Low-pressure-driven barocaloric effects at colinear-to-triangular antiferromagnetic transitions in Mn_3-xPt_1+x

INTRODUCTION

Refrigeration technology is of great significance for both industry and everyday life. Current refrigeration systems are mostly based on conventional vapor compression technology. Although highly optimized in recent decades, they still have a considerable undesirable impact on the environment^[1]. Frequently used refrigerants have thousand-time stronger global warming potentials compared to CO₂. To achieve carbon neutrality, solid-state refrigeration technology based on the caloric effects of solids has been proposed as an alternative solution. Various phase transitions caused by some calorimeter materials under external fields are accompanied by huge latent heat, which can be utilized for cooling purposes through designated thermodynamic cycles. Magnetocaloric effects (MCEs) is one of the most studied caloric effects, which is usually linked to magnetic-field-induced first-order transitions. Barocaloric effects (BCEs), as the counterpart and extension of the (MCEs), is defined as the change in the isothermal entropy or adiabatic temperature of the material during the application or withdrawal of the external pressure field. Materials with first-order phase transition are more likely to be the most potential barocaloric effect materials due to the sensitivity of the lattice to pressure.

Initially observed around 2,000 years, BCEs has been found in Pr_1-xLa_xNiO₃^[2] and CeSb^[3]. Subsequent studies of magneto-elastically coupled materials for MCEs have revealed larger BCEs, such as in magnetic shape memory alloys including NiMnIn^[4], La(Fe,Si)₁₃^[5,6], Gd₅Si₂Ge₂^[7], MnCoGe_0.99In_0.01^[8], FeRh^[9,10], and others. These materials exhibit a strong coupling between magnetic and lattice degrees of freedom. Usually, there is a magnetic phase with a larger volume and a magnetic phase with a smaller volume. The application of a sufficiently large hydrostatic pressure induces a change of the system from the large-volume to the small-volume phase, and simultaneously the magnetic phase transition takes place. Typically, the required driving pressures in these systems are as high as several hundred MPa, and a comparable pressure-induced entropy change to that induced by a magnetic field can be obtained.

In recent years, a great variety of materials have been reported with larger BCEs, such as AgI^[11], organic-inorganic hybrid chalcogenide [TPrA][Mn(dca)₃]^[12], ferroelectric (NH₄)₂SO₄^[13,14], spin-crossover complexes^[15-18], and even natural rubber^[19,20]. First-principles calculations also predicted sizable BCEs for lithium-ion conductor materials^[21], fluorine ion conductor materials^[22], and graphene^[23]. In plastic crystals, the extensive molecular orientation disorder in plastic crystals leads to huge entropy changes larger than 100 J kg^-1 K^-1, and the driving pressures have been significantly reduced down to below 100 MPa, for which they are termed as colossal barocaloric effects^[24-26].

Antiferromagnetic materials are effective in releasing their entropy change by pressure in addition to the magnetic field^[10,27], with remarkably reduced driving pressures, especially in frustrated antiferromagnets. Recent research has found that larger BCEs are observed at phase transitions from frustrated antiferromagnetic (AFM) to paramagnetic states in nitrides (Mn₃GaN^[28], Mn₃NiN^[29]) with an anti-perovskite structure. This indicates that even small hydrostatic pressures (as low as 90 MPa in plastic crystals) can effectively act on the AFM system. In this work, we report on the barocaloric properties of Mn_3-xPt_1+xalloys at first-order phase transitions from low-temperature triangle-lattice frustrated to high-temperature colinear AFM states. The composition-dependent phase transition temperature (T_t) is about 331 K for the Mn_2.82Pt_1.18. The pressure-dependent calorimetric measurements suggest that entropy changes are saturated at around 60 MPa.

