Magnetocaloric Effect in a First-Order Phase Transition in a Ferromagnet with Biquadratic Exchange

In the model of a ferromagnet with positive parameters of bilinear (I > 0) and biquadratic (K > 0) exchanges and spins S = 1, the case is investigated in which, in the range of exchange parameter ratios 2/3 < K/I < 1, a first-order phase transition occurs between the paramagnetic and magnetically ordered states. The rise and behavior of jumps in the magnetic entropy S_M and the magnetic order parameters—the relative magnetization σ_Z and the quadrupole parameter q₀—are considered both in first-order transitions in temperature (at a critical temperature T_c(H = 0) without a field or at temperatures T(H) at constant field H) and in first-order transitions in the field upon isothermal magnetization. It is shown that the magnitude of the jump in the magnetic entropy |ΔS_M(T,H_c(T))| at a critical magnetic field H_c(T) of isothermal magnetization depends on the choice of the magnetization temperature T and reaches its maximum value |ΔS_M(T_c(H = 0))| at a chosen temperature T = T_c(H = 0) + 0⁺. In turn, the magnitudes of the jumps in the entropy, |ΔS_M(T_c(H = 0))|, and order parameters, Δσ_Z and Δq₀, at a critical temperature T_c(H = 0) without a field depend significantly on the ratio K/I between the parameters of competing exchanges: they vanish at K/I → 2/3 and are maximal at K/I → 1.