Equilibrium Skyrmion Lattice Ground State in a Polar Easy-plane Magnet

Abstract

The skyrmion lattice state (SkL), a crystal built of mesoscopic spin vortices, gains its stability via thermal fluctuations in all bulk skyrmion host materials known to date. Therefore, its existence is limited to a narrow temperature region below the paramagnetic state. This stability range can drastically increase in systems with restricted geometries, such as thin films, interfaces and nanowires. Thermal quenching can also promote the SkL as a metastable state over extended temperature ranges. Here, we demonstrate more generally that a proper choice of material parameters alone guarantees the thermodynamic stability of the SkL over the full temperature range below the paramagnetic state down to zero kelvin. We found that GaV₄Se₈, a polar magnet with easy-plane anisotropy, hosts a robust Néel-type SkL even in its ground state. Our supporting theory confirms that polar magnets with weak uniaxial anisotropy are ideal candidates to realize SkLs with wide stability ranges.

Figure 1

Extended cycloidal and Néel-type SkL states in GaV₄Se₈. (a) Magnetic phase diagram for magnetic fields parallel to the polar axis, α = 0°. Below T_C = 18 K, the cycloidal (Cyc) and SkL phases, underlying the field polarized ferromagnetic state (FM), persist down to the lowest temperatures. The Néel-type SkL spin texture is schematically illustrated. Phase boundaries are assigned to anomalies in ∂M/∂H versus H (closed circles) and ∂M/∂T versus T (open circles) curves and by the SANS data (crosses). Lines are guides to the eye. The crossover region between the paramagnetic (PM) and FM states is indicated by open diamonds and color gradation. Below 12 K additional phases, labeled by question marks, emerge between the cycloidal and SkL states. (b) Magnetic phase diagram for fields applied at α = 54.7° with respect to the polar axis. In the phase labeled as Cyc, the magnetic field component normal to the polar axis continuously distorts the cycloid into a tilted conical structure, as visualized in Fig. 4g. The field component along the polar axis still establishes the SkL before the FM is reached. (c) For magnetic fields applied perpendicular to the polar axis, α = 90°, the Cyc state corresponds to the regular cycloid, which is smoothly canted by the field to form a transverse conical structure, as sketched in Fig. 4e, and eventually transforms into the FM.

Figure 2

Magnetic anisotropy of GaV₄Se₈. (a) Electron spin resonance spectra for the external field H applied along a rhombohedral axis (green curve) and tilted by 20° away from it (red curve). (b) Resonance fields (symbols) for the magnetic field rotated within the (001) plane, where φ _H is the angle between the field and the [001] direction, i.e. 0°, 45°, 90° and 135° correspond to the [100], [110], [010] and [1$\overline{1}$0] axes, respectively. Solid lines display a fit based on uniaxial anisotropy. (c) Temperature evolution of the anisotropy constant K ₁ < 0, characteristic of easy-plane anisotropy.

Figure 3

Structural and magnetic properties of GaV₄Se₈. (a) Crystal structure of GaV₄Se₈. For the sake of clarity only the face centered cubic lattice of V₄ tetrahedra is shown. The V₄ building block is shown both in the cubic state (T_d) and the rhombohedral state (C_3v), when the crystal is stretched along a 〈111〉-type axis, labeled as the c axis. (b) Field dependence of the magnetization at 12 K. (c) ∂M/∂H versus H curves measured at 12 K for H ‖ [111], [1$\overline{1}$0], [11$\overline{2}$], and[001]. The curves are vertically shifted relative to each other. Anomalies are labeled with the angles α spanned by the magnetic field and the polar c axes of the domains wherein the corresponding phase transitions take place. (d) Stability regions of the cycloidal (Cyc), SkL and ferromagnetic (FM) states at 12 K on the H_c–H_⊥ plane, where H_c and H_⊥ are the field components along and perpendicular to the polar c axis. Phase boundaries are assigned by anomalies observed in the ∂M/∂H curves in panel (c) (full symbols) and by the SANS data (crosses) for various α angles. Lines connecting full symbols are guides to the eye. In finite H_⊥ the cycloidal state is distorted to transverse or tilted conical structures as shown in Fig. 4e,g.

Figure 4

Modulated magnetic structures in GaV₄Se₈ at 12 K. (a) Representative SANS images recorded in the (111) plane with magnetic field applied along the [111] axis. The first image was taken after zero-field cooling. The magnetic field increases from left to right. (b) The same as for panel (a) but with field applied along the [1$\overline{1}$0] axis. (c) After the measurements in $\mathbf{H}\parallel [1\overline{1}\mathrm{0]}$, the magnetic field was decreased to zero and SANS images were again recorded in the (111) plane with H ‖ [111]. The colour scale on the right is common for panels (a–c). (d) Schematic of cycloidal structures present with arbitrary q-vectors distributed around a ring in the rhombohedral plane. For clarity, the cycloid is shown only for a single q-vector. (e) Magnetic fields applied perpendicular to the polar axis establish a transverse conical state with single q-vector normal to the field. (f) After switching off the magnetic field, this conical structure relaxes back to a cycloid preserving the single q-vector state. (g) For H with oblique angles, the field component normal to the polar axis distorts the cycloid into a tilted conical structure, where the axes of the cones are tilted away from the polar axis but are not exactly parallel with the field.

Figure 5

SANS intensity due to a single rhombohedral domain. Field dependence of the SANS intensity measured for selected parts of the ring structure within the white sectors, as shown in the SANS images recorded in 0, 40 and 250 mT with H ‖ [111]. The three curves correspond to the three measurement configurations presented in Fig. 4a–c.

Figure 6

Angular stability of the Néel-type SkL. Stability regions of the cycloidal (Cyc), SkL and ferromagnetic (FM) states on the H _c J/D ²–H _⊥ J/D ² plane, where H_c and H_⊥ are respectively the field components along and perpendicular to the polar c axis, as calculated for (a) AJ/D ² = 0 and (b) AJ/D ² = 0.5. The inset of panel (a) shows the distorted SkL with skyrmion cores displaced horizontally from the center of the unit cell along the H _⊥ field component.