Sr $_{3-x}$ Ca $_x$ Ru $_2$ O $_7$的非限制Hartree-Fock分析
Unrestricted Hartree-Fock Analysis of Sr$_{3-x}$Ca$_x$Ru$_2$O$_7$
摘要：
在考虑自旋轨道相互作用的双层三维多带Hubbard模型基础上，研究了Sr $_{3-x}$ Ca $_x$ Ru $_2$ O $_7$（$0 \leq x \leq 3$）的电子结构和磁性.在我们的模型中，晶格畸变被实现为传输积分或晶体场的调制。最稳定的状态估计内的无限制Hartree-Fock近似，其中共线自旋配置与五个不同的自旋量子化轴作为候选人。得到的自旋结构的一些特定的晶格畸变是一致的中子衍射结果Ca $_3$ Ru $_2$ O $_7$。此外，由于晶格畸变的变化，可能会发生一些磁相变。这些结果有助于对Sr $_{3-x}$ Ca $_x$ Ru $_2$ O $_7$相图的全面理解。
英文摘要：
We investigated the electronic and magnetic structure of Sr$_{3-x}$Ca$_x$Ru$_2$O$_7$ ($0 \leq x \leq 3$) on the basis of the double-layered three-dimensional multiband Hubbard model with spin-orbit interaction. In our model, lattice distortion is implemented as the modulation of transfer integrals or a crystal field. The most stable states are estimated within the unrestricted Hartree-Fock approximation, in which the colinear spin configurations with five different spin-quantization axes are adopted as candidates. The obtained spin structures for some particular lattice distortions are consistent with the neutron diffraction results for Ca$_3$Ru$_2$O$_7$. Also, some magnetic phase transitions can occur due to changes in lattice distortion. These results facilitate the comprehensive understanding of the phase diagram of Sr$_{3-x}$Ca$_x$Ru$_2$O$_7$.
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