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Interpretation of ferromagnetic resonance experimental results by cross-validation of solutions of the Smit-Beljers equation
Journal of Magnetism and Magnetic Materials ( IF 2.7 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.jmmm.2020.166824
P. Tomczak , H. Puszkarski

Abstract The phenomenon of ferromagnetic resonance (FMR) is still being widely used for determining the magnetocrystalline anisotropy constants of magnetic materials. We show that one can interpret the Smit-Beljers equation as the relationship between resonance frequency and curvature of the spatial distribution of free energy at resonance. Subsequently, taking this relationship into account and using cross-validation of numerical solutions of the Smit-Beljers equation (Tomczak and Puszkarski, 2018) we show how to determine accurately all the relevant constants related to the tested sample from a single FMR experiment. Specifically, three examples are given of calculating such constants from FMR data: we use historical Bickford’s measurements from 1950 for bulk magnetite, Liu’s measurements from 2007 for a 500 nm thin film of a weak ferromagnet (Ga, Mn) As, and Wang’s measurements from 2014 for an ultrathin film of YIG. In all three cases, the constants we have determined are consistent with the results of other measurements. In the fourth numerical example, we show, using Heinrich et al. FMR measurements for ultrathin Co film, that the presented method can also be a test for the correctness of the assumed form of the ferromagnet free energy at resonance. Eventually, in the fifth numerical example, the unambiguity of the determined parameters in the present approach is briefly discussed.

中文翻译:

通过 Smit-Beljers 方程解的交叉验证解释铁磁共振实验结果

摘要 铁磁共振(FMR)现象仍被广泛用于确定磁性材料的磁晶各向异性常数。我们表明,可以将 Smit-Beljers 方程解释为共振频率与共振时自由能空间分布曲率之间的关系。随后,考虑到这种关系并使用 Smit-Beljers 方程(Tomczak 和 Puszkarski,2018)的数值解的交叉验证,我们展示了如何从单个 FMR 实验中准确确定与测试样本相关的所有相关常数。具体而言,给出了从 FMR 数据计算此类常数的三个示例:我们使用 1950 年以来 Bickford 对大块磁铁矿的历史测量,Liu 于 2007 年对 500 nm 弱铁磁体 (Ga, Mn) As 薄膜的测量,以及 Wang 在 2014 年对 YIG 超薄膜的测量。在所有三种情况下,我们确定的常数与其他测量的结果一致。在第四个数值示例中,我们使用 Heinrich 等人进行展示。超薄 Co 膜的 FMR 测量,所提出的方法也可以测试共振时铁磁体自由能假定形式的正确性。最后,在第五个数值例子中,简要讨论了本方法中确定的参数的明确性。使用海因里希等人。超薄 Co 膜的 FMR 测量,所提出的方法也可以测试共振时铁磁体自由能假定形式的正确性。最后,在第五个数值例子中,简要讨论了本方法中确定的参数的明确性。使用海因里希等人。超薄 Co 膜的 FMR 测量,所提出的方法也可以测试共振时铁磁体自由能假定形式的正确性。最后,在第五个数值例子中,简要讨论了本方法中确定的参数的明确性。
更新日期:2020-08-01
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