Pd₂MnGa Metamagnetic Shape Memory Alloy with Small Energy Loss

Abstract

Metamagnetic shape memory alloys (MMSMAs) are attractive functional materials owing to their unique properties such as magnetostrain, magnetoresistance, and the magnetocaloric effect caused by magnetic‐field‐induced transitions. However, the energy loss during the martensitic transformation, that is, the dissipation energy, E _dis, is sometimes large for these alloys, which limits their applications. In this paper, a new Pd₂MnGa Heusler‐type MMSMA with an extremely small E _dis and hysteresis is reported. The microstructures, crystal structures, magnetic properties, martensitic transformations, and magnetic‐field‐induced strain of aged Pd₂MnGa alloys are investigated. A martensitic transformation from L2₁ to 10M structures is seen at 127.4 K with a small thermal hysteresis of 1.3 K. The reverse martensitic transformation is induced by applying a magnetic field with a small E _dis (= 0.3 J mol⁻¹ only) and a small magnetic‐field hysteresis (= 7 kOe) at 120 K. The low values of E _dis and the hysteresis may be attributed to good lattice compatibility in the martensitic transformation. A large magnetic‐field‐induced strain of 0.26% is recorded, indicating the proposed MMSMA's potential as an actuator. The Pd₂MnGa alloy with low values of E _dis and hysteresis may enable new possibilities for high‐efficiency MMSMAs.

Metamagnetic shape memory alloys (MMSMAs) are attracting attention as multifunctional materials, such as magnetic actuators and environment‐friendly magnetorefrigeration materials. However, the large energy loss during the phase transformation hinders their applications. In this study, a novel Pd₂MnGa MMSMA with extremely small energy loss, which may lead to high efficiency, has been developed.

1. Introduction

Metamagnetic shape memory alloys (MMSMAs), which exhibit reversible martensitic transformations when a magnetic field is applied, have recently attracted attention as multifunctional materials.^{[ 1} , ^{2 ]} One of the expected applications is their use as magnetic actuators. A large output strain of more than 5% can be obtained through the magnetic‐field‐induced reverse martensitic transformation in Ni–Co–Mn–In alloys. In addition, a strong output stress can be obtained owing to the large driving force caused by the difference in Zeeman energy between the parent and martensite phases.^{[ 3} , ⁴ , ^{5 ]} The energy density of MMSMAs is estimated to be higher than those of other known magnetostrictive alloys, such as Terfenol‐D.^{[ 4 ]} Moreover, solid‐state refrigeration techniques are highly efficient and, thus, appropriate for the realization of a sustainable society.^{[ 6} , ^{7 ]} For example, MMSMAs are expected to be applied as magnetorefrigeration materials that utilize the magnetocaloric effect,^{[ 8} , ^{9 ]} where the large entropy change during the martensitic transformation is used. Several alloy systems have been developed for MMSMAs, among which Ni–Mn‐based Heusler alloys have been widely investigated.^{[ 10} , ¹¹ , ^{12 ]}

Energy dissipation and hysteresis during phase transformation are critical obstacles that should be overcome for the application of MMSMAs. During the operating cycle of MMSMAs, a part of the input energy is wasted as heat owing to the first‐order martensitic transformation; this is referred to as the dissipation energy (E _dis). For applications such as actuators, a lower value of E _dis is advantageous; it not only leads to lower energy consumption but also causes reduced magnetic‐field hysteresis (ΔH _hys) and temperature hysteresis (ΔT _hys) during operation. On the contrary, a larger hysteresis is favorable for applications such as pipe coupling and prestressed concrete.^{[ 13} , ^{14 ]} Furthermore, an increase in ΔH _hys has been reported for Ni–Co–Mn–In alloys at low temperatures, which limits the applicable temperature range to approximately room temperature.^{[ 15 ]} In recent years, applications in low‐temperature environments have increased owing to the demands of the aerospace industry and upcoming hydrogen society. Therefore, there are several potential applications of a new MMSMA with low E _dis and ΔH _hys values at low temperatures.

An improvement in the lattice compatibility between the parent and martensite phases effectively reduces hysteresis in martensitic transformations. Cui et al. proposed that λ₂, which is the middle eigenvalue of the transformation stretch matrix,^{[ 16 ]} has a significant effect on the thermal hysteresis of Ti–Ni‐based alloys. The value of λ₂ can be calculated using the knowledge of the crystal structures and lattice constants of the parent and martensite phases.^{[ 16} , ^{17 ]} In addition, λ₂ depends considerably on the composition of the alloy; this dependence of the hysteresis has been investigated in various Ni–Mn‐based MMSMA systems.^{[ 18} , ¹⁹ , ²⁰ , ^{21 ]} Therefore, E _dis was successfully reduced to ≈5 J mol⁻¹ at a low value of ΔH _hys (≈11 kOe) in the room‐temperature range.^{[ 19 ]} However, ΔH _hys is still considered large. Some shape memory alloys, such as Ti–Ni and Fe–Pd alloys, exhibit low values of E _dis (0.3–1.0 J mol⁻¹);^{[ 22} , ^{23 ]} however, they cannot be driven by magnetic fields. To the best of our knowledge, such low values of E _dis have not been achieved for MMSMAs.

