Significant enhancement of magnetocaloric effect in a NiMnCuGa Heusler alloy through textural modification

There is a strong interest in developing an environmentally friendly near room temperature solid state refrigeration technology that utilizes magnetocaloric materials,^1–5 which exhibit large changes in magnetic ordering at the magnetic phase transition temperature. When this transition temperature also coincides with a first order structural transition, then the stability of the phase can be influenced by the application of a magnetic, electrical, or stress field. In particular, the magnetic field alone can induce or substantially aid a structural transformation in such a direction that the magnetic moment is increased. The contribution of this magnetostructural transformation leads to a large change in magnetic entropy (ΔS_M), and the phenomenon is commonly known as a “giant” magnetocaloric effect (MCE).⁶ The existence of a first order transformation does bring in hysteresis and energy loss effects that reduce the cooling efficiency. However, approaches are being developed to minimize such losses.^7–9 

Alloys that exhibit coinciding transformations near room temperature are Gd₅Si₂Ge₂,⁶ Mn-based alloys,^5,10,11 La(FeSi),¹² Heusler alloys such as non-stoichiometric Ni₂MnGa or Ni₂MnIn alloys, etc. The Heusler alloys are of particular interest because they are void of toxic elements (such as As, Be, Cd, or Pb) and generally are free of rare earth elements that sometimes can be in short supply. These alloys have the ordered bcc phase structure at high temperatures, which then transform to the Heusler L2₁ (⁠$Fm3¯m$⁠) austenite phase around 1100 K and finally undergo diffusionless martensitic transformation at lower temperatures to either a monoclinic phase or an ordered body centered tetragonal (I4/mmm) structure that is either non-modulated (NM) or of the modulated variety (5 M or 7 M) depending on the actual composition. This martensitic transformation constitutes the structural transformation for “giant” MCE in Heusler alloys. The alloys have certain additional advantages. They exhibit extended solid solubility over a range of compositions as well as limited solubility of quaternary and quinary elements such as Co, Cu, Fe, etc., which may be utilized to alter coincident transformation temperatures for specific design needs. The stoichiometric Ni₂MnGa alloy exhibits a structural transformation at 202 K along with a Curie temperature (T_C) of approximately 376 K.¹³ A decrease in the Mn content enhances the stability of the martensite phase while simultaneously decreasing the Curie temperature such that for the Ni-rich Ni_2 + xMn_1 − xGa alloys, coincident transformations with high MCE have been observed close to RT for x between 0.15 and 0.20.^14–16 Changes in the transformation temperatures as a function of composition are often characterized by the valence electron per atom (e/a) ratio,¹⁷ and in our prior work, we demonstrated using both DSC and magnetization (M) vs temperature plot at low field (μ_oH = 0.1 T) that the coinciding transformation occurred at x = 0.16 with associated ΔS_M ∼ −10 J/kg K for a field change Δμ_oH = 2 T.^18,19 However, the martensitic transformation temperature of Heusler alloys are significantly affected by long range chemical ordering.^20,21

Substitution of Cu in the place of Mn has also been found to alter the martensitic transformation temperature (T_M) and T_C in much the same way as the Ni-rich Ni_2 + xMn_1 − xGa alloys discussed above.²² Here, T_M is an approximate quantity, representing the average of martensite and austenite start and finish temperatures (M_s, M_f, A_s, A_f). The effect of the Cu content on both T_M and T_C was investigated for Ni₂Mn_1 − xCu_xGa with x between 0 and 0.3, and a coincident transformation was observed at x = 0.25. Specifically, for Ni₂Mn_0.75Cu_0.25Ga, an MCE was large; ΔS_M = −30 J/kg K for Δμ_oH = 2 T and a refrigerant cooling (RC) capacity of 72 J/kg at 308 K. Ab initio and Monte Carlo simulations have been used to rationalize the magnetic interactions where it is shown that Cu substitution leads to weakening of the Mn–Ni interactions. Reasonable agreement with trends in T_C and MCE was obtained (ΔT_ad∼ 1.2 K for Δμ_oH = 1.8 T).²³ Understanding the trend in martensitic transformation temperature T_M as a function of composition is more complex, and it has now been shown through DFT calculations that a good prediction not only requires equating ground state energies for austenite and martensite phases after including vibrational component (i.e., k_BT) but also that for ferromagnetic alloys such as NiMnGa, one must include the magnetic excitations and interactions with the vibrational degree of freedom.^24,25 This is especially important for Heusler MCE alloys, where the structural transformation near the Curie temperature contributes significantly to the MCE. Indeed, Pt substitution in the place of Mn has been shown both theoretically and experimentally to be similar to the effect of Cu, except for a larger change in T_M with increasing Pt for Ni₂Mn_1 − xPt_xGa alloys.²⁶ 

