A comparison of the spin-phonon behaviour of Fe$_2$P-based magnetocaloric materials

Magnetic refrigeration can provide an environmentally friendly technology to reduce significantly the energy consumption of cooling devices. To retain the sustainability of the device, all parts must be made from abundant materials, excluding e.g. rare earth elements. As such, materials based on Fe$_2$P have shown great potential for magnetocaloric devices. In this study, Fe$_2$P and FeMnP$_{0.55}$Si$_{0.45}$, have been studied using magnetometry, neutron scattering and theoretical modelling with the aim to understand the ferromagnetic transition, related to the magnetocaloric effect. Analysis of the diffraction data of Fe$_2$P showed that it is the Fe$_{3g}$-site that drives the magnetic transition as the Fe$_{3f}$ does not have any magnetic contribution at the magnetic transition temperature. For FeMnP$_{0.55}$Si$_{0.45}$, the magnetic transition is more gradual, on both sites, with coexistence of the para- and ferromagnetic phases close to the magnetic transition. The temperature dependent magnetic structure behaviour are well in agreement with our first principles calculations. Both Fe$_2$P and FeMnP$_{0.55}$Si$_{0.45}$ showed two distinct regions, at different length scales, in their S(\textbf{Q},$\omega$) spectra. The two length scales can be modelled using a different set of magnetic spin states (S), using S$\rm _{Fe}$~=~2 and S$\rm _{Mn}$~=~2.5, consistent with the ground state of the magnetic atoms. QENS at low Q (Q~\textless{}~0.5~\AA{}) shows similar magnetic processes in both compounds with uncorrelated magnetism below the magnetic transition temperature. The uncorrelated state highlights that the magnetic anisotropy does not play a major role in the formation of the magnetic state. Furthermore, this emphasises the existence of a two part system in FeMn(P,Si)-based compounds, that drives the magnetic transition and in turn the magnetocaloric effect.