Giant magnetocaloric effect in Co₂FeAl Heusler alloy nanoparticles

Heusler alloys (HAs) are materials of enormous interest due to their multifunctional properties including magnetoresistance (MR) [1], half-metallicity (i.e. 100 spin polarization at the Fermi edge) [2–7], spin filtering [8], spin injection [9], shape memory [10, 11] and thermoelectric effect [12]. These half-metallic ferromagnets exhibit a unique band structure at the Fermi energy (E_F), where one spin channel shows metallic nature and another spin channel displays a non-conducting or semiconducting gap. An interesting character of HAs is that the structural, magnetic and magnetocaloric properties can easily be tuned by controlling their elemental compositions or partial substitution by other elements [13–16]. In 1983, de Groot et al, firstly reported such behavior in NiMnSb HA [17]. The X₂ YZ (X/Y: transition metals; Z: main group element) Heusler compounds, generally known as full-HAs, may be crystalized in the cubic L2₁ (i.e. fully-ordered) structures under the space group ${\text{Fm}}\bar 3{\text{m}}\,\left( {\# 225} \right)$ [18]. However, the ideal L2₁ phase is difficult to achieve, especially in the nanoscale regime; therefore, they are generally crystalized in either partial-disordered (i.e. B2 type) [19] or fully disordered (i.e. A2 type) [20] phases. The half-metallic nature, large magnetic moment and high T_c of Heusler compounds (specially, in Co₂-based), make them potential candidates for spintronic applications [20–22]. Additionally, the magnetocaloric (MC) effect has also been explored in HAs [23–25]. The materials that can potentially be used as magnetic refrigerants near to or above room temperature are of great interest [13, 26, 27]. In this regard, materials exhibiting a giant magnetocaloric effect (GMCE) would be promising [16, 24, 28–30]. GMCE was initially observed in Gd₅(Si₂Ge₂) [29, 31]. Nevertheless, the high cost of Gadolinium makes it unsuitable for commercial magnetic refrigerators. Moreover, there are many other key challenges from the materials perspective to improve performance and implementation in devices [32]. The peak of the entropy change ($- \Delta {S_{\text{M}}}$) was found to be significantly higher in HAs [24, 33, 34] with first-order magnetic phase transition, which is necessary for efficient cooling. However, thermal and magnetic hysteresis present in such systems limits their practical usefulness. This further motivates researchers to search for other Heusler based materials. Lately, a few works on the MC properties of Co-based HAs have been reported [13, 35, 36]. They exhibit second-order phase transition and are found to be usable as magnetic refrigerants due to their broad working temperature range and absence of thermal and magnetic hysteresis. The spin orbit coupling is stronger in Co-based HAs [37]; therefore, the magnetocrystalline anisotropic exchange interaction might be responsible in their magnetic ordering. Practically, there is no system available which strictly follows the Stoner's itinerant model or Heisenberg theory for the localized spin. No particular theory can completely explain the magnetism of such 3d intermetallic compounds. Therefore, it is necessary to explore their magnetism near the phase transition.

As a young research field, earlier studies on Heusler nanoalloys have been focused on their synthesis, structure, and magnetic characterizations (see refs. [20, 38], and the references therein). Consequently, further investigations are required to verify their technical importance in magnetic refrigeration and microactuators. Previously, we have reported the size modulated structural and magnetic properties of Co₂FeAl (CFA) nanoparticles (NPs). CFA-NPs crystallized in cubic A2-disorder phase. Their microstructural analysis reveals that NPs are spherical and crystalline in nature with an average particle size of 16 nm. Moreover, they exhibit pronounced enhancement in M_s and T_c as compared with bulk counterpart. A record magnetic moment and T_c of 6.5 µ_B/f.u. (25% higher than the bulk) and 1261 K (15% higher than the bulk), respectively, have been observed [20]. As a rule of thumb, to get a huge MC response, the material should have a higher magnetic moment [27]; therefore, a large magnetic entropy change ($- \Delta {S_{\text{M}}}$) is expected in CFA-NPs. Here, we report the MC effect of CFA-NPs, near the FM-PM phase transition.

CFA-NPs were synthesized using the co-precipitation and thermal deoxidization method. The precursor salts were CoCl₂ · 6H₂O (99%), Fe(NO₃)₃ · 9H₂O (99%) and Al₂(NO₃) · 18H₂O (98%). The detailed description of the sample preparation was described in our previous report [20]. NPs were analyzed by x-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED) techniques. MC properties were studied using high-temperature vibrating sample magnetometer of Lake Shore Cryotronics. In magnetization measurements, the powder sample was placed into a disposable boron nitride cup as provided by Lake Shore Cryotronics.