At a phenomenological level, it is instructive to consider magnetization in terms of the magnetic domain structure that subdivides the material volume into tiny regions with individual uniform magnetic moments. They originate from exchange interactions where neighboring spins orient in the same direction. The net sum of the magnetic spins is zero at the zero magnetic field but with the application of the magnetic field one component of spin is replaced by a favorable spin such that for the sufficient large field, all domain point along the magnetic field direction. However, the domain structure is heavily influenced by crystallographic anisotropy, whereby favorable spins take on a specific crystallographic direction. In the case of the Ni-rich Ni_2 + xMn_1 − xGa alloys, the easy magnetization axis is along the 〈110〉 axis of the ferromagnetic non-modulated L1₀ (body centered tetragonal, bct) martensite phase with c/a greater than 1.¹⁸ If this crystallographic axis is aligned along the magnetic field direction, then one would anticipate that magnetic moments would more easily saturate along the field direction, i.e., a sharp transition to saturation. Also, if the austenite is trained to convert to a preferred orientation of martensite twin variants, then upon the application of a magnetic field along the aligned easy magnetization axis, the material would transform from austenite to martensite such that the martensite reaches saturation magnetization rapidly; unlike a material that would possess a random orientation of martensite twin variants. The opposite would be the case if the magnetic field is applied along a hard crystallographic axis. These differences would translate into high and low values of MCE, respectively.

Given that the material is polycrystalline, the favorable crystal and domain structure can be realized through texturing of the martensite region. The thermoelastic martensite such as in the case of Ni–Ti, Ni–Mn–Ga alloys, is highly anisotropic but possess coherent low interfacial energy interfaces between different variants. This makes the variants highly mobile, which can then switch on the application of stress (as in NiTi shape memory alloys) or a magnetic field, the latter being important in the magnetic shape memory alloy and magnetocaloric applications. In the case of mechanical stress, the switching of the variants is such that the preferred axis leads to maximum displacement that is in phase with the direction of applied stress,^27,28 and the resulting texture has been demonstrated in NiTi.^29,30 For the non-modulated L1₀ body centered tetragonal structure of martensite that was observed for Ni-rich Ni_2 + xMn_1 − xGa alloys in our previous work,^18,19 a low compressive stress assisted thermal cycling (SATC) through the transformation temperatures was used to texture the ferromagnetic martensite phase. The preferential orientation along the compression direction for the martensite was found to be 〈100〉, where we refer to the parent Heusler structure. Referring to the body centered tetragonal structure this would be the 〈110〉 axis, which is also the easy magnetization axis for c/a > 1. Magnetocaloric measurements with the field applied along this compression direction demonstrated greater than 70% increase in ΔS_M compared to the material in the as-received condition.^18,19 Since these intermetallics are generally brittle, the SATC approach was utilized to texture the material at low stress rather than the application of higher stress if it were applied below M_f. In this context, in NiTi alloys it has been shown that the stress required for texturing is significantly reduced because of a low shear modulus at the phase transformation temperature, T_M.^29,30 Single crystal (SX) Heusler alloys in the martensite state can sustain higher compressive stresses before cracking because strain incompatibility caused by different grains are absent. Therefore, favorable variants can be induced simply through mechanical cycles at higher stress below M_f.³¹ However, SX materials are difficult to process and more expensive vs the simplicity of using polycrystalline materials, where SATC is necessary, and these differences have to be considered in any final application.