EXPERIMENTS

Polycrystalline samples of Mn_3-xPt_1+xwith different Mn contents (x = 0.04, 0.08, 0.1, and 0.18) were prepared by arc-melting the high-purity (99.9%) elements under an Ar atmosphere. The true composition was determined using a ThermoFisher iCAP6300 Inductive Coupled Plasma Emission Spectrometer (ICP). The ingots were remelted three times to ensure homogeneity. 2wt.% excessive Mn elements were added to compensate for losses during the melting process. The as-prepared ingots were annealed in encapsulated quartz tubes at 973 K for 120 h and followed by furnace cooling. The nature of the single-phase was checked using a Rigaku MiniFlex 600 X-ray diffractometer. The temperature-dependent X-ray diffraction (XRD) patterns were collected using Bruker D8 Advance X-ray diffractometer. The diffraction patterns were fitted to a cubic unit cell (space group Pm$$ \scriptsize \overline{3}$$m) in Jana2006^[30]. The calorimetric data were collected as a function of temperature and pressure using a high-pressure differential scanning calorimeter (µDSC7, Setaram). The samples were enclosed in a high-pressure vessel made of Hastelloy. Constant pressure scans were performed at 0.1, 30, 60, and 90 MPa in the temperature region from 290 to 390 K, respectively. After subtracting the baseline background, the heat flow data can be converted to entropy changes. The magnetic properties are characterized using a Magnetic Properties Measurement System (MPMS-XL, Quantum Design) and a Physical Property Measurement System (PPMS-14T, Quantum Design).

RESULTS AND DISCUSSIONS

Mn_3-xPt_1+xcrystallizes in the ordered Cu₃Au-type structure^[31,32], where Mn atoms are located on the face centers of the cubic lattice formed by Pt atoms, as shown in Figure 1A. The compound with the stoichiometric composition magnetically orders into a colinear AFM state at about T_t ~365 K (magnetic transition temperature of Mn₃Pt in the literature^[32]), where a negligibly small tetragonal distortion is observed. As depicted, magnetic moments carried by Mn atoms are aligned along the c-axis, and the magnetic unit cell is constructed along the c-axis with doubled chemical unit cell. Note that the Mn atoms located on the ab-plane carry no ordered magnetic moment. The four Mn atoms form a square lattice, and the diagonal magnetic moments are parallel while the adjacent ones are anti-parallel. Spaced by the non-magnetic Mn atom, the magnetic moments of the two layers of the square lattices are antiferromagnetically coupled. As the temperature decreases below T_t, such a colinear AFM state transforms into a triangle-lattice AFM state, where magnetic moments are located on the (111) plane and point in the <211> direction, leading to a two-dimensional geometric spin frustration. This arrangement of magnetic moments ensures that the magnetic unit cell is identical to the chemical unit cell. This phase transition is a typical first-order magnetic phase transition, even if the lattice symmetry is maintained^[33]. Based on the triangular AFM structure, anomalous Hall effects have been predicted and observed in films as well as bulk single crystals^[34,35].

Figure 1. (A) Magnetic structures of Mn₃Pt alloys with triangular AFM and colinear AFM phases as reported by Tao et al.^[27]. (B-D) heat flow vs. temperature curves, the contour plots of the variable temperature XRD patterns and lattice constant vs. temperature curves for sample x = 0.1, respectively. The inset in (C) is an enlarged image of the high Q region.

In the Mn_3-xPt_1+xsystem, the magnetic properties, in particular, T_t, are strongly dependent on the composition x. Shown in Figure 1B is the heat flow data of the x = 0.1 alloy under ambient pressure, where an endothermic peak is found at 360 K while an exothermic peak at 340 K with a thermal hysteresis of about 20 K, which is a signature of the first-order phase transition. The temperature corresponding to the peak in the heat flow curve is defined as the phase transition temperature. In this paper, we uniformly regard the transition temperature of the cooling process as the phase transition temperature of the sample. The entropy change at this transition is derived from being about 12.31 J kg^-1 K^-1, which is kind of small compared to other systems that exhibit strong first-order transitions. The reason will be clarified afterward. For example, the entropy change is 22.3 J kg^-1 K^-1 in Mn₃GaN^[28] while 43 J kg^-1 K^-1 in Mn₃NiN^[29]. The temperature-dependent XRD was used to monitor the lattice distortion during the phase transition. The contour plots of the XRD patterns are shown in Figure 1C as a function of temperature (T) and scattering vector (Q). The patterns can be indexed based on the reported cubic structure. Within our resolution, there is no distinguishable symmetry change in the temperature from 300 to 410 K. Four strong Bragg peaks are observed, and the (210) peak obviously shifts towards the lower Q around 360 K. The determined lattice constant displays a sudden jump at 360 K [Figure 1D], corresponding to relative changes in lattice constant and unit cell volume of 0.75% and 2.26%, respectively. These values are similar to those reported in other literature^[36,37]. In addition, the structurally determined T_t is well consistent with the thermally determined one.

