Effect Of Ferromagnetic Material Research Articles

Ferromagnetic Resonance in Yttrium Iron Garnet at Low Frequencies

Single crystals of yttrium iron garnet (YIG) exhibit the narrowest resonant line of all known ferromagnetic materials, being as low as 2.3 oe for the full width at half height for polished spheres at 9300 mc. Ferromagnetic resonance on polished YIG disks was observed at frequencies as low as 44 mc, for an applied dc field of 1000 oe. Conversely, resonance was observed for fields as low as 300 oe, for a frequency of 2000 mc. Nonlinear effects in ferromagnetic materials can be evidenced by the excitation of unstable spin wave modes, such as were discovered at x band by Bloembergen and his colleagues. In their case the dc fields required for this subsidiary resonance were approximately one half that required for resonance of uniform precession. When measurements are made on a sphere at a frequency low enough so that Hres<8πMs/3, Suhl's theory shows that the dc field required for the minimum threshold of the subsidiary resonance is identical with that required for resonance of the uniform precession. In this case the critical rf fields required are particularly low being given in terms of the line width to an order of magnitude as hcrit=ΔH2/4πMs. Measurements have been made of hcrit, for the subsidiary resonance as a function of frequency for polished single crystal spheres of YIG. Based on a 4πMs of 1725, the frequency below which coincidence of the uniform precession and subsidiary resonances occur, is 3220 mc. Below 1610 mc the dc fields for resonance are insufficient to saturate the sphere and domains are formed. Values are given for hcrit, spin-wave angle θ, and spin-wave number k for frequencies of 1610 to 3220 mc. At 2200 mc a min in hcrit occurs. At this frequency hcrit=2.0 millioersteds, the power incident on the cavity is 20 microwatts and the power absorbed by the sample is of the order of a microwatt. The experimental results are discussed in terms of Suhl's theory.

Hall Effect in Ferromagnetics

Both the unusually large magnitude and strong temperature dependence of the extraordinary Hall effect in ferromagnetic materials can be understood as effects of the spin-orbit interaction of polarized conduction electrons. It is shown that the interband matrix elements of the applied electric potential energy combine with the spin-orbit perturbation to give a current perpendicular to both the field and the magnetization. Since the net effect of the spin-orbit interaction is proportional to the extent to which the electron spins are aligned, this current is proportional to the magnetization. The magnitude of the Hall constant is equal to the square of the ordinary resistivity multiplied by functions that are not very sensitive to temperature and impurity content. The experimental results behave in such a way also.