K $_2$ CuF $_4$和LaMnO $_3$铁磁面轨道激发的磁振子修整
Magnon dressing by orbital excitations in ferromagnetic planes of K$_2$CuF$_4$ and LaMnO$_3$
摘要：
我们表明，即使当自旋和轨道解纠缠在基态，自旋激发重整化的局部调谐的$e_g$轨道在铁磁平面的K $_2$ CuF $_4$和LaMnO $_3$。因此，在电子模型中获得的修饰自旋激发（磁振子）作为准粒子传播，其能量重整化依赖于动量${\vec k}$。因此，自旋轨道系统中的磁振子超越了具有从基态导出的最近邻自旋交换的有效海森堡模型的范例-激发态的自旋轨道纠缠预测了布里渊区边界处的大的磁振子软化，并且在LaMnO $_3$的情况下，$M=(π,π)$点处的磁振子能量可以减少$\sim 45$ %.相反，同时Goldstone模式附近的刚度常数几乎不受影响。我们阐明背后的自旋轨道系统的磁振子重整化的物理和解释为什么长波长的磁振子是unrenormalized，而同时短波长的磁振子的能量减少轨道波动。事实上，磁振子能量的${\vec k}$依赖性主要通过色散来修改，所述色散源自沿立方轴$a$和$b$的第二邻居之间的自旋交换。
英文摘要：
We show that even when spins and orbitals disentangle in the ground state, spin excitations are renormalized by the local tuning of $e_g$ orbitals in ferromagnetic planes of K$_2$CuF$_4$ and LaMnO$_3$. As a result, dressed spin excitations (magnons) obtained within the electronic model propagate as quasiparticles and their energy renormalization depends on momentum ${\vec k}$. Therefore magnons in spin-orbital systems go beyond the paradigm of the effective Heisenberg model with nearest neighbor spin exchange derived from the ground state --- spin-orbital entanglement in excited states predicts large magnon softening at the Brillouin zone boundary, and in case of LaMnO$_3$ the magnon energy at the $M=(π,π)$ point may be reduced by $\sim 45$\%. In contrast, simultaneously the stiffness constant near the Goldstone mode is almost unaffected. We elucidate physics behind magnon renormalization in spin-orbital systems and explain why long wavelength magnons are unrenormalized while simultaneously energies of short wavelength magnons are reduced by orbital fluctuations. In fact, the ${\vec k}$-dependence of the magnon energy is modified mainly by dispersion which originates from spin exchange between second neighbors along the cubic axes $a$ and $b$.
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