Theory of noncollinear magnetism in amorphous transition metals

Abstract

The noncollinear magnetism in amorphous transition metals has been investigated by developing the finite-temperature theory of amorphous-metallic magnetism, which takes into account the transverse spin degrees of freedom. The theory is based on the functional-integral technique to the degenerate-band Hubbard Hamiltonian and the distribution function method for local magnetic moments with structural disorder. Numerical results are presented for the magnetic phase diagram as a function of d electron number N and temperature T, and for the magnetization vs volume curves for d electron numbers in the vicinity of amorphous Fe. The calculated magnetic phase diagram on the $N\ensuremath{-}T$ plane exhibits three ordered phases at low temperatures: the spin glass (SG) in the region $N<~7.38,$ the noncollinear ferromagnetism (F) in the region $7.38<~N<~7.43,$ and the collinear F in the region $N>~7.43.$ The noncollinear SG is expected in the region $6.9<N<~7.38,$ while the SG transition temperatures for the collinear and the noncollinear SG are almost the same for $N\ensuremath{\lesssim}6.9.$ In the vicinity of the multicritical point on the $N\ensuremath{-}T$ plane, the transition from the collinear F to the noncollinear F is shown to occur with decreasing temperature, due to the freezing of transverse spin components. The result seems to be consistent with those of the recent M\"ossbauer measurements on Fe-rich amorphous transition-metal alloys. The calculated volume dependence at 35 K shows a clear phase transition from the F to the noncollinear SG with decreasing volume, and a subsequent transition to the paramagnetism. The type of the transition from the F to SG is found to depend on N: the first order for $N=7.0,$ and the second order for $N=7.3.$