The modified spin-wave theory is used to investigate the one-dimensional Heisenberg ferromagnet with the nearest-neighbor (NN) and next-nearest-neighbor (NNN) exchange anisotropies. The ground-state and low-temperature properties of the system are studied within the self-consistent method. It is found that the effect of the NN anisotropy on the thermodynamic quantities is stronger than that of the NNN anisotropy in the low-temperature region. The anisotropy dependence behaviors (such as the power, exponential and linear laws) are obtained for the position and the height of the maximum of the specific heat and its coefficient, as well as the susceptibility coefficient. The specific heat and its coefficient both display the low-temperature double maxima which are induced by the anisotropies and the NNN interaction. In the very low temperatures the specific heat and the susceptibility behave severally as T[Formula: see text] and T[Formula: see text] at the critical point J2/J1 = −0.25, where J1 and J2 are the NN and NNN interactions, respectively.
Effects of both the phase and the amplitude inhomogeneities of different dimensionalities on the Greens function and on the one-dimensional density of states of spin waves in the sinusoidal superlattice have been studied. Processes of multiple scattering of waves from inhomogeneities have been taken into account in the self-consistent approximation.
CsMnBr3 is a quasi-one-dimensional Heisenberg antiferromagnet. We present results of the magnetic inelastic response of CsMnBr3 across the magnetic Brillouin zone by neutron scattering techniques. Well-defined spin-wave modes, characteristic of one-dimensional magnetic insulators, are found over most of the zone in the paramagnetic phase at 15 K. The zone centre response is not sharp, but peaks in the scattering function S(k, ω) are found. No excitation branch going to zero energy at zero wavevector is found. At small wavevectors there is a mode with energy 1.7 ± 0.2 meV and we use it to identify planar anisotropy in this system. The mid-zone response as a function of temperature is analyzed in terms of a generalized Langevin equation approach (Mori formulation) to the dynamics of the one-dimensional Heisenberg antiferromagnet. The theory contains no adjustable parameters. Our results are compared with two truncation schemes of the theory. We report qualitative agreement with the theories, including the observation of upwards renormalization of spin-wave energy with temperature. Quantitative agreement is less than good for either truncation scheme.
Two methods for the numerical resolution of the Takagi-Taupin equations are compared. It is shown that for a small integration step Taupin's [Acta Cryst. (1967), 23, 25–35] extension to two dimensions of the one-dimensional Runge–Kutta third-order method is more accurate than the algorithm of Authier, Malgrange & Tournarie [Acta Cryst. (1968), A24, 126–136] but, for a given precision, Authier, Malgrange & Tournarie's method is faster than Taupin's so the former will usually be preferred for numerical calculation.
Thermodynamics of the one-dimensional frustrated Heisenberg ferromagnet with arbitrary spin