The change in temperature resulting from a change in the magnetic field applied to a magnetic material is called the magnetocaloric effect (MCE). Integrating this effect into a thermodynamic cycle could lead to a broad range of applications. One of the most attractive is magnetic refrigeration at room temperature. This cooling technique offers the possibility of advantageously replacing the conventional vapor-compression technology since it has a higher efficiency and does not use refrigerant gases that are greenhouse gases.[1, 2] The search for magnetic materials displaying a large MCE is the first step in its development and is nowadays very active. More precisely, since the discovery of “giant” MCE (G-MCE), which occurs when the latent heat of a first-order transition (FOT) is involved, research has focused on reaching ever stronger magnetic FOTs, that is to say, on reaching the largest latent heat possible, and the strongest magneto-structural coupling (e.g., cell-volume change at the FOT). However, though this approach is beneficial for reaching high MCE performances, in particular large entropy changes, it is accompanied by definite drawbacks, such as pronounced hysteretic phenomena, irreversibility of the effect, or poor mechanical stability. Here we report how a totally different approach has been used to design new materials displaying a unique combination of intense MCE and several practical advantages (based on 3d elements, limited hysteresis, no volume change at the transition), making them highly suitable for magnetic refrigeration. In MnFe(P,Si,B) compounds, large adiabatic temperature changes of 2.5 K and entropy changes of about 10 J kg−1 K−1 are achieved for a moderate field variation (1 T), while the reversibility of the effect and the mechanical stability of the samples are ensured. These results are supported by extensive experimental work combining different direct and indirect characterization methods.
The highest MCEs reported in recent years have been found in various families of intermetallic compounds: Gd5(Ge,Si)4; Mn(As,Sb); La(Fe,Si)13 and its hydrides;[6, 7] Mn2–yFey(P,x), where x = As, Ge, Si;[8-11] Heusler alloys Ni-Mn-X (X = Ga, Sn, In,…);[12-16] MnCoGe; and some other compounds.[1, 2] All these G-MCE materials show large entropy-change (ΔS) values. However, a point too often neglected in the field of G-MCE materials, even though these compounds are most prone to such drawbacks, is the negative role of hysteresis. Since all MCE applications have a cyclic character, one of the main pre-conditions is to ensure a total (or at least partial) reversibility of the effect when either field or temperature oscillations are applied. From a material point of view, this means keeping the field or thermal hysteresis that could occur as small as possible. A second drawback of G-MCE materials is related to their mechanical stability. FOTs bring not only sharp magnetization jumps but also discontinuities of other physical parameters, including the unit cell. This “structural” part can have manifold aspects: symmetry breaking or cell-volume or lattice-parameter changes. The most dramatic for the stability of polycrystalline bulk samples turns out to be the cell-volume change. During thermal or magnetic field cycles, the strains generated by a volume change may cause fractures or even destruction of the bulk piece, which severely hinders the applicability of these materials. Technical solutions can be used to overcome this problem, for instance by embedding the MCE material in a resin or by a porous shaping. However, in such cases the MCE is “diluted”, which is not satisfactory since the gap of the magnet is not efficiently used and the thermal conductivity governing the heat transfer is decreased. Bulk G-MCE materials with a good mechanical stability should remain the preferred solution. Finally, to allow large-scale applications, a last requirement that should be borne in mind is that the MCE material must consist of elements that are available in large amounts, are not expensive, and are not classified as toxic.
In this context, the MnFe(P,x) system appears to be an ideal playground. This material family is derived from the Fe2P compound, a prototypical example known for a long time to exhibit a sharp but weak (the latent heat L is only 0.25 kJ kg−1) FOT with a Curie temperature (TC) of 217 K. In this hexagonal system, the Fe atoms occupy two inequivalent atomic positions referred to as 3f (in a tetrahedral environment of non-metallic atoms) and 3g (pyramidal). An intriguing aspect is the disappearance at TC of the magnetic moments of the iron atoms at the 3f sites, whereas there is only a limited decrease of the moments at the 3g site. This theoretical prediction has led to a cooperative description of the FOT that links the loss of long-range magnetic order at TC with the loss of the local moments at the 3f site. This mechanism has recently been proposed to be the origin of the G-MCE observed in MnFe(P,Si). The disappearance of the magnetic moments is ascribed to a conversion from non-bonding d electrons to a distribution with pronounced hybridization with the surrounding Si/P atoms. A practical consequence is that the FOT mechanism can be expected to be highly sensitive to substitutions at the non-metallic site. In the present work, precisely this approach has been used to solve three problems of the previous generation of MnFe(P,Si) materials. 1) The first improvement needed is related to the enhancement of the adiabatic temperature change (ΔTad). For magnetic-refrigeration applications, it is of primary interest to optimize the heart of the device, the MCE material. This MCE is quantified either by the entropy change (ΔS) or by ΔTad, depending on whether the magnetic-field change is performed isothermally or adiabatically. Comparing different materials reveals that a large ΔS does not necessarily imply a large ΔTad, and vice versa; both quantities have to be optimized simultaneously. This is an unsatisfactory point for MnFe(P,Si) materials, which exhibit large ΔS but limited ΔTad (∼2 K in 1 T). 2) The second target is to solve the mechanical stability problem observed in MnFe(P,Si). Even though the cell-volume change of these materials at the FOT is limited (ΔV = + 0.2%), crossing the transition still leads to fractures or destruction of bulk samples. 3) The last objective is to provide materials having a large MCE at intermediate fields, that is, at those offered by permanent magnets. If the magnetic field required to fully induce the FOT is considerably higher than the field source of the magnetic refrigerator (which is often the case for a FOT with large L), the material is designed in an inefficient way, since all the drawbacks of a FOT are present but only a part of the transition is really used. A good strategy to incorporate most of the latent heat into the MCE is to optimize the temperature shift of the transition due to the applied field.