Here, we extend our SATC work to the Ni₂Mn_0.75Cu_0.25Ga composition, since this alloy was found to exhibit high MCE, both in terms of ΔS_M [using the Maxwell equation, see Eq. (1)] and ΔT_ad measured directly for Δμ_oH = 2 T.^22,23 In addition to isothermal magnetization curves, ΔT_ad was deduced from heat capacity (C_p) measurements at different magnetic fields (μ_oH). Texture measurements using neutron diffraction was used to rationalize the observed increase in MCE following SATC.

A NiMnCuGa alloy with composition Ni₂Mn_0.75Cu_0.25Ga and approximate weight 15 g was triple arc melted in argon. Typical weight loss due to arc melting was around 0.5%. The sample was heat treated at 1273 K under high vacuum (10⁻⁶Torr) for 72 h, followed by furnace cooling to room temperature. At this temperature, the alloy has a B2 crystallographic structure that permits high diffusivity and homogenization. The arc-melted button exhibited a columnar structure in which growth occurred from the bottom copper chilled face to the top crowned surface of the puck. Four cubes of approximate 4 mm cube samples were cut from the billet for structural and magnetic characterization and SATC. Samples were cut by using a slow speed diamond saw, and faces of the samples were mechanically polished to remove any imperfections.

To enhance magnetostructural coupling in the polycrystalline material, one of the 4 mm cube samples underwent SATC using an MTS servo-hydraulic load frame. The sample was compressively loaded to 20 MPa at RT along the columnar grain direction. While under load control, the sample was thermally cycled approximately 10 times from above the austenite finish (A_f) temperature to below the martensite finish (M_f) temperature so as to reach a stable stress–strain loop. Any stress greater than 20 MPa would lead to cracking of the brittle intermetallic, and this stress was sufficient to induce preferred orientation as observed from texture measurements following thermal cycling. As explained earlier, the low stress requirement is believed to be due to the low shear modulus during the thermoelastic martensitic transformation. Under a compressive load, the shortest crystallographic axis would align along the loading direction to maximize the displacement or work done,²⁷ and this would be accomplished by growing the favorable twin variant. For the current material, this would be the easy magnetization axis, namely, along the [110] direction of BCT martensite (I4/mmm) or the 〈100〉 axes when referring to the parent cubic austenite (⁠$Fm3¯m$⁠) structure.

Thermal characterization of as-heat-treated samples before and after SATC was conducted using a Perkin Elmer DSC 8 apparatus at a ramp rate of 10 K per minute. Magnetic characterization was performed using a Quantum Design® VersaLab Vibrating Sample Magnetometer (VSM) with the temperature range capability between 55 K and 390 K. Samples were extracted with approximate dimensions 1 × 1 × 3 mm with the long dimension along the columnar direction to maintain consistency between samples. Measurements were made with the magnetic field applied along the 3 mm direction. Isofield magnetization (M vs T) data at fields of μ_oH = 0.1 T and 3 T were obtained for samples before and after SATC, starting at 390 K and ending at 223 K. The cooling rate was 5 K/min. Isothermal magnetization vs magnetic field (M vs H) measurements were conducted on the same samples for evaluating ΔS_M. Samples underwent magnetization at fields from μ_oH = 0–3 T at each isotherm, starting from 330 K and ending at 317 K in temperature steps of −0.5 K. Following the approach in Ref. 32, after magnetization measurement at each isotherm, the sample was heated to 390 K under the zero magnetic field to reach the fully paramagnetic austenite phase to erase any magnetic and structural history. The sample was then cooled to the next subsequent isotherm to achieve a pristine sample state, particularly important when there may be mixed phase of austenite and martensite following a magnetization run. This testing technique for M vs H permits the capture of magnetostructural transformation at any possible isotherm.

