Magnetic dimensional resonances inFe3O4spheres

A series of new magnetic resonances were observed in magnetite (${\mathrm{Fe}}_3$ ${\mathrm{O}}_4$) spheres in microwave magnetotransmission experiments, as follows. Microwaves (32–37 GHz) traveling in a cylindrical waveguide were incident on a small magnetite sphere suspended at the center of the guide. The waveguide passed axially through a superconducting solenoid, whose field could be varied from 0 to 6 T. The waves were circularly polarized in the plane perpendicular to the applied field. The experiments were performed at 5 K. The transmitted microwave power was measured as a function of the field. In addition to ferromagnetic resonances, new size-dependent resonances were observed, and were studied as a function of sphere diameter and microwave frequency. The behavior of the new resonances cannot be explained in terms of ordinary Walker modes. The dependence of these resonances on frequency and size is quite dramatic, showing a linear relation between the variables ($B_0$-$B_R$ ${)}^{\mathrm{-}1}$ and (ωd${)}^{\mathrm{-}2}$, where $B_0$ is the field at which the resonance occurs, $B_R$ is the ferromagnetic resonance field for a given microwave frequency ω, and d is the sphere diameter. The strength of the observed effect holds promise for application in nonreciprocal microwave devices.