Large reversible caloric effect in FeRh thin films via a dual-stimulus multicaloric cycle

Giant magnetocaloric materials are promising for solid-state refrigeration, as an alternative to hazardous gases used in conventional cooling devices. A giant magnetocaloric effect was discovered near room temperature in near-equiatomic FeRh alloys some years before the benchmark study in Gd5Si2Ge2 that launched the field. However, FeRh has attracted significantly less interest in cooling applications mainly due to irreversibility in magnetocaloric cycles associated with the large hysteresis of its first-order metamagnetic phase transition. Here we overcome the irreversibility via a dual-stimulus magnetic-electric refrigeration cycle in FeRh thin films via coupling to a ferroelectric BaTiO3 substrate. This experimental realization of a multicaloric cycle yields larger reversible caloric effects than either stimulus alone. While magnetic hysteretic losses appear to be reduced by 96% in dual-stimulus loops, we show that the losses are simply transferred into an elastic cycle, contrary to common belief. Nevertheless, we show that these losses do not necessarily prohibit integration of FeRh in practical refrigeration systems. Our demonstration of a multicaloric refrigeration cycle suggests numerous designs for efficient solid-state cooling applications.

C aloric materials, which undergo an adiabatic temperature change DT or isothermal entropy change DS when some external stimulus is applied or withdrawn, are highly sought after for new refrigeration solutions to replace current vapor-cycle cooling technologies 1 . The most prominent calorics are ferroically ordered materials that often exhibit giant caloric effects near their ferroic transitions. Depending on the external stimulus, effects 1 may be called magnetocaloric (magnetic field), electrocaloric (electric field), elastocaloric (uniaxial stress) or barocaloric (hydrostatic pressure), the last two being very similar and now considered together as mechanocaloric effects. In multiferroic materials and heterostructures 2 , multicaloric effects 1,3 can exploit multiple sources of entropy and be driven by either single stimulus 3 or multiple stimuli (applied/removed simultaneously or sequentially) 1 . While theoretical descriptions of multicaloric effects are now emerging [3][4][5] , experiments are still limited to probing individual effects 6,7 . In particular, multiple-stimulus caloric cycles have yet to be realized, and their advantage over conventional cycles is not clear.
FeRh exhibits a giant negative magnetocaloric effect (MCE) near room temperature 8 , arising from an unusual first-order transition near 350 K between antiferromagnetic (AFM) and ferromagnetic (FM) order, whose physical origin is still under debate 9 . The giant MCE was discovered in FeRh 8 some years before the better-known result in Gd 5 Si 2 Ge 2 compounds 10 , and its caloric parameters DSB20 J K À 1 kg À 1 and DTB13 K (in 2 T magnetic field) 8 make FeRh a highly competitive magnetocaloric material even today 1,11 . As the transition is accompanied by a unit cell volume expansion of about 1%, FeRh is also barocaloric 12,13 and elastocaloric 14 . However, the broad hysteresis often associated with the transition 10,11,15 (and to a lesser extent the high cost of Rh) are key drawbacks for applications. The former results in a dramatic degradation of MCE versus refrigeration cycles as observed by recent direct measurements 13 , which is in contrast to the nominal reproducible MCE results calculated either by differential scanning calorimetry 12 or by magnetization-magnetic field curves 16 . The irreversibility of the MCE is associated with very broad or incomplete transitions, which arise in disordered thick films 17 and in very thin FeRh films 18,19 . While the irreversibility and hysteresis losses in other caloric materials with first-order magnetic transitions have been reduced by doping 20 , or introducing porosity 21 , such reductions have remained elusive in the case of FeRh.
In this study, we propose and realize a magnetic-electric multicaloric cycle in a multiferroic heterostructure, and use it to solve a real and longstanding problem, that is, a large hysteresis that impeded reversibility in an otherwise promising magnetocaloric material. Our heterostructure consists of a thin film (TF) of equiatomic FeRh alloy on a single-crystal BaTiO 3 (BTO) substrate. We previously showed that FeRh/BTO heterostructures exhibit the largest magnetoelectric coupling coefficient 22,23 , implying the existence of a large effective electrocaloric effect (technically an electric field-induced mechanocaloric effect 1 , as will be discussed later) driven by a voltage applied across the BTO. Unfortunately, in our previous work 22 the electric field-induced transition was mostly irreversible. Here we achieve a large reversible MCE in FeRh/BTO structures via a dual-stimulus multicaloric cycle that employs both magnetic and electric fields. Although dual-stimulus cycles do not remove intrinsic losses as previously claimed 24 , we show that those losses are not important enough to exclude practical applications, and we thus suggest a route to revive the potential of FeRh for magnetic cooling applications.

