The microscopic approach to the formulated problem is presented. For dc magnetic fields H such that \(H\mu \ll \epsilon_ F\) \((\epsilon_ F\) is the Fermi energy, \(\mu\) the particle magnetic moment) only the H- transverse spin response is affected by H. The vertices of the transverse spin and the transverse spin current and their correlation functions are investigated. General formulae are obtained expressing correlation functions of transverse spin and transverse spin current by analogous correlation functions taken at \(H=0.\)
Formulae for correlation functions are discussed in three various limits of the variable \(\lambda =kv/(\omega -2\mu H)\), namely \(| \lambda | \ll 1,| \lambda | \gg 1\), and \(| \lambda | \sim 1\), where v is the Fermi velocity and \(\omega\), k the frequency and the wave vector of the perturbing external field, respectively. In the quasihomogeneous limit, \(| \lambda | \ll 1\), the dispersion of the excitations with a gap of the order \(2\mu\) H will be found, for all orbital, l, and all magnetic, m, quantum numbers. The wave-vector longitudinal excitations \((m=0)\) contribute to the spin autocorrelation, whereas the longitudianl as well as transverse ones \((m=\pm 1)\) contribute to the spin current autocorrelation functions.
All residues of the quasihomogeneous autocorrelation functions are found if they are of the order \({\mathcal O}(\lambda^ 4)\) or greater. In the limit \(| \lambda | \gg 1\), the correlation functions do not have polar character; their imaginary parts, due to Landau damping, are of the order of their real parts. The limit \(| \lambda | \sim 1\) corresponds to the threshold of Landau damping. Nonanalytic character of such functions leads to the nonexponential damping, with the depth of the absorber, of the ac magnetic field. The main part of the calculations are performed without any restrictions imposed on the Landau parameters, though in the final formula for \(| \lambda | \gg 1\) and \(\sim 1\) it is necessary to restrict oneself to the parameters vanishing, e.g., at \(l\geq 2\) or 3, i.e. respectively to the SP and SPD approximations. For comparison, autocorrelation functions for \(m=0\) and \(m=\pm 1\) are calculated in SP and SPD approximation, respectively, without restrictions imposed on \(\lambda\).