From the M vs H measurements, the MCE and RC values can be calculated. ΔS_M was determined using integral of Maxwell's relation in Eq. (1),¹ where the magnitude of the magnetic entropy is related to the temperature change of magnetization (M), permeability of free space (μ_o), and the application of a magnetic field up to a maximum (H_max). The relevance of Eq. (1) across a structural transition has been debated in the literature; however, a good explanation for its applicability has been given in Refs. 33 and 34. This is based on the fact that the transformation is quasi-continuous, since martensite nucleation is athermal and occurs over a number of metastable steps as the temperature is reduced from M_s to M_f, during which the formed martensite is in equilibrium with the austenite, i.e., not a strict discontinuous transformation. The RC was calculated from the area within the MCE peak using the full width at half maximum (FWHM) approach.³⁵ This approach for obtaining MCE values is used for convenience, while recognizing that this parameter may not be a good indicator of adiabatic temperature change (ΔT_ad). It should also be noted that due to magnetic and thermal hysteresis in this system, the MCE value is not exact,

Texture analysis was conducted using the neutron time of flight (TOF) diffractometer high pressure preferred orientation (HIPPO) goniometer at the Los Alamos Neutron Science Center (LANSCE).^36,37 HIPPO utilizes approximately 1200 ³He detector tubes arranged on 50 detector panels positioned on rings at five different diffraction angles around the incident beam direction so that each detector probes a different sample direction. For each texture measurement, the sample is rotate around the vertical axis (perpendicular to the incident neutron beam) into three positions (0°, 67.5°, and 90°) to increase pole figure coverage. At each position, data were collected for 15 min. Samples were aligned such that the incident beam was along the columnar axis of the grains. All data collection was performed at room temperature. Data were analyzed using the Material Analysis Using Diffraction (MAUD) software using the procedure from Ref. 38. In the pole figures depicted in this paper, the columnar direction is along the center of the pole figures (perpendicular to the page).

Heat capacity (C_p) measurements at different magnetic fields were made using a Physical Property Measurement System (PPMS, Quantum Design®) under high vacuum. Apiezon N grease was used on a suspension bridge in a heat capacity puck supplied by Quantum Design. An addenda was measured with no sample to be used as a background to be subtracted from an experimental run of a given material. After the addenda was measured, a sample size of ∼1 mg was placed on the grease with care taken to not remove any grease. The addenda and measuring procedure were from high to low selected temperatures. A 2% heat rise was used, with the heat capacity measured upon the temperature decay back to the given starting temperature. Three heat capacity measurements were taken and averaged for each selected temperature. After heat capacity measurements were measured over a given temperature range, the magnetic field was increased from μ_oH = 0 to 3 T in 1 T increments. Following these measurements, ΔT_ad was calculated using the Eq. (2).¹ It should be noted that Eq. (2) is not appropriate to be used across first order phase transformations due to the dependence of C_p on an applied magnetic field, but has been shown to provide adequate comparisons within a material study.³⁹ Similarly, it is employed here to provide an approximation of the ΔT_ad to observe the effects of SATC,

The DSC plots for the as-received (AR) and SATC samples for alloy composition Ni₂Mn_0.76Cu_0.24Ga are shown in Fig. 1. Heating and cooling directions are indicated by the arrows. Second order phase transformations, such as the Curie temperature (T_C), can be observed from DSC data, as seen in our previous work.¹⁹ However, when the T_C coincides with the martensitic transformation (becomes coupled), the second order transformation can be obscured by the first order peak in DSC scans. From the DSC data, the start and finish temperature of austenite, A_s and A_f, and the martensite start and finish temperatures, M_s and M_f, were determined. These are summarized in Table I, which also includes results for the enthalpy and entropy of transformation. These values are comparable to the non-stoichiometric Ni_2 + xMn _1 − xGa samples investigated by various investigators.

