Magnetocaloric materials for energy efficient cooling

Although the direct measurement of the MCE is straightforward, the lack of commercial equipment impedes the widespread use of this technique. A recent review of home built equipment can be found in Smith et al (2012).

To measure ΔT_ad one needs to ensure adiabatic conditions and provide means for a magnetic field variation and temperature measurement. Thermocouple is commonly used to measure temperature directly (Dan'kov et al 1997, Lyubina et al 2009a, 2010, Skokov et al 2009); indirect temperature measurements can also be employed (Otowski et al 1993, Christensen et al 2010). According to the way the magnetic field variation is achieved, one distinguishes ΔT_ad measurement systems where the source of the magnetic field is stationary and a sample is moved relatively to this source (Bjørk et al 2010a, Yibole et al 2014) and systems where the magnetic field is varied in time and the sample position is fixed (Dan'kov et al 1997, Lyubina et al 2009a, 2010, Skokov et al 2009, Kuz'min et al 2011, Morrison et al 2012c, Ghorbani Zavareh et al 2015). Adiabatic conditions require the avoidance of heat exchange between a sample and environment for the duration of the measurement. Along with a good thermal insulation a fast magnetic field change is essential; this can be realised by moving permanent magnets (Lyubina et al 2009a, 2010, Skokov et al 2009) or in pulsed fields (Dan'kov et al 1997, Ghorbani Zavareh et al 2015). Exemplarily, ΔT_ad for a single crystal Gd and bulk LaFe_11.6Si_1.4 alloy measured in a device (Lyubina et al 2009a, 2010, Skokov et al 2009, Kuz'min et al 2011, Morrison et al 2012c), where the magnetic field is provided by a rotating Halbach-type permanent magnet assembly and temperature is recorded by a thermocouple, is shown in figure 8. The use of vacuum and heat shields combined with a field variation rate in the order of 1 T s⁻¹ ensures adiabaticity. In Gd, where no field or thermal hysteresis is expected to occur, essentially no difference in ΔT_ad(H) on the application and removal of the magnetic field is apparent (figure 8(a)). In contrast, substantial field hysteresis at and above T_c (191 K and 195 K in figure 8(c)) and thermal (Lyubina et al 2010) hysteresis is observed for the bulk LaFe_11.6Si_1.4 alloy, which is caused by dynamic processes within the solid (Lovell et al 2015).

Zoom In Zoom Out Reset image size

Differential scanning calorimetery (DSC) enables a direct entropy change ΔS measurement. Basso et al (2008, 2010) reported direct ΔS measurements in a home built Peltier cells heat flux DSC, where an electromagnet is used as magnetic field source. As in a commercial DSC, reference materials are used either for the determination of the calibration constant connecting the measured voltage to the heat flux or the time constant governing the kinetics. The DSC signal is due to a sum of the heat capacity and latent heat. When operated under isothermal conditions, the DSC measures a heat flux due to the change of the applied magnetic field and the induced entropy change ΔS can be directly measured.

The so-called indirect measurement of the MCE is a widely adopted technique in which either the heat capacity is measured in a calorimeter or magnetisation is measured in a magnetometer and the MCE is subsequently computed from the acquired data.

4.2.1. Heat capacity.

The calculation of the entropy S and entropy change ΔS in materials experiencing a second order transition is performed using equations (1) and (2) by numerical integration of C_p(H, T) data. Even though the transitions we are interested in are taking place around room temperature, it is important to start recording C_p(H, T) at the lowest possible temperature (typically between 2 and 5 K) to keep the error arising due to the entropy term S₀ low (Lyubina 2016). The accuracy of the MCE calculation from C_p data was studied in detail by Pecharsky and Gschneidner (1999a, 1999b).

The first order characteristics of the phase transition, latent heat (equation (9)), needs to be accounted for in the calculation of the entropy from C_p data in materials with the first order transition. Clearly, the latent heat cannot be determined by the integration of the heat capacity in materials with a very sharp first order magnetic phase transition and a singularity in C_p at the transition point (figure 3), such as that observed in ultra-pure and homogeneous Dy metal (Pecharsky et al 1996). The infinitely large heat capacity makes the accurate determination of the height of the $\Delta {{S}_{\text{L}}}$ jump impossible.

In most materials, the phase transition occurs in a finite temperature range and, as a result, although sharp, the heat capacity has a finite value (figure 7). Regardless of the first order transition type (strong, weak or inhomogeneity broadened), the latent heat must be captured appropriately in order to correctly determine the MCE (Pecharsky and Gschneidner 1999b, Morrison et al 2012a). Therefore, special procedures for the independent determination of L should be adopted.

Pecharsky et al (1996) proposed a method for capturing the latent heat at sharp first order transitions that can be used in a heat pulse calorimetry, a technique often used in both home-built and in commercial equipment operating near and below room temperature. In accordance with the thermodynamics, if the material experiences a first order transformation, the latent heat L will effectively change the amount of heat supplied to it by the calorimeter $\Delta {{Q}_{\text{pulse}}}$ ($\Delta {{Q}_{\text{pulse}}}=L+m{{c}_{\text{p}}} \Delta {{T}_{\text{pulse}}}$, m is the sample mass) and, thus, will introduce uncertainty in the measurement. The method consists in the application of heat pulses $\Delta {{Q}_{\text{pulse}}}$ with a different amplitude and recording temperature rise and decay $\Delta {{T}_{\text{pulse}}}$ (Pecharsky et al 1996). The heat pulse resulting in $\Delta {{T}_{\text{pulse}}}=0$ allows the precise determination of the latent heat of the transformation. The corresponding entropy $\Delta {{S}_{\text{L}}}$ should then be added above and below the transition point into the entropy function in equation (1) and the entropy is obtained as

$$\begin{eqnarray}&&S(T,H)={\int}_{{{T}_{0}}}^{{{T}_{\text{c}}}-\delta}\frac{{{C}_{\text{p}}}\left({{T}^{\prime}},H\right)}{{{T}^{\prime}}}\text{d}{{T}^{\prime}}+{\int}_{{{T}_{\text{c}}}+\delta}^{T}\frac{{{C}_{\text{p}}}\left({{T}^{\prime}},H\right)}{{{T}^{\prime}}}\text{d}{{T}^{\prime}}+\frac{L\left({{T}_{\text{c}}},H\right)}{{{T}_{\text{c}}}};\end{eqnarray} \tag{ 10 }$$

S₀ is neglected here. The separate measurement of the latent heat can also be realised by a temperature modulated (micro)calorimetry technique (Morrison et al 2012a, Morrison and Cohen 2014).

4.2.2. Magnetometry.

Calculation of the MCE using calorimetry requires time-consuming and non-trivial C_p measurements. The MCE can alternatively be calculated using magnetometry data; this method is often employed due to its simplicity and effectiveness in terms of reduced data collection time and accessibility of the magnetometry equipment.

Integration of the Maxwell relations (Reif 1985) yields the entropy change that is related to the magnetisation M(T, H) as

$$\begin{eqnarray} &&\Delta S(T, \Delta H)={\int}_{{{H}_{\text{i}}}}^{{{H}_{\text{f}}}}{{\left(\frac{\partial M(T,H)}{\partial T}\right)}_{H}}\text{d}H.\end{eqnarray} \tag{ 11 }$$

Since equation (11) is obtained from the free energy, thermodynamics demands that the states in the initial field H_i and final field H_f are equilibrium states. It is further assumed that the magnetisation M(T, H) has a derivative at the transition point ${{(\partial M/\partial T)}_{H}}$, i.e. it does not have a jump discontinuity.

At second order transitions, both conditions are fulfilled and the entropy change ΔS is readily calculated by numerical integration of equation (11), if isofield magnetisation curves $M{{(T)}_{H}}~$ or isotherms $M{{(H)}_{T}}$ used to build ${{(\partial M/\partial T)}_{H}}$ are known. Often, isothermal magnetisation is recorded due to a shorter data collection time and well defined lower integration limit H_i (usually zero). In the isofield measurements, recording $M{{(T)}_{H}}$ in zero field is connected to a larger uncertainty. The equivalency of both measurements was demonstrated by Morrison et al (2012c).

If open magnetic circuit magnetometry is employed, correction for demagnetising effects is required for the determination of the internal magnetic field

$$\begin{eqnarray}&&{{H}_{\operatorname{int}}}={{H}_{\text{appl}}}-NM,\end{eqnarray} \tag{ 12 }$$

where H_appl is the applied field and N is the demagnetising factor. The latter can only be neglected in thin flakes and films with M in the plane or in needles with M along the long axis.

As discussed in the preceding section, in the majority of the first order materials the phase transition occurs in a finite temperature range and, thus, the derivative ${{(\partial M/\partial T)}_{H}}$ exists. This is also the case in ultra-pure and homogeneous materials (Chernyshov et al 2005). However, the condition of the equilibrium can be violated under particular measurement conditions. In magnetocaloric material families showing a field induced metamagnetic or magnetostructural transition, the paramagnetic (PM) state is generally the equilibrium phase above T_c and in H  =  0 (Pecharsky and Gschneidner 1997a, Gschneidner et al 2005, Brück 2008, Lyubina et al 2009b, Dung et al 2012). The equilibrium state below T_c or in sufficiently high magnetic fields above T_c is the ferromagnetic state. When the transition occurs in a finite temperature range, a mixture of the PM and FM phases is observed; note that at each particular temperature only a certain PM/FM fraction is an equilibrium fraction. A frequently employed measurement protocol is a 'continuous' cooling (heating), during which an M(H)_T curve is recorded at a given temperature and a subsequent M(H)_T is recorded at a lower (higher) temperature (Caron et al 2009, Bratko et al 2012). Magnetic field sweep (zero  →  maximum field  →  zero) at a particular temperature may not always return the material to the equilibrium (e.g. PM in zero field), but some part of the sample can transform to a non-equilibrium state (e.g. FM) in the magnetic field and remain in this state in zero field. The PM/FM phase fraction will thus deviate from the equilibrium. The reason for the observation of this behaviour is a non-zero hysteresis at the transition (figure 5). Considerable errors arise as a result of the equilibrium condition violation (Caron et al 2009). In extreme cases, failure to take this effect into account can lead to a 'colossal entropy change overestimation' yielding unphysically large ΔS (Bratko et al 2012).

