Abstract
The effect of softening of the exchange in a magnetic overlayer (surface) on the temperature dependence of the surface magnetization M s( T) in the spin-wave regime is investigated. A recursion method for calculating the surface density of spin-wave states (DOS) is developed. It is applied to a magnetic overlayer of n atomic layers with softened exchange between the layers. The principal result obtained for an overlayer of any thickness between n = 1 and n = 20 is that the surface DOS and, therefore, the temperature dependence of the surface magnetization M s( T) are determined by the exchange interactions in the overlayer (surface). The classical result of surface magnetism that M s( T) follows the Bloch T 3 2 law but decreases twice as fast as in the bulk breaks down at temperatures as low as 1% of the Curie temperature T c. Above this temperature, there is a rapid crossover to a second extended region of an effective T 3 2 law with a prefactor determined by the surface exchange. This second region of the T 3 2 law which extends up to temperatures T ≈ 0.4 T c provides a perfect explanation for the observed M s( T) which was determined recently by SPLEED for Ni 40Fe 40B 20 surface and by Mössbauer spectroscopy for Fe(110) surface.
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