The influence of hydrostatic pressure and annealing conditions on the magnetostructural transitions in MnCoGe

Studies of magnetostructural phase transitions in magnetic materials have intensified due to the potential energy-saving and climate-friendly advantages of solid state cooling resulting from the magnetocaloric effect (MCE).^1–6 An increasing effort has been put on understanding the physical origins of these effects, as well as discovering better magnetocaloric materials.^7–9 Until now, many solid materials have been studied for scientific and practical purposes with regard to their magnetocaloric properties, including $Gd5SixGe4−x$⁠,^10,11 Ni-Mn-based full Heusler alloys,^12–18 MnAs-based compounds,^19–21 $Fe2$P-based alloys,^21–23 $LaFe13−xSix$ related compounds,^24,25 and intermetallic Mn$TX$ (T = transition metal and X = Ge, Si) systems.^26–32 

Among the materials listed above, intermetallic Mn$TX$ systems have drawn increasing attention recently due to their giant magnetocaloric and baroclaoric effects caused by their large volume expansion/contraction resulting from first-order martensitic structural transitions between a $Ni2$In-type hexagonal austenite phase (space group: $P63/mmc$⁠) and a TiNiSi-type orthorhombic martensite phase (space group: $Pnma$⁠).^30,31 The MnCoGe-based systems have drawn considerable interest since the structural phase transition (470 K) and Curie temperature (345 K) of the parent MnCoGe compound are relatively close to room temperature.³³ An interesting feature of MnCoGe-based alloys is the strong interplay between their structural and magnetic phase transitions. Several factors, such as the partial substitution with a fourth element,^34–56 stoichiometry modification,^57–59 interstitial doping,⁶⁰ vacancy tuning,^61–63 heat treating,^64–66 and pressure application⁶⁷ were found to influence the structural and magnetic properties considerably.

In this work, stoichiometric MnCoGe compounds were prepared by annealing the samples at temperatures ranging from $700°C$ (solid phase) to $1150°C$ (liquid phase), followed by either slowly cooling or rapidly quenching, and the phase transition properties in response to temperature, hydrostatic pressure, and magnetic field were measured. First, the raise of the quenching temperatures was found to lower the first-order martensitic structural transition by over 200 K. The lowest first-order martensitic structural transition temperature (234 K) was observed for the sample quenched at $1000°C$⁠, and the highest one (470 K) was observed for the samples cooled slowly from $1100°C$ at $30°C$/h. The largest maximum magnetic entropy change (⁠$−33.6$ J/kg K for a 7-T field change) was found for the samples quenched at $800°C$⁠, for which the magnetic and structural phase transitions are coupled. Second, as we increased the hydrostatic pressure, the first-order martensitic structural transition shifted to lower temperature until the samples were completely converted to the $Ni2$In-type hexagonal austenite phase with second-order magnetic phase transitions. Our findings show that the first-order martensitic structural transition was suppressed and transformed to a second-order magnetic phase transition of the $Ni2$In-type hexagonal austenite phase when either quenched from sufficiently high temperatures or subjected to sufficiently high hydrostatic pressures.

The formation of the MnCoGe compounds was explored using a simultaneous differential scanning calorimeter (DSC) and thermogravimetric analysis device (model: SDT Q600 manufactured by TA Instruments, Inc.). To explore the synthesis of MnCoGe alloys, the individual pure elements were placed in the DSC, and the heat flow measurement was carried out by sweeping the temperature up to $1100°C$ twice as shown in Fig. 1. The first heating experimental route is shown in Fig. 1(a), and the allotropic transformation of Mn was observed at $720°C$⁠,⁶⁸ followed by the complete liquification of MnCoGe components at $1100°C$⁠. A clear first-order phase transition peak due to crystallization was observed at $1050°C$ in the first cooling route.

After the samples were cooled, second heating and cooling scans were performed. In the second cycle, the melting/crystallization of the MnCoGe ingot was observed as shown in Fig. 1(b), and no other perceivable transitions were observed. Guided by these results, a MnCoGe ingot was prepared by melting it at $1100°C$⁠, and was then quenched either in the solid or liquid phase at the selected temperatures described in Sec. III.

In addition to exploring the potential synthesis conditions, DSC experiments were also performed for the samples with non-magnetic first-order martensitic structural transitions occurring above 400 K, the results of which together with those of magnetization measurements, will be discussed in Sec. V.