In first order materials, where a field sweep during magnetisation measurements induces a non-equilibrium state, another procedure for recording M(H)_T data is required. The essence of the method lies in 'resetting' the material to its equilibrium state by either heating well above—point c in figure 5(b) (or cooling well below—point h in figure 5(b)) the temperature of the transition. The solid thus attains equilibrium before the next isotherm is recorded (Caron et al 2009, Bratko et al 2012). It should be appreciated, however, that the formation of inhomogeneous magnetisation states (Amaral and Amaral 2010) and magnetically induced reorientation in martensitic Heusler alloys (Niemann et al 2014) can be another source of spurious effects and need to be eliminated in the calculation of ΔS.

It should be emphasised that the magnetometry technique allows the calculation of the total entropy change. Statements found in the literature that only the magnetic part of the entropy is captured by magnetisation measurements are erroneous; although the magnetic field merely influences S_mag, the change in S_mag obviously induces a variation in other relevant entropy terms (here, S_ph). Provided the equation (11) applicability conditions are not violated, the entropy change obtained from heat capacity resembles that from magnetometry (see e.g. Manosa et al 2009, Morrison et al 2010, Bratko et al 2012).

The integration of the Maxwell relation and the use of equation (1) yields the following expression for the adiabatic temperature change:

$$\begin{eqnarray} &&\Delta {{T}_{\text{ad}}}(T, \Delta H)=-{\int}_{{{H}_{\text{i}}}}^{{{H}_{\text{f}}}}{{\left(\frac{T}{{{C}_{\text{p}}}(T,H)}\right)}_{H}}{{\left(\frac{\partial M(T,H)}{\partial T}\right)}_{H}}\text{d}H.\end{eqnarray} \tag{ 13 }$$

As is apparent from equation (13), the ΔT_ad determination using magnetometry data requires the knowledge of C_p(T, H) additionally to M(T, H). The strong temperature and field dependence of the C_p(T, H) function (figure 7) does not allow to treat the heat capacity as a constant and exclude it from the integral in equation (13) (Pecharsky and Gschneidner 1999a). On the other hand, the availability of C_p data (and hence S data) in fields H_i and H_f makes the use of equation (13) obsolete, as simply equation (4) can be applied for ΔT_ad calculation. Nevertheless, it is appreciated that if the C_p(T, H) data is available only for a limited number of fields, equation (13) can be useful in the calculation of missing entropies S(T, H_i) and S(T, H_f) and the corresponding ΔT_ad determination (Pecharsky and Gschneidner 1999a).

Clausius–Clapeyron equation (Reif 1985) is an alternative method that can be used to obtain the entropy change at first order transitions:

$$\begin{eqnarray}&&\frac{\text{d}H}{\text{d}{{T}_{\text{c}}}}=-\frac{ \Delta {{S}_{\text{L}}}}{ \Delta M}.\end{eqnarray} \tag{ 14 }$$

It correlates the equilibrium line slope $\text{d}H/\text{d}{{T}_{\text{c}}}$ in the magnetic phase diagram (figure 5(b)) to the discontinuity in entropy $\Delta {{S}_{\text{L}}}~$ and magnetisation $\Delta M$ and assumes equal chemical potentials of the phases at the transition point. Since the transition between the two magnetic states must essentially be complete (which is ensured by the application of a sufficiently high magnetic field), equation (14) gives the limit of the entropy change achievable in a particular material at this transition (see e.g. Giguère et al 1999, Casanova et al 2002, Fujita et al 2013a). In practice, the magnetisation change occurs in a finite magnetic field range and not at a single H (figure 6). ΔM is as a result often underestimated (Amaral and Amaral 2010).

To justify the technology switch from vapour compression to magnetic refrigeration, ever higher performance of magnetic cooling devices must be demonstrated. In this respect, a large MCE in the magnetic refrigerant is a prerequisite for being potentially able to provide a large cooling power and high efficiency. The entropy change ΔS is a measure of the material's cooling power; adequate ΔT_ad is required to move the heat. MCE increase with the magnetic field change (see equations (11) and (13)) is limited, since the available magnetic field provided by permanent magnets is below 2 T and in high magnetic fields the MCE does not grow unlimitedly, but eventually saturates (Tishin 1990, Lyubina et al 2011). Therefore, the maximisation of MCE should be achieved through an increase of $\partial M(T,H)/\partial T$ (equations (11) and (13)).

The magnetisation derivative is maximised at magnetic phase transitions. The derivative $\partial M(T,H)/\partial T$ at first order transitions is significantly larger compared to that at second order transitions (see the magnetisation curves versus temperature in figure 3). The steep magnetisation variation leads to the observation of the giant MCE (Nikitin et al 1990, Pecharsky and Gschneidner 1997a); the latter is commonly observed in the magnetocaloric materials with a coupled magnetic and structural transformation either with or without symmetry change (figure 9). The entropy change ΔS of giant MCE materials is limited to a narrower temperature range compared to materials with a second order transition, resulting in a considerably higher ΔS_max. Figure 10 shows ΔS for a family of LaFe_13−xSi_x alloys that depending on the composition can exhibit a weak first or second order PM to FM transition; the giant MCE material, LaFe_11.6Si_1.4, possesses ΔS_max a factor of three larger compared to that of Gd.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

It should be emphasised that for the ease of ΔS comparison in various materials and from the engineering point of view, it is advisable to provide ΔS in volumetric, J m⁻³ K⁻¹, and not in gravimetric units, J kg⁻¹ K⁻¹ (Lyubina et al 2009b, Gschneidner et al 2005). The conversion between the units requires the knowledge of the material density.

The use of a single figure-of-merit reflecting ΔS and ΔT_ad for a particular magnetocaloric material could provide a convenient means for comparison and assessment of different refrigerant materials. Magnetic refrigerant capacity in the form suggested by Wood and Potter (1985), $\text{RC}= \Delta {{T}_{\text{span}}} \Delta S{{|}_{T}}$, assumes a uniform temperature across the magnetic refrigerant bed (a condition violated in AMR) and equal entropy change at the cold and hot ends, $\Delta S{{|}_{T}}$. No limitations are posed on ΔT_ad, allowing it to be unacceptably small. Likewise, from the knowledge of the relative cooling power (RCP_ΔS) alone, defined as ΔS(T) peak area or as a product of ΔS_max and the full-width-at-half maximum (FWHM) (Gschneidner and Pecharsky 2000, Lyubina et al 2009b), no conclusion can be made, whether cooling can be performed with this material. This is because a large RCP_ΔS does not necessarily imply availability of a sufficient ΔT_ad; note the additional heat capacity term in equation (13) compared to equation (11) (Pecharsky and Gschneidner 2006).

The minimum requirement for ΔT_ad is device specific. Engelbrecht and Bahl (2010) demonstrated that cooling can cease when ΔT_ad drops below 2 K. Based on this result, one can introduce a figure-of-merit parameter useful for an engineer, RCP_ΔS|ΔT_ad  >  2 K, defined as an area of the ΔS peak limited to a temperature range, where ΔT_ad is above 2 K, ($\Delta {{T}_{s}}$) (see figure 11 for a graphical visualisation):

$$\begin{eqnarray}&&\text{RC}{{\text{P}}_{ \Delta S}}| \Delta {{T}_{\text{ad}}}>2K= \Delta {{S}_{s}} \Delta {{T}_{s}}.\end{eqnarray} \tag{ 15 }$$

Zoom In Zoom Out Reset image size

Relative cooling power determined in this manner for different families of magnetocaloric materials is summarised in figure 12. It is apparent that in a single material bed regenerator, Gd by far outperforms not only material families with a second order transition, but also materials experiencing the first order transition. In some material families, such as amorphous Fe₇₈B₁₂Cr₈Ce_1–5 and Heusler alloys Ni₅₀Mn₃₄In₁₆ and Ni₅₀Mn₃₆Co₁Sn₁₃ (Khovaylo et al 2010, data not included in figure 12) the (cyclic) adiabatic temperature change is below 2 K in a field change of up to 2 T and consequently the relative cooling capacity RCP_ΔS|ΔT_ad  >  2 K is null.