Based on the Clausius–Clapeyron description dTC/dB = -TCΔM/L, where B is the magnetic flux density and ΔM the jump in magnetization, the optimizations (1) and (3) above imply that dTC/dB should be increased, that is, an increase of ΔM and decrease of the latent heat. In earlier studies of MnFe(P,Si) materials, reduction of the hysteresis was achieved by adjustment of the Mn/Fe and P/Si ratios, which, unfortunately, reduces the magnetization. To increase the magnetization and ΔM, it is required to work around the MnFeP2/3Si1/3 composition, which is a double optimum for the saturation magnetization, Mn/Fe ∼ 1 and Si ∼ 1/3.[21, 22] To control the latent heat, however, a new ingredient is required, a parameter able to decrease the latent heat while keeping the magnetization unmodified. For this purpose, boron substitution at the non-magnetic site (replacement of P by B) has been investigated.
In MnFe(P,Si) materials, the effect of B substitution on TC is similar to that in Fe2P. On the isofield MB(T) curves, Figure 1, starting from the “magnetization optimum” MnFe0.95P2/3Si1/3, substitution of B for 0.075 P (MnFe0.95P0.595B0.075Si0.33) leads to a significant increase of TC (for TC measured upon heating from 215 K to 283 K; see the Supporting Information S1 for intermediate compositions). Most interesting is the fact that the extremely large difference between heating and cooling Curie temperatures of the parent compound MnFe0.95P2/3Si1/3 (thermal hysteresis of 75 K) is strongly suppressed by B substitution, resulting in a hysteresis of only 1.6 K in the B = 7.5% compound. The average hysteresis decrease by B doping is about 10 K per percent B, a value much higher than obtained by changing the Mn/Fe ratio (−1.2 K per Mn or Fe%) or the P/Si ratio (−1.1 K per Si%). Moreover, since the control of the hysteresis is now achieved without deviating from the Mn/Fe ∼ 1 and Si ∼ 1/3 optima, the magnetization in the ferromagnetic state far below TC is kept unmodified (the two samples exhibit a magnetization of 150 A m2 kg−1 at 50 K), which is very important for the MCE performance.
The MCE evaluation of a new material requires a complete characterization of both ΔS and ΔTad. Figure 2 combines results from two direct probes and from indirect (magnetic and calorimetric (differential scanning calorimetry, DSC)) techniques. Such an extensive characterization has only recently been published for G-MCE materials, but is crucial in order to obtain a reliable picture of the thermomagnetic behavior around a FOT. The specific-heat curves of MnFe0.95P0.595B0.075Si0.33 can be found in the Supporting Information. The latent heat obtained by the integration of the curve in zero field is L = 3.8 kJ kg−1. This significantly lower value than for materials without B (L = 12.3 kJ kg−1 for MnFe0.95P2/3Si1/3 and L = 6.4 kJ kg−1 for Mn1.25Fe0.7P1/2Si1/2) is assumed to be at least partially the reason for the larger dTC/dB = 4.3(2) K T−1 found in MnFe0.95P0.595B0.075Si0.33 than the 3.5(2) K T−1 found in Mn1.25Fe0.7P1/2Si1/2. From a metrological point of view, special care has been paid to avoid miscalculations that could result in a “spike” on the ΔS(T) curves.[25-27] Moreover, since both the hysteresis and the width of the FOT are limited in the present compound, one can expect this problem to be very minor.
The ΔS(T) curves derived from isofield magnetic measurements and calorimetry upon heating, Figure 2a, are in good agreement: ΔSmax = 9.1(8) J kg−1 K−1 at 279.1 K by DSC and ΔSmax = 9.8 ± 1.0 J kg−1 K−1 at 281 K by the magnetic method. These values are much higher than those of the archetypical MCE material Gd.[1, 2] Compared with G-MCE materials, ΔS of MnFe(P,Si,B) is similar to that of Gd5Si2Ge2, higher than the values generally found in Heusler alloys, and just below the best performances found for La(Fe,Si)13Hy.[1, 2] However, it should be kept in mind that the indirect ΔS measurements we are referring to do not disclose the reversibility of the MCE, a point for which direct measurements, in particular of ΔTad, are more suitable.
