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Progress of Theoretical Physics

Collective Modes of Incommensurate Spin-Density Wave

Hideyuki Nakanishi

Published Nov 1, 1984• 3 citations
Publisher

Abstract

We investigate collective modes of the incommensurate spin-density wave state for a one-dimensional two-band model within the random phase approximation. For this model, compact expressions of the two-particle Green functions can be obtained. Three types of collective modes are found; an amplitude mode, a phase mode in a real space (a sliding mode) and a phase mode in a spin space (a spin wave mode). The amplitude mode appears in the longitudinal susceptibility and the spin wave mode appears in the transverse susceptibility, but the sliding mode is found to have no contribution to the susceptibilityes. The amplitude mode has the same energy with the energy gap of single particle excitations, but if it is couplied with phonons, its frequency is lowered and it makes a mid-gap mode.

DOI
10.1143/ptp.72.967

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We investigate collective modes of the incommensurate spin-density wave state for a one-dimensional two-band model within the random phase approximation. For this model, compact expressions of the two-particle Green functions can be obtained. Three types of collective modes are found; an amplitude mode, a phase mode in a real space (a sliding mode) and a phase mode in a spin space (a spin wave mode). The amplitude mode appears in the longitudinal susceptibility and the spin wave mode appears in the transverse susceptibility, but the sliding mode is found to have no contribution to the susceptibilityes. The amplitude mode has the same energy with the energy gap of single particle excitations, but if it is couplied with phonons, its frequency is lowered and it makes a mid-gap mode.
Dynamical spin and charge susceptibility and collective modes are studied in the framework of the random phase approximation. They are calculated from the wave function of the selfconsistently obtained ground state, including all possible higher harmonics components of the ordering vector Q . We investigate a spin wave excitation in the spin transverse mode, and phason excitation related to the domain-wall motion in the spin longitudinal and charge modes. We consider the dispersion curve of the collective mode, and discuss the dependence on the on-site U interaction and the period of the incommensurate structure.
Abstract Collective excitation modes in a general 3D homogenous spin-3/2 Fermi gas with spin-dependent contact interactions are investigated by two-particle Green’s functions and diagram techniques. Energy spectra for two branches of charge-density waves and three branches of transverse spin-density waves are obtained within the random-phase approximation. All spectra are gapless and linear in the small wave vector q, with their slopes dependent on the interaction parameters. It is also found that the spin-mixing interaction has effects on the transverse spin-density waves, but not on the charge-density modes. When the system satisfies SU(4) symmetry, the two charge-density modes become degenerate and two of the three transverse spin-density modes are degenerate, too. Furthermore, static spin susceptibilities are discussed in detail. It is found that susceptibilities increase with the enhancement of all interaction parameters, and become divergent at certain points. This phenomenon is analogous to the Stoner transition in spin-1/2 fermion gas.
The collective modes representing density fluctuation in a spin density wave (SDW) have been examined for a one-dimensional electron system of a quarter-filled extended Hubbard model with the next-nearest-neighbor interaction ( V 2 ). Within the random phase approximation (RPA), we obtain a new collective mode, which appears with increasing V 2 . The mode describes the relative motion between density wave with up spin and that with down spin. The gap in the excitation spectrum vanishes at a critical value of V 2 corresponding to the onset of the coexistence of 2 k F -SDW, 2 k F -charge density wave and 4 k F -SDW in the ground state ( k F being the Fermi wave vector).
The fluctuation around the molecular field of the spin density wave (SDW) state has been examined by calculating the collective modes and the spectral weight as a function of arbitrary strength of the repulsive on-site interaction, U , for a one-dimensional system with the half-filled band. The transverse mode is well described by the spin wave for both the small U and the large U and takes the spectral weight which is dominant compared with that of the longitudinal mode for the large U . The temperature dependence of the static magnetic susceptibility is calculated for both the longitudinal and transverse cases.
The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2 D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω ( Q )= c | Q −(π, π)| near Q ∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X ″( Q,ω →0) gives the same mode with a peak at Q ∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X ″( Q,ω →0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector.