AI 中文总结
针对钌烧绿石中强自旋轨道耦合与磁有序的矛盾，建立范弗莱克激子磁性微观理论，解释其磁有序并预测新磁相，应用于Nd$_2$Ru$_2$O$_7$并关联光谱探测。
AI 中文摘要
在$d^4$体系中，强自旋轨道耦合预计会稳定非磁性的$J=0$单重态基态，但许多钌烧绿石却表现出稳定的长程磁有序。受这一明显矛盾的驱动，我们针对烧绿石晶格发展了范弗莱克激子磁性的微观理论。从带有自旋轨道耦合的多轨道哈伯德模型出发，我们推导了Ru$^{4+}$离子低能单重态-三重态流形内的有效超交换相互作用。我们利用三重子激发谱和凝聚相的变分处理两种方法分析得到的激子哈密顿量，确定了非磁性单重态向三重子凝聚的不稳定性，并根据微观跳跃参数确定了对应的磁相图。该相图再现了传统烧绿石模型中已知的磁有序，同时还预测了一种单重态-三重态描述特有的额外磁相。最后，我们将该理论应用于烧绿石钌氧化物，重点关注Nd$_2$Ru$_2$O$_7$，并表明它非常接近激子量子临界点。我们的结果为理解烧绿石钌氧化物中的激子磁性及其磁激发谱建立了微观框架，为包括拉曼散射在内的光谱探测提供了直接关联。
英文摘要
Strong spin-orbit coupling in $d^4$ systems is expected to stabilize a nonmagnetic $J=0$ singlet ground state, yet many ruthenium pyrochlores exhibit robust long-range magnetic order. Motivated by this apparent contradiction, we develop a microscopic theory of Van Vleck excitonic magnetism on the pyrochlore lattice. Starting from a multi-orbital Hubbard model with spin-orbit coupling, we derive the effective superexchange interactions within the low-energy singlet--triplet manifold of Ru$^{4+}$ ions. We analyze the resulting excitonic Hamiltonian using both the spectrum of triplon excitations and a variational treatment of the condensed phase. We identify the instability of the nonmagnetic singlet state toward triplon condensation and determine the resulting magnetic phase diagram as a function of the microscopic hopping parameters. The phase diagram reproduces the magnetic orders known from conventional pyrochlore models while also predicting an additional magnetic phase unique to the singlet--triplet description. Finally, we apply the theory to the pyrochlore ruthenates, with particular emphasis on Nd$_2$Ru$_2$O$_7$, and show that it lies in close proximity to the excitonic quantum critical point. Our results establish a microscopic framework for understanding excitonic magnetism in pyrochlore ruthenates and their magnetic excitation spectrum, providing direct connections to spectroscopic probes, including Raman scattering.
Comments25 pages, 6 figures