The simulated and experimental XRD data of CFA-NPs are shown in figure 1. The prominent Bragg peaks of (220), (400) and (422) establish that the present system is crystallized in A2 disordered phase, but not in L2₁ phase [20]. Note that (111) and (200) superlattice reflections, which are absent in our case, are required to conclude the L2₁ structure [7]. The lattice constant, as calculated from the noticeable (220) Bragg peak is 5.72 Å. This closely matches with the bulk value [39].

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The NPs are analyzed using HRTEM imaging (figure 2). As evident from figure 2(a), particles are nearly spherical in shape. The image is further examined for particle size distribution using the ImageJ software. The size-distribution histogram, along with the fitted Gaussian profile, is shown in figure 2(b). According to the histogram, the NPs are of sizes 16 ± 10 nm. The SAED pattern (see figure 2(c)) features concentric rings accompanied by dots. This indicates that particles are crystalline in nature. The image of a single NP with an even higher resolution is shown in figure 2(d). The presence of observable lattice fringes confirm the high crystallinity of the particles. An enlarged portion of the image has been presented in the inset of figure 2(d). The interplanar spacing of 2.022 Å is equivalent to the (220) plane of the cubic phase of CFA-NPs, and is consistent with the XRD results.

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Thermomagnetic zero-field-cooled (ZFC) and field-cooled (FC) curves of CFA-NPs, measured in a 500 Oe field, in the temperature range of 300 K–1273 K, are shown in figure 3. Both the ZFC and FC curves of CFA are smooth and exhibit a clear FM to PM phase transition around the T_c. The M(T) curves resemble a continuous or second order FM-PM phase transition [40]; this argument is further supported by the absence of the thermal hysteresis in the present system. This motivated us to further investigate its phase transition and MC properties.

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The T_c is calculated from the peak value of dM/dT vs temperature (T) curve, and is found to be 1261 K (see the inset of figure 3). To analyze the MC effect of CFA-NPs, isothermal magnetization M(H) is investigated at various temperatures with a temperature interval of 2 K around the T_c, as shown in figure 4(a). The magnetization (M) increases gradually with the field up to 4 kOe and thereafter approaches a constant value. Then, the M value decreases with increasing T, suggesting the magnetic transition from a low-T ferromagnetic to a high-T paramagnetic phase. The large change in M at 1251 K–1253 K isotherms indicates the possibility of large MC effect of CFA-NPs around this temperature range. In order to see the hysteresis losses and their effects in MC properties, we have measured M(H) isotherms in a decreasing field (14 kOe–0 Oe) mode (not shown here), and have not found any difference as compared with the M(H) isotherms in the increasing field (0 Oe–14 kOe) mode. The magnetization curves taken during heating and cooling processes near the T_c coincide with each other, exhibiting a negligible hysteresis for all the temperature ranges. Such reversibility of the magnetic transition is essential from the application point of view in magnetic refrigeration.

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In order to see whether the Landau mean-field theory of the phase transition is valid for CFA-NPs system, a conventional Arrott plot (M² vs H/M) [41] is constructed as shown in figure 4(b). The Arrott plot should generate a set of parallel straight lines for the mean field values of the critical exponents $\beta = 0.5\,$ and $\gamma = 1$. The line passing through the origin should resemble the isotherm exactly at the critical temperature (T_c). As seen from figure 4(b), the Arrott plot does not generate parallel straight lines. Moreover, a substantial non-linearity with downward curvature can be seen even at the high field region. Thus, the mean field theory cannot explicate the phase transition of the present system. From Banerjee's criterion [42], the Arrott curves exhibiting a positive slope specify that the FM-PM phase transition is of second order. The magnetic entropy change, $- \Delta {S_{\text{M}}}$ is calculated by using Maxwell relation [24]:

$$\begin{equation}\,\,\,\,\,\,\,\,\,\,\Delta {S_{\text{M}}} = S\left( {T,H} \right) - S\left( {T,O} \right) = \mathop \int \limits_0^H {\left( {\frac{{\partial M}}{{\partial T}}} \right)_H}\,{\text{d}}H.\end{equation} \tag{ 1 }$$

As the experimental values of magnetization data are only available at discrete values of temperature, the integral in this equation may be replaced by the summation. It can be understood from equation (1) that the magnetic entropy change will be maximum only when ∂M/∂T is maximum. The sign of $- \Delta {S_{\text{M}}}$ is determined by the sign of ∂M/∂T. When it is positive, it will be called a conventional MC effect [43]. The change in magnetic entropy ($- \Delta {S_{\text{M}}}$) with respect to T is shown in figure 5. The magnetic entropy change show a positive anomaly at 1252 K. A large value of $- \Delta {S_{\text{M}}}$ ∼15 J kg⁻¹ K⁻¹ is detected for change of the magnetic field of 14 kOe.

