Observation of Defect-Assisted Magnetic Vortex Core Reversal at Ultralow Critical Velocity

The stability of structures with nontrivial topology is a subject of great interest, both from fundamental and technological perspectives. The topology of a magnetic vortex, for example, results in high stability of the vortex core polarity, which is attractive for applications. This high stability, however, greatly impedes the required deterministic polarity switching, which is typically only achieved with large magnetic fields or strong dynamic driving. Here, we show that the interaction between the vortex core and manufactured nanoscale defects in the magnetic material lowers the required driving strength for core polarity reversal by more than an order of magnitude. We excite vortex dynamics in thin permalloy disks, and map the two-dimensional (2D) vortex core trajectory using 3D time-resolved Kerr microscopy. In pristine samples, we observe normal gyrotropic motion of the vortex core. After laser-induced generation of defects, however, we observe repeated vortex core reversal at much-reduced driving strength. Micromagnetic simulations reveal how local reduction of exchange coupling and saturation magnetization can create vortex core reversal sites for deterministic vortex core switching.

Figure 1

Samples and the magnetic vortex. (a) A simulated ferromagnetic vortex state with the core polarity up. (b) Schematic of the sample; a permalloy disk (brown) is capped by a gold coplanar waveguide. A microscope objective is used to focus the laser light on the disks.

Figure 2

Magnetic vortex core reversal by defects. (a),(b) Gyrations of the VC before and after prolonged pulsed laser exposure. The color bar $\mathrm{\Delta }t$ indicates the time relative to the beginning of the pulse. Each red arrow represents a VC reversal. The VC velocity is shown by the values under each red arrow, which is an average velocity of the VC (m/s) on each arc before reversal, with an error of approximately $6\mathrm{m/s}$. (c),(d) The VC equilibrium position $y_0$ versus $B_x$ swept up (blue) and down (red) at three different values of ${\mathbf{x}}_0$ before and after the laser exposure, respectively.

Figure 3

From top to bottom: 2D TR MOKE of magnetization dynamics as we shift the VC from the left region towards the center. In all cases except the inset in the bottom panel we use a 3.2 mT amplitude, 35 ns magnetic field pulse. We use fixed biased fields ($B_0$) along $+\hat{x}$ to shift the VC from the left (top panel) towards the center (bottom panel). Color bars $\mathrm{\Delta }t$ indicate the time relative to the beginning of the pulse. Inset in the bottom panel shows the gyrations of the VC near the center excited by a smaller magnetic pulse of 1.6 mT. VC reversals are indicated by red arrows.

Figure 4

Region of stochastic switching (sample 1). The left panel demonstrates the 2D gyrations of the VC at $B_0=0.6\mathrm{mT}$. The $x$ and $y$ components are shown separately versus time on the right. To excite these gyrations, a 3.2 mT amplitude and 35 ns magnetic pulse is used. Color bar $\mathrm{\Delta }t$ indicates the time relative to the beginning of the pulse.

Figure 5

Single-shot switching. (a) Normal gyrations on disk 2 before the prolonged pulsed laser exposure. (b) Schematic of the procedure used to switch and test the polarity. Red arrow indicates the reversal spot appearing after pulsed laser exposure. (c),(d) Examples of VC dynamics used to respectively measure core polarities up and down after a single-shot switch. (e) Core polarities before and after each switching pulse. Green check marks (red cross) above each core polarity illustrate the successful (failed) switches. The color bars $\mathrm{\Delta }t$ show the time relative to the beginning of the 35 ns pulse.

Figure 6

VC equilibrium position $y_0$ versus $B_x$ swept up and down. Pinning and hysteresis occur as the VC traverses a 30-nm diameter region where the exchange coupling is reduced to 10 pJ/m (black squares) and to 2.5 pJ/m (red triangles) from the nominal value of 13 pJ/mm. Red (black) arrows show the direction of the field sweep for red (black) hysteresis.

Figure 7

Simulated VC trajectories. (a) VC gyrotropic trajectory with a defect strip from $x=0$ to 100 nm where $A$ is reduced to 2 from 10 pJ/m. Points are separated by 0.1 ns. Points within the defect region are circled in red. (b) Approximate VC speed versus time calculated from (a). Points where the VC is within the defect strip are circled in red. VC reversals are indicated by red arrows. Inset shows the VC speed near the first reversal in panel (a) based on simulations with higher temporal resolution. The VC speed oscillates with an average of about 200 m/s and a lowest speed approximately 120 m/s before the VC enters the defect region. (c) Same as (a), but showing a smaller amplitude trajectory with the addition of a $10\times 10{\mathrm{nm}}^2$ nonmagnetic region, indicated by the black square; (d) is same as (b), but for the trajectory shown in (c). Inset shows the approximate VC speed based on higher temporal resolution before the core is absorbed by the nonmagnetic defect in panel (d). Within the defect region with lower $A$, the VC speed is reduced to about 60 m/s before the VC accelerates as it approaches the nonmagnetic defect.

Figure 8

Snapshots of VC reversal mechanisms. (a) VC reversal at the boundary of the reduced-$A$ strip at $x>0$. Black dots indicate the path of the VC at time steps of 25 ps, starting from $x\approx -100\mathrm{nm}$. Dots are not shown when no single well-defined VC exists. (i) Negative-polarity VC is just entering the defect strip. (ii) Red wake has deepened, and started to form a positive-polarity vortex-antivortex pair. (iii) Positive polarity VC has formed outside the defect strip, with positive-polarity antivortex adjacent to the original negative-polarity VC. (iv) Original VC has annihilated with antivortex, and new positive-polarity VC is traveling to the left. (b) VC reversal at a nonmagnetic region (white square). Here black dots are separated by 50 ps, indicating lower VC velocity. (i) The VC is traveling CW with a velocity too low to have reversed upon entering the reduced-$A$ region. (ii) The VC begins to be trapped by the nonmagnetic defect. (iii) The VC itself has annihilated on the defect, and the surrounding out-of-plane magnetization has switched to the positive direction. (iv) The VC has reformed with positive polarity and leaves the defect on a CCW trajectory.