SPIN COMPLEXES IN FERROMAGNETISM

Abstract

The spin-wave theory in Heisenberg model of ferromagnetism is investigated with the Holstein - Primakoff transformation and with emphasis on the spin wave interactions. The temperature Tₒ below which the concept of magnons is valid is determined. By a special expansion formalism of operator (l-a+a/2S)1/2 which yields 1+(1-(1-1/2S)1/2 )a+a it is shown that quantized spin waves which behave like spin 1 quasiparticles (with dispersion relation ω~ k2 ) called magnons at temperatures T < Tₒ, are Bosons with an effective (negative) electrochemical potential µ that varies as T in the wave-wave interaction approximation. The various coefficients of Tv in the expression of the spontaneous magnetization M(T)/M(o) = l-(C1T3/2+C2T5/2+C3T7/2+C4T4) as well as the specific heat for some ferromagnets are calculated. The results are remarkably close to the experimental values obtained by other investigators. The method used enables one to deal especially with regimes of small spin values S for which µ differs substantially from zero. The influence of the chemical potential on some thermodynamic quantities are found for ferromagnets with Hexagonal-close-packed structures, as well as for cubic crystals, The existence of the spin wave interactions and hence of non-zero effective chemical potential is shown to give rise to a lowering of the thermodynamic internal energy with the implication that spin waves, on the average, form bound states called spin complexes. The kinematical as well as the dynamical interactions on the thermodynamic quantities are also found for some ferromagnets, by subjecting the magnons to intermediate statistics. The influence of the spin-wave-spin-wave-spin-wave interactions on the coefficients of Tv in the expression of the spontaneous magnetization of some ferromagnets are found to be negligible in comparison with wave-wave interactions. An attempt is made to extend the above calculations to spin complexes in antiferromagnetism, a phenomenon which seems to be relevant to high temperature superconductivity.