Zoom In Zoom Out Reset image size

The MCE in magnetic refrigerants can be influenced by the microstructure. Figure 13 illustrates the effect of microstructure on the entropy change for alloys of the LaFe_13−xSi_x family with a first order transition. The largest entropy change is observed in bulk microcrystalline alloy. The introduction of porosity leads to the removal of constraints imposed by grain boundaries and as a consequence ΔS is decreased by about 30% in porous alloys consisting of cold-pressed powders with surface area moment mean particle size L_m of 225 µm (Lyubina et al 2010, Lyubina 2011). Reduction of the internal strain (constraints), distribution of transition temperatures as well as material degradation due to defects and surface oxidation (Moore et al 2009, Lyubina et al 2010, 2012b, Radulov et al 2015) are discussed in relation to the reduction of the MCE on further decrease of the particle size (figure 13). A dramatic drop of the magnetocaloric effect is observed on reducing the crystallite size to the nanometer range (figure 13). In LaFe_13−xSi_x, the reduction of the grain size to 70 nm and to 40 nm gradually weakens the first order transition and ΔS_max drops by 40% and 60% compared to the microcrystalline counterpart, respectively (Lyubina 2011). The lattice microstrain is on the similar level ($\langle e\rangle$  ≈  0.13–0.15%) for both nanocrystalline materials. Thus, the gradual transition to the second-order regime may be mainly ascribed to the grain size reduction. This behaviour can be a manifestation of random anisotropy effects, when the exchange energy starts to balance the anisotropy energy yielding a so-called intergrain exchange coupling (Skomski 2003). The exchange length, a characteristic length below which atomic exchange interactions dominate magnetostatic fields, is ~10 nm in low magnetocrystalline anisotropy materials, such as LaFe_13−xSi_x. It determines, for example, the transition from a particular magnetisation rotation regime and the grain size below which the hysteresis loops of two-phase magnets appear single-phase-like (Skomski 2003). Apparently, the reduction of the crystallite size in first-order materials to the range comparable to the exchange length weakens magnetostructural coupling in first-order materials and leads to the overall MCE reduction. Similar effects were observed in Gd₅(Si_xGe_1−x)₄ alloys experiencing a first order coupled magnetostructural transition (do Couto et al 2011, Pires et al 2015). The authors did not report the grain sizes of the ball milled Gd₅(Si_xGe_1−x)₄ materials explicitly, but the presented x-ray diffraction patterns indicate their nanocrystalline nature. Also in materials with a second order transition the magnetocaloric effect is reduced on decreasing the crystallite size to the nanoscale. For example, crystallite size reduction to the nanometer regime in Gd leads to a sizable drop of ΔS (Mathew et al 2010). Thus, nanostructuring has a detrimental effect on the size of the magnetocaloric effect.

Zoom In Zoom Out Reset image size

To overcome the limitation of a narrow temperature span $\Delta {{T}_{\text{span}}}$ and correspondingly lower RCP_ΔS|ΔT_ad  >  2 K provided by a single (first order) magnetocaloric material, a graded regenerator bed comprising materials with different Curie temperature is employed (Russek et al 2010). Variation of the material composition with the aim of T_c tuning should preferably be performed in a way allowing to retain the large cooling capacity. Exemplarily, specific stoichiometry variation in Mn_xFe_1.95−xP_1−ySi_y does not change the transition type and potentially a constant and large ΔS is obtainable in $\Delta {{T}_{\text{span}}}\approx 200\,\text{K}$ (figure 14, Dung et al 2011). The condition of the constant ΔS is of utmost importance for the AMR performance (Engelbrecht and Bahl 2010). For engineering a magnetic refrigerant bed containing multiple T_c materials, it is furthermore desirable to have a sufficient and constant adiabatic temperature change along the regenerator length. The AMR performance in dependence on the temperature profile ΔT_ad(T) along the regenerator, where T is the material's temperature, was studied by Smaili and Chahine (1998), who showed that any monotonically increasing ΔT_ad(T) can provide adequate regenerator performance. 'Excessive' ΔT_ad shifts the operating temperature of a neighbouring material from its optimum and thus can reduce the overall efficiency of the refrigerator (Russek et al 2016).

Zoom In Zoom Out Reset image size

Hysteresis is observed both at field induced and temperature induced first order transitions (figure 5) and is detrimental for refrigerator operation. Figure 5(a) shows schematically the hysteresis in the field and temperature driven first order transitions with characteristic transition fields/temperatures and hysteresis widths, $\Delta {{H}_{\text{hys}}}~$ and $\Delta {{T}_{\text{hys}}}$. Hysteresis can be mapped in the (H, T)-plane by, for instance, extracting the field of the transition ${{H}_{\text{mi}}}$ from the M(H) isotherms at a temperature T_i and constructing a phase equilibrium line $\text{d}H/\text{d}{{T}_{\text{c}}}$ (figure 5(b)). In materials with the hysteresis, two phase equilibrium lines exist; the first line corresponds to the transition from a high-temperature (e.g. PM, austenite) to a low-temperature (e.g. FM, martensite) phase and the second one corresponds to the reverse transition. In the time independent or static process, the influence of the field and temperature on the transition are equivalent. It is apparent from figure 5(b) that the following relation between the thermal and field hysteresis can be established

$$\begin{eqnarray} &&\Delta {{H}_{\text{hys}}}= \Delta {{T}_{\text{hys}}}\frac{\text{d}H}{\text{d}{{T}_{\text{c}}}}= \Delta {{T}_{\text{hys}}}/\frac{\text{d}{{T}_{\text{c}}}}{\text{d}H}.\end{eqnarray} \tag{ 16 }$$

Thus, the knowledge of the thermal hysteresis width $\Delta {{T}_{\text{hys}}}$ and the shift of the transition temperature with the field $\text{d}{{T}_{\text{c}}}/\text{d}H$ or its inverse value $\text{d}H/\text{d}{{T}_{\text{c}}}$ allows one to determine the amplitude of the field hysteresis $\Delta {{H}_{\text{hys}}}$. For an ideal first order transition, the adiabatic temperature change can be approximated with the use of equations (11), (13) and (14)

$$\begin{eqnarray} &&\Delta {{T}_{\text{ad}}}\approx -{{\mu}_{0}}\,\frac{T}{{{C}_{\text{p}}}}\frac{\text{d}H}{\text{d}{{T}_{\text{c}}}} \Delta M,\end{eqnarray} \tag{ 17 }$$

provided the field $\Delta H$ is large enough to complete the transformation (Pecharsky and Gschneidner 2006). Note that cooling will cease as soon as $\Delta {{H}_{\text{hys}}}$ becomes comparable or exceeds the magnetic field change $\Delta H$. The same result is obtained on examination of the RCP (Kuz'min and Richter 2007). Obviously, magnetocaloric materials with a large $\Delta {{H}_{\text{hys}}}$ or in other words, a steep $\text{d}H/\text{d}{{T}_{\text{c}}}$ or a small rate of the T_c shift with field and large $\Delta {{T}_{\text{hys}}}$, cannot be good refrigerants. If one follows the transition along the path c  →  c^*, one notices that the lowest field hysteresis is obtained when the width $\Delta {{T}_{\text{hys}}}$ and slope of the phase equilibrium line $\text{d}H/\text{d}{{T}_{\text{c}}}$ are small (figure 5).

Materials with the strong first order transition have a large hysteresis. Exemplarily, ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}\approx 2\,\text{T}$ for Gd₅Si₂Ge₂ (table 1), ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}\approx 1\,\text{T}$ in FeRh and ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}\approx 12\,\text{T}$ for Ni₅₀Mn₃₆Co₁Sn₁₃ (Basso et al 2012). If the application in the cyclic AMR process is considered, the extremely large hysteresis (especially in the latter case) would require unacceptably high magnetic fields to induce the transformation. In contrast, materials with the weak first order transition are characterised by a much lower hysteresis, e.g. ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}\approx 0.1\,~\text{T}$ for LaFe_13−xSi_x and ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}<0.4\,~\text{T}$ for MnFeSi_xP_1−x-type compounds (table 1). Clearly, only materials with the weak first order transition are attractive for heat pumping applications. We recall that the field dependence of the MCE in these materials follows the form of equation (8).

Table 1. Properties of the magnetocaloric materials with strong and weak first order transitions: the peak temperature of the ▵S curve (T_max), the gravimetric and volumetric maximum entropy change (▵S_max) in a field change μ₀▵H  =  (0–1) T, the discontinuity of the lattice constants (▵a/a and ▵c/c) and discontinuity in volume (▵V/V), the thermal (▵T_hys) and field (▵H_hys) hysteresis and the thermal conductivity (κ) at 300 K.

Material	Tmax (K)	−ΔSmax (kJ m−3 K−1)	−ΔSmax (J kg−1 K−1)	Lattice discontinuity (%)			${{\mu}_{0}} \Delta {{H}_{\text{hys}}}$ (T)	ΔThys (K)	κ (W K−1 m−1)	Reference
				▵a/a	▵c/c	▵V/V
Gd5Si2Ge2 (homogenised)	272	68	12	−0.9	0.2	0.4	1.5–2	10	5.2	Morellon et al (1998), Pecharsky and Gschneidner (2001a), Pecharsky et al (2003) and Fujieda et al (2004)
LaFe11.6Si1.4 (bulk)	196	147	22	1.09	1.09	1.09	0.5	2.3	9.1	Fujieda et al (2004), Lyubina et al (2009b) and Lyubina (2011, 2016)
LaFe11.6Si1.4 (porous and {melt-spun})	196	76{68}	11{10}	1.09a	1.09a	1.09a	0.1	0.5	2.7–5.0	Lyubina (2011, 2016), Lyubina et al (2012b) and Radulov et al (2015)
Mn1.25Fe0.7P0.5Si0.5	274	57	9	−0.79	1.86	0.26	21(5.7)b	75(20)b		Brück (2008) and Guillou et al (2014a, 2014b)
MnFe0.95P0.582Si0.34B0.078	289	57	9	−0.73	1.57	0.09	≈0.1	2.5		Guillou et al (2014a)
MnFe0.95P0.595Si0.3B0.075	281	62	9.8			⩽0.05	0.4	1.6		Guillou et al (2014b)
Ni50Mn36Co1Sn13	281c	−110c	−13.8c				11	16.5		Khovaylo et al (2010)
Ni53.3Mn20.1Ga26.6	320d	220d	27.6d				7	5.2	15.6	Abhyankar et al (2010) and Basso et al (2012)
La0.67Ca0.33MnO3	268c	42.8c	6.9c			≈0.1		5	2.0–2.5	Radaelli et al (1995), Lin et al (2006) and Turcaud et al (2013)
Fe–Rh	313–320	−123.2	−12.5	0.27	0.27	0.27	≈1	≈10		Nikitin et al (1990), Annaorazov et al (1996), Stern-Taulats et al (2014) and Chirkova et al (2015)

^aLattice expansion accommodated by pores. ^bThe values in brackets correspond to 2nd cooling, see Brück (2008). ^cμ₀▵H  =  2 T. ^dμ₀▵H  =  1.2 T.

