Giant reversible barocaloric response of (MnNiSi)1−x(FeCoGe)x (x = 0.39, 0.40, 0.41)

MnNiSi-based alloys and isostructural systems have traditionally demonstrated impressive magnetocaloric properties near room temperature associated with a highly tunable first-order magnetostructural transition that involves large latent heat. However, these materials are limited by a small field-sensitivity of the transition, preventing significant reversible effects usable for cooling applications. Instead, the concomitant large transition volume changes prompt a high pressure-sensitivity, and therefore, promise substantial barocaloric performances, but they have been sparsely studied in these materials. Here, we study the barocaloric response in a series of composition-related (MnNiSi)1−x(FeCoGe)x (x = 0.39, 0.40, 0.41) alloys that span continuously over a wide temperature range around ambient. We report on giant reversible effects of ∼40 J K−1 kg−1 and up to ∼4 K upon application of ∼2 kbar and find a degradation of the first-order transition properties with pressure that limits the barocaloric effects at high pressures. Our results confirm the potential of this type of alloys for barocaloric applications, where multicaloric and composite possibilities, along with the high density and relatively high thermal conductivity, constructively add to the magnitude of the caloric effects. © 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5097959


I. INTRODUCTION
First-order magnetostructural transitions (FOMSTs) constitute one of the most relevant expressions within the multiferroic casuistry as they may involve an intricate network of both physical interactions and functionalities. The underlying spin-lattice coupling together with large concomitant changes in both magnitudes offers a platform where a diversity of magnetic, structural, and electronic orderings and cross-variable couplings can develop [1][2][3][4][5] and are at the origin of a variety of phenomena with promising technological applications such as the magnetic shape memory effect, 6 magnetic superelasticity, 7 giant magnetoresistance, [8][9][10] and caloric effects. 11 In particular, the latter are currently attracting great interest because they propose a clean, efficient, and down-scalable refrigeration method as an alternative to current compressors that use high-greenhouse fluids. They are based on the exchange of the latent heat associated with first-order phase transitions driven by controllable external fields. In the case of magnetocaloric (MC) materials, the latent heat in FOMSTs may entail a significant improvement of the caloric performance with respect to their second-order counterparts. 12 In addition, FOMSTs allow (i) the possibility of harvesting both magnetocaloric 11 and mechanocaloric 13 effects separately, or simultaneously, with the subsequent multicaloric advantages, 14 (ii) more compact devices as permitted by their high density, and (iii) good heat exchange due to the relatively high thermal conductivity. However, their competitiveness is restricted to the use of costless magnetic fields generated by expensive permanent magnets, which to date are limited to ∼2 T. 15 ABX-based alloys, where A and B are transition metals (typically Mn, Fe, Co, or Ni) and X is a semimetal (typically Ge or Si), are a prominent example where the occurrence of a FOMST ARTICLE scitation.org/journal/apm has revealed outstanding MC properties and rich magnetic behavior. 3,4,16,17 While MnCoGe occupies most of the attention within these types of alloys, 4,16, other structurally related compounds combining Fe, Co, Ni, and Mn, such as MnNiSi, MnNiGe, MnFeGe and CoNiGe, 2,3,19,[45][46][47][48][49][50][51][52] have also deserved considerable research efforts. The occurrence of FOMSTs in these systems is, however, not ubiquitous. In the stoichiometric forms, they usually display a martensitic transition well above the Curie temperature (Tc) from a high-temperature hexagonal Ni 2 In-type austenite (space group P63/mmc) 19,53 to a low-temperature orthorhombic TiNiSitype martensite 54 (space group Pnma), with a very large volume increase of ∼3%-4%. On further cooling, the orthorhombic phase undergoes a second-order ferromagnetic transition. In MnBX-based alloys, the magnetism of both structural phases basically originates from the Mn-3d band at the Fermi level, 18 with a different saturation magnetization for each phase. Recent studies have pointed to changes in the Mn-3d band originating from the increase in the Mn-Mn distances in the orthorhombic phase, which in turn destabilizes the hexagonal structure. 12,17,37 To achieve a FOMST near room temperature, these alloys exhibit a high sensitivity of the structural transition temperature (T 0 ) to the specific composition that has inspired abundant studies proposing rational and systematic slight chemical changes to dramatically shift T 0 to coincide with Tc, as the latter is much less sensitive to composition variations. In this sense, an extensive literature record include the introduction of vacancies, 18,42,44 addition, or substitution by dopants. 17,24,27,29,30,[32][33][34][35]37,39,40,43,45,[55][56][57] On the other hand, the doping-induced coupling is maintained in a composition range provided that T 0 does not fall below the Tc of the hexagonal phase. 32,33,45,49,50 As giant MC materials, these alloys present a major drawback, which is the fact that their transition temperatures appear to be little sensitive to the magnetic field, i.e., dT/µ 0 dH ≤ 2 K T −1 , compared to transition and hysteresis widths of ∼10 K, as reported in literature data. 17,24,37,56 Therefore, high magnetic fields would be required to fully drive the transition and overcome the hysteresis in these materials, making them unviable for MC cooling devices. Instead, the strongly nonisochoric character of the FOMSTs occurring in such alloys makes them highly sensitive to pressure 24,56 and hence good candidates to display giant barocaloric (BC) effects, 58 but only few works have been performed so far. 52,56,57 Here, we use x-ray diffraction, magnetic measurements, and calorimetry under pressure to study the magnetostructural behavior and BC response of a series of composition-related MnNiSi 1−x FeCoGex pseudobinary alloys across their FOMST occurring near room temperature. We find large and inverse BC effects that become reversible above ∼0.3 kbar and reach ∼50 J K −1 kg −1 at 2.5 kbar. The transition entropy change falls with pressure, thus indicating a weakening of the first-order character and a decrease of the BC performance at low temperature.
FeCoGe stabilizes in the hexagonal structure at any temperature, with Tc at 370 K. 52 MnNiSi is isostructural above 1200 K, whereas at this temperature, it transforms to the orthorhombic structure. 19 Therefore, in the MnNiSi 1−x FeCoGex pseudobinary alloy, it is reasonable to state that the FeCoGe elements provoke the stabilization of the hexagonal phase down to lower temperatures and may lead to a coupled magnetostructural transition. For the analyzed compositions x = 0.39, 0.40, and 0.41, a FOMST takes place from hexagonal paramagnetic to orthorhombic ferromagnetic around room temperature.