Several studies have been conducted on Ni–Mn‐based alloys; however, few studies are available on Pd–Mn‐based alloys, in which Ni is replaced by an element of the same family, Pd. Martensitic transformation has been reported in Mn‐rich Pd–Mn–Sn alloys, and a magnetic phase diagram has been constructed.^{[ 24} , ²⁵ , ^{26 ]} A magnetic‐field‐induced reverse martensitic transformation has been confirmed, and a large magnetoresistance of −30% has been reported.^{[ 27 ]} Furthermore, a spin‐flop‐type metamagnetic transition has been reported for Pd₂MnIn Heusler alloys.^{[ 28 ]}

Our previous studies presented the martensitic transformation and shape memory effect for Pd₂Mn_{2 − x} Ga _x alloys.^{[ 29} , ^{30 ]} A magnetic phase diagram was constructed, and it was reported that the martensitic transformation temperature decreased with the addition of Ga. However, this investigation was limited to high‐temperature heat‐treated alloys with a B2 structure. The stoichiometric Pd₂MnGa alloy with a B2 structure is antiferromagnetic with a Néel temperature of 198 K, and it does not undergo martensitic transformation. Furthermore, metamagnetic transitions have not been reported.

In this study, an aged Pd₂MnGa alloy exhibited a martensitic transformation for the first time and a magnetic‐field‐induced reverse martensitic transformation was also realized. A small hysteresis (ΔT _hys = 1.3 K and ΔH _hys = 7 kOe) and significantly low dissipation energy (E _dis = 0.3 J mol⁻¹) are unique characteristics of this martensitic transformation. A magnetic‐field‐induced strain of up to 0.26% was recorded; thus, the newly developed MMSMA is a potential highly efficient actuator.

2. Results

2.1. Thermoelastic Martensitic Transformation

The thermomagnetization curve for the aged Pd₂MnGa alloy is shown in Figure  1a; the solution heat‐treated (SHT) Pd₂MnGa alloy with antiferromagnetism reported in a previous study is also depicted.^{[ 29 ]} It is clear that the magnetization increases upon aging. The parent phase becomes ferromagnetic or ferrimagnetic with a Curie temperature (T _C) of 137 K, which is defined as the temperature with a maximum gradient. A sharp decrease in the magnetization was seen below the Curie temperature, which suggests another phase transformation.

Figure 1.

a) Thermomagnetization curve of the aged Pd₂MnGa alloy at 500 Oe (red line). The reported thermomagnetic response of a solution heat‐treated (SHT) Pd₂MnGa alloy is also shown as the gray line.^{[ 29 ]} b) Enlarged view of the onset of the martensitic transformation, where the forward martensitic transformation starting and finishing temperatures (T _Ms, T _Mf) and the reverse martensitic transformation starting and finishing temperatures (T _As, T _Af) are determined using the extrapolation method. c,d) Micrographs obtained through in situ optical microscopic observations at low temperatures. The surface relief at 100 K suggests martensitic transformation, which corresponds to the sharp variation in magnetization displayed in (a,b).

To clarify the origin of this phenomenon, the microstructure was observed using an in situ optical microscope, as shown in Figure 1c,d. Surface relief was observed upon cooling and disappeared upon heating, which is clear evidence of the first observation of the thermoelastic martensitic transformation of the stoichiometric Pd₂MnGa alloy. The martensitic transformation temperatures were determined using extrapolation methods, as shown in Figure 1b. The martensitic transformation starting temperature (T _Ms) and finishing temperature (T _Mf) were determined as 127.4 and 122.4 K, respectively, whereas the reverse martensitic transformation starting temperature (T _As) and finishing temperature (T _Af) were determined as 124.0 and 128.4 K, respectively. The mean martensitic temperature (T _M0) and austenitic temperature (T _A0) were calculated as $T_{\mathrm{M}0}=(T_{\mathrm{Ms}}+T_{\mathrm{Mf}})/2=124.9$ K and $T_{\mathrm{A}0}=(T_{\mathrm{As}}+T_{\mathrm{Af}})/2=126.2$ K. Therefore, an extremely small thermal hysteresis (ΔT _hys = 1.3 K) was recorded, which is defined as $T_{\mathrm{A}0}-T_{\mathrm{M}0}$. The transformation temperature width of the forward martensitic transformation, defined as $T_{\mathrm{Ms}}-T_{\mathrm{Mf}}$, was calculated as 5.0 K.

