坂井 徹

Abstract The spin- S Heisenberg antiferromagnet on the two-dimensional lattice is investigated for S = 1/2 and S = 1. We consider interaction at isolated dimers ( J _d ) and interaction bonds that form the bounce lattice ( J _b ). For J _d = J _b , the system is reduced to the maple-leaf-lattice antiferromagnet. We primarily conduct highly parallelized numerical diagonalization to examine the spin excitation gap above the ground state for various J _b / J _d cases. For S = 1/2, we report calculations for a 42-site cluster that has not been previously treated. The S = 1 case is examined for the first time for clusters up to 24 sites. Regardless of whether S = 1/2 or 1, we find that the system has a gapped nature for small J _d / J _b and becomes gapless at J _d / J _b ∼ 1.4. For S = 1, we also find that another gapped region appears between the gapless case at J _d / J _b ∼ 1.4 and the boundary of the exact-dimer phase.

The magnetization process of the S = 1/2 two-dimensional magnet where ferromagnetic dimers connected by the antiferromagnetic bond on the Shastry-Sutherland lattice is investigated using the numerical diagonalization of a finite-size cluster. We introduce the easy-axis anisotropy at the intradimer ferromagnetic interaction and consider the external magnetic field along the easy axis. It is found that the two-magnon bound state appears at higher magnetization regions for sufficiently large anisotropy. Base on the previous studies of several one-dimensional systems and the present calculation of the spin correlation function, the spin nematic order perpendicular to the external field is expected to occur in this two-magnon bound phase.

The magnetization process of the S = 1 spin ladder with two anisotropies competing each other is investigated using the numerical diagonaization of finite-size clusters and the level spectroscopy analysis. As a result, it is found that the translational symmetry broken magnetization plateaux appear at 1/4 and 3/4 of the saturation magnetization. The phase diagrams with respect to the anisotropies at the 1/4, 1/2 and 3/4 magnetizations are obtained. The magnetization curves for several typical parameters are also presented.