II. EXPERIMENTAL DETAILS
Polycrystalline (MnNiSi) 1−x (FeCoGe)x (x = 0.39, 0.40, and 0.41) samples were prepared by melting the constituent elements of >99.9% purity in an ultra-high purity Ar atmosphere using an RF-furnace. X-ray diffraction measurements were performed using Cu-Kα radiation (λ = 1.5406 Å) to determine both the phase purity of the samples and the temperature-dependent lattice parameters with the diffractometers described in Refs. 52 and 57, respectively. Pattern matching has been performed using FullProf software. 59 Magnetization measurements at normal pressure and under high hydrostatic pressure were performed as described in Ref. 52. Calorimetric measurements at normal pressure were carried out using a commercial Differential Scanning Calorimeter Q100 from TA Instruments, whereas calorimetry under hydrostatic pressure was performed employing the custom-built Cu-Be calorimeter and methods described in Ref. 58. Temperature rates were typically of ∼2 K min −1 .

III. RESULTS
X-ray measurements confirm the expected hexagonal-toorthorhombic structural change for the three compounds [see and for x = 0.41, α Hex = (5.0 ± 0.2) × 10 −6 K −1 and α Orth = (4.9 ± 0.2) × 10 −5 K −1 ]. The small volume variations with temperature of each phase but very large volume differences between phases are likely at the origin of the mechanical failure and subsequent powderization of the bulk samples when crossing the transition for the first time, which contrasts with the large hardness of the samples outside the transition. This behavior has been widely observed in alloys isostructural to those studied here and has been associated with the occurrence of the virgin effect. 48,50,[60][61][62][63][64][65][66] The temperature evolution of the magnetization under 0.1 T [see Fig. 1 . This suggests that a magnetic field of ∼9 T should be applied to overcome a ∼11 K of hysteresis and thus achieve reversible MC effects, which are prohibitively excessive for applications as anticipated previously. Second, for completeness, it is worth mentioning the presence of a hysteretic decrease of the magnetization observed on further cooling the x = 0.40 sample under 2.4 and 3.4 kbar. It indicates the presence of another firstorder magnetic transition at low temperatures, which could be contributed by antiferromagnetic interactions, as reported in similar alloys. 4,16,20,29,45,47 Temperature-dependent heat flow dQ/|dT| at atmospheric pressure for the different compositions (see Fig. S3 of the supplementary material) displays exothermic (negative) peaks on cooling corresponding to the forward martensitic transition (hereafter M) from the hexagonal austenite toward the orthorhombic martensite and endothermic (positive) peaks on heating corresponding to the backward transition (hereafter A). Defining the transition temperature as the temperature at which 50% of the material is transformed, we find that the forward and backward transition temperatures, T M and T A , depend on composition x as dT M /(100dx) = −30 ± 2 K and dT A /(100dx) = −27 ± 2 K. Integration of the peaks after baseline subtraction renders the forward and backward enthalpy (|∆H M | and |∆H A |) and entropy changes (|∆S M | and |∆S A |), and are listed in Table I, revealing large changes compared to other magnetic alloys. 1,58,[67][68][69][70][71][72][73] Temperature-dependent heat flow dQ/|dT| data at high pressures for the different compositions are shown in Figs. 2(a)-2(c). In all cases, both endothermic and exothermic peaks shift to lower temperatures when the applied pressure is increased. This behavior indicates a consistent enhancement of the stable temperature range of the lower-volume hexagonal phase at higher pressures and implies inverse BC effects. 67 Figure 2(d) shows the forward and backward transition temperatures, T M and T A , as a function of pressure for the different compositions (dT/dp < 0; see Table I). The colored regions around each temperature-pressure transition line indicate the transition width, limited by the starting and finishing temperatures for the forward (Ms and M f , respectively) and backward (As and A f , respectively) martensitic transitions. From this plot, the minimum pressure leading to reversible isothermal entropy changes ∆S can be determined as the pressure at which As at high pressure equals Ms at normal pressure. 74 In all cases, this value remains well below the modest pressure of 1 kbar, thus prognosticating a very good reversibility.