In order to fabricate stoichiometric MnCoGe, high purity Mn (99.95%), Co (99.95%), and Ge (99.999%) elemental components were placed inside $Al2O3$ crucibles, and then sealed in a quartz tube under vacuum. The materials were then brought up to $1100°C$ and annealed for 12 h. To ensure the homogeneity of their chemical compositions, the ingots were pulverized and annealed at $1100°C$ for another 12 h, and finally cooled to room temperature at $30°C$/h. This 30-g sample served as the source ingot for later sample preparation and is labeled as SC1100, where “SC” stands for “slowly cooled.”

Subsequently, 2-g pieces from the source sample were weighed and then melted in an arc furnace to preserve a single and contiguous specimen. Again, they were placed in $Al2O3$ crucibles and then sealed in a quartz tube under vacuum. Since all of the samples in this work were fabricated from the same master ingot, their compositions were expected to be identical. The samples were annealed separately at $1150$⁠, $1000$⁠, $900$⁠, 800, and $700°C$ for 12 h (labeled as AQ1150, AQ1000, AQ900, AQ800, and AQ700, respectively), and then quenched in a vessel of liquid nitrogen by breaking the quartz tube. Note that sample AQ1150 was quenched from the liquid phase, while the others remained solidified during annealing. The synthesis conditions of all the samples and their respective properties are summarized in Table I.

The crystal structures of the samples were investigated by powder x-ray diffraction (XRD), which was performed using a Scintag XDS2000 powder diffractometer with Cu K$α$ radiation at room temperature. To avoid the induced stress/stain due to the grinding process,^71,72 the XRD samples were prepared by thermal cycling the samples back and forth across their structural transitions until they were broke down into powders. The XRD results at room-temperature for all samples are shown in Fig. 2.

According to the XRD results, samples SC1000, AQ700, and AQ800 crystallized in the TiNiSi-type orthorhombic martensite phase at room temperature, while samples AQ900, AQ1000, and AQ1150 crystallized in the $Ni2$In-type hexagonal austenite phase. The lattice parameters and cell volumes of their major crystal structures are tabulated in Table II, which were obtained from Rietveld refinements using general structure analysis system (GSAS) software.^73–76 As the annealing temperature increased, the cell volumes per MnCoGe formula unit at room temperature decreased. As the volume reduces, the first-order martensitic structural transition temperatures also reduce, which has been commonly observed in similar materials,^77,78 because the $Ni2$In-type hexagonal austenite phase has a smaller volume than that of the TiNiSi-type orthorhombic martensite phase.

It is known that the TiNiSi-type orthorhombic martensite phase can be regarded as a distortion of the $Ni2$In-type hexagonal austenite phase through the relations $aorth↔chex,borth↔ahex,andcorth↔3ahex$⁠.²⁷ Based on these relations, the distortion relations between the annealing temperatures and crystal parameters/volume are presented in Fig. 3. As the annealing temperature increases, a 10.6% reduction of $aorth$ and a 6.9% expansion of $borth$ were observed, resulting in a 3.9% volume reduction overall. Note that the deformations of the cell parameters $aorth↔chex$ and $borth↔ahex$ are relatively larger than that of $corth↔3ahex$⁠, which is commonly observed in alloys with a structural transformation from a Ni$2$In-type hexagonal austenite phase to a TiNiSi-type orthorhombic martensite phase.^77,78

To investigate the structural changes across the martensitic structural transitions, samples AQ900 and SC1100 were selected for temperature-dependent XRD experiments, which were performed at the X-ray Science Division beamlines at the Advanced Photon Source, Argonne National Laboratory and the National Synchrotron Radiation Research Center (NSRRC, Taiwan) on beamline TLS-01C2, respectively. These temperature dependent XRD results are shown in Fig. 4. As the temperature increases through the martensitic structural transitions, the TiNiSi-type orthorhombic martensite phase at low temperature distorts with a 10.4% reduction of $aorth$ and 6.9% expansion of $borth$⁠, and ultimately stabilizes in the $Ni2$In-type hexagonal austenite phase. The changes in cell parameters across the martensitic structural transitions for these samples are nearly the same although their transition temperatures are significantly separated, and a coupled magnetostructural transition was observed only in sample AQ900, not sample SC1100. Comparable magnitude changes of the cell parameters were reported previously by sweeping across the first-order martensitic structural transition temperatures of MnCoGe²⁷ or $MnCoGe1−xInx$ (⁠$x=0.01,0.02$⁠),⁷⁹ or by substituting Cu in $Mn1−xCux$CoGe.⁴² 

The magnetization results presented in this section were obtained using a magnetic property measurement system manufactured by Quantum Design, in a temperature range of 20–400 K and in fields up to 7 T.