2.2. Crystal Structure Determination

The crystal structure of the parent phase was investigated using scanning transmission electron microscopy (STEM). The atomic‐resolution high‐angle annular dark‐field–STEM (HAADF‐STEM) images of the SHT and aged Pd₂MnGa alloys are shown in Figure  2a,b, respectively, and the fast Fourier transform (FFT) images are shown in the insets. The direction of the incident electron beam was parallel to the [01$\overline{1}$] direction of the BCC phase. The columns of the Pd sites are brighter because the atomic number of Pd is considerably larger than those of Mn and Ga. In the FFT images of both the SHT and aged alloys, the superlattice reflection for the B2 structure was observed (circled spots); however, the superlattice reflection for the L2₁ structure was observed only in the aged sample (squares). These results indicate that the SHT sample has a B2 structure, which is consistent with our previous study;^{[ 29 ]} further ordering towards the L2₁ structure occurred during the aging heat treatment. The line profiles also support this conclusion for the Mn and Ga sites, as indicated in Figure 2c,d, respectively. The intensities of the line profiles are almost constant for the B2 structure because Mn and Ga randomly occupy the Mn and Ga sites. In contrast, zigzag intensities were seen in the profiles when the crystal structure changed to L2₁.

Figure 2.

Scanning transmission electron microscopy–high‐angle annular dark‐field (STEM‐HAADF) images of the a) solution heat‐treated (SHT) and b) aged Pd₂MnGa alloys. The fast Fourier transform (FFT) images are shown as insets. The crystal structure of the SHT sample was determined to be B2, while that of the aged sample was L2₁. c,d) Line profiles of the Mn and Ga sites. The intensities of the Mn and Ga sites are almost constant for the B2 structure owing to the random occupation of the Mn and Ga atoms. However, there is an alternating stronger and weaker intensity for the L2₁ structure, owing to the ordering of the Mn and Ga atoms.

The exchange interactions between Mn atoms depend on the Mn–Mn distances.^{[ 31 ]} The magnetic interaction changes from antiferromagnetic to ferromagnetic through atomic ordering from B2 to L2₁ in Ni–Mn–Al and Ni–Mn–Ga–Al alloys.^{[ 32} , ^{33 ]} The ordering from B2 to L2₁ expands the Mn–Mn distances from the second to the third nearest neighbor, which is a possible origin of the increased magnetization after aging for the current Pd₂MnGa alloy.

In addition, round contrasts ≈2 nm in size appeared in the STEM‐HAADF image of the aged sample, which may be related to nanoscale composition fluctuations caused by the aging heat treatment. However, it was difficult to clarify the origin of the contrasts in this study; therefore, this will be a subject for future research.

The crystal structures at low temperatures were determined using in situ X‐ray diffraction (XRD) measurements and in situ transmission electron microscopy (TEM) observations. The powder XRD patterns of the aged Pd₂MnGa alloy at 295 and 90 K are shown in Figure  3a. The XRD pattern at 295 K is consistent with the L2₁ structure. An additional unknown peak, marked with an asterisk (*), is seen, which was also reported for the SHT sample.^{[ 29 ]} During cooling, the peaks split upon the martensitic transformation.

Figure 3.

a) In situ powder X‐ray diffraction (XRD) patterns at 295 and 90 K using Cu‐Kα (λ = 1.5418 Å) radiation for the aged Pd₂MnGa alloy. Unknown peaks are marked with an asterisk (*). The peaks indicate L2₁ and 10M structures for the parent and martensite phases, respectively. The peak splittings of 2 0 10 and 2 0 $\overline{10}$ suggest that the martensite phase is monoclinic. b,c) Selected area diffraction patterns of the aged sample measured at 290 K (b) and 81 K (c) by in situ transmission electron microscopy (TEM) observations. Four extra spots indicating a 10M structure were found at 81 K. The results of the in situ TEM observations are in good agreement with those of the in situ XRD measurements.

In situ TEM observations were also performed to determine the crystal structure of the martensite phase. The selected area diffraction patterns (SADPs) of the aged sample at 290 and 81 K are shown in Figure 3b,c. The incident electron beam was parallel to the [001] direction of the parent phase. The fundamental spots of the typical BCC structure and additional 200 superlattice reflections are seen at 290 K. Upon cooling to 81 K, as shown in Figure 3c, four extra spots are seen among the fundamental spots, which suggest a ten‐layered crystal structure; the XRD patterns are in good agreement with the 10M structure. The symmetry of the martensite phase is monoclinic because the peaks of 2 0 10 and 2 0 $\overline{10}$ split in the XRD pattern, and deviation from the right angle is seen in the SADP. Thus, a martensite phase with a monoclinic 10M crystal structure can be inferred, which has also been confirmed for Ni–Mn–Ga Heusler alloys.^{[ 34} , ³⁵ , ^{36 ]} In this study, we focus on the total lattice distortion of the phase transformation and do not consider precise atomic positions. The fitted lattice parameters of the 10M structure in the XRD patterns were $a_{10M}$ = 4.374 Å, $b_{10M}$ = 6.116 Å, $c_{10M}$ = 21.82 Å, and β = 90.2° at 90 K, and the determined β angle was in good agreement with the SADP. Recently, density functional theory studies suggested the possibility of martensitic transformation from L2₁ to a tetragonal structure with c/a ≈ 1.3 in Pd₂MnGa;^{[ 37} , ³⁸ , ^{39 ]} however, a different martensite phase was confirmed experimentally.