The mechanism for the appearance of the hysteresis can be of intrinsic and extrinsic origin. The intrinsic hysteresis stems from the fundamental characteristics of the first order transition, the latent heat L (Landau and Lifshitz 1980). The transition can proceed hysteresis-free only in a quasi-static regime (section 3). In the dynamic transition regime, the evolution of the latent heat will move the equilibrium in the endothermic or exothermic process direction depending on the direction of the temperature (or field) sweep. This will lead to the appearance of the intrinsic (i.e. thermodynamically governed) hysteresis. Intrinsic hysteresis is low in materials with the weak first order transition (section 3), as free energy profiles F(M) of such materials have very low energy barriers U comparable to the thermal energy (Yamada and Terao 2002, Kuz'min and Richter 2007, Lyubina et al 2008, Dung et al 2011, Roy et al 2016).

The underlying reason for the appearance of the extrinsic hysteresis is material microstructure and transition kinetics. In first order materials, the transition involves a structural (symmetry or/and lattice constant) change, which, in turn, is responsible for the onset of the magnetism (Bean and Rodbell 1962, Grazhdankina 1969, Yamada 1993). Microstructural features, such as crystallite size and shape, size distribution, porosity, secondary phases, inhomogeneity and strain, change the path along which this structural change actually occurs. A subtle deviation in the transition mechanism suffices to bring about a dramatic variation in the critical temperature/field of the coupled first order phase transition and consequently can bring about a substantial hysteresis (Bean and Rodbell 1962, Grazhdankina 1969).

Since most of the magnetic refrigerants are polycrystalline materials, one of the reasons for the observation of the large extrinsic hysteresis is the large volume change ΔV/V (Fujita et al 2001, Lyubina 2011) or anisotropic expansion (Morellon et al 1998, Yabuta et al 2006) of the crystallites at the first-order transition constrained by neighbouring grains (Lyubina et al 2010, Guillou et al 2014a). Table 1 summarises the lattice discontinuity for various magnetocaloric material families. It is apparent that there is a correlation between the width of the hysteresis and the lattice parameter discontinuities (Dung et al 2012).

Weakening of the first order transition by compositional modification is a common method for the reduction of the hysteresis (Provenzano et al 2004, Lyubina et al 2009b, Guillou et al 2015), but the resultant entropy change can be significantly lower. It is more attractive to retain the first order transition, but at the same time reduce the extrinsic hysteresis. Lyubina et al (2010) demonstrated that in the materials with a large ΔV/V, microstructure modification can provide significant reduction in the extrinsic hysteresis, e.g. by accommodation of the lattice expansion by the introduction of porosity (see bulk and porous LaFe_11.6Si_1.4 in table 1). Corresponding ΔS_max and $\Delta T_{\text{ad}}^{\max}$ reduction (Lyubina 2011, figure 13) can be mitigated by adjusting the degree of porosity or by embedding magnetocaloric materials in a ductile matrix, e.g. polymer, copper and silver (Lyubina et al 2012b, Turcaud et al 2013, Radulov et al 2015). Specific shaping of the magnetocaloric materials resulting in inhomogeneous magnetisation states was also shown to be useful for noticeable hysteresis reduction (Lovell et al 2015).

A magnetic refrigerator operates in the dynamic regime with a frequency limit f ~ 100 Hz (Kuz'min 2007). Note that practically achievable frequencies are currently  <10 Hz, i.e. well below this theoretical value (Tura and Rowe 2011, Engelbrecht et al 2012, Jacobs et al 2014). Since the AMR cooling power is a product of the relative cooling power of the magnetocaloric material RCP_ΔS|ΔT_ad  >  2 K and f, increasing the operation frequency could provide an attractive means for overall efficiency improvement. For this, low field hysteresis and fast kinetics of the transition are essential. Generally, magnetic isotherms M(H) expand with increasing frequency, i.e. $\Delta {{H}_{\text{hys}}}$ increases (figure 15, Lovell et al 2015). This flaring is caused by (i) the temperature variation in the material due to the magnetocaloric effect and (ii) poor thermal conductance between the material and surroundings. For the overview of further mechanisms leading to the increase of the hysteresis in magnetic materials in general (e.g. dynamic losses) the reader is referred to a book by Bertotti (1998). Improved thermal linkage and reduction of the magnetocaloric material thickness can significantly reduce the hysteresis arising at high magnetic field rates (Moore et al 2009, Kuepferling et al 2013, Lovell et al 2015). The latent heat generation and dissipation at the boundary between phases involved in the transformation (intrinsic effect) also plays an important role in determining the transition rate (Yako et al 2011, Fujita and Yako 2013, Fujita et al 2013b). Specific microstructure design and the introduction of a second phase (Lyubina et al 2012b) can be used to mitigate this effect.

Zoom In Zoom Out Reset image size

The design of the AMR requires anisotropic thermal transport properties of the magnetic refrigerants (Nielsen and Engelbrecht 2012). The thermal conductivity κ along the fluid flow should be low in order not to disturb the temperature gradient between the cold and hot side; the heat exchange transverse to the flow should be, on the other hand, very efficient. While very large anisotropy is observed in layered materials, such as graphite having the ratio of κ in the direction parallel and perpendicular to the c-axis of ~10²–10³, the thermal transport anisotropy in most materials is significantly lower (Slack 1961). The thermal conductivity of the known magnetocaloric materials is the range of 2–16 W m⁻¹ K⁻¹ at 300 K without any significant anisotropy (table 1). The thermal conductivity can to some extent be varied using synthetic routes and deploying various refrigerant bed geometries (Oezcan et al 2014). Bulk (low porosity) materials show expectedly a higher thermal conductivity. Improvement of thermal transport in higher porosity materials can be achieved by the introduction of a second component (Lyubina et al 2012b, Turcaud et al 2013, Radulov et al 2015). In composites containing a high conductivity material, a more than threefold increase in the thermal conductivity can be achieved (Lyubina et al 2012b, Turcaud et al 2013).

The majority of refrigerant beds employ epoxy fixed spheres ($\varnothing$ 200–500 µm) or plates of the magnetocaloric materials (Zimm et al 2006, Tura et al 2012, Tusek et al 2013, Jacobs et al 2014). The disadvantage of powder beds is a likely pressure drop that ultimately limits the frequency. This problem can be circumvented by using a parallel channel geometry (Nielsen et al 2012, Tura et al 2012, Tusek et al 2013). Optimum thickness of Gd plates is found to be about 100 µm in the parallel channel geometry (Tura et al 2012, Tusek et al 2013). Thermal diffusivity of first order materials is similar to Gd (Fujieda et al 2004). However, due to the evolution of the latent heat plates with a lower thickness could be required when using first-order materials (see section 5.3).

One of the key parameters for the application is the material workability. That means the magnetic refrigerant should be capable of being manufactured into an optimum regenerator shape. If brittle intermetallic compounds are concerned, providing magnetic refrigerants with dimensions in the order of and below 100 µm can be challenging. Several methods can be employed to shape the magnetic refrigerants. Spheres can be obtained by the rotating electrode process (Saito et al 2007). Metallic materials can be produced by conventional melting and melt spinning often followed by homogenisation treatment, reactive sintering (Katter et al 2009) and spark plasma sintering (Patissier and Paul-Boncour 2015). The bulk materials, when produced in the industrially relevant volumes, usually need further processing into refrigerant shapes, such as cutting, grinding, pulverising. Since cutting into thin plates of brittle materials can lead to material fracture, the latter is especially relevant in first order materials with the Curie temperature around the temperature of machining (Katter et al 2009), powder or suspension processing routes are preferred. The shaping methods include polymer bonding (Skokov et al 2014, Zhang et al 2015) and extrusion of refrigerant/polymer mixtures (Lanzarini et al 2015), electroless coating (Lyubina et al 2012b), additive manufacturing (Seeler et al 2012, Moore et al 2013) and tape casting (Bahl et al 2012). In powder processing, if the pressure/shear stress are selected too high, fracture of the powder particles can lead to thermal conductivity and MCE reduction (Lyubina et al 2012b, Skokov et al 2014, Lanzarini et al 2015).

The lattice parameter discontinuity at the first order transition (table 1) is a disadvantage both in terms of workability and cyclic stability. Microcrack formation, performance fading and pulverisation of first order materials limits their lifetime greatly (Brück et al 2008, Gschneidner and Pecharsky 2008, Lyubina et al 2010). Volume expansion accommodation is, thus, required in materials with the large ΔV; the strategies include providing porosity (Lyubina et al 2010) and creating composite materials containing an elastic matrix (Lyubina et al 2012b, Skokov et al 2014, Zhang et al 2015). Composite materials can generally provide improved cycle behaviour. In materials with a second order transition, e.g. LaFe_10.7Co_1.3Si_1.0 (Moore et al 2013), and in materials with a weak first-order transition and low volume change, e.g. MnFe_0.95P_0.582B_0.078Si_0.34 (Guillou et al 2014a), good mechanical stability is observed.

