Two-magnon excitations in resonant inelastic x-ray scattering from quantum Heisenberg antiferromagnets
Two-magnon excitations in resonant inelastic x-ray scattering from quantum Heisenberg antiferromagnets
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DOI：
10.1103/physrevb.75.214414
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发表时间：
2007-01
影响因子：
3.7
通讯作者：
T. Nagao;J. Igarashi
中科院分区：
文献类型：
--
作者：
T. Nagao;J. Igarashi
通过推广Nomura和Igarashi的公式，我们研究了Heisenberg反铁磁体共振非弹性x射线散射(RIXS)中的双磁振子谱。修订本B 71,035110(2005年)]。RIXS中间态的核-空穴势能引起$3d$电子之间交换耦合的变化，导致核空穴与$3d$电子自旋之间的有效相互作用。我们推导了一个适用于计算双磁振子RIXS强度的公式，用产生两个磁子的有效相互作用代替了原公式中负责电荷激发的裸芯-空穴势。它由两个因素组成，一个决定入射-光子-能量关系，另一个是双磁振子关联函数。我们用能带计算得到的$4p$态的态密度来评价${\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$的前一个因子。通过将磁振子-磁振子相互作用变换为可分离形式后的梯形图，我们还计算了正方形晶格上海森堡模型的能量损失和动量传递的函数--双磁振子关联函数。在磁布里渊区边界上，当$S=1/2$时，在$\ensureMath{\omega}=3j$附近形成一个宽峰，并在$\mathbf{q}=(0，0)$和$(\ensureath{\pi}，\ensureath{\pi})$处消失。RIXS谱的这种动量依赖性可以为研究海森堡模型中的动力学提供一个很好的机会。
We study two-magnon spectra in resonant inelastic x-ray scattering (RIXS) from Heisenberg antiferromagnets by extending the formula of Nomura and Igarashi [Phys. Rev. B 71, 035110 (2005)]. The core-hole potential in the intermediate state of RIXS gives rise to a change in the exchange coupling between $3d$ electrons, leading to an effective interaction between the core hole and spins of $3d$ electrons. We derive a formula suitable to calculate the two-magnon RIXS intensities, replacing the bare core-hole potential responsible for charge excitations by this effective interaction creating two magnons in our previous formula. It consists of two factors, one of which determines the incident-photon-energy dependence while the other is a two-magnon correlation function. We evaluate the former factor for ${\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$ in terms of the density of states of the $4p$ states obtained by a band calculation. We also calculate the two-magnon correlation function as a function of energy loss $\ensuremath{\omega}$ and momentum transfer $\mathbf{q}$ of the Heisenberg model on a square lattice, by summing up the ladder diagrams after transforming the magnon-magnon interaction into a separable form. The calculated spectra form a broad peak around $\ensuremath{\omega}=3J$ for $S=1∕2$ on the magnetic Brillouin zone boundary and vanish at $\mathbf{q}=(0,0)$ and $(\ensuremath{\pi},\ensuremath{\pi})$. Such momentum dependence of the RIXS spectra could provide an excellent opportunity to study the dynamics in the Heisenberg model.