Large barocaloric effect in intermetallic La1.2Ce0.8Fe11Si2H1.86 materials driven by low pressure

Barocaloric materials are particularly promising for green and efficient solid-state cooling technology because of their great potential in terms of cooling performance. However, intermetallic materials with outstanding barocaloric effects under low hydrostatic pressure are especially lacking, which has severely delayed the development of barocaloric refrigeration. Here, in a rare-earth intermetallic La-Ce-Fe-Si-H, we achieve a giant specific barocaloric temperature change of 8 K per kbar according to direct measurements of the adiabatic temperature change ΔTBCE under hydrostatic pressure, which is confirmed by a phenomenological transition simulation. This barocaloric strength is significantly better than those in previously reported phase-transitioned alloys. By using a cutting-edge in situ neutron diffraction technique operating under simultaneously varying temperature, magnetic field, and hydrostatic pressure, we reveal that the large isotropic transition volume change in La-Ce-Fe-Si-H plays a crucial role in the giant barocaloric effect. Additionally, we employ Landau expansion theory to demonstrate that the high sensitivity of the transition temperature to the applied pressure produces the sizable ΔTBCE in the itinerant electron metamagnetic transition alloys. Our results provide insight into the development of high-performance barocaloric materials and related cooling systems. A rare-earth intermetallic La-Ce-Fe-Si-H has been directly measured to cool 8 K when it is under a 1 kbar pressure. This barocaloric strength significantly outperforms those in previously reported phase-transitioned alloys. A multifield-dependent neutron diffraction has revealed that the large isotropic transition volume change for La-Ce-Fe-Si-H plays a crucial role in exploring the giant barocaloric effect.


Introduction
Novel cooling technologies based on caloric effects have attracted much attention in recent decades as efficient and environmentally friendly alternatives to conventional gas-compression refrigeration [1][2][3] . In solid-state caloric materials, phase transitions under the application of a magnetic (magnetocaloric effect) [4][5][6] , electric (electrocaloric effect) 7,8 , uniaxial stress (elastocaloric effect) 9,10 , or hydrostatic pressure (barocaloric effect) field [11][12][13][14] lead to changes in entropy and temperature. The main benefits of materials that exhibit the barocaloric effect (BCE) over other caloric materials are related to the high power density in condensed solids and the wide variety of these materials 2,3 . The giant BCE has been extensively reported for a large number of phase-transition materials, such as magnetic shape memory alloys 13,14 , antiperovskite compounds 15 , plastic crystals 11,16 , organic-inorganic hybrids 17,18 , ferrielectric ammonium sulfate 19 , and natural rubber 20,21 . However, BCE requires high hydrostatic pressure to trigger phase transitions and to generate large adiabatic temperature changes ΔT BCE , which has undoubtedly limited the development of relevant BCE refrigeration devices 2,3 . In addition, metals with high thermal conductivity are preferred for efficient heat transfer between heat-transfer fluid and barocaloric refrigerants. Regardless of the relatively abundant materials exhibiting a significant barocaloric effect, as shown in Fig. 1, more emerging intermetallic materials exhibiting the giant BCE under low pressure are highly sought to promote barocaloric techniques. NaZn 13 -typed La-Fe-Si alloys are of particular interest as high-performance magnetocaloric materials 22 . Since the degrees of freedom of the lattice and magnetism in La(Fe,Si) 13 -based alloys coexist and are strongly coupled, both magnetic fields and hydrostatic pressure are capable of driving itinerant electron metamagnetic (IEM) transitions and thus produce magnetocaloric and barocaloric effects. In this study, we focus on a Ce-doped rare-earth-rich La 1.2 Ce 0.8 Fe 11 -Si 2 H 1.86 , with an off-stoichiometric composition, owing to its strengthened magnetoelastic coupling, as revealed by earlier works 23,24 . Here, we directly measure a giant ΔT BCE of 8 K under a change in hydrostatic pressure of 1 kbar through an IEM transition in the La 1.2 Ce 0.8 Fe 11 -Si 2 H 1.86 alloy. The directly measured BCE strength (ΔT BCE /ΔP) exceeds the corresponding values that have been found for both metallic alloys and non metallics. By combining the changes in hydrostatic pressure, magnetic field, and temperature, we employ advanced in situ neutron scattering measurements under multiple fields to unveil the unique lattice-magnetism coupling mechanism under different stimuli and thus to understand the origin of the remarkable barocaloric effect for the present IEM system. Additionally, a phenomenological calculation based on the Landau expansion model is performed to optimize pressure-sensitive first-order phase transitions and to create a pathway for exploiting promising BCE materials.

