Collective Spin Excitations in Correlated Moiré Chern Ferromagnets

Abstract

Moiré-induced narrow electronic bands in transition metal dichalcogenide superlattices support many correlated quantum phases characterized by novel charge, flavor, and topological orders. Among these, magnetic ordering emerges as the most ubiquitous, often serving as the parent state for other correlated phases, including quantum anomalous Hall states, as well as chiral superconducting state. Because of electron-electron correlation, the stability of magnetic order is critically influenced by low-energy collective spin fluctuations, or magnon excitations. We investigate the nature of magnon excitations and their impact on the stability and transition temperature of the magnetic state at integer filling factor $ν= -1$. We find that the magnon spectrum exhibits isolated low-energy bands whose topological character undergoes a transition upon tuning the interlayer displacement field. The magnon gap is found to depend sensitively on the topology of the magnetic ground state, resulting in an order-of-magnitude enhancement of the transition temperature $T_c$ in the quantum anomalous Hall phase compared to the topologically trivial correlated insulator. Our findings provide insight into the interplay between electron and magnon topology and suggest new routes for controlling magnetism and topology via moiré engineering.

Figures (4)

• Figure 1: (a) Band structure of the FM ground state at twist angle $\theta = 3.5^\circ$ and zero interlayer displacement field obtained from the full self-consistent mean-field calculation. Solid (dashed) lines represet $+K(-K)$ valley and color indicates the wavefunction weight on the top (t) and bottom (b) layers. (b) Global charge gap ($E_{\rm g}$) and spin gap ($\Delta_{\rm spin}$) of the mean-field ground state as a function of displacement field. The orange and blue shading indicate regions with QAH and trivial FM insulating ground states, respectively, and the gray shading suggests the region where FM is unstable towards an IVC ground state. (c) Schematic diagram of spin-flip excitations from occupied spin down (-K) bands to the empty spin up (+K) bands.
• Figure 2: (a) Magnon bandstructure in the FM state at $D=0$. The black dashed line marks the minimum energy of the spin-flip inter-band continuum. (b) Color plot of the lowest magnon band energy with band maximum (minimum) at the $\bm{\gamma}$ ($\bm{m}$). (c) Convergence of the magnon energy at high symmetry momentum, $\bm{\kappa},\bm{\gamma},\bm{m}$ as a function of the number of filled spin-down bands, $N_v$, in the TDHF calculation (as illustrated in Fig. \ref{['MF_band']}(c)).
• Figure 3: Isolated low-energy magnon bands at representative displacement fields across the topological transition: (a) $D=7.0$ meV, (b) $D=10.5$ meV, (c) $D=12.0$ meV, and (d) $D=20.0$ meV. (e) Displacement-field dependence of the two lowest magnon energies at $\bm{\kappa}$, where the magnon band gap closes. The vertical dashed lines mark the displacement fields corresponding to panels (a)–(c).
• Figure 4: (a) Magnon gap ($\Delta_{mag}$) as a function of displacement field across different FM phases indicated by the shaded color. At $D>27.2$ meV, an instability develops toward an intervalley coherent density wave order (gray shaded region). (b) The lowest magnon band at $D=28$ meV showing the instability at finite momentum $\bm{Q}=\bm{\kappa}$. (c) Schematic illustration of magnon thermal population at finite temperature. Temperature dependence of the magnetization in (d) the QAH phase and (e) trivial insulator phase.