Insulating charge transfer ferromagnetism

Abstract

We propose a mechanism for insulating ferromagnetism in the honeycomb Hubbard model of semiconductor moiré superlattices. The ferromagnetism emerges at critical charge transfer regime, stabilizing the quantum anomalous Hall state without Hund's coupling. We further note the ferromagnetic exchange applies to general charge transfer systems when breaking particle-hole symmetry.

Figures (10)

• Figure 1: (a) Schematic diagram of a honeycomb lattice with two types of sites, A and B, illustrated in red and blue. The nearest neighbors are connected by thick gray tubes, while the second nearest neighbor is connected by red dashed lines. (b) Three exchange process for swapping two electrons spin on two A sites (cation site), by introducing an extra B site. (c) The schematic kinetic diagram for ferromagnetic ring exchange from $t_{AA}<0$. $\theta(x)$ stands for Heaviside step function. Two interfering paths are marked with blue and red arrows. (d) The phase diagram which is universal from the value of $U$ and specific lattice, calculated from $J>0$ in Eq. \ref{['effective exchange full']}. The phase diagram assumes $U_A=U_B=U$.
• Figure 2: (a) Analytical phase diagram of the strength of $J/|t_{AA}|$ as a function of $t_{AB}$ and $\Delta$. (b) The spin gap $\Delta_s$ in a $3\times3$ PBC cluster using ED. A cutoff of 1.5 is imposed for clarity. (c) The spin gap $\Delta_s$ in a $3\times12$ cylinder using DMRG. In (b) and (c), the dashed line corresponds to the phase boundary in (a).
• Figure 3: (a) The spin-spin correlation intensity difference between the $\Gamma$ and $K$ points in a $3\times3$ PBC cluster using ED. A larger value indicates greater concentration at the $\Gamma$ point. (b, c) Normalized spin-spin correlation by self-correlation in real space at $t_{AB} = 10 |t_{AA}|$, with (b) $\Delta = 100 |t_{AA}|$ and (c) $\Delta = 50 |t_{AA}|$. Arrows on sites are included for visual guidance.
• Figure 4: Calculation results for $t_{AB} = 10 |t_{AA}|$, $t_{AA} = |t_{AA}| e^{i \phi}$, $U_A = U_B = 40 |t_{AA}|$, $\Delta = 150 |t_{AA}|$ in a $3\times3$ PBC cluster using ED. (a) The difference in spin-spin correlation between the $\Gamma$ and $K$ points. (b) The energy difference $\Delta_s$ between $S_z = 3/2$ and $S_z = 1/2$, also known as the spin-one gap. (c) The $S_z$ sector in which the ground state lies. Note that although the ferromagnetic state has a small total $S_z$, it exhibits strong ferromagnetic correlation.
• Figure S1: Spin gap results using different definitions. (a) Identical to Fig. \ref{['Fig2']}(b) for reference, with the gap defined as the energy difference between $S_z=S_{max}=9/2$ and $S_z=1/2$. (b) Gap defined between $S_z=9/2$ and $S_z=7/2$. (c) Gap defined between $S_z=7/2$ and $S_z=5/2$. Dashed line here indicates phase boundary obtained from perturbation theory.