Materials and methods
The La 1.2 Ce 0.8 Fe 11 Si 2 alloy was prepared by arc melting followed by annealing at 1423 K for 24 h. Slices with thicknesses of~1.5-2 mm were cut from the parent samples to absorb hydrogen. Hydrogenation was carried out at 573 K under a high purity hydrogen gas atmosphere of 100 kPa for~5 h to saturate the H concentration. According to the neutron diffraction pattern, the resulting alloy contains mainly the 1:13 phase (~84% in volume fraction) with the chemical composition of La 0.57 Ce 0.43 -Fe 11.68 Si 1.32 H 1.86 and several secondary phases, i.e., Ce 2 Fe 17 (~7%), La 5 Si 3 (~5%), and α-Fe (~4%) (see the "Phase fraction" section in the Supplementary Information). It is known that the α-Fe and La 5 Si 3 phases do not exhibit ambient phase transformation and hence do not exhibit the barocaloric effect near room temperature. Ce 2 Fe 17 alloy undergoes spontaneous magnetostriction at 300 K accompanied by a volume shrinkage of 0.3% 25 . The volume change of Ce 2 Fe 17 is much smaller than that of La(Fe,Si) 13 alloy (~1.6%). According to the Clausius-Clapeyron equation, the barocaloric effect of Ce 2 Fe 17 alloy is much smaller than that of La(Fe,Si) 13 alloy. Moreover, the content of the Ce 2 Fe 17 phase is much smaller than that of the La(Fe,Si) 13 phase in the studied La 1.2 Ce 0.8 Fe 11 Si 2 H 1.86 alloy. Therefore, we believe that the barocaloric performance of the studied La 1.2 Ce 0.8 Fe 11 -Si 2 H 1.86 alloy is mainly due to the La(Fe,Si) 13 phase.
Magnetization measurements were acquired using a vibrating sample magnetometer (VSM, Versalab, Quantum Design) equipped with a beryllium-copper highpressure cell. The value of the pressure was determined by standard hydraulic press sets equipped with an optional-digital pressure gauge. Thermomagnetization data were recorded at a slow rate of 1.5 K min −1 to ensure that the temperature in the pressure cell kept the same pace as the ambient temperature. In-field specific heat measurements were carried out from 0 to 3 T using the heat capacity option of a VersaLab system. For the direct measurement of the adiabatic temperature change of the BCE, a high-pressure hexahedron press was used, where three pairs of symmetrical indenters simultaneously compress the sample from six directions. Cubic pyrophyllite was used as the pressure-transmitting medium to avoid heat exchange. La 1.2 Ce 0.8 Fe 11 Si 2 H 1.86 powders filled the middle of the cubic pyrophyllites, with a PT-1000 thermistor to measure the temperature of the sample during the compression process. The description of the adiabatic temperature change setup is given in the   16 , natural rubber (marked as NR) 21 , (NH 4 ) 2 SO 4 (marked as NHSO) 19 , Rb 2 KTiOF 5 (marked as RbKTiOF) 17 , (NH 4 ) 3 MoO 3 F 3 (marked as NHMOF) 18 , and (NH 4 ) 2 NbOF 5 (marked as NHNbOF) 17 . Indirectly measured data were from hydrostatic pressure-dependent differential thermal analysis (DTA) 12,47 and differential scanning calorimetry (DSC) 19,26 . The value of ΔT BCE for different materials is obtained from a low pressure of~1 kbar, at which condition the barocaloric behavior is almost linear with applied pressure.
Supplementary Information. Neutron powder diffraction data on the La 1.2 Ce 0.8 Fe 11 Si 2 H 1.86 sample were collected at the NIST Center for Neutron Research with a highresolution powder neutron diffractometer (BT1) with monochromatic neutrons of wavelength 0.20774 nm produced by a Ge(311) monochromator. Data were collected in the 2θ range of 14-140°with a step size of 0.05°i n the temperature range of 280-350 K, pressure range of 0-6.3 kbar and magnetic field range of 0-7 T. Refinements were carried out using the program GSAS to determine the phase constitution, scaling factor, background, peak shape, atomic positions, thermal vibration factor, and occupancies. The refinement results are given in the 'Neutron powder diffraction section of the Supplementary Information.

