Magnetic Excitations in the Quasi-2d Planar Magnets BaM2(XO)4)2 (M = Co,Ni ; X = P,As)

Abstract

In the past few years a great deal of effort has been devoted to studies of the phase transition in two dimensional (2d) systems with a two component order parameter and in particular to the study of 2d magnetic systems with planar anisotropy [1–8]. For this class of systems KOSTERLITZ and THOULESS [1–3] have predicted the existence of a phase transition at a finite temperature from a state with free vortices to a state in which the vortices are paired. This situation leads to an exponential divergence of the correlation length according to the relation: $$ \xi (T) = A \exp B{{(T/{{T}_{{KT}}} - 1)}^{{ - 1/2}}}(A \sim 1{\AA} , {\rm B} \sim \pi /2) $$ (1) but without any longrange order down to T=0. NELSON and KOSTERLITZ [6] have shown that the unbinding of the vortex-antivortex pairs must induce a universal jump in the superfluid density of superfluid systems or in the stiffness constant of hydrodynamic spin wave modes. The existence of such a type of transition has been established for 4He superfluid and superconducting films [9, 10]. Actually 2d magnetic systems are quasi-2d systems because it exists always a small interlayer coupling J’ which induces a 3d long range ordering at a finite temperature Tc approximatively given by: $${K_B}{T_c}\overline \sim {\text{z'|J'|}}{{\text{S}}^2}{\xi ^2}\left( {{T_C}} \right)$$ (2) where ξ(T) is the correlation length. Nevertheless the behaviour of such a system must reflect that of the pure 2d system, if all the undesirable interactions are minimized. In particular the quasi 2d planar system must have aninplane anisotropy as small as possible, with a symmetry, p > 4 in the notation of JOSE et al. [8].KeywordsCorrelation LengthMagnetic ExcitationPlanar AnisotropyFree VortexSuperfluid DensityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.