Since the magnetic refrigerant is in contact with a fluid, corrosion protection is required for stable performance (Engelbrecht et al 2011, Fujieda et al 2014). Protective coating and surface passivation of the magnetic refrigerants are the most efficient ways to provide chemical stability (Engelbrecht et al 2011, Tian et al 2013, Chennabasappa et al 2014). Ceramic materials (e.g. manganites) have inherently high corrosion resistance, which is a very favourable characteristics of these materials in terms of chemical stability.

Gadolinium is the only element that has a ferro- to paramagnetic transition near room temperature; T_c of Gd depends on homogeneity and purity and is at 294 K in a single crystal (Cable and Wollan 1968, Dan'kov et al 1998, Lyubina et al 2011). The near-room temperature transition was the reason for Gd being the first material that was considered for near room temperature refrigeration by Brown (1976). Gd is used ever since as a benchmark for comparison of performance of magnetic refrigerants. Expectedly, due to the second order nature of the Curie transition no hysteresis is observed and the entropy change ΔS is moderate (table 2, figure 10). However, the heat capacity of Gd is significantly lower compared to that of several-component materials (see equation (13)) and, consequently, Gd has a sizable ΔT_ad (table 2, figure 8). Due to its ductility Gd can be shaped into thin plates and foils, although one needs to be aware that (severe) plastic deformation can change the microstructure and reduce the MCE (Taskaev et al 2013). The formation of solid solutions with other rare earth elements allows T_c tuning (Gschneidner et al 2005). Nevertheless, despite the favourable characteristics Gd can offer, this material is not attractive for applications primarily due to its high cost (Gd belongs to heavy rare-earths that are significantly less abundant compared to e.g. Ce, La and Nd). Furthermore, it should be noted that whereas the relative cooling power RCP_ΔS|ΔT_ad  >  2 K of Gd is superior to first order materials in a single material bed (figure 12), in multiple-T_c beds, first order materials provide significantly larger cooling power compared to Gd (Russek et al 2010).

Table 2. Properties of Gd and Gd-based compounds: the peak temssperature of the ▵S curve (T_max), the gravimetric and volumetric maximum entropy change (▵S_max) and the maximum adiabatic temperature change ($\Delta T_{\text{ad}}^{\max}$) in a field change μ₀▵H  =  (0  −  H_f) T.

Material	Tmax (K)	Hf (T)	−▵Smax (kJ m−3 K−1)	−▵Smax (J kg−1 K−1)	$\bigtriangleup T_{\text{ad}}^{\max}$ (K)	Reference
Polycrystalline Gd, purity 99.7%	294	1	26	3.2	2.9	Lyubina et al (2011) and Lyubina (2016)
		2	48	6.1	5.2
		5	86	11
Single crystal Gd	295	1	32	4.0	3.1	Pecharsky and Gschneidner (1999a), Lyubina et al (2011) and Lyubina (2016)
		2	49	6.2	5.2
		5	86	11	12.0
Gd5Si2Ge2 (arc-melted)	277	1	37	6.5		Pecharsky and Gschneidner (1997a) and Pecharsky et al (2003)
		2	85	15	5
		5	114	20	11
Gd5Si4	326	2			4.3	Gschneidner and Pecharsky (2000) and Gschneidner et al (2005)
		5	61.7		7.0
Gd5Ge4	20	5	128			Gschneidner and Pecharsky (2000)

The ternary intermetallic compounds Gd₅(Si_xGe_1−x)₄ with T_c  =  295–335 K and the eminent compound Gd₅Si₂Ge₂ were discovered by Holtzberg et al (1967). It were Pecharsky and Gschneidner (1997a) who found a giant magnetocaloric effect in Gd₅Si₂Ge₂. This material class exhibits the strong first order transition for x  ⩽  0.5 (section 3); the change of the transition to second order occurs abruptly at a Si content of x  >  0.5 (Pecharsky and Gschneidner 2001b). The strong first order transition is due to a magneto-structural transformation from the monoclinic (space group $P{{112}_{1}}/a$) paramagnetic to the orthorhombic (space group $Pnma$) ferromagnetic phase (figure 9). For details of the magnetic and structural peculiarities of the transition in this system the reader is referred to papers by Pecharsky and Gschneidner (1997b, 2001b), Pecharsky et al (2003), Paudyal et al (2006) and de Oliveira and von Ranke (2010). The transition temperature in Gd₅(Si_xGe_1−x)₄ decreases linearly with decreasing Si content from about 277 K in Gd₅Si₂Ge₂ to 20 K in Gd₅Ge₄ (table 2, Pecharsky and Gschneidner 2001b). As in most materials showing a large lattice discontinuity, the first order transition in Gd₅(Si_xGe_1−x)₄ can also be induced by pressure (Tseng et al 2008).

Substitution of Gd and Ge is attractive in terms of material cost reduction. However, already the addition of small amounts (⩽1 at.%) of substitution elements, such as Fe, Al, Ga, Mn, Cu and Nb, generally leads to the formation of secondary phases (Provenzano et al 2004, Shull et al 2006, Prabahar et al 2010). The change of the element ratio in the parent phase Gd₅(Si_xGe_1−x)₄ consequently leads either to the shift of the transition temperature or/and the change of the transition type to the second order. The effect of substitution of Gd by other rare-earths was discussed by Gschneidner et al (2005) and Zhang et al (2010). Of particular interest would be the substitution of Gd by more abundant light rare earth elements, e.g. La, Ce and Nd. However, in the Ce–Si–Ge and Nd–Si–Ge systems, all compounds show a second-order type transition at temperatures below 12 K and around 110 K, respectively (Gschneidner et al 2005, Zhang et al 2010).

In Gd₅Si₂Ge₂, the rate of the transition temperature shift with the field $\text{d}{{T}_{\text{c}}}/\text{d}H$ is 5.0–6.5 K T⁻¹ (Pecharsky and Gschneidner 2001b, Pecharsky et al 2003). Combined with a significant thermal hysteresis of about 10 K it yields a fairly large ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}$ of about 2 T (table 1). The large hysteresis typical for materials with the strong first order transition and high cost of the constituent elements precludes the effective use of Gd₅(Si_xGe_1−x)₄-based materials in magnetic heat pumping.

In the La–Fe–Si system, ternary cubic LaFe_13−xSi_x compounds with the NaZn₁₃-type structure form for x  ⩽  2.5; for higher Si concentrations tetragonal compounds are formed (Palstra et al 1983, Tang et al 1994). Due to the negative heat of formation between La and Fe, no binary LaFe₁₃ is observed (the same is true for LaNi₁₃), whereas LaCo₁₃ is a stable compound (Krypiakewytsch et al 1968, Palstra et al 1983). Cubic phase LaFe_13−xZ_x can be stabilised for Z  =  Si, Al, Co (Palstra et al 1983, Helmholdt et al 1986). In LaFe_13−xSi_x (space group $Fm\bar{3}c$), La atoms are located on the 8a sites, Fe is at the 8b sites and the 96i positions are randomly occupied by Fe and Si (Lyubina 2011).

In the cubic LaFe_13−xSi_x, no sharp transition type change is observed with x variation, instead a gradual departure is observed from the weak first order transition for low Si content to second order transition for Si concentration x above approximately 1.6 (Lyubina et al 2009b, 2011, Morrison et al 2010, 2012b, Morrison and Cohen 2014). The giant MCE was first reported in LaFe_13−xSi_x for exactly this 'border' composition x  =  1.6 by Hu et al (2001).

The weak first order transition in LaFe_13−xSi_x (x  <  1.6) is due to the extraordinary flat F(M) dependence with several minima, i.e. the intrinsic hysteresis in these compounds is very low (Kuz'min and Richter 2007, Lyubina et al 2008). The temperature driven transition involves the transformation from the PM to FM state accompanied by a large volume change ~1%; the cubic symmetry is preserved (table 1, figure 9, Fujita et al 2001, 2003, Lyubina 2011). The transformation induced by the magnetic field above the Curie temperature is an itinerant-electron metamagnetic transition and is manifested in a peculiar S-shape magnetisation (figure 6, Fujita et al 2003). The field dependence of $\Delta {{S}_{\max}}$ in LaFe_13−xSi_x follows the relation in equation (8) in the whole composition range.

Figure 10 illustrates the influence of various elements on the transition temperature and on the size of the MCE in LaFe_13−xSi_x. Increase of x and Co substitution lead to the linear increase of the transition temperature (table 3, Fujita et al 2001, Lyubina et al 2009b). However, the transition gradually changes to second order and ΔS is decreasing (figure 10, table 3). Although the entropy change and transition temperature range in Co-substituted alloys is comparable to Gd (figure 6), the large heat capacity (see section 5.1 and equation (13)) of La(Fe,Co,Si)₁₃ alloys results in almost a threefold reduction of ΔT_ad (table 3, Rosendahl Hansen et al 2010).

Table 3. Properties of the LaFe_13−xSi_x-type alloys: the peak temperature of the ▵S curve (T_max), the gravimetric and volumetric maximum entropy change (ΔS_max) and the maximum adiabatic temperature change ($\Delta T_{\text{ad}}^{\max}$) in a field change μ₀ΔH  =  (0  −  H_f) T.

