Dissipationless dynamics of spin supersolid states in a spin-1/2 triangular antiferromagnet with impurities

TL;DR

This study investigates dissipationless spin dynamics in spin-1/2 triangular-lattice antiferromagnets with impurities under magnetic fields, focusing on spin supersolid states. By combining zero- and finite-temperature tensor-network methods (DMRG/TDVP and SETTN/XTRG) with linear spin-wave theory, the authors compute the dynamical spin structure factor and superfluid stiffness across Y, UUD, and V phases. They find a robust gapless Goldstone mode at the $K$ points in the spin supersolid states even in the presence of impurities, signaling persistent spin superfluidity, while the UUD state exhibits impurity-induced magnon band splitting near $K$. Impurities broaden spectral features at higher energies (e.g., near the $M$ points) but do not destroy the overall supersolid spectrum, suggesting measurable dissipationless dynamics via neutron scattering in real materials, with finite-temperature stiffness persisting up to $T/J oughly 0.1$. These results provide concrete signatures to identify spin superfluidity and guide experiments in materials such as Na$_2$BaCo(PO$_4$)$_2$.

Abstract

Motivated by recent experimental observations of the possible spin supersolid states in triangular lattice compounds, we study the dynamical properties of various ground states in the spin-1/2 easy-axis antiferromagnetic Heisenberg model with impurities under magnetic fields using numerical methods. In both low- and high-field spin supersolid states, the gapless Goldstone mode at the $K$ points remains robust against impurities, which is related to the presence of spin superfluidity. By contrast, we find that impurities induce a splitting of the magnon bands at the same density level in the conventional magnetic state, the so-called up-up-down state. In addition, the finite superfluid stiffness probed by the twisted phase in the spin supersolid states is consistent with the excitation spectrum. We argue that this excitation spectrum with impurity provides direct evidence for the dissipationless dynamics in the spin supersolid states, which could be tested in neutron scattering experiments.

Figures (13)

• Figure 1: Panel (a) shows the triangular lattice with blue solid circles representing positive spin values, and red shaded circles representing negative spin values. The purple solid circles represent the impurity sites with a positive spin value. The radius represents the magnitude where the purple ones have $\left\langle S_{i}^{z}\right\rangle \approx 0.5$. The ground state is obtained at $h_{z}=0.836$ on the $N=48 \times 6$ lattice where only the middle part is shown. Panel (b) shows the illustration of a triangular lattice. Panel (c) shows the corresponding Brillouin zone and momentum cuts for the dynamical spin structure factor.
• Figure 2: Panels (a) and (b) show the $\left\langle m_{z}^{2} \right\rangle$ and $\left\langle m_{\bot }^{2} \right\rangle$ for various $h_{z}$, respectively. P refers to the polarized state. Panel (c) shows the superfluid stiffness as a function of $h_{z}$, obtained at zero and finite temperatures $T$. Panel (d) shows the finite $T$ results of $\Delta F(\pi)$. The $\Delta F(\pi)$, $T$ and $h_{z}$ are normalized by $J$. All results are obtained on $L_{y}=6$ lattices.
• Figure 3: The dynamical structure factor near $K$ points. Panels (a) and (d) are obtained in the "Y" supersolid phase. Panels (b) and (e) are obtained in the UUD phase. Panels (c) and (f) are obtained in the "V" supersolid phase. Panels (a), (b), and (c) are obtained without the impurities, while panels (d), (e), and (f) are obtained with the impurities. The white dashed lines represent the dispersions from linear spin wave theory; see more details in the Supplemental Material SuppMaterial.
• Figure 4: The dynamical structure factor near $M$ points. Panel (a) and (d) are obtained in the "Y" supersolid phase. Panel (b) and (e) are obtained in the UUD phase. Panel (c) and (f) are obtained in the "V" supersolid phase. Panel (a), (b), and (c) are obtained without the impurities, while panel (d), (e), and (f) are obtained with the impurities. The white dashed lines represent the linear spin wave results; see more details in the Supplemental Material SuppMaterial.
• Figure S1: The dynamical structure factor obtained with different bond dimensions for the "Y" supersolid state at $h_{z}/J=0.836$ on the $L_{x}\times L_{y}=48\times 6$ lattice. Panels (a) and (b) show the dynamical structure factor near $K$ points, Panels (c) and (d) show the dynamical structure factor near $M$ points. Panels (a) and (c) are obtained with $D=1400$, Panels (b) and (d) are obtained with $D=2200$.