Research Update: The mechanocaloric potential of spin crossover compounds Open Access

Ferroic cooling is a technology in which a solid refrigerant is driven between two states by an applied field.¹ The current growth of research into candidate ferroic refrigerants at room temperature has been fuelled by two factors: firstly the promise of device efficiencies that will be greater than those found in gas-based cooling and secondly by environmental concerns over the global warming potential of current hydrofluorocarbon-based refrigerants.² 

However, there are relatively few investigations thus far of mechanocaloric effects in materials that are not already associated with the MCE or ECE. One example is Mn₃GaN, an antiferromagnetic metallic antiperovskite in which there is a volume change at the first order Néel transition. This transition is sensitive to pressure and so barocaloric effects have been observed.¹⁰ Another is ammonium sulphate, a ferrielectric in which large barocaloric effects have been studied around the first order, ferrielectric transition temperature.¹¹ In this article we examine the available literature on barocaloric effects in another class of materials—spin crossover (SCO) compounds—in order to assess their mechanocaloric potential. To our knowledge these materials have not previously been considered by the ferroic cooling community.

An interesting point of comparison between the caloric families is that while the saturation magnetisation of many d-metal magnetocaloric alloys is limited by the quantum mechanical size of magnetic moments to around 120 A m² kg⁻¹, the quantities ΔP and ΔV at a phase transition may be expected to show greater variations. Electrical polarisation is associated with the separation of charge centres and therefore has a great potential for enhancement. Meanwhile, volume changes can vary from fractions of a percent to 20%.

Perhaps as a result, there is not yet an established definition of the word “giant” in connection with all possible caloric effects, but the term has been applied to magnetocaloric materials in which an adiabatic temperature change, ΔT_ad of 2-3 K, is seen in a 2 T field. It has also been applied to materials in which the latent heat, TΔS, associated with a first order magnetic phase transition is of the order of 20–30 MJ m⁻³ or, equivalently, ΔS values in the range 0.07–0.1 J K⁻¹ cm⁻³ near room temperature. By definition, there is an entropy change at a magnetic phase transition, even without an applied field and so the latter is in some ways an easier condition to satisfy. The observed ΔT_ad depends principally on either the heat capacity of the material or, in the case of some first order compounds, on the variation of transition temperature in the applied field (∂T_t/∂Y_i). The value of ∂T_t/∂Y_i can be used to examine how close a ferroic material is to having the maximum possible adiabatic temperature change for a given change of magnetisation, volume, or polarisation (as appropriate), and large values of ∂T_t/∂Y_i are required in order to avoid the deleterious effects of thermal hysteresis on cycling the applied field.¹² (Concerns about hysteresis loss upon cycling mean that those materials close to (tri) criticality are currently favoured.)

It has been shown that the value of ∂T_t/∂Y_i can be used as a tool to search for large ΔT_ad and ΔS and hence large relative cooling powers (RCPs) associated with field-driven first order transitions.^6,13 In the simplest approximation, the adiabatic temperature change may be simplified to ΔT_ad(T, Y_applied) = (∂T_t/∂Y_i) Y_applied for values of (∂T_t/∂Y_i) that are below the value at which ΔT_ad(T, Y_applied) is maximised. Beyond the value of (∂T_t/∂Y_i) that maximises ΔT_ad, ΔT_ad(T, Y_applied) is instead related to the isothermal entropy change via the heat capacity, C_p through ΔT_ad = − TΔS/C_p.⁶ At the point at which the ΔT_ad value is maximal, either expression may be used. However, it is therefore important to know which regime of (∂T_t/∂Y_i) a given material occupies, when predicting ΔT_ad values. In addition to evaluating the regime in which SCO compounds typically sit (with regard to applied pressure and its effect on the spin crossover temperature T_SCO), we will show below that the large values of ∂T_SCO/∂p they frequently possess present an opportunity for low pressure barocaloric effects.

Spin crossover occurs in compounds where the crystal field splitting of d-orbitals associated with a magnetic moment is of the order of k_BT. The effect was discovered by Cambi¹⁴ and is typically observed in octahedrally coordinated complexes of Fe in, for example, d⁵ or d⁶ electronic configurations.¹⁵ As a result, a temperature-induced change of state from a low spin (LS) state that breaks Hund’s first rule to a high spin (HS) state can occur at temperature T_SCO. This change of state has been suggested as a tool for applications including switching and sensing.¹⁶ The low temperature state breaks Hund’s rules. Crucially for caloric applications, the change of state from LS to HS can be either continuous or first order,¹⁷ and it can occur at temperatures up to and beyond room temperature.¹⁸ 