Results
Reversible MCE through multicaloric refrigeration cycle. Our dual-stimulus multicaloric refrigeration cycle is schematized in Fig. 1a. While a similar multicaloric cycle using pressure was discussed elsewhere 24 , the full cycle was not demonstrated experimentally. For the following proposal only, we suppose that all steps can be performed fast enough to avoid heat leakage from the FeRh TF into the BTO substrate, aided, for example, by a thermal barrier layer that preserves strain coupling. Under these circumstances, we imagine the rapid changes to be adiabatic in principle.
Initially, the FeRh TF is in its AFM phase and the BTO substrate has a mixed 90°a/c ferroelastic domain structure. The cycle begins (step 1) by applying (increasing) a magnetic field H adiabatically, favouring the FM phase of FeRh and causing the FeRh film to cool down. This is followed by absorbing heat from an external source keeping H constant (step 2), due to the negative MCE 1,8,[11][12][13]15,16 . At step 3, the electric field E is applied adiabatically to the BTO substrate resulting in more c-domains and thus favouring the AFM phase of FeRh TFs 22,23 . The magnetic field H is then removed (decreased) adiabatically causing the FeRh to heat up (step 4), followed by a heat ejection towards the external source (step 5). Finally, the electric field E is removed (step 6). Our proposed refrigeration cycle differs from purely magnetic ones 11 by the introduction of electric field in steps 3 and 6, whose effect on FeRh is in principle similar to that of a magnetic field (Fig. 1b), but which in practice does not stimulate the FeRh transition. The typical MCE in FeRh follows a path with a large virgin effect, followed by a smaller reversible trajectory 13,16 (path 1-2-3, Fig. 1c). By selecting appropriate values of electric field E, we may apparently cancel the hysteresis and achieve repeatable anhysteretic magnetic loops (path 1-4, Fig. 1c), although the electric field-induced elastic strain applied in steps 3 and 6 converts an amount of mechanical work into heat that is similar to the magnetic work saved (Fig. 1d). Instead, we achieve reversible changes that are considerably larger than those achievable in a single-stimulus cycle with either magnetic or electric field. We now present an experimental demonstration of a slow, isothermal analogue of the proposed cycle in FeRh/BTO.
We grew a B40-nm-thick epitaxial FeRh film at 630°C by magnetron sputtering from an equiatomic Fe 50 Rh 50 target onto a 500-mm-thick single-crystal (001) BTO substrate. The high film quality, including epitaxy and Fe/Rh order parameter, were confirmed by reflection high-energy electron diffraction images and X-ray diffraction scans, respectively 22 . A 50-nm-thick Au layer was sputtered on the back side of the BTO as a bottom electrode, and voltages were applied across the thickness of the BTO substrate. Details of our sample preparation can be found elsewhere 22,23 . We use a film around twice as thick as in our previous work 22,23 to avoid the particularly large hysteretic losses of very thin FeRh films 18,19,22,23 , which are due to grain size reduction 18 and substrate-induced strain 22 . Magnetization measurements were carried out in a Quantum Design superconducting quantum interference device (SQUID) magnetometer with a maximum accessible temperature of 400 K and the capability to apply magnetic field up to 5 T. Given that most experimental works on the caloric effect were characterized by isothermal entropy changes rather than direct measurement of adiabatic temperature changes 1,11 , we use magnetization as a proxy for the progress of the first-order transition, because the fast heat exchange between TFs and substrates prevents us from carrying out direct thermal measurements 25 . Figure 2 shows isothermal magnetization (M) versus magnetic field (H) curves measured on increasing and decreasing magnetic field at 385 K (Fig. 2a-c) and 395 K (Fig. 2d-f) immediately after heating from room temperature, either with no applied electric  field (Fig. 2a,d), or magnetized and demagnetized under various moderate voltages DV close to the coercive voltage (± B50 V) of the BTO 22,23 : À 10 V and À 60 V (Fig. 2b,e), and 0 V and 100 V (Fig. 2c,f) Fig. 2a-f). The irreversibility is apparent in Fig. 2a where we have included the results of a second magnetic field sweep, during which the magnetization remains rigidly within this reversible range. Our main result is that optimized multicaloric cycles (Fig. 2c,f) yield larger reversible DM, and hence the reversible isothermal heat Q ¼ |TDS| pumped during one magnetocaloric cycle (Fig. 2g) is also larger compared with either magnetic field alone (Fig. 2a,d) or electric field alone (Fig. 3 of ref. 22). Here we use Q ¼ TrVDS max (DM/DM max ), where the FeRh film has mass density r ¼ 9,760 kg cm À 3 , V is the film volume and we use literature values DM max ¼ 1,190 e.m.u. per cm 3 (ref. 12) and DS max ¼ 17 J K À 1 kg À 1 (ref. 9) for the complete transition because the SQUID maximum temperature of 400 K prevents us from acquiring the full data set to estimate DS via the Maxwell relation 26 .
