Micromagnetic investigation of resonance frequencies in ferromagnetic particles

A micromagnetics study was performed to examine the dynamic magnetic susceptibility of isolated ferromagnetic nanoparticles. Cobalt and NiFe nanoparticles of dimensions L×30nm×15nm, and a Co nanoparticle of dimensions L×30nm×30nm were simulated. When L was less than or equal to one of the other dimensions, only one resonance peak was seen, with a frequency predicted using the Kittel equation and demagnetization factors calculated for a rectangular prism. However, when L was increased, a small second peak appeared with a frequency corresponding to the resonance frequency of an infinitely long needle. Simultaneously, the frequency of the first peak was shifted from the Kittel-predicted value. Additional increases in L did not change the two peak frequencies significantly but the strength of the first peak approached zero while the strength of the second peak approached a nonzero constant. At sufficiently large L, the second peak frequency converged to that of the Kittel prediction. A visual study of magnetization precession was then performed. For cubelike particles, the magnetization precession occurred uniformly throughout the particle, with the precession frequency matching the resonance frequency found in the susceptibility study. However, as L was increased, a decoupling in precession was observed. The magnetic moments in the interior volume of the particle precessed approximately uniformly at the frequency of the needlelike peak. A block of spins at each end of the particle precessed at a slower frequency corresponding to the first peak. An oscillator model was used to describe the decoupling and analyze the magnetization precession for large L.