Integration of the calorimetric peaks (1/T)(dQ/|dT|) after baseline subtraction renders pressure-dependent entropy changes at the transition [∆Si(p) with i = M, A hereafter standing for the forward and reverse martensitic transition, respectively], as shown in Figs. 2(e)-2(g) for the different compositions. The pressuredependent enthalpy changes ∆Hi(p) and volume changes ∆V i (p) as calculated via Clausius-Clapeyron, ∆V i (p) = ∆S i (p)(dTi/dp) (i = M, A) are shown in Fig. S4 0  in Fig. S5(d) of the supplementary material. Interestingly, by considering also the negative sign of the pressure-derivatives dTi/dp, d|∆Hi|/dp, d|∆Si|/dp, and d|∆Vi|/dp, [as shown in Figs Fig. S6(c) for the thermograms, and Fig. S6(d) for the resulting |∆Hi(p)| in the supplementary material]. As ∆Hi(p) values are history-independent, the decrease in |∆Hi(p)| with pressure cannot be explained by a pressure-dependent transformed fraction but should be associated with a weakening of the transition, similarly to the observed behavior in similar systems. 33,44,56 On the other hand, for x = 0.41 and p > 2 kbar, it is observed that a dramatic drop in |∆Hi(p)| and |∆Si(p)|, as suggested by previous observations in isostructural systems, 20,22,24,26,27,32,33,44,56 could be originated by the fact that the shift of the transition to lower temperatures due to composition and pressure brings the system to fall below the low-temperature limit of the range where magnetostructural coupling occurs. Consequently, such pressure-induced decoupling 24 leads the transition entropy change to lose a significant contribution coming from a (partial) magnetic ordering. The isobaric entropy curves required to determine the BC effects were calculated with respect to a reference entropy at  75 can be safely neglected because the small thermal expansion of both phases renders |∆S+| < 1.5 ± 1 J K −1 kg −1 under an increase of ∆p ∼ 2.5 kbar, TABLE III. Maximum reversible BC effects in solids reported in the literature and this work. ∆Srev stands for maximum reversible isothermal entropy changes per unit mass and per unit volume, and ∆Trev stands for maximum reversible adiabatic temperature changes upon cyclic application and removal of pressure p. Transition temperature T and pressure-dependent derivative dT/dp are averaged over heating and cooling values. Peak hyst. and Onset hyst. stand for hysteresis width as derived from the position of the peak temperature and of the onset temperature, respectively, and are useful to estimate the minimum pressure for which ∆Srev and ∆Trev can be obtained. Dots stand for unreported data.
T dT/dp Peak hyst. Onset hyst. |∆Srev| |∆Srev| |∆Trev|  Fig. S7 of the supplementary material), which also fall within the given uncertainties, whereas ∆S and ∆Srev would approximately remain invariant. BC effects were calculated according to the quasidirect method as subtraction between isobaric curves at different pressures following proper paths, i.e., isothermal entropy changes were calculated as ∆S(T, ∆p) = S(T, p f ) − S(T, p 0 ) and adiabatic temperature changes were calculated as ∆T(S, ∆p) = T(S, p f ) − T(S, p 0 ), where the lower pressure value has always been taken as normal pressure. Because of the inverse (dTi/dp < 0) and mainly athermal (hysteresis rateindependent) character of the transition, the transition line crossed on compression (decompression) coincides with the transition line crossed on heating (cooling). Consequently, both ∆S and ∆T on compression (decompression) have been calculated from the isobaric curves on heating (cooling) and are shown in Figs Table II, place our alloy family amongst the best reversible BC materials reported so far near room temperature (a comparison is given in Table III).

