Ferromagnetic Resonance of Single-Crystal Gadolinium

Abstract

Gadolinium metal is a system of relative simplicity as far as exchange interactions and ionic states are concerned. The 8S7/2 state of Gd3+ is consistent with the observed 7μb/atom and the moment contributing f electrons are most likely exchange coupled via conduction electrons. The present work concerns the measurement of the ferromagnetic resonance behavior of a single crystal at frequencies of 21 and 35 Gc/sec and at temperatures from above the Curie point (20°C) to 4.2°K. The resonance absorptions are well defined at both frequencies and at all temperatures for most crystal orientations. The minimum linewidth observed is about 400 Oe but the line shape and width degrade when the applied field departs from the easy axis, particularly at the lower frequency and at low temperatures. Strong, well-defined domain wall resonances are also frequently observed. The deduced magnetocrystalline anisotropy energy is accurately described by the standard uniaxial expansion EA = K1 sin2θ+K2 sin4θ+⋯, about the hexagonal axis. The anisotropy constants derived from the resonance data agree reasonably well with those measured by Graham1 using static torque methods. The samples used in these experiments are from the same source.2 The demagnetization fields at the surface of the coin-shaped sample are measured directly from the shift in the resonance field of a small chip of the free radical DPPH in intimate contact with the sample surface.3 The corresponding demagnetization factors lie between that calculated by Schlömann4 for a uniformly magnetized right cylinder (an accurate description of our sample shape) and that calculated for an oblate spheroid of the same axial ratio, tending toward the latter at low temperatures. Using the magnetization measurements of Graham (as a function of temperature and applied field) we find that the spectroscopic splitting factor, g, is 2.00±0.02 below 0°C, changing smoothly to 1.94±0.02 at 28°C in the paramagnetic region. This latter values agrees well with those reported by Kip5 and by Popplewell and Tebble.6 The g value at low temperatures, also deduced from the resonance data, gives better (but still not exact) agreement between the directly measured saturation magnetization and that implied by the 8S7/2 ionic state.