AI 中文总结
对铁氧体和铬尖晶石进行统一蒙特卡罗分析，引入新约化量，研究其交换常数等特性。铁氧体有特定范围和指数规律，铬系统分三个区域，还解决了 Fe$_3$O$_4$ 的维度交叉问题，确定了受挫铬酸盐普适类依赖性这一开放问题。
AI 中文摘要
我们报告了对两类磁性尖晶石的 metropolis 蒙特卡罗结果的统一分析：反铁氧体 Fe$^{3+}_{A}$[M$^{2+}$Fe$^{3+}$]$_{B}$O$_4$（M = Co、Cu、Fe、Ni），其中超交换耦合两个化学性质不同的子晶格；以及铬尖晶石 $A$Cr$_2X_4$（$A$ = Zn、Cd、Hg，$X$ = S、Se）和呼吸晶格铬酸盐 Li$M$Cr$_4$O$_8$（$M$ = Ga、In），其中单个 Cr$^{3+}$ 物种占据角共享四面体网络。我们将这些系统的交换常数、转变温度、临界指数、磁滞和磁热响应放在一起考虑，引入了两个以前未报道的约化量：铁氧体的 $\theta_{\mathrm{CW}}/T_C$ 比值和铬化合物的归一化有序尺度 $t^{*}=k_BT_C/[J_1S(S + 1)]$。铁氧体聚集在 $\theta_{\mathrm{CW}}/T_C = 0.94 - 1.19$ 的范围内，接近平均场预期的 1，这是主导的、无挫折的 A - B 超交换的特征，其指数（$\beta = 0.20 - 0.26$，$\gamma = 1.23 - 1.27$，$\delta = 4.76 - 4.78$）遵循三维伊辛类。铬系统分为三个区域：伊辛处理的硫化物的 $t^{*} \approx 1.4 - 1.9$，海森堡处理的硒化物的 $t^{*} \approx 0.99$，反铁磁呼吸铬酸盐的 $t^{*} \approx 0.24 - 0.25$，量化了连续自旋对称性和几何挫折对 $T_C$ 的联合抑制。Fe$_3$O$_4$ 的有限厚度模拟解决了两个和四个晶胞之间的维度交叉问题。我们将受挫铬酸盐中预测普适类的伊辛与海森堡依赖性确定为主要的开放问题。
英文摘要
We report a unified analysis of Metropolis Monte Carlo results for two families of magnetic spinels: inverse ferrites Fe$^{3+}_{A}$[M$^{2+}$Fe$^{3+}$]$_{B}$O$_4$ (M = Co, Cu, Fe, Ni), where superexchange couples two chemically distinct sublattices, and chromium spinels $A$Cr$_2X_4$ ($A$ = 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 $θ_{\mathrm{CW}}/T_C$ for the ferrites and the normalized ordering scale $t^{*}=k_BT_C/[J_1S(S+1)]$ for the chromium compounds. The ferrites cluster in the range $θ_{\mathrm{CW}}/T_C = 0.94$-$1.19$, close to the mean-field expectation of unity and the signature of dominant, unfrustrated A-B superexchange, and their exponents ($β= 0.20$-$0.26$, $γ= 1.23$-$1.27$, $δ= 4.76$-$4.78$) follow the three-dimensional Ising class. The chromium systems split into three regimes: $t^{*} \approx 1.4$-$1.9$ for Ising-treated sulfides, $t^{*} \approx 0.99$ for Heisenberg-treated selenides, and $t^{*} \approx 0.24$-$0.25$ 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.