Results and discussion
From the curves of field dependences of heat capacity and magnetization in Fig. 2a, b, we can see that the external magnetic field and pressure obviously affect the first-order transition behavior but in an opposite direction for La 1.2 Ce 0.8 Fe 11 Si 2 H 1.86 : the thermal-induced IEM transition temperature (T C ) increases under the application of a magnetic field but decreases under hydrostatic pressure. This is reasonable given that the lowtemperature ferromagnetic (FM) phase has a higher volume than the high-temperature paramagnetic (PM) phase. The rate of the shift in T C under a magnetic field (dT C /dH) is~3.7 K T −1 and under external pressure (dT C / dP) is~−26 K kbar −1 . It should be emphasized that the response of Tc to the application of external pressure in our sample is more sensitive than those for other magnetostructural transition alloys, e.g., Mn-Ga-N (−6.5 K kbar −1 ) 12 , Gd-Si-Ge (−3.5 K kbar −1 ) 26 , Ni-Mn-In (+1.8 K kbar −1 ) 13 , stoichiometric La(Fe,Mn,Si) 13 (−13.9 K kbar −1 ) 27 , and La(Fe,Co,Si) 13 (−9.4 K kbar −1 ) 28 . For IEM systems, T C is determined by the band structure near the Fermi surface. In the case of the studied La 1.2 Ce 0.8 Fe 11 -Si 2 H 1.86 alloy, the hydrostatic pressure shortens the exchange of the 3d electrons of Fe atoms and thus affects the band structure near the Fermi surface. Therefore, the nature of the first-order transition strengthens, and the transition hysteresis increases with applied hydrostatic pressure (0.5 K for 0 kbar, 3 K for 1.9 kbar, and 9 K for 2.8 kbar), as shown in Fig. 2b. Importantly, such an ultrahigh sensitivity indicates that low pressure is expected to trigger the IEM transition and thus generate a giant adiabatic temperature change (ΔT BCE ) in our sample.
First, we theoretically evaluate how the sample cools during adiabatic pressurization using a phenomenological simulation called the "transition distribution model". This convergence method has been employed to approach the real cooling behavior for MCE materials by analyzing the controlling parameters of phase transitions 5 . Analogous to the magnetic field, we show the change in temperature influenced by pressure. Details of mathematical deduction can be seen in the section "Transition distribution model under pressure" of the Supplementary Information. As shown in Fig. 2c, at the initial temperature of 290 K, the sample maintains the FM state when the pressure is lower than 0.4 kbar and then starts to undergo the FM-PM transition. The magnetostructural transition is completed with pressurization up to 1.4 kbar, resulting in a maximum ΔT BCE of 11 K. More strikingly, a giant BCE strength of ΔT BCE = 8 K at 1 kbar is achieved by fulfilling a phase transition fraction of~80%. Such an exceptional ΔT BCE under low pressure has also been verified by pressure-dependent calorimetric measurement with the quasi-direct method (described in the section "DSC under pressure" in the Supplementary Information).
As a straightforward assessment of BCE, a direct measurement of the adiabatic temperature change upon the rapid application and removal of hydrostatic pressure was carried out (see the section "Description of direct ΔT BCE measurements" in the Supplementary Information). The time-dependent temperature change is presented in Fig. 2d. Upon the application of a pressure of 1 kbar within 50 s, the sample cools from 290 to 282 K, causing a large ΔT BCE of 8 K. Then, it remains at a nearly constant temperature for 70 s when the pressure is maintained, indicating very good adiabatic pressurization conditions that guarantee the accuracy of the measured ΔT BCE in this experiment. Upon the release of pressure, the sample heats back to the initial temperature. This confirms the reversibility of the phase transition and BCE temperature variation. It should be noted that the sharp temperature peaks prior to BCE are due to the signal from the temperature sensor subjected to the applied pressure. The directly achieved temperature change is highly consistent with the theoretically predicted value from the aforementioned phenomenological model, as well as the results from quasi-direct measurements. Furthermore, the influence of pressure cycles on ΔT BCE is measured. Although for each cycle the giant temperature change exhibits good recoverability (a symmetric rise and drop in temperature), there is a slight degradation of the absolute value of ΔT BCE down to 6 K under pressurization-depressurization cycles (Fig. 2e). Such energy losses could be ascribed to mechanical friction at particle and grain boundaries 29 , which might be overcome by lattice tuning and microstructural optimization 30,31 .