The isofield, temperature-dependent magnetization measurements in an applied 0.1-T field were performed using field-cooled cooling and field-cooled warming protocols, and the results are shown in Fig. 5. At ambient pressure, all the samples except AQ1150 exhibit first-order martensitic structural transitions with thermal hysteresis. First-order martensitic structural transitions were not observed in sample AQ1150, which is consistent with the MnCoGe samples prepared by melt spinning,⁶⁶ while the sample SC1100 shows similar structural and magnetic transitions as reported in Ref. 33.

The first-order martensitic structural transition temperatures, $Tm$⁠, estimated from the temperature-dependent magnetization measurements and the calorimetric experiments, are listed in Table I. Increasing annealing temperatures were found to decrease the first-order martensitic structural transition temperatures rapidly, and to decrease the Curie–Weiss temperature of austenite phase comparatively slowly. The lowest first-order martensitic structural transition temperature (234 K) was observed for the sample quenched at $1000°C$⁠, and the highest one (470 K) was observed for the sample cooled slowly from $1100°C$⁠. The effect of the annealing temperatures on the first-order martensitic structural transitions and Curie–Weiss temperatures is illustrated in Fig. 6.

Magnetization measurements under hydrostatic pressure were performed using a commercial BeCu cylindrical pressure cell manufactured by HMD Inc.^80,81 The temperature-dependent magnetization results in 0.1-T field shown in Fig. 5 (dashed lines) demonstrate the effect of pressure on the phase transitions under the indicated hydrostatic pressures. With the specified hydrostatic pressures, the thermal hysteresis due to the first-order martensitic structural transitions was suppressed in samples AQ900 (8.9 kbar) and AQ1000 (8.3 kbar), while the first-order martensitic structural transition temperatures decreased in samples SC1100 (11.3 kbar) and AQ700 (6.4 kbar). These temperature-dependent magnetization results under pressures suggest that the hydrostatic pressure application induces the negative temperature shift of martensitic structural transitions, and the absence of the first-order martensitic structural transition was observed as long as sufficiently high pressure is applied. Note that the first-order martensitic structural transition was expected to convert to second-order phase transition in samples SC1100, AQ700, and AQ800 if sufficiently high pressures were applied. In summary, it is found that the first-order martensitic structural transitions were converted to second-order magnetic phase transitions of the $Ni2$In-type hexagonal austenite phase by either applying pressures or raising the quenching temperatures.

To further investigate the magnetizations of the samples at low temperatures, saturation magnetization measurements at 2.0 K were performed up to 7 T, as shown in Fig. 7. The saturation magnetization (⁠$Msat$⁠) values were estimated by fitting the experimental magnetization data by the law of approach-to-saturation

where $a$ and $b$ are fitting parameters.^82,83 These fitted $Msat$ values are listed in Table I. Different from the other quenched samples, sample AQ1150 shows a much lower saturation magnetization and also exhibits no thermal hysteresis in the temperature-dependent magnetization, as shown in Fig. 5. With the application of hydrostatic pressures, similar phenomena were observed in samples AQ900 (8.9 kbar) and AQ1000 (8.3 kbar). It is known that the saturation magnetization of the MnCoGe parent phase is 3.9 and 2.6 $μB$ for the TiNiSi-type orthorhombic martensite phase and the $Ni2$In-type hexagonal austenite phase, respectively.^27,84–87 Therefore, the abrupt reduction of the saturation magnetization along with the absence of thermal hysteresis observed here are concluded to be evidence that the TiNiSi-type orthorhombic martensite phase was completely suppressed, and only the $Ni2$In-type hexagonal austenite phase was present under the specified annealing and pressure conditions.

The Curie–Weiss law⁸⁸ 

where $NA$ is Avogadro’s number, $kB$ is the Boltzmann constant, $μeff$ is the effective magnetic moments per formula unit, and $θCW$ is the Curie–Weiss temperature, was used to fit the temperature-dependent magnetization in the paramagnetic temperature region. The linearity between $1/χ$ and $T$ shown in Fig. 8 demonstrates the paramagnetic behavior of both the martensite and austenite phases. The fitted Curie–Weiss temperatures for the $Ni2$In-type austenite phase and for the TiNiSi-type orthorhombic martensite phase are listed in Table I, and these values are consistent with previous reports.^67,85,87 It is worth noting that the Curie–Weiss temperatures of both the TiNiSi-type orthorhombic martensite phase and the $Ni2$In-type austenite phase remain relatively unchanged regardless of the annealing and pressure conditions, while the first-order martensitic structural transition temperatures are sensitive to both.

