Exchange topology and criticality in ferrite and chromium spinels: a unified Monte Carlo analysis

Abstract

We report a unified analysis of Metropolis Monte Carlo results for two families of magnetic spinels: inverse ferrites Fe${}_A^{3+}$[M${}^{2+}$Fe${}^{3+}$]${}_B$O${}_4$ (M = Co, Cu, Fe, Ni), where superexchange couples two chemically distinct sublattices, and chromium spinels $A$Cr${}_2{X}_4$ ($A$ = Zn, Cd, Hg, $X$ = S, Se) together with the breathing-lattice chromates Li$M$Cr${}_4$O${}_8$ ($M$ = Ga, In), where a single Cr${}^{3+}$ species occupies a corner-sharing tetrahedral network. Placing the exchange constants, transition temperatures, critical exponents, hysteresis, and magnetocaloric responses of these systems on a common footing, we introduce two reduced quantities not previously reported: the ratio ${\theta }_{\mathrm{CW}}/T_C$ for the ferrites and the normalized ordering scale $t^{\ast }=k_B{T}_C/[J_{1}S(S+1)]$ for the chromium compounds. The ferrites cluster in the range ${\theta }_{\mathrm{CW}}/T_C=0.94$-$1.19$, close to the mean-field expectation of unity and the signature of dominant, unfrustrated A-B superexchange, and their exponents ($\beta =0.20$-$0.26$, $\gamma =1.23$-$1.27$, $\delta =4.76$-$4.78$) follow the three-dimensional Ising class. The chromium systems split into three regimes: $t^{\ast }\approx 1.4$-$1.9$ for Ising-treated sulfides, $t^{\ast }\approx 0.99$ for Heisenberg-treated selenides, and $t^{\ast }\approx 0.24$-$0.25$ for the antiferromagnetic breathing chromates, quantifying the combined suppression of $T_C$ by continuous spin symmetry and by geometric frustration. Finite-thickness simulations of Fe${}_3$O${}_4$ resolve a dimensionality crossover between two and four unit cells. We identify the Ising-versus-Heisenberg dependence of the predicted universality class in frustrated chromites as the principal open problem.