In situ XRD measurements were performed at various temperatures down to 10.5 K. The XRD pattern of the aged Pd₂MnGa alloy at 10.5 K is shown in Figure  4a. All the peaks were indexed as the 10M structure, and the crystal structure did not change during cooling. The XRD patterns in the range of 71° ⩽ 2θ ⩽ 80° for cooling and heating are summarized in Figure 4b, c, respectively. The reversibility of the martensitic transformation was also confirmed by in situ XRD measurements. The lattice constants were determined for each temperature, and the results are summarized in Figure 4e. $\sqrt{2}{a}_{10M}$, $b_{10M}$, and $\sqrt{2}/5c_{10M}$ are plotted for comparison with $a_{L{2}_1}$ because the β angle is almost vertical (β ≈ 90.2°). The lattice constants of the martensite phase vary gradually with variations in temperature.

Figure 4.

a) X‐ray diffraction (XRD) patterns of the aged Pd₂MnGa at 10.5 K. All the peaks seen were indexed as the 10M structure. b,c) In situ powder XRD patterns of the aged Pd₂MnGa alloy from 10.5 to 130 K during cooling (b) and heating (c). Below 120 K, the peaks corresponding to the martensite phase were clearly observed, and their positions shifted by changing the temperature. d) Lattice constants determined from 10.5 to 150 K: $\sqrt{2}{a}_{10M}$, $b_{10M}$, and $\sqrt{2}/5c_{10M}$ are plotted for comparison with $a_{L{2}_1}$. The hysteresis in the lattice constants of the martensite phase should be noted. The dashed lines are observation guides. e) Comparison of the XRD patterns at the same temperature of 100 K during heating and cooling. f) Molar volume calculated from lattice constants.

Interestingly, hysteresis exists for the cooling and heating processes in the lattice constants of the martensite phase. A comparison of the XRD patterns at 100 K during heating and cooling is shown in Figure 4d, where a clear difference in the angles of the peaks is confirmed. The exact origin of the hysteresis of the lattice constants is not understood; however, the magnetization difference between cooling and heating in the martensite phase, shown in Figure 1a, may be related to this phenomenon. The molar volumes calculated from the lattice constants are depicted in Figure 4f. The volume change due to the martensitic transformation was found small.

2.3. Magnetic‐Field‐Induced Phase Transformation

Magnetic properties were investigated under a strong magnetic field. The thermomagnetization curves under various magnetic fields up to 70 kOe are shown in Figure  5 . Magnetization increased, and the martensitic transformation temperatures decreased by ≈7.8 K as the magnetic field increased to 70 kOe, which is similar to the results of Ni–Mn‐based MMSMAs.^{[ 3 ]}

Figure 5.

Thermomagnetization curves of the aged Pd₂MnGa alloy under various magnetic fields. The T _Ms and T _Af were determined using extrapolation methods.

Magnetization measurements were performed for the aged Pd₂MnGa alloy at various temperatures. The magnetization curves obtained using the AC measurement system (ACMS) option of the physical properties measurement system (PPMS; Quantum Design Inc., USA) and strong pulsed magnetic fields are shown in Figures  6a,b, respectively. Hysteresis was observed in the magnetization curves below 120 K, which suggests a magnetic‐field‐induced transition.

Figure 6.

Magnetization curves for the aged Pd₂MnGa alloy under a) relatively lower magnetic fields obtained using the physical properties measurement system–AC measurement system (PPMS‐ACMS) and b) strong magnetic fields obtained using pulsed magnets. Hysteresis are seen in the magnetization curves. c,d) In situ optical microscopy images under a pulsed magnetic field at 10 K. The surface relief disappeared with the application of the magnetic field. e) High‐field X‐ray diffraction (HFXRD) patterns of the aged powder sample under magnetic fields up to 50 kOe at 119 K. The peaks of the martensite phase changed to that of the parent phase when the magnetic field was applied. These results confirmed a magnetic‐field‐induced reverse martensitic transformation in the Pd₂MnGa alloy for the first time. The critical magnetic fields for the phase transformation (H _Ms and H _Mf) were determined by extrapolating the magnetization curves (a,b).

To confirm the transformation, in situ optical microscopy (OM) observation was performed in high‐pulsed magnetic fields to directly see the variation in the microstructure (Video S1, Supporting Information). The OM images captured under magnetic fields of 0 and 330 kOe at 10 K are shown in Figure 6c,d, respectively, where the disappearance of the surface relief during the reverse martensitic transformation can be observed when the magnetic field is applied. Further, variations in the crystal structure were directly investigated using high‐field XRD (HFXRD) measurements, as shown in Figure 6e. The powdered sample was cooled to 10.5 K without a magnetic field, and measurements under magnetic fields were performed after heating the sample to 119 K. The sample was in the martensite phase at 119 K under 0 kOe, and the peaks indicating the martensite phase changed to those indicating the parent phase when the magnetic field was applied. Based on the results of the magnetization measurements, microstructure observations, and XRD measurements, the magnetic‐field‐induced reverse martensitic transformation was confirmed in a Pd₂MnGa alloy for the first time.

