Characteristics of ferroelectric-ferroelastic domains in Néel-type skyrmion host GaV4S8

Abstract

GaV₄S₈ is a multiferroic semiconductor hosting Néel-type magnetic skyrmions dressed with electric polarization. At T_s = 42 K, the compound undergoes a structural phase transition of weakly first-order, from a non-centrosymmetric cubic phase at high temperatures to a polar rhombohedral structure at low temperatures. Below T_s, ferroelectric domains are formed with the electric polarization pointing along any of the four 〈111〉 axes. Although in this material the size and the shape of the ferroelectric-ferroelastic domains may act as important limiting factors in the formation of the Néel-type skyrmion lattice emerging below T_C = 13 K, the characteristics of polar domains in GaV₄S₈ have not been studied yet. Here, we report on the inspection of the local-scale ferroelectric domain distribution in rhombohedral GaV₄S₈ using low-temperature piezoresponse force microscopy. We observed mechanically and electrically compatible lamellar domain patterns, where the lamellae are aligned parallel to the (100)-type planes with a typical spacing between 100 nm-1.2 μm. Since the magnetic pattern, imaged by atomic force microscopy using a magnetically coated tip, abruptly changes at the domain boundaries, we expect that the control of ferroelectric domain size in polar skyrmion hosts can be exploited for the spatial confinement and manipulation of Néel-type skyrmions.

Figure 1

Panel (a) shows the crystal structure of GaV₄S₈. The red V₄S₄ clusters and the green VS₄ clusters are arranged in an fcc lattice. Panel (b) illustrates the tetrahedral arrangement of the vanadium sites within the V₄S₄ clusters in the cubic phase of the crystal. The rhombohedrally distorted V₄ cluster is shown in panel (c). The distortion is exaggerated for visibility. The local electric polarization developing upon the phase transition along the remaining C₃ axis of the distorted tetrahedron is indicated by a red arrow. Panel (d) demonstrates the schematic setup for out-of-plane piezoresponse force microscopy (PFM), with the lateral x and y scanning directions indicated by red and green arrows, respectively. Panels (e–g) present optical micrographs of the three different GaV₄S₈ single crystals used in this study, i.e. #1 and #3 with (001) surfaces, and #2 exhibiting the (111) crystallographic surface. The typical dimensions of the cuboid-shaped crystals are approximately 1–2 mm. The high-symmetry directions within the as-grown surfaces are indicated with reference to the x and y PFM scanning directions.

Figure 2

Simultaneous measurements of the PFM phase, PFM amplitude and AFM topography performed above (a–c) and below (d–f) the temperature of the structural phase transition. All images (a–f) stem from the same surface area on the (001) surface of Sample #1, as clearly seen from the topographic AFM pictures (c,f). The crystallographic directions are indicated in panel (d) according to Fig. 1(e). The yellow dashed rectangle in panel (a) marks the area of the measurements presented later in Fig. 3.

Figure 3

PFM phase (a) and amplitude (b) images along with the AFM topography image (c) taken on the (001) surface of Sample #1 over the area marked by a yellow dashed rectangle in Fig. 2(a). Panels (d–f) present the corresponding profiles along the same line indicated by white bars in panels (a–c). The alternating yellow-red backgrounds of the line profiles indicate domains distinguishable by the AFM topography and the PFM measurements. The difference in the surface inclination angle in adjacent domains, denoted as γ, is displayed by a blue arc in panel (f). Panel (g) shows the polarization directions in the four rhombohedral domains in a single inversion variant of the crystal. Red and yellow colors represent the different sign of the out-of-plane PFM signal observable on the (001) surface. Panel (h) presents one of the two possible compatible solutions for the observed alternating structure along the line profile. The top image shows the in-plane and out-of plane polarization vectors with reference to the scanning directions and the alternating electric field applied by the PFM tip, denoted by E^ω. The bottom image illustrates the three-dimensional structure of this solution with the color coding corresponding to panels (d–g).

Figure 4

Simultaneous measurements of the PFM phase, amplitude and AFM topography performed above (a–c) and below (d–f) the temperature of the structural phase transition. All images (a–f) stem from the same surface area on the (111) surface of Sample #2. The crystallographic directions are indicated in panel (d) according to Fig. 1(f). The yellow dashed rectangle in panel (a) marks the area of measurements presented in Fig. 5.

Figure 5

PFM phase (a) and amplitude (b) images along with the AFM topography image (c) taken on the (111) surface of Sample #2 over the area marked by a yellow dashed rectangle in Fig. 4(a). Panels (d–f) present the corresponding profiles along the same line indicated by white bars in panels (a–c). The alternating yellow-red backgrounds of the line profiles indicate domains distinguishable by the AFM topography and PFM measurements. The difference in the surface inclination angle in adjacent domains, denoted as γ, is displayed by a blue arc in panel (f). Panel (g) shows the polarization directions in the four rhombohedral domains in a single inversion variant of the crystal. Red and yellow colors represent the different sign and magnitude of the out-of-plane PFM signal observable on the (111) surface. Panel (h) presents the only compatible solution that yields PFM contrast, as observed along the line profile. The top image shows the in-plane and out-of -plane polarization vectors with reference to the scanning directions. The bottom image displays the three-dimensional structure of this solution with the color coding corresponding to panels (d–g).

Figure 6

(a) Transition of alternating domain pairs into a uniform domain in Sample #3 and (b) the junction of two different lamellar structures observed in Sample #2. The matching of incompatible domains results in the deformation of the domain walls, producing needle-like endings, or irregular domain wall inclinations.

Figure 7

m-AFM topography (a) and magnetic dissipation (b–f) maps recorded on the (001) surface of GaV₄S₈ in increasing external magnetic fields. The inset in Panel (a) displays the topography profile along the white arrow shown in the AFM image. The reversal of the surface inclination angle indicates different structural domains. The white dashed line in all images represents the structural domain boundary, acting as a magnetic domain boundary as well. The magnetic order characteristic to the given external field is indicated in each image as ‘Cyc’ for cycloidal order, ‘SkL’ for skyrmion lattice and ‘FM’ for the ferromagnetic order with different anisotropy axes in the two structural domains.