论文标题
磁八极张量分解和二阶磁电效应
Magnetic octupole tensor decomposition and second-order magnetoelectric effect
论文作者
论文摘要
我们讨论了二阶磁电效应，其中二次或双线性电场从磁性八杆的铁序列化方面诱导线性磁化。我们将一般级别3张量的分解为其不可还能的球形张量，然后将磁性八极张量的特定情况减少分解，$ \ Mathcal {M} _ {ijk} = \ \ intμ_i（\ intμ_i（\ intbf {r}）我们使用第一原理密度功能理论来计算原型磁电磁性CR $ _2 $ o $ $ _3 $中铬离子上局部磁多物的大小，并表明，除了稳固的局部磁性偶极子和磁性多极端，磁性octupoles还为非non-nker。 Cr $ _2 $ o $ _3 $中的磁八杆具有抗侵蚀布置，因此其净二阶磁电响应为零。因此，它们形成了一种隐藏秩序，可以显示为对非区域中心（均匀）二次电场的线性磁性（抗磁性）响应。
We discuss the second-order magnetoelectric effect, in which a quadratic or bilinear electric field induces a linear magnetization, in terms of the ferroic ordering of magnetic octupoles. We present the decomposition of a general rank-3 tensor into its irreducible spherical tensors, then reduce the decomposition to the specific case of the magnetic octupole tensor, $\mathcal{M}_{ijk} = \int μ_i (\mathbf{r}) r_j r_k d^3 \mathbf{r}$. We use first-principles density functional theory to compute the size of the local magnetic multipoles on the chromium ions in the prototypical magnetoelectric Cr$_2$O$_3$, and show that, in addition to the well established local magnetic dipoles and magnetoelectric multipoles, the magnetic octupoles are non-zero. The magnetic octupoles in Cr$_2$O$_3$ have an anti-ferroic arrangement, so their net second-order magnetoelectric response is zero. Therefore they form a kind of hidden order, which could be revealed as a linear magnetic (antiferromagnetic) response to a non-zone-center (uniform) quadratic electric field.
