Ferrochiral, antiferrochiral, and ferrichiral skyrmion crystals in an itinerant honeycomb magnet

Topological spin textures, such as a skyrmion crystal, are a source of unusual physical phenomena owing to the interplay between magnetism and topology. Since physical phenomena depend on the topological property and the symmetry of underlying spin structures, the search for new topological spin textures and emergent phenomena is one of the challenges in condensed matter physics. In this study, we theoretically explore topological spin textures arising from the synergy between spin, charge, and sublattice degrees of freedom in an itinerant magnet. By performing simulated annealing for an effective spin model of the honeycomb Kondo lattice model, we find a plethora of skyrmion crystal instabilities at low temperatures, whose topological spin textures are classified into three types: ferrochiral, antiferrochiral, and ferrichiral skyrmion crystals. We show that the obtained skyrmion crystals are the consequence of the spin-orbit-coupling-free honeycomb structure. Our results reveal the potential for itinerant honeycomb magnets to host a wide variety of skyrmion crystal and emergent phenomena.

Figure 1

Skyrmions characterized by $(p,v,N_{\mathrm{sk}})$. The arrow and color show the spin direction and $z$ component, respectively, where red (blue) corresponds to the positive (negative) $z$ component.

Figure 2

(a) Phase diagram on the $\mathrm{\Theta }-K\left(\right|X^{\mathrm{AB}}\left|\text{−}K\right)$ plane at $T=0.01$. CS, FC SkX, and AFC SkX represent the chiral stripe state, ferrochiral SkX, and antiferrochiral SkX, respectively. Inset: The honeycomb structure with sublattices A (white) and B (gray). ${\mathit{d}}_{\eta }^{*}$ ($\eta =1$–3) is the vector of three nearest-neighbor bonds. Snapshots of the (b) FC and (c) AFC SkXs II at $\mathrm{\Theta }=\pi /12$ and $K=0.4$. Upper left (right) panel: Spin (${\mathit{S}}_i$) and chirality (${\chi }_{\mathit{r}}$) configurations on sublattice A (B). Lower panel: Spin configuration on the honeycomb lattice. The arrows, contours of arrows, and contours of circles show the $xy$ spin component, $z$ spin components, and spin scalar chirality, respectively. $(p^{\alpha },v^{\alpha },N_{\mathrm{sk}}^{\alpha })$ and $(N_{\mathrm{sk}}^{\mathrm{tot}},N_{\mathrm{sk}}^{\mathrm{stagg}})$ are shown in the upper and lower panels, respectively.

Figure 3

(a) Phase diagram on the $\mathrm{\Theta }-H$ plane at $X^{\mathrm{AB}}<0, K=0.4$, and $T=0.01$. FC SkX, AFC SkX, and FerriC SkX represent the ferrochiral SkX, antiferrochiral SkX, and ferrichiral SkX, respectively. I–V are nontopological phases. Snapshots of (b) FC SkX I at $\mathrm{\Theta }=\pi /8$ and $H=0.5$, (c) AFC SkX I at $\mathrm{\Theta }=\pi /8$ and $H=0.4$, and (d) FerriC SkX at $\mathrm{\Theta }=\pi /8$ and $H=0.375$, which corresponds to Figs. 2  and 2.

Figure 4

(a) Phase diagram at zero field with $K_c\left(\mathrm{\Theta }\right)$. The $K_c\left(\mathrm{\Theta }\right)$ curve divides the phase diagram into regions I and II. (b) $K$ dependence of the energy difference between the SkX II and $1Q$ spiral I states for $\mathrm{\Theta }=\pi /60$ (black), $\mathrm{\Theta }=\pi /30$ (red), $\mathrm{\Theta }=\pi /20$ (orange), $\mathrm{\Theta }=\pi /15$ (pink), and $\mathrm{\Theta }=\pi /12$ (blue), where we set $\delta =0.025$ based on the simulation results. We plot the data in region I, i.e., $K>K_c\left(\mathrm{\Theta }\right)$.

Figure 5

First (fourth) column: Spin (${\mathit{S}}_{\alpha i}$) and chirality (${\chi }_{\alpha \mathit{r}}$) configurations on sublattice A (B) of (a) the trivial state I at $\mathrm{\Theta }=\pi /24$ and $H=0.3$, (b) the trivial state II at $\mathrm{\Theta }=\pi /24$ and $H=1$, (c) the trivial state III at $\mathrm{\Theta }=5\pi /48$ and $H=1$, (d) the trivial state IV at $\mathrm{\Theta }=\pi /6$ and $H=1$, and (e) the trivial state V at $\mathrm{\Theta }=\pi /4$ and $H=1$. The arrows, contours of arrows, and contours of circles show the $xy$ spin component, $z$ spin component, and spin scalar chirality, respectively. Second and third (fifth and sixth) columns: The in-plane $\left[S^{\perp }(\alpha ,\mathit{q})\right]$ and out-of-plane $\left[S^z(\alpha ,\mathit{q})\right]$ spin structure factors for sublattice A (B) in momentum space, respectively. The circle and square highlight the dominant and subdominant peaks, respectively. The hexagons with a solid line show the first Brillouin zone. The $\mathit{q}=\mathit{0}$ component is removed for better visibility.