We solve for the finite temperature collective mode dynamics in the Holstein-double-exchange problem, using coupled Langevin equations for the phonon and spin variables. We present results in a strongly anharmonic regime, close to a polaronic instability. For our parameter choice, the system transits from an undistorted ferromagnetic metal at low temperature to a structurally distorted paramagnetic insulator at high temperature, through a short-range charge-ordered (CO) phase near the ferromagnetic crossover at $T_{\text{FM}}$. The small amplitude harmonic phonons at low temperature cross over to large amplitude dynamics around $0.5T_{\text{FM}}$ as spin disorder promotes formation of short-range correlated polarons. The CO background in turn leads to the softening of phonons near momentum $\mathbf{q}=(\pi ,\pi )$ with temperature, while strong anharmonicity close to the magnetic transition leads to unusually large damping. The most remarkable phonon feature, however, arises from the rare thermal tunneling of CO domains, generating a momentum selective spectral weight at very low energy. The spin dynamics is similar to that of a nearest-neighbor Heisenberg model with sharp spin waves at low $T$, transiting to diffusive modes near $T_{\text{F}\text{M}}$. We compare our results to inelastic neutron data in the manganites and suggest how the singular low-energy features can be probed.

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电子-声子-自旋耦合问题中的强非调和集体模

我们使用耦合的声子和自旋变量的Langevin方程求解Holstein-双交换问题中的有限温度集体模态动力学。我们目前的结果是在强非调和状态下，接近极化不稳定性。对于我们的参数选择，系统从低温的未变形铁磁金属过渡到高温下的结构变形的顺磁绝缘体，通过位于铁磁交叉点附近的短程电荷有序（CO）相。${Ť}_{\text{调频}}$。低温下的小振幅谐波声子在周围发生大振幅动力学$0.5{Ť}_{\text{调频}}$因为自旋障碍会促进短程相关极化子的形成。反过来，CO背景导致声子在动量附近变软$\mathbf{q}=（\pi ，\pi ）$随温度变化，而靠近磁转换的强非谐性会导致异常大的阻尼。然而，最显着的声子特征来自于CO域的罕见热隧穿，从而在非常低的能量下产生了动量选择性光谱权重。自旋动力学与最近的海森堡模型相似，自旋动力学在低速时具有尖锐的自旋波$Ť$，过渡到附近的扩散模式 ${Ť}_{\text{F}\text{中号}}$。我们将我们的结果与锰矿中的非弹性中子数据进行比较，并提出如何探测奇异的低能特征的建议。