Spin-Atomic Vibration Interaction and Spin-Flip Hamiltonian of a Single Atomic Spin in a Crystal Field

Abstract

We derive the spin-atomic vibration interaction $V_{\mathrm{SA}}$ and the spin-flip Hamiltonian $V_{\mathrm{SF}}$ of a single atomic spin in a crystal field. We here apply the perturbation theory to a model with the spin-orbit interaction and the kinetic and potential energies of electrons. The model also takes into account the difference in vibration displacement between an effective nucleus and electrons, $Δ{\boldmath $r$}$. Examining the coefficients of $V_{\mathrm{SA}}$ and $V_{\mathrm{SF}}$, we first show that $V_{\mathrm{SA}}$ appears for $Δ{\boldmath $r$}$$\ne$0, while $V_{\mathrm{SF}}$ is present independently of $Δ{\boldmath $r$}$. As an application, we next obtain $V_{\mathrm{SA}}$ and $V_{\mathrm{SF}}$ of an Fe ion in a crystal field of tetragonal symmetry. It is found that the magnitudes of the coefficients of $V_{\mathrm{SA}}$ can be larger than those of the conventional spin-phonon interaction depending on vibration frequency. In addition, transition probabilities per unit time due to $V_{\mathrm{SA}}$ and $V_{\mathrm{SF}}$ are investigated for the Fe ion with an anisotropy energy of $-|D|S_Z^2$, where $D$ is an anisotropy constant and $S_Z$ is the $Z$ component of a spin operator.

55 pages, 17 figures, to be published in J. Phys. Soc. Jpn. 79 (2010) No. 11, typos corrected

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