Superexchange interactions in orthorhombically distorted titanates RTiO3 (R = Y, Gd, Sm and La)
Superexchange interactions in orthorhombically distorted titanates RTiO3 (R = Y, Gd, Sm and La)
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DOI：
10.1088/1367-2630/11/9/093003
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发表时间：
2009-06
影响因子：
3.3
通讯作者：
I. Solovyev
中科院分区：
文献类型：
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作者：
I. Solovyev
从RTiO 3（R=Y、Gd、Sm和La）t2 g带的多轨道Hubbard模型出发，其中所有参数都是从第一性原理电子结构计算中推导出来的，通过将转移积分视为微扰，我们构建了一个有效的超交换（SE）自旋模型。我们考虑了SE相互作用的四种近似：（i）正则晶体场（CF）理论，其中占据t2 g轨道的形式由每个Ti位的CF分裂决定;和CF理论的三种扩展，即（ii）相对论CF理论，其中占据轨道被限制在由CF和相对论自旋轨道（SO）相互作用对角化得到的最低Kramers二重态内;（iii）有限温度扩展，它考虑了CF组态附近的热轨道涨落对自旋之间原子间相互作用的影响;（iv）多电子扩展，它是基于对系统中每个键的两电子态分别构造的完全哈密顿量的对角化。主要研究结果如下。(i)轨道自由度的热波动可以显著降低磁转变温度的值。(ii)相对论SO耦合通常负责各向异性和反对称Dzyaloshinsky-Moriya相互作用。所有的相互作用严格推导和RTiO 3的磁性能的影响进行了讨论。(iii)CF理论，虽然适用于YTiO 3和高温结构的GdTiO 3和SmTiO 3，打破在LaTiO 3的情况下。在后者中，CF分裂较小。因此，键中的多电子效应以及相对论SO相互作用开始起重要作用。有人认为，这两种效应的组合可能是负责原子间的关联在LaTiO 3的AFM字符。(iv)在YTiO 3中的SE相互作用强烈地依赖于晶体结构的细节。低温结构中的晶体畸变倾向于削弱铁磁相互作用。
Starting from the multiorbital Hubbard model for the t2g-bands of RTiO3 (R=Y, Gd, Sm and La), where all the parameters have been derived from the first-principles electronic structure calculations, we construct an effective superexchange (SE) spin model, by treating transfer integrals as a perturbation. We consider four approximations for the SE interactions: (i) the canonical crystal-field (CF) theory, where the form of the occupied t2g-orbitals is dictated by the CF splitting at each Ti-site and three extensions of the CF theory, namely (ii) the relativistic one, where occupied orbitals are confined within the lowest Kramers doublet obtained from the diagonalization of the CF and relativistic spin–orbit (SO) interactions; (iii) the finite-temperature extension, which considers the effect of thermal orbital fluctuations near the CF configuration on interatomic interactions between the spins; (iv) the many-electron extension, which is based on the diagonalization of the full Hamiltonian constructed in the basis of two-electron states separately for each bond of the system. The main results are summarized as follows. (i) Thermal fluctuations of the orbital degrees of freedom can substantially reduce the value of the magnetic transition temperature. (ii) The relativistic SO coupling is generally responsible for anisotropic and antisymmetric Dzyaloshinsky–Moriya interactions. All interactions are rigorously derived and their implications for the magnetic properties of RTiO3 are discussed. (iii) The CF theory, although applicable for YTiO3 and high-temperature structures of GdTiO3 and SmTiO3, breaks down in the case of LaTiO3. In the latter, the CF splitting is small. Therefore, the many-electron effects in the bonds as well as the relativistic SO interaction start to play an important role. It is argued that the combination of these two effects could be responsible for the AFM character of interatomic correlations in LaTiO3. (iv) The SE interactions in YTiO3 strongly depend on the details of the crystal structure. Crystal distortions in the low-temperature structure tend to weaken the ferromagnetic interactions.