相对论自旋轨道相互作用驱动的半填充态电子极化的超交换理论
Superexchange theory of electronic polarization driven by relativistic spin-orbit interaction at the half-filling
摘要：
应用有效半满Hubbard模型的Berry相位理论，推导了相对论自旋轨道耦合驱动下电子极化的解析表达式。模型本身是在Wannier基础上构建的，使用局域密度近似下第一原理电子结构计算的输入，然后按照超交换理论的精神进行处理。所获得的极化具有以下形式：${\bf P}_{ij} = \boldsymbolε_{ji} \boldsymbol{\cal P}_{ij} \cdot [\boldsymbol{e}_i \times \boldsymbol{e}_j]$，其中$\boldsymbolε_{ji}$是键$\langle ij \rangle$的方向，$\boldsymbol{e}_i$和$\boldsymbol{e}_j$是该键中自旋的方向，并且$\boldsymbol{\cal P}_{ij}$是包含关于所考虑系统的晶体对称性的所有信息的伪矢量。该表达式描述了具有非共线但非极性磁性结构的各种磁体中的铁电活性，如果没有SO相互作用，则不会产生极化，包括磁电（ME）效应，由外部磁场中自旋的铁磁倾斜引起，以及自旋螺旋多铁性。用该理论分析了Cr $_2$ O $_3$和BiFeO $_3$的线性ME效应以及多铁性MnWO $_4$和$β$ -MnO $_2$的性质.在所有考虑的例子中，该理论完美地描述了激发极化的对称性。然而，在某些情况下，这种极化的值被低估了，这表明除了自旋和电子效应之外，其他效应也可以发挥重要作用。
英文摘要：
By applying Berry-phase theory for the effective half-filled Hubbard model, we derive an analytical expression for the electronic polarization driven by the relativistic spin-orbit (SO) coupling. The model itself is constructed in the Wannier basis, using the input from the first-principles electronic structure calculations in the local-density approximation, and then treated in the spirit of the superexchange theory. The obtained polarization has the following form: ${\bf P}_{ij} = \boldsymbolε_{ji} \boldsymbol{\cal P}_{ij} \cdot [\boldsymbol{e}_i \times \boldsymbol{e}_j]$, where $\boldsymbolε_{ji}$ is the direction of the bond $\langle ij \rangle$, $\boldsymbol{e}_i$ and $\boldsymbol{e}_j$ are the directions of spins in this bond, and $\boldsymbol{\cal P}_{ij}$ is the pseudovector containing all the information about the crystallographic symmetry of the considered system. The expression describes the ferroelectric activity in various magnets with noncollinear but otherwise nonpolar magnetic structures, which would yield no polarization without SO interaction, including the magnetoelectric (ME) effect, caused by the ferromagnetic canting of spins in the external magnetic field, and spin-spiral multiferroics. The abilities of this theory are demonstrated for the the analysis of linear ME effect in Cr$_2$O$_3$ and BiFeO$_3$ and properties multiferroic MnWO$_4$ and $β$-MnO$_2$. In all considered examples, the theory perfectly describes the symmetry properties of the induced polarization. However, in some cases, the values of this polarization are underestimated, suggesting that other effects, besides the spin and electronic ones, can also play an important role.
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