Zhang Yin, Wang X S, Yuan H Y, Kang S S, Zhang H W, Wang X R
Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. HKUST Shenzhen Research Institute, Shenzhen 518057, People's Republic of China.
J Phys Condens Matter. 2017 Mar 8;29(9):095806. doi: 10.1088/1361-648X/aa547e. Epub 2017 Jan 27.
The dynamic magnetic susceptibility of magnetic materials near ferromagnetic resonance (FMR) is very important in interpreting the dc voltage obtained in its electrical detection. Based on the causality principle and the assumption that the usual microwave absorption lineshape of a homogeneous magnetic material around FMR is Lorentzian, the general forms of the dynamic magnetic susceptibility of an arbitrary sample and the corresponding dc voltage lineshapes of its electrical detection were obtained. Our main findings are as follows. (1) The dynamic magnetic susceptibility is not a Polder tensor for a material with an arbitrary magnetic anisotropy. The two off-diagonal matrix elements of the tensor near FMR are not, in general, opposite to each other. However, the linear response coefficient of the magnetization to the total radio frequency (rf) field (the sum of the external and internal rf fields due to precessing magnetization is a quantity which cannot be measured directly) is a Polder tensor. This may explain why the two off-diagonal susceptibility matrix elements were always wrongly assumed to be opposite to each other in almost all analyses. (2) The frequency dependence of dynamic magnetic susceptibility near FMR is fully characterized by six real numbers, while its field dependence is fully characterized by seven real numbers. (3) A recipe of how to determine these numbers by standard microwave absorption measurements for a sample with an arbitrary magnetic anisotropy is proposed. Our results allow one to unambiguously separate the contribution of the anisotropic magnetoresistance to the dc voltage signals from the anomalous Hall effect. With these results, one can reliably extract the information of spin pumping and the inverse spin-Hall effect, and determine the spin-Hall angle. (4) In the case that resonance frequency is not sensitive to the applied static magnetic field, the field dependence of the matrix elements of dynamic magnetic susceptibility, as well as the dc voltage, may have another non-resonance broad peak. Thus, one should be careful in interpreting the observed peaks.
铁磁共振（FMR）附近磁性材料的动态磁化率对于解释其电检测中获得的直流电压非常重要。基于因果律原理，并假设均匀磁性材料在FMR附近通常的微波吸收线形为洛伦兹线形，得到了任意样品动态磁化率的一般形式及其电检测对应的直流电压线形。我们的主要发现如下。（1）对于具有任意磁各向异性的材料，动态磁化率不是泡利张量。该张量在FMR附近的两个非对角矩阵元通常并不彼此相反。然而，磁化强度对总射频（rf）场（由于进动磁化产生的外部和内部rf场之和，这是一个无法直接测量的量）的线性响应系数是泡利张量。这可能解释了为什么在几乎所有分析中，两个非对角磁化率矩阵元总是被错误地假定为彼此相反。（2）FMR附近动态磁化率的频率依赖性由六个实数完全表征，而其场依赖性由七个实数完全表征。（3）提出了一种通过标准微波吸收测量来确定具有任意磁各向异性样品的这些数的方法。我们的结果使人们能够明确地将各向异性磁阻对直流电压信号的贡献与反常霍尔效应区分开来。利用这些结果，可以可靠地提取自旋泵浦和逆自旋霍尔效应的信息，并确定自旋霍尔角。（4）在共振频率对施加的静磁场不敏感的情况下，动态磁化率矩阵元以及直流电压的场依赖性可能会有另一个非共振宽峰。因此，在解释观察到的峰时应谨慎。
