Magnetomechanical coupling and ferromagnetic resonance in magnetic nanoparticles

We address the theory of the coupled lattice and magnetization dynamics of freely suspended single-domain nanoparticles. Magnetic anisotropy generates low-frequency satellite peaks in the microwave absorption spectrum and a blueshift of the ferromagnetic resonance (FMR) frequency. The low-frequency resonances are very sharp with maxima exceeding that of the FMR, because their magnetic and mechanical precessions are locked, thereby suppressing the effective Gilbert damping. Magnetic nanoparticles can operate as nearly ideal motors that convert electromagnetic into mechanical energy. The Barnett damping term is essential for obtaining physically meaningful results.

Figure 1

(a) Laboratory frame $(x,y,z)$ and (moving) body frame $(x_b,y_b,z_b)$ of a nanomagnet with principal axis $\mathbf{n}$ along the $z_b$ axis. The directions of $\mathbf{n}$ and magnetization $\mathbf{m}$ are shown for (b) oblate and (c) prolate spheroids with dipolar magnetic anisotropy.

Figure 2

Low- and high-frequency resonances in the FMR spectrum of an Fe nanosphere of $2\mathrm{nm}$ diameter in a static magnetic field of $0.65\mathrm{T}$ with Gilbert damping constant $\alpha =0.01$; quality factor $Q_f=\omega /\left(2\eta \right)$.

Figure 3

Low-frequency magnetomechanical modes ${\omega }_{l_1}$ and ${\omega }_{l_2}$ of an Fe nanosphere of $2\mathrm{nm}$ diameter.

Figure 4

FMR spectrum of an Fe disk with $15\mathrm{nm}$ diameter and $2\mathrm{nm}$ thickness in a static magnetic field of $0.25\mathrm{T}$ with Gilbert damping constant $\alpha =0.01$.

Figure 5

Real and imaginary parts of the magnetic susceptibility tensor $\chi \left(\omega \right)$ of the low-frequency modes ${\omega }_{l_1}$ and ${\omega }_{l_2}$ for an Fe nanosphere of $2\mathrm{nm}$ diameter with Gilbert damping $\alpha =0.01$.