$A{B}_2{\mathrm{O}}_4$ are a special class of spinel structured compounds exhibiting unique multiferroic properties. Recent experimental observation confirms switchable polarization in $A{\text{Cr}}_2{\text{O}}_4$ $(A=\text{Co}, \mathrm{Mn}, \mathrm{Fe})$, arising out of noncollinear magnetic spin order. In this paper we unfold the microscopic origin behind such magnetic spin order, hysteresis, polarization, and the so-called magnetic compensation effect in $A{\text{Cr}}_2{\text{O}}_4$ $(A=\text{Co}, \mathrm{Mn}, \mathrm{Fe}, \mathrm{Ni})$ using Monte Carlo simulation. We have carefully constructed a set of exchange interaction parameters, which help to explain various experimental findings such as magnetization vs temperature $\left(T\right)$, conical stability, magnetic ordering, and polarization in a representative compound ${\text{CoCr}}_2{\text{O}}_4$. When substituted with Fe, ${\text{CoCr}}_2{\text{O}}_4$ shows few exotic phenomena such as sign reversible exchange bias effect and magnetic compensation. ${\text{CoMn}}_2{\text{O}}_4$ and ${\text{CoFe}}_2{\text{O}}_4$ are two other compounds in the spinel family where we found no conical spin order and polarization, and thus facilitate a distinct contrast compared to others.

中文翻译：

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尖晶石结构的AB2O4化合物的圆锥序，磁补偿和符号可逆交换偏置：蒙特卡洛研究

$\mathrm{一种}{乙}_{\mathrm{2个}}{\mathrm{Ø}}_4$是一类特殊的尖晶石结构的化合物，具有独特的多铁性。最近的实验观察证实了偏振的可切换$\mathrm{一种}{\text{铬}}_{\mathrm{2个}}{\text{Ø}}_4$ $（\mathrm{一种}=\text{有限公司}， 锰， 铁）$，是由非共线磁性自旋顺序引起的。在本文中，我们揭示了磁自旋顺序，磁滞，极化和所谓的磁补偿效应背后的微观起源。$\mathrm{一种}{\text{铬}}_{\mathrm{2个}}{\text{Ø}}_4$ $（\mathrm{一种}=\text{有限公司}， 锰， 铁， 你）$使用蒙特卡洛模拟。我们精心构建了一组交换相互作用参数，这有助于解释各种实验结果，例如磁化强度与温度的关系。$（Ť）$代表性化合物中的，圆锥稳定性，磁有序性和极化 ${\text{钴铬}}_{\mathrm{2个}}{\text{Ø}}_4$。当用铁取代时，${\text{钴铬}}_{\mathrm{2个}}{\text{Ø}}_4$ 几乎没有异常现象出现，例如符号可逆交换偏置效应和磁补偿。 ${\text{钴锰}}_{\mathrm{2个}}{\text{Ø}}_4$ 和 ${\text{钴铁}}_{\mathrm{2个}}{\text{Ø}}_4$ 是尖晶石家族中的另外两种化合物，我们没有发现其锥形自旋顺序和极化，因此与其他化合物相比，形成了鲜明的对比。