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The obtained value of $- \Delta {S_{\text{M}}}$ is comparable in magnitude with the peak value of another GMCE material Gd₅Si₂Ge₂ [29], which is very well known in the field of refrigeration technology. It is much larger, i.e. at least three times the peak value of expensive Gd [29]. Our results show higher or at least comparable MC values as compared to other Heusler materials such as Fe₂CoAl [44], Mn_1−x Cr_x CoGe [45], MnCo_1−x Zr_x Ge [46] and Mn_1-xAl_xCoGe [47]. We also compare our results to the Heusler based thin films (see table 1). As a matter of fact, the small mass of thin films makes it challenging to evaluate MC properties quantitatively, particularly the adiabatic temperature change (D T_ad). Because of this, a limited number of publications are available on the MC properties of thin films of metals and compounds. Most of them are concerned with the study of MC effect in Ni–Mn–X (X = Ga, In, Sn) thin films. Recarte et al [48] deposited NiMnGa film with thickness of 0.4 µm onto alumina substrate. The film exhibited a magnetostructural phase transition at 346 K, and the magnetic entropy change ($- \Delta {S_{\text{M}}}$) was found to be 8.5 J kg⁻¹ K⁻¹, at the 60 kOe field. Niemann et al [49] observed inverse MC effect in epitaxially grown metamagnetic Ni–Co–Mn–In film (0.2 µm) on MgO (001) substrate. The resulting $- \Delta {S_{\text{M}}}$, was −8.8 J kg⁻¹ K⁻¹ at 353 K for the magnetic field change of 90 kOe. Lately, Yüzüak et al [50] detected inverse MCE in epitaxial Ni–Mn–Sn/MgO thin films of 200 nm thickness. The $- \Delta {S_{\text{M}}}$ and relative cooling power (RCP) were −1.5 J kg⁻¹ K⁻¹ and 33.9 J Kg⁻¹ at 10 kOe field, respectively. A comparison of all the values, as discussed above, are tabulated in table 1.

Table 1. A comparison of the magnetic entropy change ($- \Delta {S_{\text{M}}}$), RCP, Δ H, T_c, and nature of the phase transition in present system and other magnetocaloric materials.

Materials		$- \Delta {S_{\text{M}}}$ (J kg−1 K−1)	RCP (J kg−1)	Field range (ΔH) in kOe	Tc (K)	Nature of the phase transition	Refs.
Heusler alloy NPs	Co2FeAl	∼15	89	14	1261	Second order	Present work
	Fe2CoAl	2.65	44	20	830	Second order	[44]
Bulk Heusler alloys	Mn1−x Crx CoGe	∼28.5		50	322	First order	[45]
	MnCo1−x Zrx Ge	7.2	266	50	274	First order	[46]
	Co2Cr0.25Mn0.75Al	3.5	∼285	90	720	Second order	[13]
	Mn1−x Alx CoGe	12	303	50	286	First order	[47]
Giant MC Materials	Gd5Si2Ge2	18		20	276	First order	[29]
	(MnNiSi)1−x (FeCoGa)x	25	191.8	50	323	First order	[16]
	Fe-Rh	20	—	20		First order	[30]
MCE in Heusler thin films	NiMnGa	8.5					[48]
	Ni–Co–Mn–In	−8.8	—	90	353	—	[49]
	Ni–Mn–Sn	−1.5	33.9	10	∼270	—	[50]
Others	Fe68.5Mo5Si13.5B9Cu1Nb3	∼1.1	63	15	∼475		[27]
	Fe50Rh50 particles	9.7	230	30	—	First order	[55]