SCO materials are paramagnets and it is found that the driving field most effective in shifting the transition temperature is that of elastic strain or pressure. (The T_SCO is sensitive to a magnetic field, but at rates of around 0.03 K/T.¹⁹) Table I gives examples of known pressure variations of several T_SCO in compounds studied in the literature; from these values, upper bounds on the ΔT_ad values may be calculated. The application of pressure will stabilise the LS state, resulting in a negative ΔS value in the cases shown. Since for typical SCO materials, the magnitude of the entropy change associated with spin crossover, $Δ S =100$ J kg⁻¹ K⁻¹ and C_p = 2000 J kg⁻¹ K⁻¹,²⁰ the value of (∂T_SCO/∂p) p_applied at which we must switch from calculating ΔT_ad using (∂T_SCO/∂p) p_applied to using −TΔS/C_p is around 10 K (at 200 K) or 15 K (at 300 K), due to the high heat capacity, per kg, of these materials. In Table I we may use the regime for which ΔT_ad = − TΔS/C_p, in order to estimate the maximum possible ΔT_ad values and the value of the ∂T_SCO/∂p to estimate the pressure required to generate this ΔT_ad value.

We note from the table that the available isothermal entropy change is considerable; in molar units its magnitude is typically in the range 50–80 J/K mol (∼100–160 J/K kg or ∼0.2–0.3 J K⁻¹ cm⁻³ given the normal density of spin crossover compounds). This puts the SCO materials in a comparable range of volumetric entropy change density to that of giant magnetocaloric materials (see above). Furthermore, as shown in the table, the pressure required to obtain the maximum ΔT_ad possible is often relatively low, since the ∂T_SCO/∂p values for each material are higher than in the case of intermetallics. As a result, the pressures that may be used to obtain technologically relevant ΔT_ad values may be an order of magnitude lower than those used in experiments on intermetallics already known to the MCE and BCE community. A related conclusion was drawn by Moya et al. in the case of the pressures required to induce the ferrielectric transition in ammonium sulphate. That material had a comparable heat capacity and entropy change (in J K⁻¹ kg⁻¹). (At applied pressure values p_applied that are lower than the pressure required to obtain the maximum ΔT_ad value, the adiabatic temperature change is simply given by (∂T_SCO/∂p) p_applied.)

Finally, we make two further remarks. First, we note that the isothermal transition entropy change in materials such as ammonium sulphate and SCOs is rather more similar to that found in intermetallic barocaloric materials such as shape memory alloys and FeRh when it is expressed in units of J K⁻¹ m⁻³. The technologically relevant unit in the case of MCE materials is certainly J K⁻¹ m⁻³ since permanent magnetic fields are the cost centre of a magnetic cooling device.³⁰ The relevant unit for expressing the entropy change of BCE materials may also turn out to be the same. Second, the above analysis does not take into account any energy loss due to transition hysteresis in the cyclic application of an applied pressure. Such losses are an important variable that precludes the application of caloric materials with strongly first order transitions, where the reversible component of an isothermal entropy change or adiabatic temperature change may be significantly reduced.³¹ Since the purpose of this manuscript is to highlight the potential of the entire SCO class, however, we here only bring to the reader’s attention that transition hysteresis will necessarily have to be tuned. There are very good indications that such tunability is possible, for example, in the guest dependence of thermal hysteresis on the SCO transitions of a spin crossover framework (SCOF) compound, [Fe^II(pz)Ni^II(CN)₄] ⋅ xGuest.¹⁸ 

The above survey of SCO materials is designed to motivate further work including material optimisation for caloric purposes. We note with regard to material design that ab initio calculations of even single molecule SCO compounds are non-trivial, given the high degree of dynamical correlations that can be present.³² However, one significant advantage of SCO compounds is their tunability; a change of ligand can be used to alter the crystal field and thereby the SCO temperature and the order of the phase transition. This could be a very useful attribute, for example, in minimising thermal hysteresis. As in studies of other (in particular magneto-) caloric materials, one may also ask what the origin of the transition entropy is in SCO materials, and how it may be maximised. A large percentage of the latent heat at a first order SCO is due to the entropy associated with the giant change in the moment, from LS to HS, or vice versa. However, the strength of the so-called cooperativity, the coupling of the change of spin state to the atomic lattice, can lead to a phonon contribution of similar (or greater) size to the magnetic one.¹⁷ Such complementary use of phonon and magnetic entropy allows further opportunities for material optimisation.

In summary, from a brief consideration of the literature on spin crossover compounds, we may reasonably expect that these are materials that possess mechanocaloric effects which are as large as those seen to date in more conventional intermetallic compounds. Moreover, their low density and bulk modulus may make them an attractive technological prospect. There remains much to be done to fully evaluate the caloric potential of these materials experimentally and theoretically, and to explore and optimise a range of materials with spin crossover transitions around room temperature.

We are grateful to I. Gass, M. Halcrow, and C. Kepert for useful discussions and The Royal Society and CUNY-Brooklyn College for financial support.