The isofield magnetization (M vs T) plots at magnetic fields μ_oH = 0.1 T and 3 T for the AR and SATC samples are illustrated in Fig. 2. The data confirm coinciding structural and magnetic transformation for the ferromagnetic alloy, i.e., the material transforms from paramagnetic austenite to ferromagnetic martensite upon cooling. The start and finish temperatures for austenite and martensite exhibit remarkable agreement with the DSC measurements and are summarized in the bottom two rows of Table I. More importantly, Fig. 2 shows a significant sharpness in the magnetic transition for the SATC sample compared to the AR sample at μ_oH = 0.1 T. Thus, saturation in magnetization occurs over a smaller temperature range in the SATC sample (compare row 4 with row 3 in Table I) along with suppression of magnetization in the paramagnetic state. These differences in behavior also manifest in the isothermal magnetization data presented later. Figure 2(b) shows that the change in sharpness also persists under a μ_oH = 3 T magnetic field and confirms stabilization of the ferromagnetic martensite under a magnetic field. One may also observe a longer tail in the paramagnetic region at μ_oH = 3 T and is believed to be due to partial organization of magnetic spins under a high magnetic field.

The isothermal M vs H plot for samples before and after SATC using the loop protocol are shown in Fig. 3. For the as-received sample, the magnetostructural transformation is directly visible over the temperature range 325 K–322 K, where the required magnetic field for transformation to the ferromagnetic state decreases with temperature. Saturation in magnetization only occurs at temperatures close to M_f. Correspondingly, for the SATC sample, magnetostructural transformation starts at approximately 326 K that is well above M_s (see Table I). Furthermore, magnetization is close to saturation almost immediately following the magnetostructural transformation. Such sharp and large transitions are rarely observed in Heusler alloys and suggest that the crystallography in the SATC sample is likely oriented for easy magnetization of the formed martensite combined possibly with ease of martensite variant reorientation under a magnetic field. The latter we surmise from the small kinks that we observe for the isotherms that exhibit large magnetization changes. We note that these magnetostructural transformations at each isotherm over a small temperature range are particularly observable because of the loop protocol to capture M vs H behavior for the pristine material. With this loop process, the material is heated into the paramagnetic austenite state after each isotherm, thereby erasing magnetic history and associated remnant mixed phases.

An additional insight from the M vs H curves of Ni₂Mn_0.76Cu_0.24Ga is that SATC changed the susceptibility, saturation magnetization of martensite near the phase transformation temperature, and coercivity. In the martensite, the SATC sample reached about 33 A m²/kg with an applied field of μ_oH = 0.2 T, while for the as-heat-treated material, the magnetization ranges between 20 and 27 A m²/kg. The saturation magnetization at 317 K increases nominally from 40 A m²/kg to about 44 A m²/kg following SATC; however, the rapid transition to saturation is what distinguishes the two material conditions and contributes significantly to ΔS_M. Lastly, the coercivity values in the martensite were seen to be greatly reduced from about μ_oH = 25 × 10⁻⁴T in the as-heat-treated material to only 2 × 10⁻⁴T after SATC. This is likely due to a lesser degree of energy barriers associated with reorienting twin variants with an applied magnetic field in the martensite of the SATC sample.

The MCE calculated using Maxwell's equation [Eq. (1)] is shown in Fig. 4. Both samples exhibited an extended M vs H behavior. For Δμ_oH = 2 T, maximum ΔS_M values were about −10 and −25 J/kg K for the as-received and SATC sample, respectively. It is possible that the 0.5 K temperature steps in the M vs H protocol enhanced somewhat the MCE values and error (estimated to be about 1 J/kg K), but the difference between the material before and after SATC is clearly visible. Thus, SATC increased the MCE by about 100% over the as heat treated material, which is a very significant increase. Furthermore, the peaks are fairly broad at Δμ_oH = 2 T and 3 T, as opposed to the narrower peaks we had observed for a Ni_2.16Mn _0.84Ga alloy that also exhibited high ΔS_M.^18,19 The refrigerant capacity, RC, was obtained from the magnetic entropy plot and were approximately 23 and 50 J/kg at Δμ_oH = 2 T for the as-received and SATC samples, respectively;, i.e., an increase of about 100% as a result of SATC. Hysteresis effects would temper the RC values and remain to be adequately characterized in future work.

The heat capacity of the materials was evaluated at magnetic fields of μ_oH = 0, 1, 2, and 3 T and are illustrated in Fig. 5 for the material in the as heat treated (AR) and SATC conditions. The curves are generated during cooling from 372 K. The plots show similar behavior for the two material conditions and exhibit expected peaks close to the phase transformation temperature. In addition, the temperature at the peaks increases with the magnetic field, consistent with the stabilization of ferromagnetic martensite at higher magnetic fields. We also observe a difference in the baseline value between the AR and SATC samples. Adequate care was taken in accounting for the addenda baseline, so the reason for the difference remains unclear.