As seen from the inset of figure 5, the $- \Delta {S_{\text{M}}}$ peak height is very sensitive to the field change (ΔH) from H = 5 kOe onwards. It increases linearly relative to ΔH and the width of the peak decreases. RCP is an important parameter to evaluate the usefulness of the material for magnetic refrigeration. This parameter is also used for a comparison with other MC materials. It is a measure of the amount of heat transferred between the hot and cold reservoirs in an ideal refrigeration cycle and defined as: RCP = $- \Delta {S_{{{\text{M}}_{{\text{peak}}}}}} \times \Delta {T_{{\text{FWHM}}}}$, where $\Delta {T_{{\text{FWHM}}}}$ represents full width at half maximum of the $- \Delta {S_{\text{M}}}$ vs T curve [51]. The large value of RCP of 89 J Kg⁻¹ (see figure 6) was observed at the change of magnetic field of 14 kOe, which signifies a large heat conversion capacity in a refrigeration cycle. $\Delta {T_{{\text{FWHM}}}}$ also represents the span of working-temperature, which is found to be around ∼6 K in the present system. Zverev et al [52] and Engelbrecht et al [53] previously suggested that a material having a broad peak of $- \Delta {S_{\text{M}}}$ is much better than that of materials with a sharp peak of magnetic entropy change for cooling applications. Therefore, in order to fine-tune the T_c and the temperature span of the CFA-NPs, studies of composition optimization are in progress. The refrigeration capacity (RC) and entropy change ($- \Delta {S_{\text{M}}}$) have shown a linear behavior (see figures 5 and 6) with respect to magnetic field. The increasing nature of the peak value of the entropy change with ΔH can be suitable for Ericsson-cycle refrigeration applications [54]. And therefore, the study of magnetic and MC properties on Co₂-based HAs might be useful for the application of multistage magnetic refrigeration [13]. From a simple linear extrapolation of our data to 50 kOe, will give an approximate value of RCP = 305 J Kg⁻¹, and $- \Delta {S_{\text{M}}}$ = 50 J kg⁻¹ K⁻¹. In comparison to the recently reported high-T MC material Co₂Cr_1−x Mn_x Al HA [13], having T_c of 720 K on the same field scale (i.e. 50 kOe), our value of entropy change ($- \Delta {S_{\text{M}}}$) is 20 times larger and the RC value is slightly larger or at least comparable with that material.

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Franco et al [56] proposed a master curve that is used to see the nature of the magnetic phase transition. This curve can be plotted as the normalized entropy change ($\Delta {S{^{^{\prime}}}_{\text{M}}}$) where $\Delta {S{^{^{\prime}}}_{\text{M}}} = \Delta {S_{\text{M}}}/\Delta S_{\text{M}}^{{\text{peak}}}$, with respect to the rescaled temperature (θ) defined by

$$\begin{equation}\theta = \left\{ {\frac{{ - \left( {T - {T_{\text{c}}}} \right)}}{{({T_{{\text{r}}1}} - {T_{\text{c}}})}}{ },{\text{ for }}T \leqslant {T_{\text{c}}};{ }\frac{{\left( {T - {T_{\text{c}}}} \right)}}{{({T_{{\text{r}}2}} - {T_{\text{c}}})}}{ },{\text{ for }}T > {T_{\text{C}}}} \right\}.\end{equation} \tag{ 2 }$$

In equation (2), T_c represents the temperature at which $\Delta S_{\text{M}}^{{\text{peak}}}$ is attained. The reference temperatures ${T_{{\text{r}}1}}$ and ${T_{{\text{r}}2}}$ below and above the T_c, are taken as the temperatures corresponding to $\frac{1}{2}\Delta S_{\text{M}}^{{\text{peak}}}.{ }$ In figure 7, all the curves ($\Delta {S{^{^{\prime}}}_{\text{M}}}$ vs θ) of CFA-NPs, taken at different magnetic fields, are merged into a single universal curve (see the inset of figure 7 for a comparison), which confirms a second-order magnetic phase transition. Such types of phenomenological curves were previously reported for materials exhibiting second-order phase transition [56–58]. The present study suggests a possibility of using this material in high temperature cooling applications such as multi-stage magnetic refrigeration, where cooling from high temperature is desired in more than one stage [59]. Such multistage refrigerators are highly suitable in industry, where the low temperature of one stage acts as the upper temperature for the next stage [59, 60].

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We have performed a detailed investigation on the structure, magnetic phase transition and magnetocaloric effect in Co₂FeAl NPs. The positive slope of the Arrot curve suggests second order FM to PM phase transition near the T_c. The normalized entropy change ($\Delta {S{^{^{\prime}}}_{\text{M}}}$) with respect to the rescaled temperature (θ) at different fields collapsed into a single universal curve, further confirms the phase transition to be of second-order. Owing to the abrupt change in magnetization and a large peak value (∼15 J kg⁻¹ K⁻¹) of the magnetic entropy change, CFA-NPs system exhibits GMCE across the phase transition (T_c). The observed peak value is superior or at least comparable to those of the other MC materials on a comparison of the peak heights. The present study provides a window for future research on tuning the T_c and MC effect of Co₂-based Heusler nanoalloys by controlling the elemental composition and/or partial substitution of the other elements.

A Ahmad acknowledges the University Grants Commission, New Delhi and Ministry of Education (MoE), India for providing the research fellowship. Amal Kumar Das acknowledges the financial support from the Department of Science and Technology (DST), India (Project No. EMR/2014/001026). The fruitful discussion with Dr Ramchandra Sahoo is highly acknowledged.

The data that support the findings of this study are available upon reasonable request from the corresponding authors.