The critical magnetic fields of H _Ms (forward martensitic transformation starting magnetic field) and H _Af (reverse martensitic transformation finishing field) were determined by the extrapolation method, as shown in Figure 6a,b. Figure  7 shows the magnetic phase diagram constructed from the thermomagnetization and magnetization measurements. The equilibrium temperature ($T_0=(T_{\mathrm{Ms}}+T_{\mathrm{Af}})/2$) and magnetic field ($H_0=(H_{\mathrm{Ms}}+H_{\mathrm{Af}})/2$) are defined. The relationship between H ₀ and temperature is described using the Clausius–Clapeyron equation

$$\frac{\mathrm{d}{H}_0}{\mathrm{d}T}=-\frac{\mathrm{\Delta }S}{\mathrm{\Delta }M}$$ (1)

where ΔM (= M _M − M _P) and ΔS (= S _M − S _P) represent the differences in the magnetization and entropy between the parent (P) and martensite (M) phases, respectively. ΔS was estimated to be −0.03 J mol⁻¹ K⁻¹ at 120 K using Equation (1) with dH ₀/dT = −5.5 kOe K⁻¹ (Figure 7) and ΔM = −0.6 emu g⁻¹ (Figure 6a). It should be noted that the shift in the transformation temperature against the magnetic field (dT ₀/dH) corresponds well with the shift in the critical magnetic field against the changing temperature (dH ₀/dT), as can be seen in Figure 7. The value of dT ₀/dH(= −0.18 K kOe⁻¹) in the Pd₂MnGa alloy is lower than those in Ni–Mn‐based MMSMAs, that is, usually approximately −0.6 K kOe⁻¹.^{[ 19 ]} An increase in ΔM may be effective in improving the response against the magnetic field.

Figure 7.

Magnetic phase diagram of the aged Pd₂MnGa alloy determined through thermomagnetization and magnetization measurements. The dashed lines are observation guides.

The values of ΔT _hys at the various applied magnetic fields are depicted in Figure  8a. The ΔT _hys increased with an increase in the magnetic field. The magnetic‐field hysteresis (ΔH _hys) was also evaluated using $\mathrm{\Delta }{H}_{\mathrm{hys}}=H_{\mathrm{A}0}-H_{\mathrm{M}0}$, where $H_{\mathrm{A}0}=(H_{\mathrm{As}}+H_{\mathrm{Af}})/2$ and $H_{\mathrm{M}0}=(H_{\mathrm{Ms}}+H_{\mathrm{Mf}})/2$, respectively. The results are plotted in Figure 8b. A small magnetic‐field hysteresis (ΔH _hys) (=7 kOe only) was confirmed at 120 K, and ΔH _hys increased with a decrease in the temperature.

Figure 8.

a) ΔT _hys plotted against the applied magnetic field. b) Temperature dependence of ΔH _hys for the magnetic‐field‐induced phase transformation. ΔH _hys increases at low temperatures.

2.4. Magnetic‐Field‐Induced Strain

The magnetic‐field‐induced strain was investigated using a dilatometer equipped with a PPMS. The setup is illustrated in Figure  9a, where the sample was placed on one side of the groove and a clip was placed on the other side to hold the sample. When the length of the sample changed under the application of a magnetic field, the width of the W‐shaped gap changed. This width was measured using the capacitance method, from which the length of the sample was evaluated. The sample holder was rotated such that the measurement direction was parallel to the applied magnetic field.

Figure 9.

Magnetic‐field‐induced strain measurements for the aged single‐crystal Pd₂MnGa alloy using a dilatometer equipped with a PPMS. a) Photograph of the dilatometer. b) Results of magnetic‐field‐induced strain measurements for a single crystal of the aged Pd₂MnGa alloy.

A single crystal of the aged Pd₂MnGa alloy was used for these measurements under magnetic fields up to 89 kOe. The crystal orientation along the direction of the magnetic field (that is, the direction of the magnetic‐field‐induced strain) is indicated in the inset of Figure 9b, which is close to the [001] direction. The measurements of the second cycle at each temperature are shown in Figure 9b. The test temperatures were 105, 110, and 115 K, which were slightly lower than T _Mf under 500 Oe, as shown in Figure 5. Moreover, the reverse transformation is expected to occur under a high magnetic field at these temperatures. Reversible magnetic‐field‐induced strains of up to 0.26% were recorded for the Pd₂MnGa alloy. The strains measured under the application of a magnetic field are caused by the reverse martensitic transformation, and the reversible strain recorded by removing the field indicates that the same martensite variants were formed.

In this study, the measurements of the magnetic‐field‐induced strain were performed without any pre‐strains. Therefore, the measured magnetic‐field‐induced strains are indicative of a phase transformation between the multivariant martensite and parent phases. As depicted in Figure S1, Supporting Information, the maximum transformation strain was estimated as 0.76% using the phenomenological theory of martensitic transformations.^{[ 40} , ^{41 ]} This value is smaller than those of Ni–Mn‐based MMSMAs (more than 6%)^{[ 4 ]} but larger than those of typical magnetostriction materials such as Tb–Dy–Fe (Terfenol‐D) alloys, which are reported to be ≈0.2–0.4%.^{[ 42} , ^{43 ]} The measurement of magnetic‐field‐induced strain on a single‐variant‐martensite state will be carried out in future work. Furthermore, the large transformation width for the full martensitic transformation (≈40 kOe at 115 K) should be reduced to suppress the required magnetic fields, and an adjustment of the martensitic transformation temperatures is also necessary if the material is to be used near room temperature.