After confirming the first-order phase transition as the core of this study typically occurs at x = 0.1, we systematically extend the magnetic characterizations to x = 0.04, 0.08, 0.1, and 0.18. Their field-cooled magnetizations as a function of temperature are plotted in Figure 2A-D. As the temperature decreases, magnetizations abruptly drop at 331 K for x = 0.18, 336 K for x = 0.1, 355 K for x = 0.08, and 384 K for x = 0.04, indicating the first-order phase transitions. As for x = 0.1, the determined T_t at the magnetization is a few kelvins lower than that in the heat flow data. We summarize the T_t values of these four samples, along with their lattice constants at room temperature, in Figure 2E. As x changes from 0.18 to 0.04, T_t monotonically increases while the lattice constant a decrease. Unlike the linear behavior of a, T_t exhibits a saturation feature, remaining nearly constant when x is greater than 0.1. Such a tendency is consistent with the previous report^[31,32,36]. This phenomenon is also explained in the literature^[31] based on the theoretical phase diagram of Mn₃Pt in the molecular field approximation.

Figure 2. (A-D) Magnetization curves for samples x = 0.18, 0.1, 0.08, and 0.04, respectively. (E) Curves of phase transition temperature vs. manganese content x (blue squares and red dots indicate measurement by M-T and heat flow, respectively) and lattice constant vs. manganese content x for the samples. (Taking x = 0.08 as an example, the fitting parameters obtained using the lebail method to fit the XRD curve are: GOF = 1.47, Rp = 4.18, Rwp = 5.99). (F) The magnetization loop of x = 0.18. The inset shows the enlarged plot at low fields.

Selecting x = 0.18 as an example, the high-field isothermal magnetization is considered at 300 and 380 K, where the compound is in the triangular AFM and colinear AFM states, respectively. As shown in Figure 2F, the magnetizations essentially obey a linear relation as a function of applied fields up to 14 T, which reflects the dominating AFM interactions. However, the low-field regions (the inset of Figure 2F) show a weak nonlinearity at both temperatures, which might be attributed to the uncancelled moments due to the off-stoichiometry. In particular, there are small remanence and coercivity at 300 K. The exact origin is still unknown. Previous studies have also shown that a ferromagnetic component perpendicular to the (111) plane is allowed on both Mn and Pt atoms, except for the component in the (111) plane pointing in the [112] direction in the magnetic structure of the triangular AFM phase^[31]. Furthermore, it has been pointed out that the origin of this ferromagnetism may be because the third site of the colinear AFM phase generates a net magnetic moment due to electron interactions at low temperatures of 100 K or even lower^[38]. In contrast to the presence of net moments along the <111> direction, the magnetization curve of the single-crystal material along the <111> direction did not show ferromagnetic behavior^[34].

Except for the influence of magnetic fields on the first-order phase transitions, we explore the impact of applied hydrostatic pressures. Heat flow data as a function of temperature are plotted under 0.1, 30, 60, and 90 MPa for x = 0.08 and x = 0.18 in Figure 3A and B, respectively. As the pressure increases, the endothermic and exothermic peaks move toward the high-temperature region simultaneously. The peak intensity has a small increase with pressure, while the peak width has a tendency to narrow, which is especially obvious in the x = 0.18 sample. In addition, the thermal hysteresis at 0.1 MPa for the x = 0.08 sample is the same as that at x = 0.1, which is 19 K. However, the thermal hysteresis at atmospheric pressure for x = 0.18 sample is 9 K and decreases to 5 K at 90 MPa with increasing pressure.