IV. DISCUSSION
Rough estimates used to predict good caloric materials habitually come from transition entropy changes at normal pressure ∆S ∼ ∆Si(patm) and the field-sensitivity of the transition temperature, ∆T ∼ (dTi/dp)∆p. In the present case, however, and despite our giant values, we obtain ∆S < ∆Si(patm) and ∆T < (dTi/dp)∆p. This is due to the nontrivial decrease of the transition entropy change when increasing pressure as revealed by our high-pressure calorimetry, which demonstrates the importance of this technique for a proper BC characterization. Otherwise, assuming a pressure-independent transition entropy change as done elsewhere 56 may give rise to large inaccuracies or incorrect conclusions. Our observed decrease can be explained by the contributions of two factors: On one hand, as shown in Ref. 85, the isobaric entropy of the hexagonal phase decreases more rapidly with decreasing temperature than the isobaric entropy of the orthorhombic phase. As a result, the shift of the transition to lower temperatures results in a decrease of the entropy difference between the two phases, assuming that pressure dependence on the entropy is much weaker than the temperature dependence. On the other hand, it is widely accepted that the fact that the Tc of both phases exhibits much smaller sensitivity to pressure and composition than the structural transition leads the magnetostructural coupling to occur only in a temperature range nearly limited by the Tc of the two phases. 32,33,45,49,50 Therefore, the application of pressure may eventually shift the FOMST temperature below the Tc of the hexagonal phase, resulting in a (partial) decoupling of the structural from the magnetic transition. 24 Subsequently, this decoupling entails a decrease of the entropy change and the weakening of the first-order character of the surviving transition. This is further supported by experimental evidences reported elsewhere in temperature-dependent magnetization measurements at some specific values of composition and/or at high pressure, that reveal either a smoothing of the magnetization change across the transition or a two-stage transition, a second-order step followed by a first-order step. 20,22,24,26,27,32,33,44

V. SUMMARY AND CONCLUSIONS
Our study demonstrates the great barocaloric potential near room temperature and at moderate pressures of some magnetic alloys that are also less expensive than those containing Gd. They offer an alternative to the MC effects traditionally reported in the same and similar alloys that would require too large and expensive magnetic fields to achieve reversibility. The values of the giant BC effects in our MnNiSi-FeCoGe alloys are amongst the largest BC effects reported for magnetic materials. Although they are smaller than the largest BC effects observed in nonmagnetic materials, magnetostructural alloys should not be left behind in an integral BC research as, in addition to a notable reversible BC response, they offer additional significant advantages that compare favorably to other systems with larger BC effects, as clearly set out by our work: (i) fine tuning of operational temperatures via doping that enables the fabrication of composites with a very wide temperature span using close-composition alloys, and (ii) high density which improves the compactness. Also, a relatively large thermal conductivity improves the heat transfer efficiency and the possibility of multicaloric effects through the simultaneous or successive application of mechanical and magnetic fields allows the enhancement of the reversible operational range and other multicaloric advantages.

SUPPLEMENTARY MATERIAL
See supplementary material for selected x-ray diffraction patterns, lattice parameters and volume over a wide temperature range, conventional differential scanning calorimetry at atmospheric pressure, pressure-dependent and composition-dependent transition thermodynamic quantities, and details about the protocol to check the pressure-independence of the transformed fraction and propagation of errors derived from Cp.