Surface anisotropy and vortex states in ferromagnetic wires

Summary form only given. The magnetic anisotropy induced by lateral surfaces of magnetic nanowires may overcome demagnetizing forces and and may stabilize vortex states. The distribution of the normalized magnetization m=(sin /spl theta/ cos /spl psi/, sin /spl theta/ sin /spl psi/, cos /spl theta/) written in cylindrical coordinates r=(/spl rho/ cos /spl phi/, /spl rho/ sin /spl phi/, z) is determined by minimization of the energy W=2/spl pi/ /spl int//sub 0//sup R/ {A[(d/spl theta//d/spl rho/)/sup 2/+sin/sup 2/ /spl theta/ [(d/spl psi//d/spl rho/)/sup 2/+1//spl rho//sup 2/(d/spl psi//d/spl phi/)/sup 2/]]+K(m/spl middot/n/spl circ//sub z/)/sup 2/-Hcos/spl theta/+2/spl pi/ (m/spl middot/n/spl circ//sub /spl rho//)/sup 2/} /spl rho/d/spl rho/+2/spl pi/R/spl Omega/(/spl theta/,/spl psi/)|/sub /spl rho//=R.