Field-induced pseudo-skyrmion phase in the antiferromagnetic kagome lattice

We study the effects of an in-plane Dzyaloshinskii-Moriya interaction under an external magnetic field in the highly frustrated kagome antiferromagnet. We focus on the low-temperature phase diagram, which we obtain through extensive Monte Carlo simulations. We show that, given the geometric frustration of the lattice, highly nontrivial phases emerge. At low fields, lowering the temperature from a cooperative paramagnet phase, the kagome elementary plaquettes form noncoplanar arrangements with nonzero chirality, retaining a partial degeneracy. As the field increases, there is a transition from this “locally chiral phase” to an interpenetrated spiral phase with broken ${\mathcal{Z}}_3$ symmetry. Furthermore, we identify a quasi-skyrmion phase in a large portion of the magnetic phase diagram, which we characterize with a topological order parameter, the scalar chirality by triangular sublattice. This pseudo-skyrmion phase consists of a crystal arrangement of three interpenetrated non-Bravais lattices of skyrmionlike textures, but with a non-(fully)-polarized core. The edges of these pseudo-skyrmions remain polarized with the field, as the cores are progressively canted. Results show that this pseudo-skyrmion phase is stable up to the lowest simulated temperatures and for a broad range of magnetic fields.

Figure 1

Kagome lattice. The labels 1,2,3 indicate the three sublattices (the dashed blue line indicates the unit cell). Small green arrows are Dzyaloshinskii-Moriya vectors ${\mathbf{D}}_{ij}, {\mathbf{D}}_{jk}$, and ${\mathbf{D}}_{ik}$ involved in sites (labeled as) $i,j,k$.

Figure 2

Magnetization curves vs external field $h/J$ for $L=60$ lattice size at $T/J=2\times {10}^{-3}$. Average magnetization $\langle M\rangle$ (blue open circles), magnetization modulus $\left|M\right|$ (green open triangles), and susceptibility ${\chi }_M=dM/dh$ (yellow open squares). The black arrows indicate four features in these curves. The values of the fields where these feature emerge, the critical fields, $h_{c1},h_{c2},h_{c3}$, are indicated by dashed lines. The critical field $h_{c4}$ corresponds to the saturation field where all the spins are polarized.

Figure 3

Snapshots of the spin textures and the corresponding structure factors for $L=42, D/J=0.2, T/J=2\times {10}^{-3}$. As the external magnetic field increases, different structures can be identified. For this plot we select one $h/J$ value in representation of each phase: (a) and (d) the locally chiral phase at $h/J=0.8$, (b) and (e) interpenetrated spirals at $h/J=1.8$, and (c) and (f) pseudo-skyrmion crystal at $h/J=2.8$.

Figure 4

(a) Specific heat as a function of temperature for low magnetic field at $h/J=0.5$ (yellow open squares), a spiral at $h/J=1.6$ (green open triangles), and pSkX at $h/J=2.7$ (blue open circles). (b) Structure factor obtained from Monte Carlo simulations at temperature $T/J=8\times {10}^{-2}, h/J=0.5$, for $D/J=0.2$.

Figure 5

Histogram of the nearest-neighbor chirality ${\chi }_{ijk}$ per triangular plaquette for two snapshots at $T/J=2\times {10}^{-3}, L=60, h/J=0.8$ (red) and $h/J=0.4$ (blue).

Figure 6

Spherical snapshot at $T/J=2\times {10}^{-3}$ for (a) the locally chiral phase at $h/J=0.8$ and (b) the spiral phase at $h/J=1.8$. Each color indicates a different triangular sublattice. The right column is the top view of the spherical snapshot.

Figure 7

Order parameter ${\varphi }_{tot}$ as a function of the external magnetic field at $T/J=2\times {10}^{-3}, L=60$. Nonzero values of $\varphi$ indicate the sublattice magnetization is not the same for each sublattice. Inset: ${\varphi }_{tot}$ vs $T/J$ at $h/J=1.8$ for $L=48, L=54$, and $L=60$.

Figure 8

(a) Snapshot for $D/J=0.2, h/J=2.6, T/J=2\times {10}^{-3}$. Every colored hexagon indicates the rim of a pseudo-skyrmion in each of the three interpenetrated pseudo-skyrmion sublattices. (b) A single pseudo-skyrmion structure. The different triangular sublattices of the kagome lattice are indicated. (c) One of the pseudo-skyrmion sublattices.

Figure 9

Sublattice chirality density as a function of $h/J$ for $L=60$ (green open triangles) at $T/J=2\times {10}^{-3}$. Inset: sublattice chirality density as a function of $T/J$ for $L=48,54,60$ at $h/J=3.5$.

Figure 10

Spherical snapshots in the pSkX phase for $L=60$, (a) $h/J=2.6$ and (b) $h/J=3.8$ and(c) for the “chiral polarized” high-field phase at $h/J=5.2$ with $T/J=2\times {10}^{-3}, D/J=0.2$. Each color indicates a different triangular sublattice of the kagome lattice.

Figure 11

Complete $T/J$ vs $h/J$ magnetic phase diagram obtained from Monte Carlo simulations. The solid green line was obtained by analyzing the peaks in the specific heat, the dashed white lines restrict the nonzero ${\varphi }_{tot}$ area $h_{c1}<h<h_{c2}$, and the CP phase was obtained computing the structure factor $S_{\mathbf{q}}$.