Possible skyrmion-lattice ground state in the $B20$ chiral-lattice magnet MnGe as seen via small-angle neutron scattering

We have investigated the magnetic structure in a polycrystalline sample of the $B20$-type MnGe by means of small-angle neutron scattering. On the projected diffraction plane normal to the incoming neutron beam, a Debye-ring-like pattern appears due to the random orientation of the spin helix $q$ vectors ($\parallel \langle 100\rangle$). When an external magnetic field is applied normal to the incoming neutron beam, an intense peak with wave vector ($q$) perpendicular to the applied magnetic field is observed as the hallmark of the formation of a skyrmion lattice with a multiple-$q$ helix in a wide temperature-magnetic-field region. This scattering intensity remains even after removing the magnetic field, which indicates that a skyrmion lattice is stabilized as the ground state. A different form of skyrmion lattice, either square or cubic, is proposed, which is also shown to be in good agreement with previous high-angle neutron diffraction results. Calculations based on such structures also describe the magnetic-field profile of the topological Hall resistivity.

Figure 1

(a) Crystal structure of $B20$-type MnGe. (b) A contour map of magnetization normalized by its value at 14 T at every temperature. The black circles indicate the temperature variation of the critical field, at which the spin-collinear (ferromagnetic) state is realized. (c) SANS setup used in the present study. The powdered MnGe sample is put into a single-crystalline silicon cell. The magnetic field is applied perpendicular to the incident neutron beam.

Figure 2

(a)–(f) SANS patterns at zero magnetic field during zero-magnetic-field cooling (ZFC). (g) The angle-averaged SANS intensity during ZFC as a function of wave vector $q$. (h) Temperature dependence of the magnetic modulation vector $q$ (open circles) as measured in the present SANS study, compared with the data from the high-angle neutron diffraction study taken from Ref. 18 (solid circles).

Figure 3

Variation of SANS patterns with magnetic field ($H$) at 30 K. The magnitude of the applied magnetic field changes from (a) 0 T to (e) 9.9 T and back to (h) 0 T in the sequential order indicated by thick arrows. Three typical intensities are clearly observed in panel (b): (i) crescent-shaped diffractions parallel to the field (diffractions 1 and 2); (ii) a local maximal intensity observed perpendicular to the field (diffraction 3), which indicates the formation of a skyrmion lattice; (iii) a diffusive diffraction around the center (diffraction 4), which is assigned to the double scattering stemming from the crescent shape of diffractions 1 and 2. The solid and dashed lines in panel (b) are guides to the eyes.

Figure 4

Magnetic-field dependence of SANS intensities (a) parallel and (b) perpendicular to the field at 30 K. Solid and open circles represent different field-decreasing scans. The dashed line in panel (a) indicates the relation $M_{\mathrm{s}}^2-M^2$ vs $H$. (c) SANS intensity as a function of angle in the sector bounded by the dashed line in the inset of panels (a) and (b). The angle origin ($\theta =0$) is defined at the $I(\mathit{q}\perp \mathit{H})$ position (the bottom of the half-circle).

Figure 5

SANS patterns under zero magnetic field after an application of high magnetic field exceeding critical magnetic field at each temperature; 9.9 T for 30, 70, and 100 K and 5.0 T for 140 K. [See also Fig. 1b.]

Figure 6

Schematic illustrations of (a) a square, (b) a simple-cubic, and (c) a triangular skyrmion lattice. The color and the hue of the arrows represent the $z$ component of the magnetic moments; red (blue) arrows indicate up (down) magnetic moments. Comparison between the experimental results of topological Hall resistivity[18] (black solid lines) and the calculated ones with varying cutoff magnetization ($M_{\mathrm{c}}$) in (d) a square, (e) a simple-cubic, and (f) a triangular skyrmion lattice.