SPIN-WAVE MODEL FOR SYSTEMS WITH COMPETING MAGNETIC ANISOTROPIES AND UNDERGOING SPIN REORIENTATION TRANSITIONS

An adapted spin-wave model has been developed to explain spin reorientation (SR) processes in rare-earth ferromagnetic (or ferrimagnetic) systems with competing axial-planar anisotropies. The model involves only second order in the effective spin S and single-ion crystal electric field (CEF) interactions, and several results of interest have been achieved, in particular the temperature dependence of the SR angle-theta. The conditions required to have an SR transition have been established. Of importance is that the 0 K SR angle-theta(0) becomes a consequence of the frozen-in uniform zero-point quantum spin fluctuations, and depends only on the ratio-DELTA = -(D(p)/D(a)) between the planar and axial second-order CEF strengths. A consequence is that the SR temperature T(SR) and the 0 K second-order magnetic anisotropy free energy, K1(0) sin2-theta(0), become proportional. The angle-theta fluctuates critically for T less than or similar T(SR) and its exponent has been calculated, beta = 1/2, as well as the dependence of T(SR) with DELTA and the exchange strength. At low temperatures the dependence of sin2-theta becomes of T3/2 Bloch-like type. A comparison of these results with current experimental findings in hard magnetic intermetallics, such as (RE(x)'RE1-x)2Fe14B and RE(x)'RE1-xCo5, has been made. The effective anisotropy constant K1(0) and the magnon energy at the Brillouin zone boundary for some of the above series of intermetallics have been obtained from previous experiments, the K1(0) values being in good agreement with theory.