Spin Waves in Nickel Nanorings of Large Aspect Ratio

The spin dynamics of high-aspect-ratio nickel nanorings in a longitudinal magnetic field have been investigated by Brillouin spectroscopy and the results are compared with a macroscopic theory and three-dimensional micromagnetic simulations. Good agreement is found between the measured and calculated magnetic field dependence of the spin wave frequency. Simulations show that as the field decreases from saturation, the rings switch from a “bamboo” to a novel “twisted bamboo” state at a certain critical field, and predict a corresponding dip in the dependence of the spin wave frequency on the magnetic field.

Figure 1

Scanning electron microscope micrograph of the hexagonal array of the high-aspect-ratio nickel nanorings.

Figure 2

Simulated magnetization distributions ($H_0=5\mathrm{mT}$) for a nickel nanoring in the twisted bamboo phase. (a) A cross section containing the ring axis, and (b) top, (c) middle, and (d) bottom cross sections normal to the ring axis (viewed along the $-{\mathit{H}}_0$ direction).

Figure 3

Magnetic field dependence of the frequencies of spin waves in a nickel nanoring. Measured frequencies are represented by closed circles, while calculated ones by open circles (micromagnetic simulations) and a solid curve (analytical equation $\omega =\gamma [H_t\{4\pi M_S+H_t\}{]}^{1/2}$).

Figure 4

Brillouin spectrum of a nickel nanoring array in a 0.8 T magnetic field applied parallel to the symmetry axis of the rings. Experimental data are denoted by dots. The spectrum is fitted with a Lorentzian function (dotted curve) and a background (dashed curve), and the resulting fitted spectrum is displayed as a solid curve. Left inset: Simulated time dependence of the transverse magnetization component of the spin wave at $H_0=0.8\mathrm{T}$. Right inset: Corresponding spin wave frequency obtained via a Fourier transform.

Figure 5

Calculated Zeeman, demagnetization, and exchange contributions to the total energy of a nickel nanoring as a function of longitudinally applied magnetic field.