Fig. 4. Experimental determination of the skyrmion Hall angle of FeGe.

First, the temperature was set to 268 K (T_C =273 K) and a skyrmion-stabilising magnetic field was applied to reach the skyrmion phase pocket. The resonant elastic X-ray scattering (REXS) pattern in a shows the typical signature of a skyrmion lattice containing several domains, with multiple sets of six-fold symmetric peaks, see ‘Methods’ for details. b In order to assure stable starting conditions without uncontrolled lattice reorientation, the diffraction experiment was repeated after a sufficient waiting period (15 min), showing a virtually identical pattern. c After applying a linear field gradient (I on) for 15 min, the shear force (F) introduced by the field gradient drives the skyrmion lattice to completely reorient along its direction of motion, resulting in single, six-fold symmetric spot pattern. A video of the evolution from a to b to c is provided in the Supplementary Materials (Supplementary Video 1). Owing to its six-fold symmetry, there are three possible directions of motion that result in the same diffraction pattern: v₁ at 55°, v₂ at −5°, and v₃ at −65° (note that the skyrmion Hall angle is restricted to [−90°, 90°]). In order to resolve this ambiguity, the stiffness of the skyrmion lattice was tuned from its soft state just below T_C to a harder lattice at a reduced temperature of 250 K, in which strain can build up. d The final orientation of the skyrmion lattice is generally the same as for the soft lattice shown in (c), however, now the presence of strain leads to a characteristic anisotropic peak broadening (highlighted and magnified, see red ellipse; note that another pair of broadened peaks is masked by the beamstop). The direction of peak broadening is consistent with v₁ and a Hall angle of 55°, as shown in the simulated REXS pattern in the inset in the top right for which the direction of the shear is 55^∘ away from the direction of the applied force.