The potential MCE performance of materials was characterized by the magnetic entropy change $ΔS(T,0→H)$⁠, which was estimated by using the thermodynamic relation⁸⁹ 

A series of isothermal magnetization measurements were performed to obtain $M(T=const.,H)$⁠. To eliminate any residual ferromagnetic response from the martensite phase, prior to each isothermal magnetization measurement the samples were heated to complete the paramagnetic austenite phase, and then cooled down to the target measurement temperature under zero field. This thermodynamic reset protocol was referred to as the cooling protocol or the loop process in Refs. 90 and 91, because the results obtained using this protocol can also be acquired by calorimetric experiments during the cooling process.

The magnetic entropy changes of samples under different quenching temperatures for a 7-T field are shown in Fig. 9. The values of the maximum magnetic entropy change and relative cooling power for each sample are listed in Table I. Sample AQ800 shows the largest maximum magnetic entropy change for a 7-T field change (⁠$ΔSmax=−33.6$ J/kg K) while the other samples have nearly equivalent magnitudes with $ΔSmax=−9.7$ J/kg K for AQ900, and $−9.6$ J/kg K for AQ1000. Among all the samples, AQ1000 shows the largest relative cooling power (⁠$RCP=682$ J/kg for a 7-T field change) although its full width at half maximum, $δFWHM$⁠, is much larger than that of AQ800. Comparable maximum magnetic entropy changes and martensitic structural transition temperature shifts were also observed in Ref. 59 by controlling the valence electron concentration of $Mn1−xCoGe1+x/Mn1+yCoGe1−y$⁠, and in Ref. 34 by controlling the Au-doping concentration in $Mn1−xAuxCoGe$⁠. Nevertheless, the results presented here were achieved for samples with a single composition, MnCoGe.

The sample AQ800 that shows the largest maximum magnetic entropy change was selected for further investigation of the magnetic entropy changes under different pressures, the results of which are shown in Fig. 10. Similar to the effect of quenching temperature, hydrostatic pressure drives the martensitic structural transition temperature lower as the pressure increases, and the magnetostructural transitions decoupled. Meanwhile, the maximum magnetic entropy change at 1.8 kbar was found to be largest, and then tended to decrease as the pressure further increased up to 7.9 kbar. It is clear that the pressure induces the negative temperature shift of the martensitic structural transition and would ultimately suppress the first-order martensitic structural transition as long as sufficiently high pressure were applied. Therefore, the maximum magnetic entropy change is expected to be further reduced above 7.9 kbar until the first-order martensitic structural transition is completely absent and only the second-order magnetic transition is present in sufficiently high pressures.

In this work, the structural and magnetic properties of MnCoGe upon systematic variation of the annealing/quenching conditions and applied hydrostatic pressure were investigated. First-order martensitic structural transitions from the TiNiSi-type orthorhombic martensite phase to the $Ni2$In-type hexagonal austenite phase decreased in a wide temperature range (⁠$>200$ K) by increasing the quenching temperatures of the samples in the solid phase up to $1000°C$⁠. As the samples were quenched from the liquid phase (⁠$1150°C$⁠), the first-order martensitic structural transition disappeared, and only the second-order magnetic transition remained. Similarly, as we applied hydrostatic pressures, all of the samples converted to the $Ni2$In-type hexagonal austenite phase with a second-order magnetic transition for sufficiently high pressures. It is concluded that the TiNiSi-type orthorhombic martensite phase would eventually be absent, and only the second-order magnetic phase transitions of the $Ni2$In-type hexagonal austenite phase would be present, if sufficiently high annealing temperatures or hydrostatic pressures were reached. Meanwhile, the coupled magnetostructural transitions and the corresponding magnetic entropy enhancements were found to also be achievable by either applying proper hydrostatic pressures, quenching conditions, or both.

S. Stadler acknowledges support from the U.S. Department of Energy (DOE), Office of Basic Energy Sciences under Award No. DE-FG02-13ER46946. N. Ali and I. Dubenko acknowledge support from the U.S. Department of Energy, Office of Basic Energy Sciences under Award No. DE-FG02-06ER46291. D. P. Young acknowledges support from the U.S. National Science Foundation (NSF), Division of Materials Research under Award No. NSF-DMR-1904636. Y.-C. Huang acknowledges support from the Ministry of Science and Technology of Taiwan (No. MOST 107-2218-E-131-007-MY3). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by the Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The DSC data used in this work were collected at the Center for Advanced Microstructures and Devices (CAMD) under the supervision of A. Roy.

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