Theory of Dynamical Behaviors of Ferromagnetic Spins

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The dynamical behavior of ferromagnetic spins is studied on the basis of the statistical mechanics of irreversible processes. A macroscopic equation determining the change in time of an inhomogeneous magnetization is derived with explicit expressions for the frequency spectrum and damping constant. With the use of the general expressions thus obtained, the following problems are discussed on the basis of the Heisenberg model of ferromagnetic spins: (1) the pair correlation of spins, (2) the magnetic scattering cross section of neutrons, (3) the frequency spectrum and the damping constant of spin waves, (4) the damping of the longitudinal spin component above and below the Curie point. In the low temperature limit, a straightforward reduction of our expressions leads to the spin wave frequency and damping equivalent to Dyson's theory of spin wave interactions. A general expression is given for van Hove's parameters describing the asymptotic behavior of the spin pair correlation at large distances. It is shown that the longitudinal spin damping in the low temperature limit exhibits a variety of k dependences, depending upon the relative magnitudes of the spin wave energy Dk^2, the effective magnetic field H coming from other than the exchange interaction and the thermal energy k_BT; in particular, for gμ_BH≪Dk^2≪k_BT, the longitudinal damping is proportional to k^2, namely, the change in time of the longitudinal spin density obeys the diffusion equation. In the vicinity of the Curie point and in the paramagnetic region, the longitudinal damping is shown to obey the diffusion equation. The diffusion constant thus obtained vanishes at the Curie point and is in good agreement with the values observed by Ericson and Jacrot for iron above the Curie point.
理論物理学刊行会の論文
1962-03-25

Theory of Dynamical Behaviors of Ferromagnetic Spins

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