3. Discussion

3.1. Lattice Compatibility and ΔT _hys

Recently, Cui et al. investigated Ti–Ni‐based alloys and related the hysteresis of the martensitic transformation to the middle eigenvalue (λ₂) of the transformation stretch matrix (U), which represents the lattice compatibility of the martensitic transformation.^{[ 16 ]} A similar investigation was carried out for the ΔT _hys value of Ni–Mn‐based alloys, and the tendency of ΔT _hys to decrease was confirmed when λ₂ approaches unity.^{[ 19 ]} According to James et al., there are 12 transformation stretch matrices for the cubic‐to‐monoclinic martensitic transformation; the following matrix was applied to the Pd₂MnGa alloy^{[ 17 ]}

$$\mathbf{U}=\left(\begin{array}{ccc}1.0022& 0& -0.0018\\ 0& 0.9916& 0\\ -0.0018& 0& 1.0057\end{array}\right).$$ (2)

The following lattice constants were used for the calculations: a _10M = 4.384 Å, b _10M = 6.112 Å, c _10M = 21.84 Å, and β = 90.2° at 120 K for heating, and $a_{L{2}_1}$ = 6.164 Å at 130 K. The value of λ₂ was calculated to be 1.0015, and this value was compared with those of other reported Ni–Mn–Ga‐based alloys, as shown in Figure  10 .^{[ 44} , ⁴⁵ , ⁴⁶ , ^{47 ]} The λ₂ value of the Pd₂MnGa alloy was seen to be very close to unity. Thus, it is concluded that the good lattice compatibility of the martensitic transformation is one of the possible reasons for low hysteresis in Pd₂MnGa alloys.

Figure 10.

Comparison of the λ₂ value of the aged Pd₂MnGa alloy with those of Ni–Mn–Ga‐based alloys.^{[ 44} , ⁴⁵ , ⁴⁶ , ^{47 ]}

For this alloy, both ΔT _hys and ΔH _hys increase as the temperature decreases, as depicted in Figures 7 and 8b. In addition, the value of ΔM of the metamagnetic transition also increases with a decrease in the temperature, as depicted in Figure 6a,b. A similar phenomenon has also been confirmed in Ni–Mn‐based MMSMAs, and the temperature dependence of ΔH _hys was fitted based on a phenomenological model describing the kinetics of the martensitic transformation.^{[ 48 ]} However, the temperature dependence of hysteresis for the Pd₂MnGa alloy could not be explained using this model. For this alloy, the lattice constants vary significantly with temperature (Figure 4e); thus the value of λ₂, which affects hysteresis, is also expected to vary significantly. Further investigation of the lattice constants in the parent and martensite phases under high magnetic fields is required, which will be taken up as future work.

3.2. Comparison of E _dis and ΔH _hys

In this section, we further discuss the value of E _dis, which represents the energy loss during the martensitic transformation. The E _dis value for the magnetic‐field‐induced martensitic transformation ($E_{\mathrm{dis}}^{M-H}$) can be calculated through integration over the hysteresis loop of the magnetization curve, as follows

$$E_{\mathrm{dis}}^{M-H}=-\left({\int }_0^{H_1}{M}_{\mathrm{inc}}\mathrm{d}H+{\int }_{H_1}^0{M}_{\mathrm{dec}}\mathrm{d}H\right)$$ (3)

where M _inc and M _dec represent the magnetizations during the processes of increasing and decreasing the magnetic fields to H ₁, respectively. The E _dis of the Pd₂MnGa alloy was estimated using Equation (3). This equation can be further approximated as follows

$$E_{\mathrm{dis}}^{M-H}\approx \mathrm{\Delta }M·\mathrm{\Delta }{H}_{\mathrm{hys}}$$ (4)

where ΔM is the difference in magnetization between the parent and martensite phases. Thus, a low value of E _dis is also beneficial for obtaining a low value of ΔH _hys. A large E _dis is beneficial for use in energy‐absorption materials such as dampers.^{[ 49} , ^{50 ]} However, for most applications, such as actuators, magnetocaloric refrigerants, and sensors, a small value of E _dis is favored owing to the reduced energy loss and decreased hysteresis.

Figure  11 shows a comparison of the magnetization curve of the aged Pd₂MnGa alloy with those of conventional MMSMAs at 120 K.^{[ 51} , ^{52 ]} The colored areas in the magnetization curves correspond to E _dis. It can be seen that the E _dis of Pd₂MnGa alloy is much smaller than those of Ni–Co–Mn–In and Ni–Co–Mn–Ga.

Figure 11.

Comparison of the magnetization curves of Pd₂MnGa, Ni–Co–Mn–In^{[ 51 ]}, and Ni–Co–Mn–Ga^{[ 52 ]} alloys at 120 K. The colored areas of the hysteresis loops correspond to the dissipation energy (E _dis); the E _dis of Pd₂MnGa is the smallest.

