Control of Gilbert damping using magnetic metamaterials

We studied, from a theoretical standpoint, the Landau-Lifshitz-Gilbert equation of magnetic metamaterials consisting of magnetic nanoparticles. The dynamics of the metamaterials magnetization was numerically investigated in order to elucidate the mechanism of Gilbert damping. Our results revealed that the interacting dipole field synchronized to the magnetization precession causes the variation in the effective Gilbert damping factor. Nevertheless, we found that a metamaterial with a specific structure has almost the identical effective Gilbert damping factor, although the interacting dipole field increases. This work demonstrates that the effective Gilbert damping factor can be analytically predicted and designed using the structure factors in magnetic metamaterials, opening an avenue to a new relationship between metamaterials and spintronics.

Figure 1

Illustrations of magnetic metamaterials: (a) Model 1, (b) Model 2, and (c) Model 3. A $9\times 9\times 5$ simple cubic lattice with the lattice spacing $r_0$ is considered. Model 1 consists of single-sized particles with 8 nm in diameter, which correspond to the magnetic moment $m=1.3\times {10}^{-16}$ emu. Contrastingly, randomness of the magnetization magnitude was introduced in Models 2 and 3. These models are composed of dual-sized particles, in which the large and small particles respectively correspond to the magnetic moment $m=2.6\times {10}^{-16}$ emu and $m=1.3\times {10}^{-16}$ emu. In Model 2, the large and small particles are alternately arranged just similar to an NaCl-type structure. On the other hand, in Model 3, the large and small particles randomly occupy a lattice point.

Figure 2

Line profile of the susceptibility $\chi$ in field sweep with (a) Model 2 and (b) Model 3. Lattice constant $r_0$ is set to be $r_0=10$ nm (filled circles and filled triangles), 12 nm (open triangles), 15 nm (open circles and filled squares) and 20 nm (crosses and open squares).

Figure 3

Comparison between Model 2 (green line and blue circles) and Model 3 (pink line and red triangles) when $r_0=10$. Effective Gilbert damping factor ${\alpha }^{\prime }$ is obtained from the fitting curves.