Material	Tmax (K)	Hf (T)	−ΔSmax (kJ m−3 K−1)	−ΔSmax (J kg−1 K−1)	$\Delta T_{\text{ad}}^{\max}$ (K)	Reference
LaFe11.6Si1.4 (homogenised bulk)	196	1	147	22	4.2	Lyubina et al (2009b) and Lyubina (2016)
		2	160	24	7.8
LaFe11.6Si1.4 (porous)	196	1	76	11	3.3	Lyubina (2011, 2016)
		2	109	16	5.8
LaFe11.6Si1.4 (nanocrystalline)	200	2	54	8	2.2	Lyubina (2011)
		5	96	14
LaFe11.6Si1.4 (homogenised melt-spun)	201	1	68	10	2.2	Lyubina et al (2008) and Lyubina (2011, 2016)
		2	107	16	4.1
		5	151	22
LaFe11.4Si1.6 (homogenised melt-spun)	220	2	35	5		Lyubina et al (2009b)
		5	102	15
LaFe11.2Si1.8 (homogenised melt-spun)	234	2	25	4		Lyubina et al (2009b)
		5	83	12
LaFe11.14Co0.76Si1.1	267	1	52	7.2	1.8	Rosendahl Hansen et al (2010)
LaFe10.92Co0.98Si1.1	293	1	38	5.3	1.2	Rosendahl Hansen et al (2010)
LaFe10.61Co1.29Si1.1	327	1	30	4.2		Rosendahl Hansen et al (2010)
LaFe11.6Si1.4H1.2	273	5	118	17		Lyubina et al (2009b)
LaFe11.6Si1.4H1.6	333	5	140	21		Lyubina et al (2008)
LaFe11.6Si1.4H2.3	342	5	120	18		Lyubina et al (2009b)
LaFe11.35Mn0.39Si1.26H1.53	282	1.6	75	11		Barcza et al (2011)
LaFe11.35Mn0.39Si1.26H1.53	289	1.6	88	13		Barcza et al (2011)
LaFe11.35Mn0.39Si1.26H1.53	295	1.6	82	12		Barcza et al (2011)

Also on interstitial hydrogen insertion T_c raises (figure 10, Lyubina et al 2009b), which is a result the lattice expansion (Fujieda et al 2008, Lyubina 2011) and electronic structure modification of the parent compound (Hannemann et al 2012). Hydrogen insertion can be realised at high temperature in a hydrogen containing atmosphere (Fujieda et al 2008, Barcza et al 2011) or electrochemically at low temperature (Lyubina et al 2012a). The advantage of the use of La(Fe,Si)₁₃H_y hydrides is the preservation of the weak first order transition and, consequently, large MCE (figure 10). However, due to the desorption of hydrogen starting at approximately 150 °C, the operation and (post-)processing temperature are limited. Instability of partially hydrided materials can be circumvented by lowering T_c of the parent compound with Ce or Mn substitution (Fujita et al 2009, Wang et al 2011) followed by full hydrogen loading (Barcza et al 2011).

Table 3 summarises the magnetic properties of the LaFe_13−xSi_x materials for various compositions and various microstructures. The large volume discontinuity at the transition in the LaFe_13−xSi_x-based compounds (table 1) results in a noticeable contribution of the microstructure to the hysteresis amounting to ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}\approx 0.5\,\text{T}$ in bulk materials (see section 5.3). The fact that the contribution to the hysteresis is of extrinsic, microstructure-driven nature is further corroborated by the essentially equal rate of T_c shift with field $\text{d}{{T}_{\text{c}}}/\text{d}H$ in the bulk LaFe_11.6Si_1.4 (≈4.4 K T⁻¹) and porous and melt-spun alloys of the same composition (≈4.2 K T⁻¹). That means that the fundamental feature of the transition, latent heat, is at the same level in the bulk alloy and in the materials, where the lattice expansion can be accommodated (see Clausius–Clapeyron equation (14)). In the latter materials, $\Delta {{T}_{\text{hys}}}$ is significantly reduced and ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}\approx 0.1\,\text{T}$ (table 1); this value is representative for the intrinsic hysteresis in the LaFe_13−xSi_x materials and means to achieve such values were devised by Lyubina et al (2010, 2012b), Lyubina et al (2011) and Lovell et al (2015).

The large MCE, cooling power RCP_ΔS|ΔT_ad  >  2 K (figure 12, table 3) and a low hysteresis (tables 1 and 3) are very attractive characteristics for the magnetic heat pumping. Furthermore, the LaFe_13−xSi_x materials are based on abundant and inexpensive elements and can be produced by technologies that can be easily scaled up, such as rapid solidification (Lyubina et al 2009b, Mayer et al 2014), reactive sintering (Katter et al 2009), electrolytic hydriding (Lyubina et al 2012a). Surface protection by a polymer, copper or other protective layer may be required for these materials to avoid corrosion. Exemplarily, the specific cooling power achievable in an AMR with a multiple-T_c refrigerant bed containing La(Fe,Si)₁₃H_y was reported to be in the range of 450–1300 W kg⁻¹ (Russek et al 2010, Jacobs et al 2014). The specific cooling powder of the AMR employing Gd is significantly below these values (170 W kg⁻¹). It should be emphasised, however, that the achievable specific cooling power is very much design-specific.

MnFeSi_xP_1−x (0  ⩽  x  ⩽  0.7) represents another very attractive material class showing for certain compositions a weak first order transition. These materials crystallise in the hexagonal Fe₂P crystal structure (space group $P6\bar{2}m$). Para- to ferromagnetic transition in the binary Fe₂P occurs at 217 K; the transition is of first order and occurs without the symmetry change (figure 9, Beckman et al 1982, Yamada and Terao 2002). In MnFeSi_xP_1−x, the Fe and Mn atoms preferentially occupy the 3f and 3g positions, respectively, and comprise different alternating layers (Roy et al 2016). The giant MCE in this material family was first reported by Tegus et al (2002) in MnFeP_0.45As_0.55. Despite the large MCE and low hysteresis (table 4), potential toxicity makes As-containing materials less appealing for applications, especially in domestic devices.

Table 4. Properties of (Mn,Fe)₂P-type compounds: the peak temperature of the ΔS curve (T_max), the gravimetric and volumetric maximum entropy change (ΔS_max) and the maximum adiabatic temperature change ($\Delta T_{\text{ad}}^{\max}$) in a field change μ₀ΔH  =  (0  −  H_f) T.

Material	Tmax (K)	Hf (T)	−ΔSmax (kJ m−3 K−1)	−ΔSmax (J kg−1 K−1)	$\Delta T_{\text{ad}}^{\max}$ (K)	Reference
MnFeP0.45As0.55	303	1	82	13	2.8	Tegus et al (2002) and Brück et al (2005)
		2	95	15
MnFeP0.78Ge0.22	323	2	189	30		Brück et al (2012)
MnFe0.94Co0.06P0.78Ge0.22	294	2	126	20		Brück et al (2012)
MnFe0.88Co0.12P0.78Ge0.22	260	2	107	17		Brück et al (2012)
MnFe0.88Co0.12P0.74Ge0.26	300	2	69	11		Brück et al (2012)
MnFeP0.55Si0.3Ge0.15	292	2	38	6		Cam Thanh et al (2007)
MnFeP0.59Si0.3Ge0.11	288	2	88	14		Cam Thanh et al (2007)
MnFeP0.59Si0.34Ge0.07	280	2	101	16		Cam Thanh et al (2007)
MnFe0.95P0.55Si0.45	282	1	63	10		Guillou et al (2014a)
Mn1.25Fe0.7P0.5Si0.5	274	1	57	9		Guillou et al (2014a)
MnFe0.95P0.582Si0.34B0.078	289	1	57	9		Guillou et al (2014a)
MnFe0.95P0.595Si0.3B0.075	281	1	62	9.8	2.7	Guillou et al (2014b)
		2	91	14.5

Silicon and germanium were later shown to be the elements whose substitution for arsenic allows retaining the first order transition (figure 14, Brück 2008, Dung et al 2011). However, these alloys are characterised by an immense hysteresis: ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}=21\,\text{T}$ and $\Delta {{T}_{\text{hys}}}=75\,\text{K}$ (table 1). Apparently, this hysteresis is of extrinsic nature and arises due to the discontinuous anisotropic change in the lattice parameters (table 1, Cam Thanh et al 2007, Guillou et al 2014b). The fact that Fe₂P and seemingly MnFeSi_xP_1−x compounds have very flat F(M) dependence, i.e. low intrinsic hysteresis (Yamada and Terao 2002, Roy et al 2016) and that the hysteresis is reduced to 5.7 T and 20 K on the second and subsequent temperature cycles due to cracking and pulverisation of the material (Brück 2008, Brück et al 2008, Guillou et al 2014a) supports the observation.

Cobalt, nickel and boron substitution leads to the gradual departure from the first to second order transition (Brück et al 2012, Guillou et al 2014b, 2015). In certain compositions containing B, a large MCE and low hysteresis can be obtained (table 1). Boron substitution increases the rate of transition temperature shift $\text{d}{{T}_{\text{c}}}/\text{d}H$ from 3.5 K T⁻¹ in B-free to 4.3 K T⁻¹ in the MnFe_0.95(P,Si,B) materials (Guillou et al 2014b), which is a very favourable effect for applications (see section 5.3). Low temperature hysteresis $\Delta {{T}_{\text{hys}}}~=~1.6\,\text{K}$ and low field hysteresis ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}<~0.4\,\text{T}$, inexpensive constituent elements and scalable production routes (melt spinning) make MnFe_0.95(P,Si,B) very attractive for heat pumping applications. In fact, these alloys have been used as refrigerant material in the first industrial prototype (ChemistryViews 2016).