Figure 6 shows the adiabatic temperature change calculated from the heat capacity and isothermal magnetization data. The data correspond to magnetization runs during cooling from the austenite phase, see Fig. 3. For the as heat treated material, ΔT_ad is approximately 1.2 K for a magnetic field change Δμ_oH = 2 T. This is slightly lower than 1.5 K observed through direct ΔT_ad measurements for an alloy with very similar composition (Ni₂Mn_0.75Cu_0.25Ga),²³ and strikingly identical to their 1.2 K prediction using their Monte Carlo simulation. For the same field change, ΔT_ad is approximately 2 K for the SATC sample, i.e., an increase of about 60% over the as heat treated material. Although 2 K value appears small, significant temperature change can be realized through current refrigerator design concepts based on the AMR cycle.

Neutron diffraction was used to determine the martensite texture for both the as heat treated and SATC samples. Figure 7 shows a screen capture with some labeled hkl peaks of the diffraction pattern from the MAUD analysis for the as received sample with the 90° bank ring of detectors at 0° sample rotation.

Here, the blue dots mark the diffraction data points while the red line represents the best fit from Rietveld analysis using the MAUD software.³⁸ From the best-fit calculation procedure, it was found that at RT there was about 90% of tetragonal non-modulated (NM, I4/mmm space group) martensite phase and 10% volume fraction of 7 M martensitic phase (I12/m1) present in both the as heat treated and SATC samples. Some of the hkl peaks are marked for the NM phase, and the very small peaks for the 7 M structure are also pointed out in the graph. The poor fit for the (101) reflection for this detector bank is a result of texture and is partially amplified in the fit routine at high d-spacing where the contribution to the peak fit is small. The fitting at low d-spacing is seen to be near exact in Fig. 7 and is consistent across all other detector banks and sample rotations.

By compiling and analyzing over multiple detector banks and sample rotations, pole figures were generated for both samples and are shown in Fig. 8. The center of each pole figure is the columnar direction. The intensity of each set of pole figures should be the same, but in this case, no value was seen to provide a clear picture without obscuring information. This discrepancy is due to the material being heavily oriented, which occurs in these intermetallics during arc melting. The billet contained multiple grains that could be seen by either breaking part of the arc melted billet or by thermally etching during heat treatment of a clean cut face of the material. For the as heat treated sample, the lattice parameters of a = b and c were 3.842 Å and 6.369 Å, respectively, for the body centered tetragonal BCT lattice. The resulting c/a ratio is 1.172 after using a factor of √2 with a to relate the BCT lattice to the parent austenite $Fm3¯m$ space group. The texture index is extremely high, 66, and the spots suggest two main orientations of the grains. For the SATC sample the texture index was considerably lower, 7, as seen from the wider region of higher intensity. The lattice parameters for this material were slightly different, with of a = b = 3.866 Å and c = 6.410 Å, but the c/a ratio remained identical, namely, 1.172.

The pole figures for the as heat treated material suggest a (200) preferred orientation along the columnar axis of the small billets, referring to the BCT structure.¹⁹ Correspondingly, the pole figures show that the (002) and (110) poles are approximately at 45° to the columnar axis. The (002) and (110) pole figures match one another because these two twin variants pair 90° to each other with a (112) twinning plane in the [$111¯$] direction.¹⁹ In terms of magnetization, (110) is the easy magnetization axis, (002) is the hard axis, and (200) is somewhere between the two.⁴⁰ 

After SATC, the pole figures take on a new appearance. Like with a non-stoichiometric Ni₂MnGa alloy, the (110) plane aligns along the columnar and loading direction due to SATC. The (002) pole, being the counterpart to (110) twin variant, moves radially out to 90° from the columnar axis. These orientation shifts move the (200) pole away from the columnar direction, as may be observed for the SATC sample. Most importantly, although the appearance of a bi-crystal and extremely high texture index is lost, the preferred orientation of the columnar grains move toward the (110) easy magnetization axis. We believe this is precisely the reason why we observe a sharp transition in magnetization at the Curie temperature for the SATC sample. It contributes to an enhanced magnetostructural coupling and thereby a significant increase in MCE.

