In a microdevice made of a thin (~100 nm) plate of the chiral helimagnet FeGe, a dc current density of order 102 A cm−210^2\,\mathrm{A\,cm^{-2}} — several orders of magnitude below what conventional spin-transfer torque needs to move domain walls — first rotates and then continuously translates a two-dimensional skyrmion crystal near room temperature (Yu et al., Nat. Commun. 3, 988 (2012)). The observation left the physics of this ultralow-current flow undetermined: the dominant motive forces behind the skyrmion-crystal rotation were not identified, the pinning landscape was not quantified, the critical current's temperature dependence was opposite to that of bulk MnSi without explanation, and no drift velocity was measured. The open problem is: identify which microscopic forces (spin-transfer torque, Magnus/skyrmion Hall force, spin-orbit-mediated chiral lattice torque, boundary- and defect-mediated lattice deformation) drive the observed rotation and sliding; determine how the sample's pinning landscape sets local depinning thresholds and the opposite Jc(T)J_c(T) trend relative to bulk MnSi; measure the drift velocity as a function of current density in the ultralow-current regime; and construct a predictive model connecting material and defect parameters to the measured JcJ_c.

Background

A magnetic skyrmion is a nanometer-scale, particle-like whirl of the magnetization that is topologically protected: its spin texture wraps the unit sphere an integer number of times and so cannot be unwound by smooth deformations. In chiral magnets such as MnSi and FeGe (both with the non-centrosymmetric cubic B20 structure), the absence of inversion symmetry combined with strong spin-orbit coupling produces the Dzyaloshinskii-Moriya interaction (DMI), an exchange term that favors slowly twisting spin structures. Below the helimagnetic ordering temperature (Tc≈278 KT_c\approx278\,\mathrm{K} for bulk FeGe, ∼275 K\sim275\,\mathrm{K} in the thin-plate device) these materials form helical spin spirals, and under a moderate magnetic field the spirals condense into a triangular skyrmion crystal (lattice constant ≈70 nm\approx70\,\mathrm{nm} in a ∼100 nm\sim100\,\mathrm{nm}-thick FeGe plate).

In 2010 Jonietz et al. (Science 330, 1648 (2010)) showed by neutron scattering that in bulk MnSi a current density of only ∼102 A cm−2\sim10^2\,\mathrm{A\,cm^{-2}} — five orders of magnitude below the 107 ⁣− ⁣108 A cm−210^{7}\!-\!10^{8}\,\mathrm{A\,cm^{-2}} typically required to move a ferromagnetic domain wall — rotates the skyrmion lattice; they attributed the rotation to the macroscopic temperature gradient along the current, which combines drag and Magnus forces. On the theory side, Everschor et al. (Phys. Rev. B 84, 064401 (2011)) showed that spin-orbit coupling generically produces rotational torques on a skyrmion lattice driven by current.

Yu et al. (Nat. Commun. 3, 988 (2012)) studied a microdevice patterned from a thin FeGe plate by Lorentz transmission electron microscopy (a TEM mode that images magnetic domains through the deflection of electrons by the sample's in-plane magnetization). Near room temperature (250-270 K) in a 150 mT150\,\mathrm{mT} field, a dc current first caused intermittent rotations of the skyrmion crystal and, above a critical current Jc∼102 A cm−2J_c\sim10^2\,\mathrm{A\,cm^{-2}}, continuous flow so fast that the lattice blurred beyond the 250 ms250\,\mathrm{ms} frame exposure. Their discussion enumerated the candidate motive forces — spin-transfer torque (drag from the spin polarization of the current), the Magnus force associated with the skyrmion Hall effect (the transverse deflection of a moving skyrmion, the counter-action to the topological Hall effect experienced by the conduction electrons), and a rotational force — in competition with pinning by impurities, lattice imperfections, and grain boundaries. The thermal-gradient mechanism of bulk MnSi was judged implausible over their ∼100\sim100-nm-thick view area; instead they suggested spin-orbit-mediated coupling between the skyrmion crystal and the chemical lattice, or deformation of the skyrmion lattice by sample boundaries and dislocations, and stated that the origin of the rotation 'remains elusive at the moment'. They also found that JcJ_c decreases with increasing temperature toward the paramagnetic transition — opposite to bulk MnSi, tentatively ascribed to the difference between two-dimensional and three-dimensional pinning — and did not measure any drift velocity.

Later work illuminated pieces of this physics without settling it: Iwasaki, Mochizuki and Nagaosa (Nat. Commun. 4, 1463 (2013)) derived, from Landau-Lifshitz-Gilbert simulations and the Thiele equation (the collective-coordinate equation of motion for a rigid magnetic texture), a universal current-velocity relation and explained the small JcJ_c by the Magnus force and the skyrmion's flexible shape, which lets it flow around pinning centers; Jiang et al. and Litzius et al. (Nature Physics 13, 162 and 170 (2017)) directly imaged the skyrmion Hall effect of isolated skyrmions in ultrathin multilayers; Luo et al. (Commun. Mater. 1 (2020)) found thermally-activated skyrmion-lattice creep in bulk MnSi well below JcJ_c; Okuyama et al. (Commun. Phys. 2 (2019)) observed inhomogeneous, edge-friction-driven lattice rotation under current in bulk MnSi; and Jin et al. (Nano Lett. 24 (2024)) demonstrated a chiral lattice torque that rotates skyrmion crystallites in the insulating magnet Cu2_2OSeO3_3 under a temperature gradient. What these results mean for the original FeGe thin-plate device is precisely the unresolved question.

Problem Statement

Establish the microscopic mechanism and the quantitative description of current-driven skyrmion-crystal flow at ultralow current densities in thin-plate FeGe microdevices near room temperature. Concretely, in a device as in Yu et al. (Nat. Commun. 3, 988 (2012)) — a thin (∼100 nm\sim100\,\mathrm{nm}) FeGe plate hosting a two-dimensional skyrmion crystal (lattice constant ≈70 nm\approx70\,\mathrm{nm}) at 250-270 K in a ∼150\sim150-mT field, driven by dc current of order Jc∼102 A cm−2J_c\sim10^2\,\mathrm{A\,cm^{-2}} — determine:

  1. Which microscopic force or combination of forces — spin-transfer torque, the Magnus (skyrmion Hall) force, the spin-orbit-mediated chiral lattice torque coupling the skyrmion crystal to the chemical lattice, or lattice deformation imposed by sample boundaries and dislocations — dominates the observed rotation of the skyrmion crystal below and at the onset of continuous flow, and how this assignment can be tested experimentally.

  2. How the pinning landscape (impurities, lattice imperfections, grain boundaries) quantitatively sets the local depinning thresholds, how those thresholds depend on skyrmion dimensionality and topology (two-dimensional thin-plate versus three-dimensional bulk lattices), and specifically why JcJ_c decreases with increasing temperature in the thin FeGe plate while the opposite trend is observed in bulk MnSi.

  3. The drift velocity of the skyrmion crystal as a function of current density in the ultralow-current sliding regime, together with the dominant microscopic dissipation mechanism, and a predictive model that connects material parameters (Dzyaloshinskii-Moriya interaction strength, exchange stiffness, anisotropy) and defect statistics to the measured JcJ_c and velocity in thin microdevices.

These three questions are inseparable aspects of one objective — the mechanistic and quantitative account of ultralow-current skyrmion-crystal dynamics in thin-plate FeGe: the force assignment (1) requires the pinning and dissipation understanding (2, 3) to explain why the threshold is so low and temperature-dependent, and the predictive model (3) is validated by the mechanism and velocity data (1, 2).

References

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