* Corresponding author. Fax: #55-19-2893137. E-mail address: villares@i".unicamp.br (A.V. Ferrer). Journal of Magnetism and Magnetic Materials 226}230 (2001) 510}511 Domain wall dynamics in 1D quantum antiferromagnets A. Villares Ferrer*, A.O. Caldeira Instituto de Fn& sica **Gleb Wataghin++, Departamento de Fn& sica do Estado So& lido e CieL ncia dos Materiais, Universidade Estadual de Campinas, 13083-970, Campinas, SP, Brazil Abstract The problem of dissipative motion of domain walls (DW) in the case of tetramethyl ammonium manganese chloride (TMMC) is studied as a function of the external magnetic "eld and the temperature. Two speci"c situations are analyzed separately; the "rst, above the transition temperature ¹  , in which the classical motion of the spin degree of freedom may be described by a sine-Gordon equation of motion and, the second, below ¹  , in which the system may be described by a double sine-Gordon equation of motion. The existence of a dissipative regime for the DW motion and its in#uence on the dynamical structure factor * which might be experimentally detected * are investigated.  2001 Elsevier Science B.V. All rights reserved. Keywords: Antiferromagnetism*quantum; Antiferromagnets*one dimensional; Domain wall dynamics, Di!usion*Brownian; Di!usion In the past few decades, it has become well-established that the physical properties of some magnetic materials, tetramethyl ammonium manganese chloride (TMMC), CsNiF  and CuCl  2NC  H  , for instance, have essen- tially one-dimensional character above their transition temperature [1]. In magnetic materials, the physical region separating two di!erent magnetic domains can be associated with solitonic solutions of the non-linear equation of motion for the magnetization. Therefore, solitons or solitary-waves can be regarded as &kinks' or &twists' in the spin space moving with constant speed. For su$ciently low temperatures, when the linear modes (spin-waves) are not excited, the magnetic system can be represented in "rst approximation by a gas of non- interacting solitons [2]. Using this idea, Mikeska [1] calculated the soliton contribution to the dynamical structure factor of the classical one-dimensional magnets showing that the assumption of ballistic motion for solitons is the origin of the &central peak' behavior observed in neutron-scattering experiments [3]. A di!er- ent situation could be found from the quantum "eld theory point of view when the temperature is raised. In this case, the spin-wave (SW) modes are excited; there- fore, not all of the degrees of freedom of the system contribute to the soliton formation and a residual inter- action (which couples the center of mass of the soliton to the SW modes) shows up. In practice, the speci"c form of this kind of interaction is obtained via the collective coordinate method in the quantization process of the classical Hamiltonian [4]. The domain wall DW}SW coupling may result in a dissipative regime for the soliton motion depending on the form of the potential generated by the presence of the non-linear excitation [5]. As it is known, the equation of motion for the spin variable in the TMMC below the transition temperature ¹  has a double sine-Gordon (2SG) form [6]. Although this kind of equation is not completely integrable, it has solitonic solutions in the form of 2-kinks(antikinks) in the spin space. At the same time, the presence of this non-linear excitation in the system generates a potential that is felt by the magnons. In this particular situation the potential acting over the magnons has a non-zero re#ection coe$cient and, there- fore, the motion of DW happens to be dissipative. The damping coe$cient (, basically the inverse of the mobil- ity) for DW motion as a function of temperature drops exponentially to zero due to the existence of a energy gap 0304-8853/01/$ - see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 9 9 0 - 2