On the Failure of the Bloch–Kubo–Dyson Spin Wave Theory

Abstract

Further investigations on magnets with pure spin moments are presented showing that the temperature dependence of the order parameter can accurately be described over a large temperature range by a single T ε power term. The exponent ε is found to be independent of the spin order type but it depends on whether the spin quantum number is integral or half-integral and, of course, on the dimensionality of the magnetic interactions. The six empirical spin wave exponents ε defined in this way are 9/2, 2 and 3 for isotropic, anisotropic and axial interactions and integral spin quantum number but 2, 3/2 and 5/2 for isotropic, anisotropic and axial interactions and half-integral spin quantum number. Thermodynamic crossover between neighbouring exponents is frequently observed: antiferromagnetic NiO having S =1 is cubic above T N but undergoes a progressive trigonal lattice distortion with decreasing temperature. For this material a crossover from isotropic ( ε =9/2) to anisotropic ( ε =2) interactions is observed as a function of decreasing temperature (see Table tI). The hexagonal ferromagnet gadolinium having S =7/2 exhibits a crossover from ε =3/2 to ε =5/2 indicative for a gradual change from anisotropic to predominantly axial interactions with decreasing temperature. Also the itinerant ferromagnets Fe, Ni and Co show the same exponents ε as insulators with S =1/2. While cubic Fe and Ni exhibit ε =2 the same crossover from ε =3/2 to ε =5/2 as for hexagonal Gd is observed for hcp cobalt.