A Ni₂Mn_0.76Cu_0.24Ga alloy, which in prior studies exhibited good MCE properties,^22,23 was studied in this work. As indicated in the Introduction, substitution of Cu in the place of Mn in the Ni₂MnGa alloy increases the stability of the martensitic phase, thereby increasing the structural transition temperature while simultaneously decreasing the Curie temperature such that the two transformations coincide close to RT. This contributes to an enhanced magnetic coupling to the first order phase transformation, and an increased MCE have been observed.

A goal of this work was to evaluate whether improved texture could be imparted to this material to further enhance MCE properties. In our past research with non-stoichiometric Ni₂MnGa alloys,^18,19,41 we had shown that simple compressive stress assisted thermal cycling (SATC) through M_f and A_f could be utilized to impart favorable texture to the ferromagnetic martensite phase, where the low shear modulus at the phase transformation temperature during cycling contributes to low stress requirement. Else, at higher stresses, these brittle materials would fracture.

Our results show that SATC has a drastic effect in the sharpness of the magnetic transition, whereby the magnetization change at the Curie temperature under a nominal magnetic field is significant and occurs over a very narrow temperature window; compare the as-received and SATC plots in Fig. 2. We had observed a similar behavior earlier in non-stoichiometric NiMnGa alloys,^18,19 but the effects were more drastic for this alloy. Certainly, the composition of the alloy affects the extent to which SATC influences the temperature interval; however, it is relevant to explore the sharpening because it contributes to higher MCE. Below, we attempt to provide a phenomenological explanation.

From a thermodynamic perspective, the chemical free energy difference between the austenite and martensite at an undercooling (ΔT_u) below the equilibrium temperature (T_m) drives the martensitic transformation; recall G vs T plots. The martensite growth rates are of the order of sonic velocities. However, at any given temperature below M_s, the growth is insufficient to take the transformation to completion because work has to be continually done to overcome the strain energy associated with growth of lenticular martensite plates or laths. The process is athermal and, therefore, the temperature has to be reduced to M_f to take the process to completion or near completion. Indeed it is believed that the transformation occurs over a number of metastable states as the temperature is reduced during which the martensite is in thermoelastic equilibrium with the martensite.^28,33 Now, the chemical free energy is typically of the order of 1 kJ/mole for steels, and it has been shown that the activation energy for nucleation event can be so high (∼100–1500 eV/atom) that thermal activation is not possible. The current understanding is that dislocations, dislocation arrangements, partial dislocations, and other similar defects serve as nucleation sites.^42,43 Viewed in this context, local strain centers and residual stresses caused by SATC likely serve as nucleation sites for martensite and thereby would likely help in reducing (M_s− M_f). When the applied field is mechanical stress, then a sharper length change would be expected and has been observed in our work on NiTi.³⁰ When a magnetic field is present, however (Fig. 2), and if the initially nucleated variants are favorable to align along the magnetic field, these initially formed variants, especially their tips that locally have high stresses, can aid the nucleation process of additional variants. This type of re-nucleation behavior can lead to reduced (M_s− M_f) value. Furthermore, the magnetization change would necessarily be larger at small fields because of the favorable alignment of variants. This may explain why we observe such a sharp and large transition in Fig. 2 at low field, which is also exhibited in the isothermal magnetization plots in Fig. 3 at higher fields.