We used two types of direct methods to measure the adiabatic temperature change (denoted as ΔTcyclic hereafter). The first direct measurements were carried out in a device using a continuous sweep of the temperature during field oscillations (ΔB = 1.1 T). Figure 3a presents a typical raw-data curve. Application and removal of the magnetic field creates a tower shape response overlaying a linear temperature versus time evolution, which corresponds to the sweep rate of the measurement. The same values ΔTcyclic = 2.8 K are obtained irrespectively of the direction of the magnetic-field change, which is a first indication of total reversibility of the MCE in this material. To avoid any inconsistencies that may result from the dynamic character of this measurement, especially when dealing with a material still displaying a small thermal hysteresis, a second kind of direct ΔTcyclic measurement was performed. Instead of being swept, the external temperature was maintained in such a way that the same starting temperatures before each field application and removal were used. In this case, the resulting temperature versus time profile, Figure 3b, simulates a Brayton magnetic-refrigeration cycle.[1, 2] Therefore, this cyclic measurement directly reflects the material performance for applications. For ΔB = 1 T, a ΔTcyclic of 2.55 K is achieved and maintained during all subsequent cycles. These two direct ΔTcyclic measurements are finally compared with the indirect calorimetric method (DSC) in Figure 2b. One observes good agreement of the adiabatic temperature changes, the values derived from ΔTcyclic in sweeping mode are slightly higher (2.8 K) since this corresponds to a field change of 1.1 T.
Compared to the best materials, ΔTad of MnFe0.95P0.595B0.075Si0.33 is similar to that of Gd and most of the G-MCE compounds.[1, 2] For instance, the present performances are close to the “giant ΔTad” reported in Heusler alloys (ΔTad = 2.8 K at 1 T for Ni45.2Mn36.7In13Co5.1). However, in sharp contrast with this latter example, where only a small part of ΔTad is reversible, the large MCE presently observed is fully reversible when the field is cycled, which is an overwhelming advantage of MnFe(P,Si,B) compounds. These new materials are also a significant improvement over the previous MnFe(P,Si) generation, since the same ΔS values are observed while ΔTad has been enhanced by more than 30%. This enhancement of ΔTad at intermediate magnetic fields is ascribed to the larger dTC/dB, so indirectly comes from the higher magnetization and lower latent heat of this new material.
The last progress achieved for MnFe(P,Si,B) materials concerns the mechanical stability. This problem, already noticed in G-MCE materials, manifests itself by, for instance, the degradation of ΔTad during cyclic measurements. Qualitatively, we observe that bulk pieces of MnFe0.95P0.595B0.075Si0.33 do not show any degradation when cycled across the transition. Quantitatively, even after 10000 cycles of magnetization/demagnetization used in the ΔTcyclic measurements, the sample geometry remains intact and the mechanical integrity is maintained while the MCE does not show any degradation (Supporting Information S3). We believe that this improved mechanical stability in comparison with MnFe(P,Si) compounds or other G-MCE materials is partially related to the absence of a cell-volume change at the transition. In MnFe0.95P0.595B0.075Si0.33, the jump of the c/a ratio at TC is almost as pronounced as in Mn1.25Fe0.7P0.5Si0.5, but no discontinuous volume change is observed within the experimental accuracy, Figure 4. This exceptionally small ΔV turns out to be smaller than in all other MnFe(P,x) compounds, for instance smaller than in As-based materials (where ΔV/V = −0.44%), in Ge-based materials (where ΔV/V = +0.1%), and in Si-based materials.
Generally speaking, the present study highlights that, besides magnetism, the key parameter to be controlled in the design of promising G-MCE materials is the latent heat of the FOT. More precisely, L has to be large enough to ensure high ΔS values but should be “kept under control” to maintain a large dTC/dB and ΔTad. Regarding the MnFe(P,x) MCE family, it is found that B substitution has a similar effect as in Fe2P, a point which was not straightforward at first glance since we are actually dealing with FOTs about 50 times stronger than in Fe2P. From an application point of view, the combination of a tunable TC (Mn/Fe, P/Si, and B composition parameters), no toxic or critical elements, high ΔS, high ΔTad, total reversibility of the effect, and good mechanical stability gives MnFe(P,Si,B) compounds considerable advantages, making them highly promising for magnetic refrigeration. Compared to La(Fe,Si)13 hydrides, it is still unclear which material has the largest reversible MCE but, in any case, these new MnFe(P,Si,B) materials neither contain a rare-earth element nor suffer from dehydrogenation.