32, 33]. With the aim of investigating the effect of the demagnetizing factor N on the magnetocaloric properties, we

Figure 4 shows the temperature dependence of the magnetic entropy change, |1SM |, for the Er2 Fe17 alloy using the previously calculated values for the demagnetizing factor: N = 0.25 (figure 4(a)) and N = 0.28 (figure 4(b)). Data 3

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J. Phys.: Condens. Matter 25 (2013) 496010

Figure 5. The internal magnetic field dependence of the refrigerant capacity, RC. For each definition of RC the curves corresponding to the three values of N are plotted for comparison.

This model does not consider the demagnetizing factor, hence we have analysed the effect of including N in the calculations; in our case, N = 0, 0.25 or 0.28 gives the same value, within the error, n = 0.69 ± 0.01. It is worth noting that the obtained value almost matches that corresponding to the mean field theory (n = 2/3). We also have studied the effect of the demagnetizing factor on the refrigerant capacity (see figure 5). Due to the temperature limit of the magnetometer (T = 350 K), the temperature corresponding to the hot reservoir (i.e., Thot for the definition of both RC-1 and RC-2, and Tb for RC-3) is exceeded for µ0 1H ≈ 4 T. Generally speaking, the RC values for Er2 Fe17 (regardless of the demagnetizing field) are smaller than those found in other R2 Fe17 materials undergoing second-order magnetic phase transitions [17–19]. This is a consequence of the reduced net magnetic moment of Er2 Fe17 due to the ferrimagnetic character of the alloy [30]. Concerning the effect of the demagnetizing factor on the magnetic field dependence of RC, we observed that the RC values are larger for N = 0.25, even though the value of |1SM |Peak is almost the same for either N = 0.25 or 0.28; this difference comes out of the wider |1SM | (T) of the former N value (see figure 3). For N = 0 the values are lower, as can be expected from the |1SM |Peak (H) curves shown in the inset of figure 4. It is worth noting that the present findings in Er2 Fe17 show that the correction of the magnetization curves with an appropriate demagnetizing factor gives rise to only slight changes in the magnetocaloric response. However, neglect of the demagnetizing correction could give rise to erroneous estimation of the MCE, depending on the shape of the sample and the direction of the applied magnetic field, because the value of N affects the MCE through the modification of the M(H) curves.

Figure 4. The temperature dependence of |1SM | under different internal magnetic field changes. The values N = 0.25 (a) and N = 0.28 (b) have been used for the demagnetizing factor. The inset shows the internal magnetic field dependence of |1SM | for the different N values. Lines are guides for the eyes.

corresponding to N = 0 can be found in [30]. The |1SM |(T) curves exhibit a peak at T ≈ 300 K, which corresponds to a direct magnetocaloric effect due to the magnetic transition between the ferrimagnetic and the paramagnetic state. The maximum of |1SM |(T) for µ0 H = 5 T is 3.7 J kg−1 K−1 in both cases, in good agreement with the value reported in [39]. Although Er2 Fe17 exhibits an inverse MCE with its maximum located at T ≈ 40 K, originated by the different magnetic field and temperature dependences of the Er and Fe magnetic sublattices at low temperature [30], in this work we will focus only on the ferri-to-paramagnetic transition. As can be seen in the inset of figure 4, where the internal magnetic field dependence of the |1SM |Peak is plotted, the values are slightly larger when the demagnetizing field is considered for the calculations. This coincides with what other authors have found for the adiabatic temperature change [20, 40]; however, we do not observe any shift to higher temperature in the position of the |1SM |Peak , as previously reported for pure Gd [41]. Franco et al have shown that for second-order magnetic phase transitions the magnetic entropy change at TC follows a power law with the exponent n as the main parameter, which, in turn, is related to the critical exponents of the magnetic phase transition [25] according to the following expression: n=1+

β −1 . β +γ

3.4. Critical behaviour Once the magnetization versus internal magnetic field curves have been obtained, we can focus on the critical behaviour

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J. Phys.: Condens. Matter 25 (2013) 496010

around the Curie temperature, TC . The exponent δ, related to the magnetic field dependence of the magnetization at TC , M = mH 1/δ (m is a factor proportional to the saturation magnetization), was estimated from the M(H) isothermal curves closest to the order temperature, TC , and the empirical relation [42] TC = T − A[δ(TC ) − δ(T)]

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with A being a sample-dependent constant. The obtained value was δ = 5.1 ± 0.2. Fitting the peak of the heat capacity versus temperature at zero-magnetic field (raw data taken from [30]) with the equation [43] A1 + B1 α(−ε −α − 1) A2 Cp = + B2 α(ε−α − 1) Cp =