Interestingly, we also reduce the magnetic work (or magnetic hysteresis losses) W mag , defined by the difference in area R M dH between curves with increasing and decreasing H, by up to 96%  (Fig. 1b) we do not make this claim, and we use the term hysteresis losses to describe W mag here. Comparing our work with ref. 27, the epoxy bonding in Ni-Mn-In-Co/PMN-PT is much weaker than our epitaxial contact, and the resulting relatively weak magnetoelectric coupling may limit the reversibility of MCE for applications. The important mechanical work was also overlooked in the elastic cycle 27 . Therefore we emphasize the need for caution when analysing multicaloric refrigeration cycles of the type we propose in Fig. 1.
To understand whether losses in our FeRh/BTO system would prohibit practical applications, in Table 1, we compare them with undoped and doped Gd 5 Si 2 Ge 2 (ref. 20) in terms of the fundamental parameters of magnetocaloric cooling devices 1 , that is, the isothermal heat Q and the pumped heat/total work ratio Q/W, which constitutes an upper bound to the thermodynamic coefficient of performance (COP), COP max , for refrigerators. Here we take Q for FeRh/BTO at 395 K and DV ¼ 100 V, but we use W ¼ W mag for the cycle at 395 K without voltage, because the total W should be approximately the same for all multicaloric cycles. While the value COP max ¼ 26.9 for our highly lossy FeRh TF is lower than for even undoped Gd 5 Si 2 Ge 2 , this should not at all be the dominant inefficiency in the system. For example, in a non-isothermal refrigeration cycle with a hot reservoir at T h ¼ 395 K and a temperature span (T h À T c ) ¼ 8.5 K (ref. 15), the COP is bounded by the Carnot limit ) These figures are competitive, and it is likely that the real COP would be dominated by other losses in the device, which in our case would include losses in the substrate ferroelectric cycle (which can themselves be reduced by optimization). We do not calculate the refrigerant capacity (ref. 20) here, as our data does not reveal the full temperature dependence of the entropy change.
Although here we report data only at 385 K and 395 K, an advantage of using FeRh TFs is that the large reversible caloric effects can be potentially achieved at any temperature within the B100 K wide tetragonal phase field of BTO (including room temperature) because the FeRh transition temperature can be tuned over hundreds of kelvins and through room temperature by doping with other metallic elements 28 . This extreme tunability is in contrast with, for example, the La 0.7 Ca 0.3 MnO 3 /BTO system (B6 K) where reversible MCE is restricted to the vicinity of the rhombohedral-orthorhombic transition of BTO at B200 K 25 . We note that the tuning of the metamagnetic phase transition temperature (420 K) by electric field as we have already achieved in refs 22,23 is also ideal to achieve a large temperature span in an active magnetic regenerator 27 . Moreover, the tunability of our FeRh/BTO system is considerably greater than that in Ni-Mn-In-Co/PMN-PT (o10 K, ref. 27).
The fact that the transition from AFM phase to FM phase at 385 K is not fully achieved under 5 T (see Fig. 2a,b), in line with previous results on ultrathin FeRh TFs 18,19 , suggests that even larger effects could be obtained by microstructural optimization, for example, by nanopatterning to artificially introduce porosity. Also, as the strain states in FeRh are discrete, that is, related to either an a-or c-domain of BTO, it is difficult to access a wider range of strain states in FeRh 22,23 . In contrast, a continuous range of electro-strains can be achieved if FeRh TFs are grown on a relaxor substrate like PMN-PT, which would also fortuitously reduce the losses in the substrate (as in ref. 27).
