The anisotropy of the internal magnetic field on the central ion is capable of imposing great impact on the quantum tunneling of magnetization of Kramers single-ion magnets

In this work, a theoretical method, taking into account the anisotropy of the internal magnetic field (B-int), is proposed to predict the rate of quantum tunneling of magnetization (QTM), i.e., tau(-1)(QTM), 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 B-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 tau(-1)(QTM) on various parameters is analyzed for model systems. The averaged magnitude of B-int (B-ave) and principal g value of the axial direction (g(Z)) are the parameters on which tau(-1)(QTM) is linearly dependent. The ones on which tau(-1)(QTM) is quadratically dependent are g(XY), i.e., the principal g value of the transversal direction, and x(aniso) characterizing the anisotropy of B-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 tau(-1)(QTM).

Automated summary

A theoretical method considering the anisotropy of the internal magnetic field was proposed to predict the rate of quantum tunneling of magnetization in Kramers single-ion magnets. The method's predictions were consistent with previous theoretical results and indicated the importance of including the anisotropy of B-int for accurate description of QTM. The dependence of QTM rate on various parameters was analyzed, with some parameters showing linear dependence while others showing quadratic dependence.