dc Detection of Spin Resonance in Thin Metallic Films
Authors: Juretschke H. J. 
Published: April 2005

Ohm's law in strongly magnetic, though not necessarily ferromagnetic materials, has leading terms in the presence of a magnetization M and an induction B of the form E=ρJ−R0J×B−R1J×M+Δρ/M2(J·M)M+…,which represent the ordinary and extraordinary Hall effects and a magnetoresistance. The M-dependent terms, in particular, describe interactions due to polarized scattering centers and to the left-right asymmetry of polarized mobile charge carriers.1
An electromagnetic wave interacting with such a material will, under resonance conditions, cause a precession of M, while at the same time inducing an eddy current density J. According to Eq. (1), the presence of two such terms at microwave frequencies introduces local dc electric fields related to the time average of the various products. These fields will be largest near spin resonance. Such fields are observable only in films thin compared to the electromagnetic skin depth,2 and they may be used either to study spin resonance in very thin films or to determine their transport properties at microwave frequencies. In particular, for a configuration in which the static field is in the film plane and the electromagnetic wave is at normal incidence 〈J×B〉 has no contribution in the film plane; such an experiment allows a separation of R0 and R1 even in materials which show no magnetic saturation.
The detailed electromagnetic theory of this configuration has been worked out3 for an isotropic material and experiments have been carried out on nickel films to test the various features of the theory, and to determine the usefulness of the method in studying high-frequency magnetic and conduction properties in thin films.4 The experimental arrangement consists of placing the sample close to a wave guide or cavity wall, but insulated from it, and measuring the dc voltages, either steady or modulated, induced by the microwaves. The major precaution necessary for a quantitative study is that the microwave field pattern within the film must be well known, so that sample geometry, its electrical boundary conditions, and placement of detection wires is very critical.
The experimental results reproduce all the qualitative features of the theory, with regard to sample thickness, local field configuration, power, and magnetic field orientation. The agreement with the theory is better than reported by Seavey5 for Permalloy films, most likely because of differences in local field configuration, and by Heinz and Silber6 for a ferrite, whose experiment did not permit separation of all parameters. A quantitative analysis of the data7 gives consistent values of the magnetic resonance parameters g, M0, and τ. It also requires that the films be described at microwave frequencies by a complex conductivity which is generally smaller than at low frequencies. Within the over-all accuracy of the analysis—about 15%—the magnetoresistance Δρ is the same as at low frequencies, and the increase of R1 is related to that of ρ, so that no dispersion of these constants is observed.
The same method has been applied to thin films of gadolinium, and while the signals are much smaller, the dc effects clearly persist in the paramagnetic region above room temperature.8 Quantitative analysis of the data has been impeded because the power levels necessary to observe the signals cause considerable heating of the sample. Since both the magnetic and galvanomagnetic properties of gadolinium are very temperature sensitive, a careful determination of the local temperature within the film during the microsecond long pulse of microwaves is required. The data obtained so far indicate that the g value of our gadolinium films is higher than in bulk, and that the extraordinary Hall constant appears to be larger than in bulk material.