Our results here demonstrate that the historical irreversibility of MCE in FeRh discovered almost 25 years ago 8 can be solved by using an electric field, although the magnetic hysteresis losses are not destroyed but simply transferred to an elastic cycle. Since research in multicaloric materials has intensified recently 1 , we believe that our work will stimulate more efforts in multiferroic systems 2 where strong mechanical coupling between ferroic order parameters may provide more diverse choices for the design of efficient solid-state refrigeration, including purely electric fielddriven systems (see below). Revisiting overlooked compounds like FeRh using hybrid heterostructures can also provide a new life for many magnetocaloric materials. Alternative geometries including multilayer structures, core-shell nanoparticles or nanocomposites (NCs) 5,25 may also be of interest for achieving comparable volume fractions of magnetic and electric components.
Electric field-induced mechanocaloric effect. Finally, an optimized device may also permit a purely electric field-driven refrigeration cycle consisting of steps 3 and 6 alone. This overlooked electric field-induced mechanocaloric effect 2 may also open a new paradigm to potentially overcome the inevitable uneconomic investments on clumsy magnets in magnetic cooling. Unlike traditional magnetocalorics 1,11 , the entropy change is induced on application of an electric field on BTO substrate rather than a magnetic field directly applied on FeRh (step 1) thanks to the magnetoelectric coupling. As the elastic hysteresis losses might not be critical, the novel mechanocaloric effect subjected to the electric field-induced two-dimensional stress/ strain could be a low-cost approach for developing the next generation of solid-state refrigeration. Figure 3a,b shows the promise of FeRh/BTO in the electric field-induced mechanocaloric effect by comparing its performance with a representative sample of competitive electrocaloric materials [29][30][31] . FeRh/BTO would perform comparably to all of these systems except for P(VDF-TrFE-CFE)/Boron nitride nanosheets/Ba 0.67 Sr 0.33 TiO 3 NC (ref. 31), which apparently outperform all other systems. There are few mechanocaloric data available for FeRh, possibly due to concerns about irreversibility and the high price of Rh. Here we use elastocaloric parameters (|DS E |B7.8 J K À 1 kg À 1 and |DT E |B5.2 K, ref. 14) rather than larger barocaloric parameters (that is, |DS p |B12.5 J K À 1 kg À 1 , ref. 12) to deduce approximately the mechanocaloric effect. Interestingly, Fig. 3c,d shows that the caloric strengths |DS E /DE| (3.9 J cm V À 1 K À 1 kg À 1 ) and |DT E /DE| (2.6 K cm kV À 1 ) under an electric field DE of B2 kV cm À 1 are at least 1 order of magnitude larger than previous best reports on electrocaloric effect in BTO single crystals 29 (SC), and nearly 3 orders of magnitude larger than those in P(VDF-TrFE) TFs 32 . Our results also make a significant improvement on previous mutiferroic heterostructures: |DS E | is significantly larger than that (1.43 J K À 1 kg À 1 ) in La 0.7 Sr 0.3 MnO 3 /PMN-PT while |DS E /DE| is over 1 order of magnitude larger than that (0.20 J cm V À 1 K À 1 kg À 1 ) in La 0.7 Sr 0.3 MnO 3 /PMN-PT 33 .
We emphasize that our multicaloric effects rely on strainmediated coupling 2 but not on any phase transition of BTO, and are thus exempt from the requirement that the magnetic and ferroelectric/piezoelectric layers should have similar phase transition temperatures 3 , as suggested in a recent theoretical study 34 . However, other parameters including the layer thicknesses and heat capacities are important in the eventual design of a cooling system, so that their values in a composite multiferroic should be taken into account to determine the optimal design parameters 34 . In addition, a purely magnetic heatpump scheme without any second stimulus was proposed theoretically in FeRh without experimental evidence 35 while our proposed multicaloric refrigeration cycle is realized by experimental support.
In summary, our results here demonstrate that the historical irreversibility of MCE in FeRh discovered almost 26 years ago 8 can be solved by using an electric field. The dual-stimulus multicaloric cycle creates larger caloric effects, although the magnetic hysteresis losses are not destroyed but simply transferred to an elastic cycle. Since research in multicaloric materials has intensified recently 1 , we believe that our work will stimulate more efforts in multiferroic systems 2 where strong mechanical coupling between ferroic order parameters may provide more diverse choices for the design of efficient solidstate refrigeration, including purely electric field-driven systems. Finally, revisiting overlooked compounds like FeRh using hybrid heterostructures can also provide a new life for many magnetocaloric materials.
Data availability. The data that support the findings of this study are available from the corresponding author (Y.L. (liuyang-phy52@gmail.com) or L.C.P. (lee.phillips@cantab.net)) on request.