For comparison to the BCE, the magnetic field-induced adiabatic temperature change (ΔT MCE ) was investigated by direct and indirect measurements based on heat capacity data. As shown in Fig. 2f, under a magnetic field of 2 T, which in general is accessible with permanent magnets, the maximum ΔT MCE is approximately +4 K, which is only half of the value of the ΔT BCE generated by 1 kbar pressure (Fig. 2f). This comparison clearly reveals that relatively low pressure is prone to producing a more significant caloric effect than a magnetic field is for our La 1.2 Ce 0.8 Fe 11 Si 2 H 1.86 refrigerant.
From the Clausius-Clapeyron equation, the ΔT BCE in a complete first-order phase transition can be determined by the crucial parameters of (i) the volume change of transition Δω and (ii) the sensitivity of the transition temperature to applied pressure dT C /dP: where T is the temperature, P the pressure, C p the heat capacity, V the volume, and ρ the density. Both Δω and dT C /dP are strongly dependent on magnetostructural coupling 12 . To obtain experimental insight into the physical mechanism of the field-triggered IEM transition and particularly to examine the bond structural changes, cutting-edge neutron scattering measurements were carried out as a function of pressure, magnetic field, and temperature (Fig. 3a). The collected diffraction spectrum shows the shift in the diffraction peaks, which indicates that the sample undergoes complete phase transitions under different fields.
The crystallographic structure of La-Fe-Si-based compounds is described as a CsCl-type packing of rare-earth atoms and Fe-I centered icosahedra (Fig. 3a). La/Ce atoms occupy the 8a sites, and the Fe-I sites at 8b are fully occupied by Fe atoms. Each Fe-I atom is surrounded by an icosahedron of 12 Fe-II atoms at 96i, which is randomly   32 . The lattice exhibits a discontinuity in the magnetic ordering. As shown in Fig. 3b, the sample remains in the PM state under a pressure of 3.4 kbar. However, the pressure-dependent thermomagnetization data (Fig. 2b) indicate that 3.4 kbar pressure is sufficient to fully induce the transition at 280 K. Such an inconsistency is very likely because the actual pressure value on the powder sample is less than the calculated pressure in the high-pressure neutron diffraction experiment. During the pressurization process, some particles of the sample inevitably fill in the tiny gap between the rig and pressurized cylinder of the high-pressure units in the neutron diffraction device. The resultant large friction offsets a considerable part of the pressure, and thus, the pressure might be overestimated. Therefore, the pressuredependent neutron diffraction experiment can only be used to qualitatively discuss the difference in the effects of pressure, magnetic field, and temperature on lattice structure and bond length.
The application of a nominal pressure of 6.3 kbar at 280 K drives the sample to undergo the FM-PM transition and produces a giant Δω of 2%. Such a volume change consists of two parts: shrinkage by phase transition and normal elastic volume compression. Using the bulk elastic modulus of 2.29 × 10 3 kbar taken from the close composition of LaFe 11 Si 2 33 , the volume change by the compression effect is calculated to be 0.3%. Therefore, the dominant contribution to the total volume change can be ascribed to the magnetostructural transition (~1.7%). In comparison, the application of a magnetic field leads to a volume change of 1.6% in the phase transitions, which is similar to the volume change caused by hydrostatic pressure. However, the temperature-induced volume change is detected to be an even smaller value of 1.2%.
To understand the discrepancy in volume change induced by different external stimuli, we employ general local-moment volume magnetostriction theory in the framework of the Callen-Callen model 34 . The volume magnetostriction Δω on the IEM transition is proportional to the squared magnetization ΔM 2 , compressibility k, and magnetoelastic coupling coefficient C mv , while it is negatively proportional to the squared thermal spin fluctuations Δξ 2 : Here, Δξ 2 is proportional to the squared temperature. Considering that the temperature range in our in situ neutron diffraction experiment is quite narrow, the contribution from Δξ 2 to the volume change is similar under different external stimuli. Therefore, the large transition volume change triggered by external fields is mainly ascribed to the change in the local magnetic moment. For La-Fe-Si-based alloys, ferromagnetism originates from the exchange interaction of the 3d itinerant electrons of Fe-II atoms 35 . In La(Fe,Si) 13 -based alloys, the shortened bond length between the Fe atoms weakens the ferromagnetic coupling between Fe atoms and therefore lowers the magnetization of the alloy. Compared with the bonds between Fe-I and Fe-II atoms, the lengths of Fe-II -Fe-II bonds (marked as B2, B3, B4, and B5) are the determining factors in mastering the magnetic moment 36 . With an indepth investigation of the fine structure of La 1.2 Ce 0.8 -Fe 11 Si 2 H 1.86 by in situ neutron diffraction methods, we can see that the Fe-II -Fe-II bonds display the most significant shrinkage, by 0.66 and 0.53% with the application of pressure and magnetic field, respectively (Fig. 3c). It should be clarified that the difference in bond length changes under hydrostatic pressure and the magnetic field is due to the compression effect of hydrostatic pressure and experimental error. The field-dependent neutron diffraction results indicate that the symmetry of the icosahedra in the La 1.2 Ce 0.8 Fe 11 Si 2 H 1.86 alloy remains constant during the IEM transition triggered by external hydrostatic pressure and magnetic field. Interestingly, in terms of the thermal phase transition, the icosahedron cluster is deformed. In the case of the temperature-driven PM-FM transition, however, the B4 bond varies by a much smaller magnitude, 0.2%, and the B5 bond remains nearly unchanged. In addition, the B2 bond changes by a smaller magnitude (0.1%) than B3 (0.55%). Since the IEM transition is closely related to the distance-dependent exchange, the deformation of the cluster could cause weakening of the IEM transition 37 . Thus, we assume that the small value of Δω in the thermally triggered phase transition is very likely due to its lattice distortion. In other words, the application of pressure and magnetic field are assumed to induce a more drastic change in the magnetic moment and to drive a larger phase transition volume change than the temperature.
