Direct observation of anisotropic magnetic field response of the spin helix in FeGe thin films

We report the observation by small-angle neutron scattering (SANS) of a magnetic helical structure confined in a thin film of the chiral lattice magnet FeGe. Twofold magnetic Bragg spots appearing below the magnetic transition temperature indicate the formation of a spin helix with a single propagation vector $\mathit{q}$ aligned perpendicular to the film plane. Due to magnetic anisotropy, the direction of $\mathit{q}$ is unaffected by an external magnetic field $\mathit{H}$. Instead we observe anisotropic deformations of the spin helix with respect to the $\mathit{H}$ direction. In the configuration with $\mathit{H}\perp \mathit{q}$, the helical pitch exhibits hysteretic elongation with $\mathit{H}$, while the system tends to maintain an integer number of spiral turns within the film thickness by continuously pushing out one turn. For $\mathit{H}\parallel \mathit{q}$, the helix is smoothly distorted to a conical structure with minimal change in the magnetic period. The direct measurement of $\mathit{q}$ by SANS establishes a correspondence between helix deformation and macroscopic features observed in magnetization and magnetoresistivity.

Figure 1

(a) $\theta -2\theta$ x-ray diffraction pattern of the FeGe thin film. (b) Reciprocal-space map around the Si (331) peak. The peak position estimated from the lattice parameter of bulk FeGe is indicated by an open circle. (c) Cross-sectional transmission electron microscopy image. (d) Experimental setup for the SANS experiment. The stack of 32 thin films of 15 mm $\times$ 15 mm size are aligned with their surfaces along the incident neutron beam when the rocking angle is zero. Magnetic fields were applied both parallel $\left({\mathit{H}}_{\mathrm{in}}\right)$ and perpendicular $\left({\mathit{H}}_{\mathrm{out}}\right)$ to the film surfaces.

Figure 2

(a) Typical SANS pattern at zero magnetic field. Due to the strong reflected neutron intensity from the periodic array of Si substrates, the magnetic Bragg scattering is discerned above a small offset rocking angle $\left(\approx \pm 4^{\circ }\right)$ [34]. (b) Rocking scan of magnetic Bragg peaks. Intensities in the left and right boxes in panel (a) are indicated by red and blue markers, respectively. Both rocking profiles are well fitted by single Lorentzians. (c) Temperature dependence of magnetic scattering intensity, which corresponds to magnetization profile $\left(\propto M^2\right)$. (d) Weakly temperature-dependent magnetic propagation vector $q$. Scattering pattern at 290 K and 0 T at a respective rocking angle was used as a background subtracted from the measured patterns below $T_{\mathrm{N}}$.

Figure 3

Magnetic-field dependences of the magnetic modulation period $\lambda$ [(a) and (b)], magnetization $M$ [(c) and (d)], and magnetoresistivity [(e) and (f)] under in-plane and out-of-plane fields at 2 K. In the background of panels (a) and (b), we show scattering intensity distribution maps as a function of $\lambda$ at various magnetic fields. The color maps are produced from the radial dependence of scattering intensity in the reciprocal space $(q_x,q_y)$ by conversion via the relation $\lambda =2\pi /q$. At characteristic magnetic fields during decreasing-field processes, which are respectively labeled as $H_i$ ($i=0$–6) for ${\mathit{H}}_{\mathrm{in}}$ configurations, the following features are identified: At $H_1$, a pair of magnetic Bragg spots become discerned and $M$ and MR start to exhibit gradual decrease and increase, respectively. At $H_2$, the Bragg spots begin to change their positions and $M$ and MR show abrupt variations. At $H_3$, change in positions of the Bragg spots ceases and both $H$ dependence of $M$ and MR indicates small kinks. At $H_4$, positions of the Bragg spots start to change again, and stepwise variations of $M$ and MR profiles set off. At $H_5$, change in positions of the Bragg spots ceases, and $M$ and MR show abrupt variations. At $H_6$, the Bragg spots disappear and variations of $M$ and MR with variation of $H$ become reduced. (g)–(j) Example SANS patterns for the development of helicoidal state with decreasing ${\mathit{H}}_{\mathrm{in}}$: (g) $H_2>0.04\mathrm{T}>H_3$; (h) $H_3>0\mathrm{T}>H_4$; (i) $H_4>-0.09\mathrm{T}>H_5$; (j) $H_5>-0.11\mathrm{T}>H_6$. Scattering patterns at $T=2$ K and ${\mu }_0{H}_{\mathrm{in}}=0.25$ T and at $T=2$ K and ${\mu }_0{H}_{\mathrm{out}}=1.0$ T were used as a background subtracted from the measured patterns under respective field directions.

Figure 4

Magnetic phase diagrams under decreasing (a) ${\mathit{H}}_{\mathrm{in}}$ and (b) ${\mathit{H}}_{\mathrm{out}}$ from large magnetic fields (e.g., ${\mathit{H}}_{\mathrm{in}}=0.25$ T and ${\mathit{H}}_{\mathrm{out}}=1.0$ T). Schematic illustrations of helicoidal and conical states are inset in panels (a) and (b), respectively.

Figure 5

(a) ADF-STEM image and (b)–(d) EDX mappings for Si, Fe, and Ge elements.

Figure 6

Data sets for magnetic modulation period $\lambda$, magnetization $M$, and magnetoresistivity under in-plane and out-of-plane magnetic fields at various temperatures. Scattering patterns at ${\mu }_0{H}_{\mathrm{in}}=0.25$ T and at ${\mu }_0{H}_{\mathrm{out}}=1.0$ T at respective temperatures were used as a background subtracted from the measured patterns under the different field directions.