Skyrmion lattice structural transition in MnSi

Abstract

Magnetic skyrmions exhibit particle-like properties owing to the topology of their swirling spin texture, providing opportunities to study crystallization of topological particles. However, they mostly end up with a triangular lattice, and thus, the packing degree of freedom in the skyrmion particles has been overlooked so far. We report a structural transition of the skyrmion lattice in MnSi. By use of small-angle neutron scattering, we explore a metastable skyrmion state spreading over a wide temperature and magnetic field region, after thermal quenching. The quenched skyrmions undergo a triangular-to-square lattice transition with decreasing magnetic field at low temperatures. Our study suggests that various skyrmion lattices can emerge at low temperatures, where the skyrmions exhibit distinct topological nature and high sensitivity to the local magnetic anisotropy arising from the underlying chemical lattice.

Keywords: Small angle neutron scattering; magnetic skyrmion.

Fig. 1. SANS measurements on equilibrium magnetic phases and quenched SkL state under a magnetic field of 0.2 T.

(A) H-T magnetic phase diagram of MnSi. The open symbols denote phase boundaries between helical, conical, SkL, and field-induced ferromagnetic phases determined by resistivity measurements using the identical sample used in the SANS measurements. Inset: Typical time profiles of an electric current pulse and the resulting temperature change. (B) Schematic showing the experimental setup, orientation of the crystal, and directions of neutron beam and magnetic field. (C to E) SANS patterns measured in the H || k_i configuration (C) in the equilibrium SkL phase, at 12.5 K and 0.2 T before applying the current pulse (D), and after the application of the pulse (E). (F to H) Corresponding SANS patterns measured in the H ⊥ k_i configuration.

Fig. 2. Magnetic field induced transitions in the lowest temperature (1.5 K) after quenching.

(A) Magnetic field dependence of integrated intensity of the magnetic reflections measured in the H || k_i configuration after quenching at 0.2 T with increasing and decreasing fields and (B) measured with increasing magnetic field after reaching the square SkL state in zero field. (C) Field dependence of average values of peak position in q measured in the H || k_i configuration at 1.5 K. Filled and open symbols denote data measured with increasing and decreasing field, respectively. Gray data points in (B) are the data shown in (A). (D) Hall resistivity data redrawn from fig. S3a in the Supplementary Materials of the study by Oike et al. (23). Expected square SkL contribution in Hall resistivity is highlighted in pink. Slight discrepancies in transition fields are due to differences in temperature and demagnetizing effect. (E to H) Azimuthal angle profiles of the annular-averaged intensities measured at (E) 0.2 T, (F) 0.08 T, and (G) 0 T with decreasing field and at (H) 0.2 T with increasing field from 0 T. (I to P) The SANS patterns measured in the H || k_i and H ⊥ k_i configurations at the selected magnetic fields. In (K), (L), and (O), the intensities (I) are multiplied by factors of 3, 3, and 10, respectively, to enhance clarity.

Fig. 3. Metastable state diagram mapped on the H-T magnetic phase diagram.

Metastable state diagram mapped on the H-T magnetic phase diagram. The filled circles denote the boundaries between the metastable triangular SkL, square SkL, and (equilibrium) conical and helical magnetic states.

Fig. 4. Triangular SkL and square lattice arrangements of particles with the same modulation period λ.

(A) The triangular SkL described by superposition of three screw magnetic modulations of q₁, q₂, and q₃ (|q_i| = 2π/λ, i = 1 to 3) shown in its inset and a uniform magnetization component along the z direction. Colors and arrows denote out-of-plane and in-plane components of the magnetic moments, respectively. (B) Schematic showing square lattice arrangements of particles characterized by two wave vectors of q₁ and q₂ (|q_i| = 2π/λ, i = 1, 2) shown in its inset.