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Spin waves and instabilities in the collinear four component antiferromagnetic materials

Pavel A. Andreev

Abstract

The small amplitude perturbations of spins are considered in the four component antiferromagnetic materials with the equilibrium state of form up-up-down-down (uniaxial samples). Other configurations for the four component antiferromagnetic materials and two component antiferromagnetic materials are briefly considered for the comparison with main regime. Dispersion dependencies of two spin waves existing in the system are found if equilibrium spins are parallel to the anisotropy axis. Dispersion equation leading to a possibility of four spin waves is derived if equilibrium spins are perpendicular to the anisotropy axis. It is found that at least one solution has negative frequency square for all possible modules and signs of the anisotropy constants. Calculations are made for the one dimensional chain of classical spins in the approximation of the nearest neighbours interaction. Next, we also addressed the nearest neighbours interaction approximation in the limit of the continuous medium (for the Landau--Lifshitz--Gilbert equation). Mostly applied form of the Landau--Lifshitz--Gilbert equation goes beyond the nearest neighbours interaction approximation. The difference is described. Required assumptions are described.

Spin waves and instabilities in the collinear four component antiferromagnetic materials

Abstract

The small amplitude perturbations of spins are considered in the four component antiferromagnetic materials with the equilibrium state of form up-up-down-down (uniaxial samples). Other configurations for the four component antiferromagnetic materials and two component antiferromagnetic materials are briefly considered for the comparison with main regime. Dispersion dependencies of two spin waves existing in the system are found if equilibrium spins are parallel to the anisotropy axis. Dispersion equation leading to a possibility of four spin waves is derived if equilibrium spins are perpendicular to the anisotropy axis. It is found that at least one solution has negative frequency square for all possible modules and signs of the anisotropy constants. Calculations are made for the one dimensional chain of classical spins in the approximation of the nearest neighbours interaction. Next, we also addressed the nearest neighbours interaction approximation in the limit of the continuous medium (for the Landau--Lifshitz--Gilbert equation). Mostly applied form of the Landau--Lifshitz--Gilbert equation goes beyond the nearest neighbours interaction approximation. The difference is described. Required assumptions are described.

Paper Structure

This paper contains 19 sections, 67 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Spin waves in one-dimensional spin chains
  3. Spin waves in one-dimensional spin chains -- the easy-axis regime for the four component AFM of form up-up-down-down
  4. Regime of two sets of spins of different magnitude
  5. Simplified regime of four spins of equal magnitude
  6. Regime of easy-axis for the four component AFM with configuration up-down-up-down
  7. Spin waves in one-dimensional spin chains -- the easy plane regime for the two component AFM
  8. Spin waves in one-dimensional spin chains -- the easy-plane regime for the four component AFM with configuration up-up-down-down
  9. Landau--Lifshitz equation for the four-component AFM
  10. Landau-Lifshitz equation for two-component AFM
  11. Energy density in the nearest-neighbor interaction approximation
  12. Two component regimes for the energy density: account of next-nearest neighbor interaction
  13. Four component regimes for the energy density: nearest neighbor interaction
  14. Configuration up-up-down-down
  15. Configuration up-down-up-down
  16. ...and 4 more sections

Figures (4)

  • Figure 1: The equilibrium spin structures considered in this paper and corresponding exchange integrals. The anisotropy axis is not presented since two regimes are considered: anisotropy axis parallel to the spins and the anisotropy axis perpendicular to the spins.
  • Figure 2: The dispersion dependence of the spin waves existing in four component up-up-down-down system, if the equilibrium spins are parallel to the anisotropy axis. It is presented as the function of the dimensionless frequency $\textrm{w}=\omega/JS_{0}$ depending on the dimensionless wave vector $kl$, with $l=4a$ and $a$ is the interparticle distance. This figure demonstrates functions given by equation (\ref{['MFMemf dispersion dependence uudd no an']}).
  • Figure 3: The dispersion dependence of the spin waves existing in four component up-down-up-down system, if the equilibrium spins are parallel to the anisotropy axis. The dimensionless notations are the same as in previous figure. This figure illustrated equation (\ref{['MFMemf disp dep 4 AFM udud ea']}).
  • Figure 4: The frequency square as the function of the dimensionless anisotropy constant is demonstrated for the lowest branch of the dispersion dependence following from equation (\ref{['MFMemf disp eq easy plane uudd']}).