A comparison of the temperature dependence of the E _dis value for the aged Pd₂MnGa alloy with those of other MMSMAs is presented in Figure  12a.^{[ 15} , ⁵¹ , ⁵² , ⁵³ , ⁵⁴ , ^{55 ]} Some alloys such as La–Fe–Si,^{[ 56 ]} Mn–Co–Ge,^{[ 57 ]} and Mn₃ZnInN^{[ 58 ]} also exhibit metamagnetic transitions with small magnetic‐field hysteresis. However, these materials are not included in this comparison because their transitions are not accompanied by variations in the crystal structures; thus, these materials are not categorized as MMSMAs. In this study, the E _dis of Pd₂MnGa is only ≈0.3 J mol⁻¹ at 120 K, which is extremely small when compared with other MMSMAs. One possible reason for the small E _dis is the good lattice compatibility of the martensitic transformation, as exhibited in Figure 10. Furthermore, at temperatures below 120 K, the aged Pd₂MnGa alloy has the smallest E _dis among the reported MMSMAs.

Figure 12.

Comparison of a) E _dis and b) ΔH _hys for metamagnetic shape memory alloys (MMSMAs). The E _dis value was estimated from the areas of the hysteresis loops in either MH or the stress–strain curves. The E _dis and ΔH _hys values of the aged Pd₂MnGa alloy are the smallest when compared with those of other MMSMAs. The dashed lines are observation guides.^{[ 15} , ¹⁹ , ²³ , ⁵¹ , ⁵² , ⁵³ , ⁵⁴ , ^{55 ]}

In the cases of thermal or stress‐induced martensitic transformations, low values of E _dis have been confirmed in a few materials, such as the B2‐R phase transformation in Ti–Ni alloys (0.3–1.0 J mol⁻¹) and the FCC‐FCT transformation in Fe–Pd alloys (0.3 J mol⁻¹).^{[ 22} , ^{23 ]} Some alloys, such as Fe–Pd, Ti–Ni, and Ni–Co–Fe–Ga, also exhibit superelasticity with narrow hysteresis;^{[ 22} , ²³ , ⁵⁹ , ^{60 ]} however, these alloys cannot be driven by magnetic fields. When limited to MMSMAs, the value of E _dis is generally as high as 5–150 J mol⁻¹,^{[ 19} , ²¹ , ^{61 ]} and the realization of a low value of E _dis is difficult; thus, the proposed Pd₂MnGa alloy is a breakthrough in this family of alloys.

A comparison of the ΔH _hys value with those of other MMSMAs is presented in Figure 12b. For MMSMAs, a low value of ΔH _hys is necessary for applications because the creation of a strong magnetic field is energy‐consuming. Several investigations have been conducted to reduce ΔH _hys, particularly for Ni–Mn‐based alloys. The suppression of ΔH _hys (11 kOe) was successfully demonstrated for the Ni–Co–Mn–In alloy at approximately room temperature;^{[ 19 ]} however, this value is still higher than 10 kOe. Moreover, obtaining a small hysteresis at low temperatures for Ni–Mn‐based alloys is more difficult because ΔH _hys increases at low temperatures.^{[ 15} , ^{51 ]} The proposed Pd₂MnGa alloy exhibits a small hysteresis of 7 kOe at 120 K, which is smaller than that of any known Ni–Mn‐based MMSMA.

4. Conclusions

This study reports for the first time a new Pd₂MnGa MMSMA with extremely low dissipation energy and hysteresis. The microstructure, crystal structure, magnetic properties, martensitic transformation behavior, and magnetic‐field‐induced strain were investigated, and the results are summarized as follows.

The Pd₂MnGa alloy ordered from the B2 to L2₁ structure through an aging heat treatment at 573 K. The aged alloy exhibited a thermoelastic martensitic transformation from the L2₁ to 10M structure at 127.4 K with an extremely small ΔT _hys of 1.3 K. The martensitic transformation exhibited a difference in magnetization between the parent and martensite phases, and a magnetic‐field‐induced reverse martensitic transformation was confirmed. The values of E _dis and ΔH _hys were extremely low: 0.3 J mol⁻¹ and 7 kOe, respectively. The low E _dis and hysteresis values can be explained by the good lattice compatibility of the martensitic transformation with λ₂ = 1.0015, which is very close to 1. For a single‐crystal sample, a maximum magnetic‐field‐induced strain of −0.26% was obtained at 105 K through the magnetic‐field‐induced phase transformation.

The small ΔT _hys, ΔH _hys, and E _dis are unique characteristics of the Pd₂MnGa MMSMA. This alloy has the potential to be used as a low‐temperature actuator, which is an essential technology for meeting the demands of both the aerospace industry and the upcoming hydrogen society.

5. Experimental Section

The Pd₂MnGa alloys were prepared by repeated arc melting or induction melting in an argon atmosphere from pure Pd (99.9%), Mn (99.9%), and Ga (99.9999%) metals. The prepared samples were sealed in quartz tubes in an argon atmosphere for an SHT at 1473 K from 24 to 72 h and then quenched in ice water after the quartz tubes were broken. The samples were bounded by tungsten wires to prevent contact with the quartz tubes. The quenched samples were further aged at 573 K for 72 h in sealed quartz tubes under an argon atmosphere. The SHT and aged samples were cut into small pieces, and the experiments described below were performed.

The thermomagnetization curves were measured using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design Inc., USA) at 2 K min⁻¹ under applied magnetic fields of up to 70 kOe. Magnetization measurements up to 89 kOe were performed using the ACMS equipped with PPMS at a rate of 50 Oe s⁻¹. The magnetization measurements and microstructure observations using an in situ optical microscope (OM) in high‐pulsed magnetic fields were carried out at the Institute for Solid State Physics, The University of Tokyo. The maximum magnetic field and duration of the pulsed magnetic fields were ≈550 kOe and 36 ms for the magnetization measurements, respectively, and 330 kOe and 4.6 ms for the in situ OM observations, respectively. Details of the experimental methods are described in the literature.^{[ 62} , ^{63 ]}

The crystal structures and lattice constants at low temperatures under magnetic fields were determined through HFXRD measurements using powdered samples.^{[ 64 ]} The SHT sample was crushed into powders with grain sizes from 65 to 150 µm, sealed in quartz tubes in an argon atmosphere, and heat‐treated at 1473 K for 90 s to relieve the strain introduced during crushing. After the strain‐relief heat treatment, the powders were quenched in ice water without breaking the quartz tube. The quenched sample was aged at 573 K for 72 h before the XRD measurements. The chemical composition of the aged powders was analyzed by an electron probe microanalyzer equipped with wavelength dispersive X‐ray spectroscopes. The analyzed composition (Pd_{50.29 ± 0.05}Mn_{24.29 ± 0.06}Ga_{25.42 ± 0.04}) is consistent with that of the bulk sample (Pd_{50.26 ± 0.04}Mn_{24.34 ± 0.07}Ga_{25.40 ± 0.08}). The HFXRD measurements were performed at 10 ⩽ T ⩽ 300 K and 0 ⩽ H ⩽ 50 kOe.

TEM was used for the microstructural observation and crystal structure determination. Disk‐shaped samples were cut using an electrical discharge machine and then wet‐polished to a thickness of 50–100 µm. Subsequently, jet polishing was performed using an electrolyte comprising 6% perchloric acid, 12% acetic acid, 12% ethylene glycol, and 70% ethanol. Atomic‐resolution HAADF‐STEM images were obtained using an electron microscope (JEM‐ARM200F, JEOL Ltd., Japan). In situ TEM observations were performed with an electron microscope (JEM‐2100 HC, JEOL Ltd., Japan) using a sample‐cooling holder. The acceleration voltage used for the observations was 200 kV.

The magnetic‐field‐induced strain was measured using a dilatometer equipped with PPMS. A cuboid‐shaped single crystal was cut using an electron discharge machine from the large grain of the aged sample, and the oxide layer formed during processing was removed by wet polishing. The sample size was ≈2 mm × 2.5 mm × 3 mm, and the length of the 2 mm side was measured using a dilatometer. The crystal orientation of the sample was determined using electron backscattered diffraction. A magnetic field of up to 89 kOe was applied parallel to the direction of measurement, and the magnetic‐field‐induced strain was investigated. The dilatometer is described in Section 2.4 (Figure 9a).

Statistical Analysis

For the measurements of chemical compositions of bulk and powdered Pd₂MnGa samples using an electron probe microanalyzer, seven analyses were conducted for each sample. The average of the seven data points for each sample was taken as the determined composition with the standard error. For the magnetization measurements using high‐pulsed magnetic fields up to ≈550 kOe, time derivatives of magnetic flux density (dμ₀ H/dt) and magnetization (dM/dt) were directly obtained by induced voltages in pick‐up coils at the desired temperature. Since dM/dt contains signals from background and uncompensated induced voltage, two measurements, with the specimen and the background, that is, sample holder, were conducted; their difference is the net dM/dt signal from the specimen. Both dμ₀ H/dt and subtracted dM/dt were integrated with respect to time, and the preliminary M–H data were obtained. The absolute value of magnetic flux density was calibrated using the metamagnetic transition fields of MnF₂. Thus, obtained preliminary values of M, M _preliminary, were subjected to a calibration. Using M _calibrated(H) = aM _preliminary(H) + bH + c, calibration was performed by determining the coefficients a, b, and c in comparison with the absolute values of M, M _calibrated, up to 70 kOe obtained by a SQUID magnetometer at the same temperature. Since other data were directly obtained, neither data processing nor statistic procedures were applied.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Supplemental Movie 1

Ito T., Xu X., Miyake A., Kinoshita Y., Nagasako M., Takahashi K., Omori T., Tokunaga M., Kainuma R., Pd₂MnGa Metamagnetic Shape Memory Alloy with Small Energy Loss. Adv. Sci. 2023, 10, 2207779. 10.1002/advs.202207779

Data Availability Statement

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