Alternately, if we were to consider the free energy equation (per unit mass) and explicitly consider the contribution of individual variants, we have

where ΔG is the free energy change of a phase, given changes in the intrinsic variables, namely, pressure (p), temperature (T), magnetic field (H) and applied stress (σ). Here, V is specific volume and μ₀ is permeability of free space. In particular, the magnetic contribution is expressed as a sum of contributions of individual variants with their respective magnetocrystalline anisotropy. Considering only the magnetic contribution, the difference in free energy between the austenite and martensite is composed of the chemical free energy difference between the austenite and martensite (typically approximated as LΔT_u/T_m, where L is the enthalpy of transformation at T_m), plus the difference in magnetization imposed by H on the austenite and martensite phases. For the paramagnetic austenite, the magnetic contribution can be taken as zero. Now, if it is assumed that the contribution of the few selected variants, perhaps as few as two in a given grain, produces a lower free energy due to the magnetic field, than if all variants are present because of magnetocrystalline anisotropy, then the enhanced free energy driving force would contribute to increasing the extent of transformation below M_s, essentially lowering the (M_s− M_f). We note that the two alternate ways to describe the reduction in (M_s− M_f) are based on the nucleation of favorable variants when austenite transforms to martensite under a magnetic field. This is only a working explanation, based on our observation that SATC enhances the volume fraction of favorable variants, as seen in the pole figure plot (Fig. 8). Molecular dynamics (MD) simulations combined with ab initio calculations may provide partial confirmation of the mechanisms suggested here.

In previous work with magnetic NiMnGa alloys in magnetic shape memory alloys, a slightly different form of load and magnetic cycling was used to enhance shape memory characteristics.⁴⁴ The material was in single crystal form, and stress–strain curves showed significant reduction of the plateau stress during deformation of the martensite following their loading experiments. It was suggested that the loading protocol contributed to reduced resistance to twinning and hence reduced plateau stress. It is possible that ease of twin nucleation also contributes to an enhanced magnetostructural coupling; but in these polycrystalline materials, it is difficult to observe such changes because of premature fracture. Therefore, although ease of twin nucleation following SATC may have contributed to enhanced magnetostructural coupling, the texture work suggests that preferential alignment of martensite is likely the primary contributor.

Our work shows that ΔS_M increases from ∼10 to 25 J/g and ΔT_ad increase from 1.2 to 2 K, following SATC for a magnetic field change of Δμ_oH = 0 to 2 T. The RC increased also by a factor of two. Texturing the Ni₂Mn_0.75Cu_0.25Ga alloy with SATC has shown larger magnetocaloric response than NiMnCuGa alloys that have been directionally solidified.⁴⁵ These represent major increases and can significantly improve the material landscape for near RT refrigeration applications. The protocol is simple and can be applied to other materials such as elastocaloric applications, where again martensitic transformation are involved.

A Ni₂Mn_0.76Cu_0.24Ga alloy, which in prior research exhibited good MCE characteristics, was subjected to compressive stress assisted thermal cycling (SATC) through the M_f and A_f temperatures. The rationale was to impart favorable texture for improved MCE. Isofield magnetization measurements showed that SATC significantly sharpened the magnetic phase transformation and contributed to an enhanced magnetostructural coupling, as observed from isothermal magnetization curves. With a Δμ_oH = 0 to 2 T applied magnetic field, the MCE increased from ∼10 to ∼25 J/kg K and the RC almost doubled due to SATC. Using heat capacity measurements at different magnetic fields and the isothermal magnetization data, the adiabatic temperature increase was approximately 1.2 and 2.0 K for the as heat treated and SATC samples, respectively, for Δμ_oH = 0 to 2 T. Texture analysis using neutron diffraction confirmed the realignment of martensite twin variants such that the (110) easy magnetization axis was oriented along the loading and magnetic field directions. This we believe largely contributed to enhanced magnetostructural coupling and the significant increase of MCE due to SATC.

We would like to thank Sven Vogel at Los Alamos National Laboratories for the neutron diffraction experiments on the HIPPO and with the data analysis with MAUD. Los Alamos Neutron Science Center was supported by Department of Energy (DoE) BES under Contract No. W-7405-ENG-36. Thanks to Gregory Kozlowski, Serhiy Leontsev, Yuhui (Helen) Shen, and John Horwath for discussions on this work while in development. We would also like to thank Kyu Cho from the Army Research Laboratory for the initial funding for this project through the Cooperative Program Agreement No. W911NF-11-2-0036.

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