Direct Observation of Zhang-Li Torque Expansion of Magnetic Droplet Solitons

Magnetic droplets are nontopological dynamical solitons that can be nucleated in nanocontact based spin torque nano-oscillators (STNOs) with perpendicular magnetic anisotropy free layers. While theory predicts that the droplet should be of the same size as the nanocontact, its inherent drift instability has thwarted attempts at observing it directly using microscopy techniques. Here, we demonstrate highly stable magnetic droplets in all-perpendicular STNOs and present the first detailed droplet images using scanning transmission X-ray microscopy. In contrast to theoretical predictions, we find that the droplet diameter is about twice as large as the nanocontact. By extending the original droplet theory to properly account for the lateral current spread underneath the nanocontact, we show that the large discrepancy primarily arises from current-in-plane Zhang-Li torque adding an outward pressure on the droplet perimeter. Electrical measurements on droplets nucleated using a reversed current in the antiparallel state corroborate this picture.

Figure 1

(a) Schematic of an all-perpendicular STNO. The current ($I_{\mathrm{d}\mathrm{c}}$) flows through the NC fabricated on top of the stack. The magnetic field $H$ is applied at an angle ${\phi }_H$ from the plane. (b) Full (black circles) and minor (red and blue dots) out-of-plane hysteresis loops of the unpatterned material stack showing decoupled free and fixed layers. (c) Full (black circles) and minor loop (red dots) low-current ($-0.6\mathrm{mA}$) magnetoresistance (MR) measurements of the STNO showing $\mathrm{MR}\sim 1\%$ and some process induced interlayer coupling of about–0.03 T.

Figure 2

(a) Change in resistance ($\mathrm{\Delta }R$) of a 100 nm NC vs $I_{\mathrm{d}\mathrm{c}}$ showing droplet nucleation at a field-dependent negative current on a parabolic Joule heating background. Inset: same data after background subtraction. The color plot is the power spectral density (PSD) up to 0.4 GHz in a field of 0.35 T, showing how the step in $\mathrm{\Delta }R$ is accompanied by the onset of low-frequency microwave noise. (b) $\mathrm{\Delta }R$ vs field at different negative currents for the same NC as in (a). At a small negative $I_{\mathrm{d}\mathrm{c}}$ ($-1\mathrm{mA}$), the state switches directly from AP to P at about 0.25 T. For larger negative $I_{\mathrm{d}\mathrm{c}}$, the AP state first switches to an intermediate resistance consistent with a droplet before gradually switching to the P state. The droplet is again accompanied by microwave noise. Inset: PSD in a field tilted 30° from the plane showing both the precession frequency and much broader and stronger microwave noise. (c) Field-swept $\mathrm{\Delta }R$ measurements at different negative $I_{\mathrm{d}\mathrm{c}}$ for NC diameters ranging from 50 to 150 nm, plotted on a color scale defined by the P and AP states. The droplet state is seen as an intermediate resistance state. The dashed red line marks the linear droplet nucleation boundary. In the bottom of (c), nucleation boundary slope vs NC area together with a linear fit (dashed line).

Figure 3

(a) Photograph of three STNOs on a SiN membrane. (b), (c) Spatial STXM maps of the $m_z$ component of the Ni (b) and Co (c) moments of the free layer, where the green circle outlines the nanocontact. Both STXM maps are obtained at–15 mA and in 0.18 T. Both maps reveal a fully reversed droplet with a diameter of about 160 nm. (d) Cartoon of the STNO with the current (red) flowing only in the perpendicular direction underneath the nanocontact (yellow). (e) Plots of the perpendicular (green) and lateral (red) current vs $x$ coordinate. (f) Micromagnetic simulation of the resulting droplet. (g)–(i) Same as in (d)–(f) but with a realistic lateral current spread. The micromagnetic simulation includes the realistic spatial profile of the perpendicular current density but ignores the Zhang-Li torque from the lateral current. (j)–(l) Same as in (g)–(i) with the Zhang-Li torque included. (m)–(o) Same for a droplet in the AP state, including both the current spread and the Zhang-Li torque.

Figure 4

The red data show how a droplet is nucleated from an AP state at $+10\mathrm{mA}$. The blue data show an ordinary droplet nucleated from the P state by a negative current. The resistance step associated with each droplet is highlighted by the red (AP) and blue (P) arrows, respectively. The insets show the corresponding magnetic state and the directions of the current and the pressure from the Zhang-Li torque.