Electron spin resonance of Mn2+ in LiNbO3 single crystal by using quantum Liouville equation
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The line shape functions (LSF) electron spin resonance for Mn2+ in LiNbO3 and the resulting crystal structure were investigated using a projection operator method. The LSF, which directly apply the spin Hamiltonian describing the system to the projection operator, can be obtained relatively easily by series expansion of propagation factors. Mn, a transition metal with electron spin S=5/2, has unfilled 3d electron shells in its outermost shell, which causes spin crystal structure interactions to spread in the LSFs. The magnetic field dependence of the LSFs the +1/2 -1/2 and +5/2 -5/2 optical transitions, among several allowable optical transitions, and the optical absorption power for the resonance magnetic field were investigated at magnetic field dependence when an external incident electromagnetic wave of 9.27 GHz was applied. The calculation results show that the line-widths decrease slightly with increasing magnetic field, which is believed to be due to the hoping of Nb5+ and Li+ toward the oxygen layer center or plane with increasing magnetic field. The LSF of the system was obtained by the projection operator method, and it was found that Mn2+ was substituted for Li or Nb, which had axial symmetry with respect to the c-axis.
Abstract
The line shape functions (LSF) electron spin resonance for Mn2+ in LiNbO3 and the resulting crystal structure were investigated using a projection operator method. The LSF, which directly apply the spin Hamiltonian describing the system to the projection operator, can be obtained relatively easily by series expansion of propagation factors. Mn, a transition metal with electron spin S=5/2, has unfilled 3d electron shells in its outermost shell, which causes spin crystal structure interactions to spread in the LSFs. The magnetic field dependence of the LSFs the +1/2 -1/2 and +5/2 -5/2 optical transitions, among several allowable optical transitions, and the optical absorption power for the resonance magnetic field were investigated at magnetic field dependence when an external incident electromagnetic wave of 9.27 GHz was applied. The calculation results show that the line-widths decrease slightly with increasing magnetic field, which is believed to be due to the hoping of Nb5+ and Li+ toward the oxygen layer center or plane with increasing magnetic field. The LSF of the system was obtained by the projection operator method, and it was found that Mn2+ was substituted for Li or Nb, which had axial symmetry with respect to the c-axis.