In connection with the spin frustration, the phase transitions of hexagonal ABX3 compounds are experimentally studied. For the XY-like CsMnBr3, it is revealed that the phase transition belongs to a new universal class governed by Z2×S1 symmetry. It is also revealed that though the phase transition is well established, the ordered phase in this substance as well as the intermediate phases in the Ising-like CsCoCl3, CsCoBr3 and CsNiCl3 dynamically fluctuate in a time scale slightly longer than the observation time of neutron diffraction. Crucial effects of strong one-dimensionality of the substances are discussed.
In the evaluation of the spin-orbit coupling (SOC), the use of the L · S formula is invalid in the interatomic region where the effective potential is not spherically symmetric. This problem occurs in the LCAO, LMTO, and APW methods, while the plane-wave pseudopotential and PAW methods cannot treat the spin-orbit splitting (SOS) of core orbitals. To avoid these problems, the all-electron mixed basis approach is adopted, which uses both plane waves (PWs) and atomic orbitals (AOs) as a basis set. The general form S · V × p can be used for PWs, while the standard form L · S can be used for AOs, which are well localized inside the non-overlapping atomic sphere in the spherical potential region and composed of the numerical radial function on a logarithmic radial mesh and analytic cubic harmonics. The explicit formula of the AO-AO, PW-AO, and PW-PW matrix elements of the SOC for spin-polarized systems is presented. In particular, the AO-AO matrices are explicitly derived for p, d, and f orbitals. The method is applied to the SOS of core and valence levels in X-ray photoelectron spectra. The results are in excellent agreement with the available experimental data, which suggests the validity of the present method.
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