Ti substituting Ru in ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$ in small concentrations induces incommensurate spin density wave order with a wave vector $\mathit{Q}\simeq (2\pi /3,2\pi /3)$ corresponding to the nesting vector of two of three Fermi surface sheets. We consider a microscopic model for these two bands and analyze the correlation effects leading to magnetic order through nonmagnetic Ti doping. For this purpose we use a position-dependent mean-field approximation for the microscopic model and a phenomenological Ginzburg-Landau approach, which both deliver consistent results and allow us to examine the inhomogeneous magnetic order. Spin-orbit coupling additionally leads to spin currents around each impurity, which in combination with the magnetic polarization produce a charge current pattern. This is also discussed within a gauge-field theory in both charge and spin channel. This spin-orbit coupling effect causes an interesting modification of the magnetic structure if currents run through the system. Our findings allow a more detailed analysis of the experimental data for ${\mathrm{Sr}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Ti}}_x{\mathrm{O}}_4$. In particular, we find that the available measurements are consistent with our theoretical predictions.

中文翻译：

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杂质在Sr2RuO4中的磁有序化

用Ti代替Ru in $r_{\mathrm{2个}}茹{\mathrm{Ø}}_4$ 浓度低时，波矢量会引起自旋密度波阶不相称 $\mathit{问}\simeq （\mathrm{2个}\pi /3，\mathrm{2个}\pi /3）$对应于三个费米表层中的两个费米表层的嵌套向量。我们考虑了这两个带的微观模型，并分析了通过非磁性Ti掺杂导致磁序的相关效应。为此，我们使用微观模型的位置相关平均场近似和现象学的Ginzburg-Landau方法，二者均能提供一致的结果并允许我们检查不均匀的磁阶。自旋轨道耦合还导致每个杂质周围的自旋电流，这与磁极化结合会产生充电电流模式。在电荷和自旋通道的规范场理论中也对此进行了讨论。如果电流流经系统，则这种自旋轨道耦合效应会引起磁结构的有趣变化。$r_{\mathrm{2个}}{茹}_{\mathrm{1个}-X}{钛}_X{\mathrm{Ø}}_4$。特别是，我们发现可用的测量结果与我们的理论预测相符。