Structure Of Energy-level Degeneracy Of A Single-spin Model From A Viewpoint Of Symmetry Of The Spin Anisotropy And Its Nontrivial Spin Dependence On The Higher-order Anisotropy

摘要

We study structure of the gapless points (diabolical points) at zero magnetic field (H_z=0) of single-spin models with spin anisotropies. Nontrivial appearance of diabolical points at finite transverse field H_x has been studied from the viewpoint of interference of the Berry phase and related phenomena have been experimentally found in the single molecular magnet Fe_8. We study effects of the orthorhombic single-ion anisotropy E(S_+~2+S_-~2) and find a symmetry associated with the degeneracy, which provides a clear picture of the global structure of energy-level diagram including the excited states. Moreover, we study effects of the higher-order anisotropy C(S_+~4+S_-~4) and find that, in contrast to the semiclassical limit (S→∞), location of a pair annihilation of the diabolical point does not coincide with a point at which a pair of diabolical points appears in nonzero H_y space (bifurcation points). Distance between the annihilation and bifurcation points vanishes when S→∞, which restores the semiclassical result. We obtain a complete structure of the diabolical points in the (C,H_x) plane.