SURFACE-ROUGHNESS AND LONG-RANGE ORDER OF A SEMIINFINITE FERROMAGNET

We consider the effect of random surface roughness on a semi-infinite ferromagnetic film. We calculate the magnetization as a function of di stance from the surface and the spin-spin correlation as a function of lateral separation. We show that, even in the absence of crystalline anisotropy or an external field, the surface of the ferromagnet is sta ble against random torques created by the roughness. Near the surface, the magnetization reduction is inversely proportional to the square o f a ''healing'' length lambda0 = (D/2piM0)1/2, where D is an exchange stiffness and M0 is the saturation magnetization. The correlations in fluctuations of the magnetization orientation der-ay exponentially wit h distance parallel to the surface, lambda0 being in the exponent. In contrast, fluctuations decrease only as the reciprocal of the square o f the distance perpendicular to the surface. Results are discussed and compared with other calculations of the effects of random surface per turbations.