T < TC T ≥ TC

(5) (6)

where ε = (T −TC )/TC , we obtained the critical exponent α = −0.59 ± 0.04. Once the values for the α and δ exponents are determined, we can estimate those for β and γ , thanks to the relationships given by α = 2(1 − β) and δ = 1 + γ /β [44], as β = 0.42±0.01 and γ = 1.74±0.08. Regarding equation (3), and using these values for β and γ , the exponent n is 0.73, which agrees rather well with the value given in section 3.3 (n = 0.69 ± 0.01). In figure 6(a) we represent the Arrott plots (β = 0.5 and γ = 1); note that the lines are no longer parallel, indicating that the mean field theory does not fit properly (as expected from the critical exponents). We examined the critical behaviour of the transition by the modified Arrott–Noakes equation of state [45] (Hint /M)1/γ = (T − TC )/T1 + (M/M1 )1/β

Figure 6. (a) Arrott plots for the demagnetizing factor N = 0. (b) Modified Arrott plots for the demagnetizing factor N = 0.25. The inset depicts the temperature dependence of the spontaneous magnetization (zero-field) and the inverse of the initial susceptibility (see the text for details).

[18, 30, 47, 48] play an important role in the shape of the M(H) curves around the magnetic transition temperature that could strongly affect the values of the critical exponents. A similar trend has also been observed in other Fe-rich alloys including metallic glasses [49, 50], where the Fe–Fe interatomic distances drive the magnetic coupling between Fe atoms. Therefore, additional measurements in other Fe-based magnetocaloric materials with and without magneto-volume anomalies will be needed to shed light on this topic.

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with Hint the internal field. The correct choice of the critical exponents leads to straight and parallel isothermal M 1/β versus (Hint /M)1/γ curves over a wide range of Hint /M values in the surroundings of TC [46]. Furthermore, the extrapolation of the isothermal M 1/β versus (Hint /M)1/γ curve at T = TC from the linear regime crosses through the origin of coordinates. In figure 6(b) we show the modified Arrott plots using the values of the critical exponents previously calculated. Besides that, we can obtain the temperature dependence of the spontaneous magnetization, MS (for T ≤ TC ), and that of the inverse initial susceptibility, χ0−1 (for T ≥ TC ), if we take into account the crossover point of the isothermal M 1/β versus (Hint /M)1/γ curves on the vertical axis (through Hint = 0) corresponding to the high field linear fit (for (Hint /M)1/γ < 0.2 T the curves bend to zero, as is usual for low magnetic fields [46]). The inset of figure 6(b) shows the plot of MS and χ0−1 as a function of temperature. From the linear fit of the χ0−1 versus T curve a paramagnetic Curie temperature of θP = 303 ± 1 K is obtained. Importantly, the notable deviation observed in the values of the critical exponents β and γ with respect to those corresponding to the mean field theory could be related to the Invar character of R2 Fe17 alloys. The magnetovolume anomalies observed in these intermetallic alloys

4. Summary and conclusions In this work, we have investigated the effect of the demagnetizing factor on both the magnetic entropy change and the refrigerant capacity in Er2 Fe17 . We have found that the magnetic entropy change is undervalued if the demagnetizing factor is not considered, even though the exponent n corresponding to the magnetic field dependence of |1SM |Peak remains almost unchanged. Accordingly, the refrigerant capacity increases when corrections for demagnetization field effects are properly taken into account. In addition, the critical exponents determined from magnetic, M(H, T), and heat capacity, Cp , measurements agree with the magnetic field dependence of |1SM |Peak . Further investigations in other magnetocaloric materials exhibiting second-order magnetic phase transitions are needed to elucidate a possible correlation 5

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between the values of the critical exponents at the magnetic ordering temperature, the maximum value of the magnetic entropy change and the shape of the |1SM |(T) curves.

Acknowledgments Financial support from the Spanish MINECO (research project MAT2011-27573-C04) is acknowledged. JLSLl acknowledges the support received from CONACYT, Mexico, under the project CB-2010-01-156932, and Laboratorio Nacional de Investigaciones en Nanociencias y Nanotecnolog´ıa (LINAN, IPICyT). The SCTs at the University of Oviedo, the technical support received from MSc G J Labrada-Delgado and B A Rivera-Escoto (DMA, IPICyT) and the assistance of Dr I de Pedro (CITIMAC, Univ. Cantabria) with some of the magnetic measurements are also acknowledged.

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