Magnetization reversal via internal spin waves in magnetic nanoparticles

By numerically solving the equations of motion for atomic spins we show that internal spin-wave processes in large enough magnetic particles, initially in unstable states, lead to complete magnetization reversal and thermalization. The particle’s magnetization $m$ strongly decreases in the middle of reversal and then recovers. The closer is the initial orientation of $\mathbf{m}$ to the energy minimum, the slower is the relaxation toward it and the smaller is the decrease in $m$ in the course of relaxation. We identify two main scenarios, exponential and linear spin-wave instabilities. For the latter, the longitudinal and transverse relaxation rates have been obtained analytically. Orientation dependence of these rates leads to a nonexponential relaxation of the particle’s magnetization at long times.

Figure 1

(Color online) Magnetization switching out of the disappearing metastable state via exponential spin-wave instability in a particle of a box shape with uniaxial anisotropy and oblique magnetic field.

Figure 2

(Color online) Magnetization switching out of the maximal-energy state via exponential spin-wave instability in a spherical particle with uniaxial anisotropy and transverse field. Switching occurs via longitudinal relaxation without rotation. (b) shows the short-time magnification. The “Plateau” at $t\lesssim 2000$ describes the initial exponential increase in $1-m$.

Figure 3

(Color online) Magnetization switching via exponential spin-wave instability in a box-shaped particle with uniaxial anisotropy and transverse field. (a) The particle is prepared with all spins opposite to the magnetic field (the maximal-energy state). Again the longitudinal relaxation is the main mechanism of switching. (b) The particle is prepared with all spins perpendicular to the magnetic field.

Figure 4

(Color online) Magnetization switching via linear spin-wave instability in a particle with random anisotropy. (a) Particle prepared with all spins antiparallel to the magnetic field. The small-$t$ asymptote of Eq. (41) is shown by the dashed line. For this initial condition, switching occurs predominantly via changing the magnetization length $m$. (b) Particle prepared with all spins perpendicular to the magnetic field.

Figure 5

(Color online) Time dependence of the magnetization magnitude $m$ for a cubic particle of $5\times 5\times 5=125$ spins with random anisotropy. For the resonant value of the field $h$ spin waves are generated out of the false vacuum (magnetization opposite to the field) but they cannot be converted into other modes so that the process is bottlenecked. For the nonresonant value of $h$ spin waves are practically not generated.

Figure 6

(Color online) Time dependence of the magnetization component $m_z$ for the box-shaped particle of $5\times 7\times 10=350$ spins with random anisotropy, initially oriented opposite to the field $h/J=0.382$.

Figure 7

Spin configurations at different times for the box-shaped particle of $5\times 7\times 10=350$ with random anisotropy in the middle of the $x$ plane $\left(i_x=3\right)$.

Figure 8

Fourier spectra at different times for the box-shaped particle of $5\times 7\times 10=350$ spins with random anisotropy, initially oriented opposite to the field $h/J=0.382$. (a) Initial stage of the instability: growth of the first-generation peak and the secondary peak. (b) Spread of the excitation over all modes and thermalization.