Solitons in one-dimensional antiferromagnetic chains

Abstract

We study the quantum-statistical mechanics, at low temperatures, of a one-dimensional antiferromagnetic Heisenberg model with two anisotropies. In the weak-coupling limit we determine the temperature dependences of the soliton energy and the soliton density. We have found that the leading correction to the sine-Gordon (SG) expression for the soliton density and the quantum soliton energy comes from the out-of-plane magnon mode, not present in the pure SG model. We also show that when an external magnetic field is applied, the chain supports a new type of kink, where the sublattices rotate in opposite directions.

Spin superconductivity in the frustrated two-dimensional antiferromagnet in the square lattice

“…The frustrated Heisenberg model, sometimes called the J 1 − J 2 model, is a prototype model for several magnetic materials and is of considerable interest in the context of statistical physics 2, 3 . For another side, quantum phase transitions have been subject of intense research over the last decades 4,5 .…”

Intrinsic localized spin waves in an antiferromagnetic spin system with next nearest neighbour interactions

“…There are several mathematical methods to solve the nonlinear spin problems analytically that provide an exact approximate solution for the system. Generally, solitons are obtained for a continuum version of the classical linear Heisenberg spin chain [7,8] by classical approximation, whereas the bosonic representation of the spin operator turns out to be the extremely acceptable method for studying soliton excitation in quantum theory. In contrast to classical approximation, bosonic representation uses operators with no approximation to the Hamiltonian [9] to develop an exact nonlinear equation for the quantum spin system.…”

Solitary magnon excitations in a one-dimensional antiferromagnet with Dzyaloshinsky–Moriya interactions

“…It is well known that the ferromagnetic (FM) and antiferromagnetic (AFM) chain compounds such as CsNiF 3 and TMMC [(CH 3 ) 4 NMnCl 3 ] are systems exhibiting soliton-like excitations [2]. Several theoretical and experimental methods for studying nonlinear excitations of 1D and 2D magnets have been proposed [2][3][4][5][6][7][8][9]. One of the most interesting methods is that of coherent state treatment.…”