INSTABILITY OF INPLANE VORTICES IN 2-DIMENSIONAL EASY-PLANE FERROMAGNETS

An analysis of the core region of an in-plane vortex in the two-dimens ional Heisenberg model with easy-plane anisotropy lambda = J(z)/J(xy) leads to a clear understanding of the instability towards transformati on into an out-of-plane vortex as a function of anisotropy. The anisot ropy parameter lambda(c) at which the in-plane vortex becomes unstable and develops into an out-of-plane vortex is determined with an accura cy comparable to computer simulations for square, hexagonal, and trian gular lattices. For lambda < lambda(c), the in-plane vortex is stable but exhibits a normal mode whose frequency goes to zero as omega is-pr oportional-to (lambda(c) - lambda)1/2 as lambda approaches lambda(c). For lambda > lambda(c), the static nonzero out-of-plane spin component s grow as (lambda -lambda(c))1/2. The lattice dependence of lambda(c) is determined strongly by the number of spins in the core plaquette, i s fundamentally a discreteness effect, and cannot be obtained in a con tinuum theory.