Origin of the magnetic-field dependence of the nuclear spin-lattice relaxation in iron

Abstract

The magnetic-field dependence of the nuclear spin-lattice relaxation at Ir impurities in Fe was measured for fields between 0 and $2\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ parallel to the [100] direction. The reliability of the applied technique of nuclear magnetic resonance on oriented nuclei was demonstrated by measurements at different radio-frequency (rf) field strengths. The interpretation of the relaxation curves, which used transition rates to describe the excitation of the nuclear spins by a frequency-modulated rf field, was confirmed by model calculations. The magnetic-field dependence of the so-called enhancement factor for rf fields, which is closely related to the magnetic-field dependence of the spin-lattice relaxation, was also measured. For several magnetic-field-dependent relaxation mechanisms, the form and the magnitude of the field dependence were derived. Only the relaxation via eddy-current damping and Gilbert damping could explain the observed field dependence. Using reasonable values of the damping parameters, the field dependence could perfectly be described. This relaxation mechanism is, therefore, identified as the origin of the magnetic-field dependence of the spin-lattice relaxation in Fe. The detailed theory, as well as an approximate expression, is derived, and the dependences on the wave vector, the resonance frequency, the conductivity, the temperature, and the surface conditions are discussed. The theory is related to previous attempts to understand the field dependence of the relaxation, and it is used to reinterpret previous relaxation experiments in Fe. Moreover, it is predicted that the field dependences of the relaxation in Fe and Co, on one side, and in Ni, on the other side, differ substantially, and it is suggested that the literature values of the high-field limits of the relaxation constants in Fe are slightly too large.