Rp. Erickson et Jr. Cullen, SURFACE-ROUGHNESS AND LONG-RANGE ORDER OF A SEMIINFINITE FERROMAGNET, Journal of applied physics, 73(10), 1993, pp. 5981-5983
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.