After investigating the impact of Δω on the BCE, we discuss another important parameter, dT C /dP, for the enhancement of ΔT BCE . The pressure dependence of the transition temperature is regarded as an approximate measure of the stability of the ordered state against pressure 12 . Assuming an ideal condition of infinite pressure in Eq. (1), ΔT BCE varies inversely with dT C /dP. However, the real phase transition occurs in a finite temperature range rather than at a specific temperature. In the case of a small dT C /dP, it is extraordinarily difficult to complete phase transition at low pressure, and thus the obtained ΔT BCE is significantly smaller than the upper bound of ΔT BCE . Similar to magnetocaloric materials 38 , the magnitude of dT C /dP must be at an optimal value to maximize ΔT BCE under limited pressure. It must be noted that most of the available room temperature BCE material systems exhibit a relatively small dT C /dP that needs to be critically improved to achieve a larger BCE under low pressure. As modulating the IEM transition order has been proposed as a feasible way to increase dT C /dP and to reduce the strength of the required driving pressure 39 , we attempt to explore the potential of dT C /dP based on the IEM transition model.
According to Landau's theory, the slope of the H/M-M 2 curve (Arrott curve) is nearly equal to B(T). Therefore, the secondary Landau coefficient B(T C ), similar to the Arrott curve, can be used as the basis for judging the transition order of the La(Fe,Si) 13 -based alloys 40 . Generally, a negative B(T C ) leads to a first-order phase transition, and a positive B(T C ) corresponds to a second-order phase transition 41 . By taking the influence of spin fluctuations and magnetoelastic coupling into account, the Landau expansion theory can describe the IEM transition behavior under hydrostatic pressure well: the pressure dependence of T C around zero pressure is maximized when the secondary Landau coefficient B at T C approaches zero 42 . We derived the value of B at T C by fitting the magnetization data for reported La-Fe-Si-based alloys (described in the section "Landau expansion model" in the Supplementary Information). As plotted in Fig. 4, the magnitude of dT C /dP for La-Fe-Si alloys in the literature varies from 6 to 22 K kbar −1 owing to the scattered B at Tc far from zero 25,28,34,39,[43][44][45] . For the present work, we manipulate the IEM transition by simultaneously introducing large Ce atoms and interstitial H atoms. Consequently, the studied composition of La 1.2 Ce 0.8 Fe 11 Si 2 H 1.86 is near the boundary of the phase transition, where the value of B at Tc is rather small. Such a unique phasetransition feature indicates that our La 1.2 Ce 0.8 Fe 11 Si 2 H 1.86 alloy simultaneously possesses both a giant volume change and small hysteresis, especially under low pressure. Thus, low pressure of~1 kbar can convert a large phase fraction of almost 80%, leading to a giant reversible ΔT BCE of 8 K.

Conclusions
From the present findings, we demonstrate that giant barocaloric performance at low pressure can be realized by enhancing the transition volume change Δω and manipulating the pressure-sensitive phase transitions dTc/dP. Both crucial parameters are closely related to the magnetoelastic coupling coefficient. In this sense, the strengthening of magnetoelastic coupling is one key step for developing more efficient BCE materials. This criterion goes beyond La-Fe-Si IEM-type alloys and should be applicable to other first-order transition materials.