Heusler alloys are materials with a formula X₂YZ, where X is a transition element, Y atoms can belong either to transition or rare-earth or alkaline rare earth elements and Z are the elements from the IIIA–VA group. The first report on MCE in the Heusler compound Ni₂MnGa is due to Hu et al (2000). The observation of the MCE in magnetic Heusler alloys relies on the presence of the martensitic transformation (Acet et al 2011, Manosa et al 2013). A temperature and field induced strong first order transformation between the martensite and austenite phases is responsible for the observation of a large MCE (table 5, Hu et al 2000, Marcos et al 2002, Acet et al 2011). Some Heusler alloys, such as Ni₂MnZ with Z  =  Sn, In and Sb, exhibit an inverse magnetocaloric effect (Krenke et al 2005, Manosa et al 2008, Liu et al 2009). This effect occurs due to a lower magnetisation of the low temperature phase, martensite, compared to the magnetisation of the high-temperature phase, austenite (see the sign of the M derivative in equation (11)).

Table 5. Properties of the Heusler alloys: the peak temperature of the ΔS curve (T_max), the gravimetric and volumetric maximum entropy change (ΔS_max) and the maximum adiabatic temperature change ($\Delta T_{\text{ad}}^{\max}$) in a field change μ₀ΔH  =  (0  −  H_f) T.

Material	Tmax (K)	Hf (T)	−ΔSmax (kJ m−3 K−1)	−ΔSmax (J kg−1 K−1)	$\Delta T_{\text{ad}}^{\max}$ (K)	Reference
Ni55.2Mn18.6Ga26.2	315	5	163	20.4		Zhou et al (2005)
Ni50Mn34In16	174–181	1	−19	−2.4		Manosa et al (2008) and Lyubina (2016), this work
		2	−37	−4.6	−1.3(−0.5)a
		5	−75	−9.4
Ni45Mn37In13Co5	312–321	1			−1.3(−0.2)a	This work
		2			−4.3(−1.3)a
Ni50Mn37Sn13	295	1	−26	−3.3		Krenke et al (2005)
		2	−55	−6.9
		5	−144	−18.0
Ni50Mn36Co1Sn13	283	1			−0.4	Khovaylo et al (2010)
		2	−110	−13.8	−1.25

^aThe values without brackets correspond to $\Delta T_{\text{ad}}^{\max}$ measured on heating, the values in the brackets are for $\Delta T_{\text{ad}}^{\max}$ measured on cooling.

Very large thermal hysteresis $\Delta {{T}_{\text{hys}}}=16.5\,\text{K}$ and a slow rate of the transition temperature change with field $\text{d}{{T}_{\text{c}}}/\text{d}H~=~-~1.5~\,\text{K}\,{{\text{T}}^{-1}}$ (Khovaylo et al 2010) yield extremely large field hysteresis ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}$ of 11 T. Consequently, the adiabatic temperature change in the Heusler alloys differs greatly upon cooling and heating (figure 16). A large ΔT_ad in Ni₄₅Mn₃₇In₁₃Co₅ is observed only on heating and drops significantly on reversing the temperature sweep direction, i.e. cooling (figure 15(a)). The low ΔT_ad observed on cooling is caused by the thermodynamic stability of the martensite and the large hysteresis: once the martensite is formed on cooling, it will not transform back to the ferromagnetic austenite unless it is heated to the temperature of the start of the austenite transformation or subjected to very high magnetic fields ~10 T; the high field is required due to the large thermal hysteresis and steep $\text{d}H/\text{d}{{T}_{\text{c}}}$ phase boundary lines (figure 5(b), Khovaylo et al 2010, Ghorbani Zavareh et al 2015). Regarded as a function of the field (not shown here), only the first magnetic field application results in a large MCE of  −4.3 K; subsequent field application induces only a low ΔT_ad of about  −1 K in µ₀ΔH  =  1.9 T, since no transformation can be completed in this field. Both situations are inacceptable in the conventional AMR cycle. The difference between the heating and cooling curve, though not so drastic, since the overall MCE magnitude is significantly lower, can also be observed in another Heusler alloy, Ni₅₀Mn₃₄In₁₆ (figure 15(b)). The 'reversible part' of the MCE near the martensitic transformation in the Heusler alloys is below 2 K and is comparable to the MCE near the conventional second order PM-FM transition of the austenite $T_{\text{c}}^{\text{A}}$ (figure 15(b)). The relative cooling power RCP_ΔS|ΔT_ad  >  2 K of the Heusler alloys is null (figure 12). The described behaviour essentially precludes their efficient use in the AMR cycle.

Zoom In Zoom Out Reset image size

Ferromagnetic manganites R_1−xM_xMnO₃ are oxides with the perovskite structure, where R is at least one rare earth element and M belongs to the group including e.g. Ca, Pb, Ba, Na¹⁺, Ag¹⁺ and K¹⁺. As oxide materials, manganites have significant advantage over intermetallic magnetocaloric compounds in terms of excellent chemical stability allowing low cost synthesis and various shaping opportunities (Bahl et al 2012, Turcaud et al 2013). A review of the manganite properties can be found in Phan and Yu (2007).

Most ferromagnetic manganites exhibit a second order transition (Phan and Yu 2007, Zhang et al 2012). An exception is La_1−xCa_xMnO₃ with x between 0.25 and 0.5 that exhibits a first order PM insulator to FM metal transition with the concomitant volume change (table 1, Radaelli et al 1995). Due to the low density compared to the metallic materials, the volumetric entropy change in the manganites is moderate (table 6, Mira et al 2002, Phan et al 2005, Phan and Yu 2007). The large heat capacity (see equation (13)) is responsible for the low adiabatic temperature change; only for the La_0.67Ca_0.33MnO₃ composition ΔT_ad slightly exceeds 2 K in a field change of 2 T (table 6, Lin et al 2006). Consequently, only a small RCP_ΔS|ΔT_ad  >  2 K can be obtained (figure 12, Bahl et al 2012).

Table 6. Properties of manganites: the peak temperature of the ΔS curve (T_max), the gravimetric and volumetric maximum entropy change (ΔS_max) and the maximum adiabatic temperature change ($\Delta T_{\text{ad}}^{\max}$) in a field change μ₀ΔH  =  (0  −  H_f) T.

Material	Tmax (K)	Hf (T)	−ΔSmax (kJ m−3 K−1)	−ΔSmax (J kg−1 K−1)	$\Delta T_{\text{ad}}^{\max}$ (K)	Reference
La0.67Sr0.33MnO3	370	1	9.9	1.6	1.0	Rostamnejadi et al (2011)
		2	16.7	2.7	1.6
		5	31.9	5.15	3.3
La0.67(Ca0.95Sr0.05)0.33MnO3	275	1	20.2	3.26		Mira et al (2002), Phan et al (2005)
		5	65.1	10.5
La0.67(Ca0.887Sr0.113)0.33Mn1.05O3	275	1	22.9	3.7	1.3	Bahl et al (2012)
La0.67Ca0.33MnO3	268	1			1.3	Lin et al (2006)
		2	42.8	6.9	2.4

Soft magnetic Fe-based amorphous and nanocrystalline alloys as well as rare-earth-based bulk metallic glasses show the conventional second order PM to FM transition with the Curie temperature adjustable in the range of 100–600 K (Maeda et al 1983, Franco et al 2006b, 2012, Gorsse et al 2008, 2011, Ipus et al 2009). A recent review on the MCE in these materials can be found in Franco et al (2012). Favourable characteristics of the Fe-based alloys are good mechanical stability, low cost and chemical resistance. Common to this material type is, however, low absolute value of the entropy change ΔS_max, which is only about half of that observed in Gd (see tables 2 and 7). This is caused by a very wide temperature range (~100 K), where the transition is taking place. The adiabatic temperature change is below 2 K even in a field change of about 2 T (table 7, Law et al 2011). The wide temperature span is often used to calculate the relative cooling power of these materials without taking into account that a sufficient ΔT_ad is required to move the heat in the regenerator (section 5.1). Since the amorphous and nanocrystalline alloys show ${{T}_{\text{ad}}}<2\,\text{K}$, cooling will not be efficient (figure 12). As discussed in section 5.1, the reduction of the MCE, albeit not so drastic, is also observed in materials with the first and second order transitions, when the grain size is reduced to the nanometer range (Mathew et al 2010, Lyubina 2011).

Table 7. Properties of amorphous alloys: the peak temperature of the ΔS curve (T_max), the gravimetric and volumetric maximum entropy change (ΔS_max) and the maximum adiabatic temperature change ($\Delta T_{\text{ad}}^{\max}$) in a field change μ₀ΔH  =  (0  −  H_f) T.

Material	Tmax (K)	Hf (T)	−ΔSmax (kJ m−3 K−1)	−ΔSmax (J kg−1 K−1)	$\Delta T_{\text{ad}}^{\max}$ (K)	Reference
Fe90Zr10	230	1.4	9.5	1.4		Maeda et al (1983)
		5	27	4.0
Fe84Nb7B9	299	1.5	9.8	1.44		Min et al (2007)
Fe75B12Cr8Ce5	295	1.8		1.1	1.4	Law et al (2011)
Fe79B12Cr8La1	348	1.8		1.1	1.3	Law et al (2011)

Order–order transitions occur between magnetically ordered states and are distinct from the order–disorder transitions, such as FM  →  PM transition. The order–order transitions can be subdivided into (i) transitions involving the change in the orientation of the sublattice moments, e.g. transitions between ferromagnetic and antiferro- or ferrimagnetic states, and (ii) transitions, where orientation of the moments is altered only in respect to the crystallographic axes, i.e. spin reorientation transitions (SRT).

