Magnetothermal Properties and Magnetocaloric Effect in the 3d Ferromagnetic Elements: Fe, Co, and Ni

Abstract

AbstractWe present a calculation of magnetothermal properties and magnetocaloric effect (MCE) for the ferromagnetic elements: Fe, Co, and Ni. In particular, we calculated the temperature and field dependences of magnetization, heat capacity, entropy, isothermal entropy change $$\Delta {S}_{m}$$ Δ S m , adiabatic temperature change ΔTad, and the two figures-of-merit: the relative cooling powers RCP(S) and RCP(T). We have used the mean-field theory in calculating the magnetization, magnetic heat capacity, and magnetic entropy. The lattice and electronic contributions to the total heat capacity and entropy were calculated using standard relations to subsequently calculate $$\Delta {T}_{ad}$$ Δ T ad . Those contributions depend on the Debye temperature ϴD and the coefficient of the electronic heat capacity γe respectively. The Maxwell relation is used to calculate $$\Delta {S}_{m}$$ Δ S m and $$\Delta {T}_{ad}$$ Δ T ad . As an example of our results, the maximum $$\Delta {S}_{m}$$ Δ S m for the three elements, in 6 T, is between 0.17 to 0.36 J/mol K and the maximum $$\Delta {T}_{ad} \mathrm{}$$ Δ T ad  is between 0.46 to 1.5 K/T for the same field change. The relative cooling power RCP(S) is in the 15–36 J/mol range for the three elements in a 6 T field. Also, the relative cooling power, RCP (T), is in the 162–1044 $${K}^{2}$$ K 2 range for the same field. For Fe and Co the RCP (T) per Tesla values, i.e., 139 and 174 $${K}^{2}/T$$ K 2 / T respectively are comparable to that of Gd and other Gd-based magnetocaloric materials. The behavior of the magnetization, magnetic heat capacity, and magnetic entropy shows that the phase transition in these three elements is of the second order. The universal curve and Arrott plots further support this conclusion.