In this work, a theoretical method, taking into account the anisotropy of the internal magnetic field (_int), is proposed to predict the rate of quantum tunneling of magnetization (QTM), i.e., τ_QTM⁻¹, for Kramers single-ion magnets (SIMs). Direct comparison to both experimental and previous theoretical results of three typical Kramers SIMs indicates the necessity of the inclusion of the anisotropy of _int for accurate description of QTM. The predictions of the method here are consistent with the theory proposed by Prokof'ev and Stamp (PS). For Kramers SIMs of high magnetic axiality, the QTM rates, predicted by the method here, are almost linearly proportional to the results by the PS method. The dependence of τ_QTM⁻¹ on various parameters is analyzed for model systems. The averaged magnitude of _int (B_ave) and principal g value of the axial direction (g_Z) are the parameters on which τ_QTM⁻¹ is linearly dependent. The ones on which τ_QTM⁻¹ is quadratically dependent are g_XY, i.e., the principal g value of the transversal direction, and x_aniso characterizing the anisotropy of _int. Compared to B_ave and g_Z, g_XY and x_aniso provide a higher order of dependence for QTM. Therefore regulation of the SMM property via introduction of desired values of g_XY and x_aniso ought to be a strategy more efficient than the one via B_ave and g_Z. Being different from the one via g_XY, the strategy via x_aniso to regulate the QTM has been rarely touched upon according to our best knowledge. However, this strategy could also lead to significant improvement since it is the same as g_XY in the aspect of the dependence of τ_QTM⁻¹.

中文翻译：

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内部磁场在中心离子上的各向异性能够对Kramers单离子磁体的磁化量子隧穿产生很大影响

在这项工作中，理论上的方法，考虑到内部磁场（的各向异性_INT），提出了预测磁化量子隧穿的（QTM），速率即，τ _QTM ^-1，对于克拉默斯单离子磁铁（模拟人生）。与三种典型Kramers SIM的实验结果和先前的理论结果直接比较，表明必须包含_int的各向异性才能准确描述QTM。此处方法的预测与Prokof'ev and Stamp（PS）提出的理论一致。对于具有高磁轴性的Kramers SIM，通过此处的方法预测的QTM速率几乎与PS方法的结果线性相关。的依赖τ _QTM ^-1上的各种参数被分析模型系统。的平均幅度_INT（乙_AVE）和主克轴向（的值克_Ž）是参数在其τ _QTM ^-1线性依赖。的那些在其τ _QTM ^-1被平方依赖性是克_XY，即，将主要克横向方向的值，并且X _ANISO表征的各向异性_INT。相比于乙_AVE和克_ž，克_XY和X _ANISO提供QTM依赖性的高阶。因此，通过引入g _XY和x _aniso的期望值来调节SMM属性应该比通过B _ave和g _Z进行调节更有效。与通过g _{XY的方法不同}，通过x _aniso调节QTM的策略根据我们的最佳知识很少涉及。但是，此策略也可以导致重大改进，因为它与克_XY中的依赖性的方面τ _QTM ^-1。