Fe–Rh alloys (space group $Pm\bar{3}m$) exhibit a strong first-order transition from the FM to antiferromagnetic (AF) state at 320–350 K (figure 9, Shirane et al 1963, Kouvel and Hartelius 1962). Fe₄₉Rh₅₁ was the alloy, where the first experimental observation of the giant MCE was made (Nikitin et al 1990). The MCE in the Fe–Rh alloys is of the inverse type, since the high-temperature phase in these materials is FM and the low-temperature phase is AF with zero net magnetisation. Consequently, on cooling or field application Fe–Rh shows a negative adiabatic temperature change of about $-~13~\text{K}$ (µ₀ΔH  ≈  2 T) and positive entropy change of about 120 kJ m⁻³ K for µ₀ΔH  >  1 T (table 8, Stern-Taulats et al 2014). A large volume change is observed at the transition (table 1). The thermal hysteresis and the rate $\text{d}{{T}_{\text{c}}}/\text{d}H~$ can differ to a great extent depending on the alloy microstructure: between 7.5 K and 50 K and $-~3.3~\,\text{K}\,{{\text{T}}^{-1}}$ and $-~8.5~\,\text{K}\,{{\text{T}}^{-1}}$, respectively (Nikitin et al 1990, Manekar and Roy 2008, Chirkova et al 2015). In the most favourable case, the parameters yield ${{\mu}_{0}} \Delta {{H}_{\text{hys}}}\approx 1\,\text{T}$. As a result of the large hysteresis, the MCE on the second and subsequent cycles is lower compared to the first cycle (Manekar and Roy 2008, Chirkova et al 2015). The considerable hysteresis and high cost of rhodium are disadvantageous characteristics for heat pumping.

Table 8. Properties of materials with order–order transitions: the peak temperature of the ΔS curve (T_max), the maximum entropy change (ΔS_max) and the maximum adiabatic temperature change ($\Delta T_{\text{ad}}^{\max}$) in a field change μ₀ΔH  =  (0  −  H_f) T.

Material	Tmax (K)	Hf (T)	−ΔSmax (kJ m−3 K−1)	−ΔSmax (J kg−1 K−1)	$\Delta T_{\text{ad}}^{\max}$ (K)	Reference
FeRh	313–320	1	−123.2	−12.5	≈−5.6	Nikitin et al (1990), Annaorazov et al (1996) and Stern-Taulats et al (2014)
		2	−123.2	−12.5	≈−13
		5	−123.2	−12.5
Er2Fe14B (H||c-axis)	323	0.5; 1; 2; 5	−6.6	−0.7	−0.5	Pique et al (1996), Skokov et al (2009), Basso et al (2011)
NdCo5 (rotation from c- to a-axis)	280	1.3a	15.9	1.9	1.6	Nikitin et al 2010

^aConstant magnetic field H.

At SRT, rotation of the magnetisation induces a change in the anisotropy part of the free energy ${{F}_{\text{an}}}$ with the corresponding change in the entropy term ${{S}_{\text{an}}}$. In a uniaxial crystal, the adiabatic temperature change can be written as (Vonsovsky 1971)

$$\begin{eqnarray} &&\Delta T_{\text{ad}}^{\text{an}}=-\frac{T}{{{C}_{\text{p}}}} \Delta {{S}_{\text{an}}}=\frac{T}{{{C}_{\text{p}}}}\frac{\partial {{K}_{1}}}{\partial T}\left[{{\sin}^{2}}\theta \left({{H}_{\text{f}}}\right)-{{\sin}^{2}}\theta \left({{H}_{\text{i}}}\right)\right],\end{eqnarray} \tag{ 18 }$$

where K₁ is the uniaxial anisotropy constant and $\theta \left({{H}_{\text{i}}}\right)$ and $\theta \left({{H}_{\text{f}}}\right)$ is the angle between the magnetisation and the c-axis in the initial and final fields, respectively. Different to the operation of the conventional AMR (section 2), the adiabatic temperature change can be realised by rotation of the magnetic refrigerant in a constant magnetic field or by rotation of the field vector H while keeping the refrigerant stationary.

From the form of equation (18) it is apparent that the MCE is large, when the derivative $\partial {{K}_{1}}/\partial T$ is large, which ultimately requires materials with a high magnetocrystalline anisotropy and a SRT of the first order type. The condition is fulfilled e.g. in the R₂Fe₁₄B (R  =  Er, Tm) compounds (space group $P{{4}_{2}}/mnm$) showing SRT between the 'easy axis' ($\boldsymbol{M}\parallel$ c-axis) and the 'easy plane' ($\boldsymbol{M}\bot$ c-axis) (Pique et al 1996). In a single crystal Er₂Fe₁₄B, $| \Delta T_{\text{ad}}^{\text{an}}|$ saturates at a value of 0.5 K in µ₀H  =  0.5 T and $| \Delta {{S}_{\text{an}}}|$ at 6.6 kJ m⁻³ K in µ₀H ~ 0.01 T; in fields above this value the entropy peak broadens (table 8, Skokov et al 2009, Basso et al 2011). A light-rare earth-based compound, NdCo₅, also shows a first order SRT from 'easy axis' to 'easy cone' at 280 K (figure 9, Nikitin et al 2010). Larger MCE can be obtained by rotating this refrigerant in 1.3 T compared to R₂Fe₁₄B (table 8). However, $| \Delta T_{\text{ad}}^{\text{an}}|\,\,\,=1.6\,\text{K}$ yields negligible relative cooling capacity RCP_ΔS|ΔT_ad  >  2 K.

Magnetocaloric effect in thin films is less of application interest, but is mainly interesting from the point of view of understanding the basic phenomena and exploring the ways to improve the performance or even radically change the way the magnetocaloric materials are applied. One of the first publications reporting the MCE in the film form are due to Babkin and Urinov (1989), who studied ΔT_ad on rotation (see equation (18)) of single-crystal Ni and Fe₂O₃ films, and Morelli et al (1996), who reported the MCE in 2.4 µm thick La_0.67M_0.33MnO₃ films (M  =  Ca, Ba, Sr) on LaAlO₃ substrates in the vicinity of the magnetic phase transition coinciding with the metal–insulator transition. The entropy change in the manganite films is significantly below that in bulk counterparts, compare ΔS  =  0.5 J kg⁻¹ K⁻¹  ≈  3.1 kJ m⁻³ K⁻¹ for a field change of 0–1 T in films (Morelli et al 1996) to ΔS values in table 6. Suppression of the ΔS peak height with the concomitant smearing out of the ΔS peak width is also observed in 1–3 µm thick Gd films (Mansanares et al 2013), Gd/W multilayers on MgO substrate (Miller et al 2010) and Gd₅(Si,Ge)₄ thin films (Hadimani et al 2015). The reduction can be attributed to the finite size scaling effects in nanostructures that has also been observed in bulk systems (Mathew et al 2010, Lyubina 2011) and discussed in section 5.1.

Mukherjee et al (2009) proposed a concept of AF interlayer coupling of the FM layers that would potentially allow one to tailor a metamagnetic transition with a prominent magnetisation discontinuity at the transition. Experimentally observed values of the MCE in a model Co/Cr multilayer system are rather low. Nevertheless, the concept of artificial structures may provide a pathway for the discovery of new materials.

The entropy change in epitaxial 200 nm thick films of La_0.8Ca_0.2MnO₃ on LaAlO₃ substrate and La_0.7Sr_0.3MnO₃/SrRuO₃ superlattices is of the same value or even exceeds ΔS observed in bulk counterparts (Zhang et al 2011, Debnath et al 2013). The observed ΔS in epitaxial films exhibits an anisotropy with the values of about 36 kJ m⁻³ K⁻¹ in the ab plane and 25 kJ m⁻³ K⁻¹ along the c-axis for a field change of 1 T. Debnath et al (2013) attributed the anisotropy in the MCE to a stronger exchange interaction in the manganite intralayer compared to that in the interlayer, forcing the magnetic moments to lie in the ab plane.

A further effect that can play a role in thin film systems is the strain induced in the magnetocaloric film by a substrate. The effect of epitaxial strain induced by various substrates allowing to vary the size and direction (compressive/tensile) of the imposed stress was studied by Kumar et al (2013) in La_0.67Sr_0.33MnO₃ films and by Maat et al (2005) in FeRh films. Moya et al (2013) exploited a first-order structural phase transition in BaTiO₃ substrates to create giant and reversible magnetocaloric effects in epitaxial films of La_0.7Sr_0.3MnO₃ via the entropic interconversion of ferromagnetic and paramagnetic phases.

A step further in the direction of manipulating the MCE by stimuli other than the magnetic field was demonstrated by Binek and Burobina (2013). In their theoretical concept, the entropy change in two-phase films consisting of the magnetocaloric material La_0.7Sr_0.3MnO₃ and piezoelectric PbMg_0.33Nb_0.67O₃–PbTiO₃ (PMN–PT) is induced by voltage. Various possible geometries (figure 17) were suggested and isothermal voltage-controlled entropy change ~1 J kg⁻¹ K⁻¹ was predicted. Although the effect of voltage on the MCE still needs to be demonstrated experimentally, a step towards experimental realisation of magnetocaloric/piezoelectric heterostructures was devised by the successful growth of epitaxial Heusler-type Ni–Mn–Ga–Co films on PMN–PT substrates (Schleicher et al 2015).

Zoom In Zoom Out Reset image size

Mechanical control of the magnetic properties in thin films with a large magnetostriction offers an interesting route to employ the interaction of surface acoustic waves (SAW) with magnetic excitations to trigger MCE in materials with first order transition. Duquesne et al (2012) demonstrated large ultrasound attenuation in thin epitaxial MnAs films on GaAs that can be ascribed to the strain-induced triggering of the giant MCE in MnAs. The observed effect opens up a new way to control the magnetocaloric effect.