Strain-tunable magnetic correlations in spin liquid candidate Nb$_3$Cl$_8$

TL;DR

This study investigates the magnetic properties of monolayer Nb3Cl8, a 2D breathing Kagome candidate hosting $S=1/2$ Nb3 trimers on an effective triangular lattice. Using ab initio DFT+$U$+SOC calculations and the four-state energy-mapping formalism, the authors extract a generalized Heisenberg-like Hamiltonian with anisotropic exchange, Dzyaloshinskii–Moriya interactions (DMI), and single-ion anisotropy, and then analyze the temperature-dependent susceptibility via classical Monte Carlo simulations. They find short-range antiferromagnetic correlations with negative Weiss temperatures and a frustration index $f \,\approx\;2.3$–$2.4$, indicating pronounced magnetic frustration. Moreover, biaxial strain tunes the system between antiferromagnetic, paramagnetic, and ferromagnetic local correlations, with DMI magnitude comparable to anisotropic exchange, suggesting the potential for strain-engineered quantum states and noncollinear spin textures in Nb3Cl8.

Abstract

Recent research suggests the possibility of the two-dimensional breathing-Kagome magnet Nb$_3$Cl$_8$ hosting a quantum spin liquid state, warranting further study into its magnetic properties. Using ab initio calculations, we show that monolayer Nb$_3$Cl$_8$ has short-range antiferromagnetic correlations among Nb$_3$ trimers with S = 1/2, and becomes magnetically frustrated due to the underlying effective triangular lattice geometry, and is evidenced by a frustration index of f > 1. The high-temperature susceptibility shows a negative Weiss temperature from Monte Carlo calculations. Considering spin-orbit coupling, we investigate the magnetic anisotropy, including anisotropic exchange, single-ion anisotropy and the Dzyaloshinskii-Moriya interaction using the four-state energy mapping formalism. Although the elements have relatively small atomic numbers, the Dzyaloshinskii-Moriya interaction is comparable in magnitude to the anisotropic exchange. Additionally, we show that biaxial strain tunes the short-range correlations between antiferromagnetic, paramagnetic and ferromagnetic. These findings strengthen our understanding of Nb$_3$Cl$_8$ and advance its applications in current condensed matter physics and materials science research, including nanoscale mechanical and spintronics applications.

Figures (10)

• Figure 1: Nb$_3$Cl$_8$ crystal structure shown as a $4\times 4\times 1$ supercell, viewed along the $c$-axis momma2008vesta. Semi-transparent spheres represent Nb (green) and Cl (purple) atoms of the breathing Kagome lattice, with alternating large and small Nb$_3$ triangles. Selected Nb$_3$ trimers (small triangles, each hosting a single $S=1/2$ moment) are highlighted in yellow. Consider each yellow trimer as a single unit that produces the overlying triangular lattice. Arrows indicate NN (blue), 2NN (red), and 3NN (black) trimer-trimer interactions used in our calculations. The triangle with three arrows pointing to it is taken as the first index of each bond.
• Figure 2: Inverse magnetic susceptibility $1/\chi_d$ (arb. units) vs. temperature $T (K)$ in the $d=x$-direction for $0\%$ (unstrained), $-3\%,$ and $-4\%$ biaxial strain. Data from Monte Carlo simulations are shown as dots. For clarity in illustration, we show Monte Carlo data for only the $50 \leq T \leq 300$$K$ range used in the fitting, with the exception of $0\%$ strain, which exemplifies the kink indicating $T_N$. The Weiss temperature $\theta_d$ and uncertainty for each case is given alongside the vertical dashed lines denoting the intersection of the linear fits with the $T$ axis.
• Figure 3: Diagonal matrix elements $J_{xx},J_{yy}$ and $J_{zz}$ of $J^1$ and $J^3$, with respect to strain (horizontal axis). Note that some of the $J_{xx},J_{yy},J_{zz}$ curves in each case heavily overlap with each other. The red circles highlight the three test cases explored in our Monte Carlo calculations: $0\%$, $-3\%$ and $-4\%$.
• Figure 4: Spin-spiral energies as a function of ordering vector for $0\%$ and $-4\%$ biaxial strain, with the energy at $\Gamma$ set to $0$.
• Figure 5: $\mathbf{D}^1$ for the unstrained case, visualized in the $xy$ (left) and $yz$ (right) planes. The $D_z$ component is $-0.15$ meV for all NN bonds.