Strain Induced Vortex Core Switching in Planar Magnetostrictive Nanostructures

The dynamics of magnetic vortex cores is of great interest because the gyrotropic mode has applications in spin torque driven magnetic microwave oscillators, and also provides a means to flip the direction of the core for use in magnetic storage devices. Here, we propose a new means of stimulating magnetization reversal of the vortex core by applying a time-varying strain gradient to planar structures of the magnetostrictive material ${\mathrm{Fe}}_{\mathbf{8}\mathbf{1}}{\mathrm{Ga}}_{\mathbf{1}\mathbf{9}}$ (Galfenol), coupled to an underlying piezoelectric layer. Using micromagnetic simulations we have shown that the vortex core state can be deterministically reversed by electric field control of the time-dependent strain-induced anisotropy.

Figure 1

Average magnetization fluctuation $\delta m_z$ as a function of the driving frequency of the piezoelectric layer and applied field. (a) Bias field along [100] and (b) bias $\text{field}=0.3\mathrm{T}$.

Figure 2

The effect of a time and spatially varying strain on the dynamics of a magnetic vortex core. (a) Differences between using a time-varying magnetic field (upper right figure) and the case of no spatial gradient in the time-varying strain-induced anisotropy (lower right figure). (b) Dynamics of the $x$ position of the vortex core as a function of time and strain gradient during the first 25 ns. (c) Steady state radius of the oscillations as a function of strain gradient. (d) Steady state radius of the orbit of the vortex core as a function of the driving frequency of the PE. (e) Schematic of the device concept.

Figure 3

The result of a combination of a time-varying Zeeman field and time and spatially varying strain gradient. (a) The maximum vortex core displacement, with the inclusion of the time-varying Zeeman term of amplitude 0.2 mT, occurs at 270°. (b) The effect of the magnitude of the time-varying Zeeman field when the phase shift between the two driving terms is $+90°$. The black solid line represents a fit to the modulus of a linear line and the point at which it goes to zero represents a balancing of the Zeeman and time-varying strain anisotropies, occurring at around 0.14 mT.

Figure 4

Snapshots of the vortex core motion during switching by a time-varying strain. At 8.075 ns the vortex core motion is counterclockwise as indicated by the green arrow. At 8.670 ns the antivortex-vortex pair, which has arisen due to the driving force, annihilates with the expected ejection of spin waves from the core. After the core switches the motion of the vortex is in the opposite direction and the switching is complete. The color of the macrospins corresponds to the $z$ component of the magnetization. The full time sequence is available in the Supplemental Material [21].