Quantum skyrmions in the antiferromagnetic triangular lattice

TL;DR

The study investigates quantum antiferromagnetic skyrmions on a triangular lattice by simulating the $S=1/2$ Heisenberg model with in-plane DMI using DMRG. It identifies three phases as a function of the external field: low-field AF helices, an intermediate three-sublattice AF skyrmion texture, and a high-field polarized state, with structure-factor, chirality, and magnetization analyses corroborating the skyrmionic phase. The skyrmion textures are shown to be robust to boundary geometry and variations in $D/J$, and quantum entanglement measures (half-chain entropy and nearest-neighbor concurrence) demonstrate the genuine quantum nature of these textures. These results connect classical AF skyrmion textures with their quantum counterparts and highlight potential avenues for AF skyrmion-based devices that suppress the skyrmion Hall effect.

Abstract

Magnetic skyrmions are topological quasiparticles potentially useful for memory and computing devices. Antiferromagnetic (AF) skyrmions present no transverse deflection, making them suitable candidates for data storage applications. After the discovery of skyrmions with length scales comparable to the lattice constant, several works presented quantum analogues of classical ferromagnetic skyrmions in spin systems. However, studies about quantum analogues of AF skyrmions are still lacking. Here, we explore the phases of the AF quantum spin-1/2 Heisenberg model with Dzyaloshinskii-Moriya interactions on the triangular lattice using the density matrix renormalization group (DMRG) algorithm. We study the magnetization profile, spin structure factor and quantum entanglement of the resulting ground states to characterize the corresponding phases and signal the emergence of quantum AF skyrmions. Our results support that three-sublattice quantum antiferromagnetic skyrmion textures are stabilized in a wide range of magnetic fields.

Figures (12)

• Figure 1: Left: Sites that belong to each of the three sublattices of the triangular lattice, where "A", "B", "C" label spin sites in each of the sublattices. Sites having the same color form part of the same sublattice. Arrows indicate the directions of the DMI vectors $\mathbf{D}_{\mathbf{r'},\mathbf{r}}$. Right: Two representative sets of sites $(i,j,k)$ used to compute the chirality in Eq.\ref{['eq:quir']}. We label the sites of the vertices of each triangular plaquette as $i$, $j$ and $k$ following a counterclockwise order. Note that each site belongs to a different sublattice.
• Figure 2: Average magnetization per site $m$ in the magnetic field direction (purple circles) and its derivative, the susceptibility (dark blue triangles), as a function of magnetic field $B/J$. As expected, $m$ approaches the value $1/2$ for high $B/J$. The susceptibility is discontinuous at $B/J \simeq 1.16$ and $B/J \simeq 4.8$ (dashed dark blue vertical lines).
• Figure 3: Representative magnetization profiles for the obtained ground states: (a) AF helical phase at $B/J=0.8$, (b) AF skyrmions at $B/J=1.76$, (c) higher-field AF skyrmion-like phase at $B/J=3.4$, and (d) field-polarized at $B/J=5.4$. Local magnetization of the entire lattice for each phase is presented on the first row. For the first three cases, we also display the profiles for each triangular sublattice (A, B and C, as in Fig. \ref{['fig:sitios_quir']}). The colorbar indicates the $\langle \hat{S}^z\rangle$ scale.
• Figure 4: Chirality $Q$ (blue circles) and magnetic susceptibility (dark blue triangles) as a function of $B/J$. We multiply $Q$ by $-1$ so that $Q$ and the susceptibility take mostly positive values, which allows for an easier comparison of changes in their behavior. Solid blue lines indicate $B/J$ values where $Q$ changes sign and dashed dark blue lines mark discontinuities in the susceptibility. Note that at higher fields both lines show up at $B/J\simeq4.8$.
• Figure 5: Classical chirality $Q_{clas}$ (red diamonds) and quantum chirality $Q$ (blue circles) as a function of $B/J$.