We present a comprehensive study of the spin excitations—as measured by the dynamical spin structure factor $S(q,\omega )$—of the so-called block-magnetic state of low-dimensional orbital-selective Mott insulators. We realize this state via both a multi-orbital Hubbard model and a generalized Kondo-Heisenberg Hamiltonian. Due to various competing energy scales present in the models, the system develops periodic ferromagnetic islands of various shapes and sizes, which are antiferromagnetically coupled. The $2\times 2$ particular case was already found experimentally in the ladder material $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{Se}}_3$ that becomes superconducting under pressure. Here we discuss the electronic density as well as Hubbard and Hund coupling dependence of $S(q,\omega )$ using density matrix renormalization group method. Several interesting features were identified: (1) An acoustic (dispersive spin-wave) mode develops. (2) The spin-wave bandwidth establishes a new energy scale that is strongly dependent on the size of the magnetic island and becomes abnormally small for large clusters. (3) Optical (dispersionless spin excitation) modes are present for all block states studied here. In addition, a variety of phenomenological spin Hamiltonians have been investigated but none matches entirely our results that were obtained primarily at intermediate Hubbard $U$ strengths. Our comprehensive analysis provides theoretical guidance and motivation to crystal growers to search for appropriate candidate materials to realize the block states, and to neutron scattering experimentalists to confirm the exotic dynamical magnetic properties unveiled here, with a rich mixture of acoustic and optical features.

中文翻译：

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块状轨道选择莫特绝缘子：自旋激发分析

我们对自旋激发进行了全面的研究，以动态自旋结构因子来衡量 $\mathrm{小号}（q，\omega ）$所谓的低维轨道选择性莫特绝缘子的块磁态。我们通过多轨道Hubbard模型和广义的Kondo-Heisenberg Hamiltonian来实现这种状态。由于模型中存在各种竞争的能量尺度，因此系统会开发出各种形状和大小的周期性铁磁岛，这些铁磁岛是反铁磁耦合的。的$2\times 2$ 在梯子材料中已经通过实验找到了特殊情况 $巴{铁}_2{硒}_3$在压力下变得超导。在这里，我们讨论电子密度以及Hubbard和Hund耦合依赖性$\mathrm{小号}（q，\omega ）$使用密度矩阵重归一化组方法。确定了几个有趣的特征：（1）发展了声（色散自旋波）模式。（2）自旋波带宽建立了一个新的能量尺度，该能量尺度在很大程度上取决于磁岛的大小，并且对于大的星团，异常变小。（3）光学（无色散自旋激发）模式存在于此处研究的所有块态。此外，已经研究了多种现象学上的自旋哈密顿量，但没有一个与我们主要在哈伯德中期获得的结果完全吻合$ü$长处 我们的综合分析为晶体生长者寻找合适的候选材料以实现块态提供了理论指导和动力，并为中子散射实验者确定了此处揭示的奇特的动磁特性提供了丰富的声学和光学特性的混合物。