Figure 3. (A and B) Heat flow data as a function of temperature for x = 0.08 and x = 0.18 at 0.1, 30, 60, and 90 MPa pressure, respectively. (C and D) Entropy change curves for x = 0.08 and x = 0.18 at different pressures, respectively. (E and F) The temperature-pressure phase diagrams for x = 0.08 and x = 0.18, respectively.

Entropy changes at the phase transition under constant pressure, ΔS_P, are determined by integrating the heat flow data. The pressure-induced entropy changes ($$\Delta S_{P_{0}\rightarrow P}$$) when pressure is increased from ambient pressure (P₀) to applied pressure (P) is defined as $$\Delta S_{P_{0}\rightarrow P}$$ = ΔS_P - $$\Delta S_{P_{0}}$$. Figure 3C and D show $$\Delta S_{P_{0}\rightarrow P}$$ at the final pressure of 30, 60, and 90 MPa for x = 0.08 and 0.18, respectively. It can be seen that more than 80% of the maximum entropy changes are achieved at pressures as low as 30 MPa, and the entropy changes tend to be saturated at about 60 MPa. Note that the maximum entropy of 13.79 J kg^-1 K^-1 acquired in x = 0.08 at 90 MPa is larger than that in x = 0.18 whereas the so-called reversible region (overlapped region for the cooling and heating curves) is much larger for x = 0.18. The temperature-pressure phase diagrams are constructed based on the heat flow data [Figure 3E and F]. It can be seen that the thermal hysteresis is much smaller in x = 0.18, which is the reason why its reversible region is larger^[14]. Furthermore, its thermal hysteresis is obviously reduced at higher pressures.

To understand the uniqueness of this system, Table 1 compares its barocaloric factors to those of other typical compounds, including organic plastic crystals, inorganic salts, magnetocaloric intermetallics, and other frustrated AFM systems. The slope of the phase boundary (dT_t/dP) of this system is the largest, and the driving pressure (ΔP) is the smallest among all intermetallics, which are impressively comparable to those of prototype plastic crystal neopentyl glycol with colossal BCEs. However, the larger dT_t/dP must lead to smaller entropy changes in terms of the Clausius-Clapeyron relation^[39], even though the volume change is not too small. The small entropy change at this first-order phase transition is due to unique magnetic fluctuations in nature. Magnetic fluctuation refers to the fluctuation of magnetic (electron spin) moment in magnetic systems^[40]. The interaction between the local moment and the itinerant electron matrix may enhance spin fluctuation. Frustration structures are often accompanied by strong spin fluctuations^[41,42]. Neutron diffraction measurements suggest that the ordered moment is 3.3 µ_B/Mn atom in the colinear AFM state, whereas 2.2 µ_B/Mn atom in the triangular AFM^[37]. The reduction in the latter should be attributed to spin fluctuations due to geometric frustration. As a result, the triangle-lattice AFM state is magnetically less ordered than the colinear AFM one, which leads to an increase of magnetic entropy across T_t. At the same time, the crystal lattice shows a normal contraction, and a reduction of entropy of the lattice subsystem is expected. We infer that the contributions of individuals to the total entropy change partially cancel each other out, and the remaining entropy change represents the overall entropy change of the material. According to the previous theoretic study, the system can be described by a nearest-neighboring exchange interaction J₁ and a next-nearest-neighboring exchange interaction J₂. J₁ is always negative, but J₂ can be negative or positive, dependent on the interatomic distance between Mn atoms^[31]. At T_t, J₂ just changes its sign due to the shrinkage of the Mn-Mn distance. In this sense, such a picture is similar to the exchange striction observed in NiMnIn alloys^[43].

CONCLUSIONS

In summary, the first-order phase transitions of Mn_3-xPt_1+x(x = 0.04, 0.08, 0.1, and 0.18) compounds have been studied at varying temperatures, pressures, and magnetic fields. At the phase transitions, both magnetizations and lattice constants showed abrupt drops as the temperature decreased. While the phase transition temperatures decreased at lower Mn content, they increased at higher pressures. This system is highly susceptible to pressure, and the pressure-induced entropy changes are saturated at 60 MPa, which is the lowest among current intermetallics. This may be due to the intense geometric magnetic frustration.