We have used the method of Wannier functions to calculate the frequencies and profiles of spin waves localized in one-dimensional magnonic crystals due to a gradient in the bias magnetic field. This localization of spin waves is analogous to the phenomenon of Bloch oscillations of quantum-mechanical electrons in crystals in a uniform electric field. As a convenient yet realistic model, we consider backward volume magnetostatic spin waves in a film of yttrium-iron garnet in a bias magnetic field comprising spatially uniform, cosine and gradient contributions. The spin-wave spectrum is shown to have the characteristic form of a Wannier–Stark ladder. The analytical results are verified using those obtained using numerical micromagnetic simulations. The physics of spin-wave Bloch oscillations combines the topics of magnonic crystals and graded magnonic index — the two cornerstones of modern magnonics.

中文翻译：

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梯度一维磁子晶体中磁偶极自旋波布洛赫振荡的 Wannier-Stark 阶梯谱

我们已经使用万尼尔函数的方法来计算由于偏置磁场中的梯度而位于一维磁子晶体中的自旋波的频率和轮廓。自旋波的这种局部化类似于晶体中量子力学电子在均匀电场中的布洛赫振荡现象。作为一个方便但现实的模型，我们考虑偏磁场中钇铁石榴石薄膜中的后向体积静磁自旋波，包括空间均匀、余弦和梯度贡献。自旋波谱被证明具有 Wannier-Stark 阶梯的特征形式。使用通过数值微磁模拟获得的结果来验证分析结果。