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

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

2010-09-19

arxiv.org/abs/1009.3634v2

J. Phys. Soc. Jpn. 79 (2010) 114721-1 - 114721-24

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

10.1143/JPSJ.79.114721

We derive the spin-atomic vibration interaction $V_{\rm SA}$ and the spin-flip Hamiltonian $V_{\rm SF}$ 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, $\Delta {{\boldmath $r$}}$. Examining the coefficients of $V_{\rm SA}$ and $V_{\rm SF}$, we first show that $V_{\rm SA}$ appears for $\Delta {{\boldmath $r$}}$$\ne$0, while $V_{\rm SF}$ is present independently of $\Delta {{\boldmath $r$}}$. As an application, we next obtain $V_{\rm SA}$ and $V_{\rm SF}$ of an Fe ion in a crystal field of tetragonal symmetry. It is found that the magnitudes of the coefficients of $V_{\rm SA}$ can be larger than those of the conventional spin-phonon interaction depending on vibration frequency. In addition, transition probabilities per unit time due to $V_{\rm SA}$ and $V_{\rm SF}$ 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.

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