Resonance Absorption and Transverse Magnetization of an Anti-Ferromagnetic Spin System Interacting with a Phonon Reservoir in the Spin-Wave Region

A form of the transverse magnetic susceptibility is derived and the resonance absorption and transverse magnetization are studied for an anti-ferromagnetic spin system interacting with a phonon reservoir in the spin-wave region, employing the TCLE method of linear response in terms of the non-equilibrium thermo-field dynamics (NETFD), which is reformulated for the revised spin-phonon interaction taken to reflect the energy transfer between the spin system and phonon reservoir. Here, the TCLE method of linear response is a method in which the admittance of a physical system is directly derived from time-convolutionless equations with external driving terms. The approximate formulas of the resonance frequencies, peak-heights (heights of peak) and line half-widths in the resonance region of the power absorption and the amplitude of the expectation value of the transverse magnetization, which is referred as "the magnetization-amplitude", are derived for the anti-ferromagnetic system in a transversely rotating magnetic-field. For an anti-ferromagnetic system of one-dimensional infinite spins in the transversely rotating magnetic-field, the power absorption and magnetization-amplitude are investigated numerically in the region valid for the lowest spin-wave approximation. The approximate formulas of the resonance frequencies, peak-heights and line half-widths, are shown to coincide well with the results investigated calculating numerically the analytic results of the power absorption and magnetization-amplitude in the resonance region, and also are shown to satisfy "the narrowing condition" that as phonon reservoir is damped quickly, the peak-heights increase and the line half-widths decrease, and thus are verified numerically. In the resonance region of the power absorption and magnetization-amplitude, it is shown that as the temperature T becomes high, the resonance frequencies increase slightly, the peak-heights decrease and the line half-widths increase, and that as the wave number k becomes large, the resonance frequencies and peak-heights increase, and the line half-widths decrease, and also that as the spin-magnitude S becomes large, the resonance frequencies and peak-heights of the power absorption and magnetization-amplitude become large. The effects of the memory and initial correlation for the spin system and phonon reservoir, which are represented by the interference terms in the TCLE method and are referred as "the interference effects", are confirmed to increase the power absorption and magnetization-amplitude in the resonance region, and are shown to produce effects that cannot be disregarded for the high temperature, for the non-quickly damped reservoir or for the small wave number k.