Mutual enhancement of altermagnetism and ferroelectricity

TL;DR

The paper addresses the coexistence and mutual interplay of ferroelectric polarization and metallic altermagnetism in a Rashba spin-orbit coupled 2D Hubbard model. It employs a self-consistent mean-field treatment, deriving a $4\times4$ Hamiltonian $H_{\boldsymbol{k}}$, solving for the altermagnetism order parameter $m_N$ and chemical potential $\mu$, and minimizing the total free energy $F_{\text{tot}}=F_0+F_P$ with respect to the polarization $P$ (where $F_P=\tfrac{1}{2}\gamma P^2+\eta P^4$). The key findings show a strong doping dependence: near half-filling, Rashba SOC suppresses altermagnetism and FE, while away from half-filling, metallic AM and FE coexist with mutual enhancement, and the system can be electrically tuned between nodal and nodeless AM phases. This suggests that doping and lattice energetics offer a practical route to control spin-splitting and ferroelectricity in metallic altermagnets, with potential spintronic applications where FE polarization modulates non-relativistic spin-splitting alongside Rashba-driven effects.

Abstract

We consider theoretically the possibility of coexisting ferroelectric and metallic altermagnetic order, which has recently been predicted in insulating and semiconducting systems via ab initio calculations. Solving self-consistently a mean-field Hubbard model, accounting also for the energy cost of distorting the lattice to produce an electric polarization, our results show that metallic altermagnetism and ferroelectricity suppress or enhance each other depending on the doping level of the system. Close to half-filling, the system can lower its energy by becoming altermagnetic, but at the expense of losing the electric polarization. Away from half-filling, the coexistence of ferroelectricity and altermagnetism is much more robust toward an increase in the energy cost associated with the deformation of the lattice. Therefore, our results suggest that filling fractions corresponding to doping relatively far away from half-filling constitute the most promising regime to look for coexistent ferroelectricity and metallic altermagnetism with mutual enhancement. Moreover, we propose a way to electrically tune altermagnetism between nodal and nodeless phases as well as achieving coexistence of a nodal and nodeless phase for the two spin species.

Figures (3)

• Figure 1: (a) The schematic diagram of the model Hamiltonian with sublattices A and B and (b) the associated magnetic Brillouin zone.
• Figure 2: $m_N$ vs $U$ for different carrier density $n_0$ in the first row and the corresponding Fermi surfaces in the second (third) row in the absence (presence) of Rashba SOC $\lambda_R$. The four eigenenergies satisfy $E_1<E_2<E_3<E_4$, which can be identified by the color of the in-plane spin arrows. The parameters used are: $t=1$, $t^{'}/t=0.3$, $\delta=0.2$, and $T/t=0.1$. In panels (d) and (e), there is no in-plane component of the spin expectation value at the Fermi surface and hence the individual contributions $E_1-E_4$ cannot be discerned. Similar to (g), the inner (outer) FS in the presence of nodes corresponds to $E_2$ ($E_1$) in (d). In (e), the FS corresponds to $E_3$, the same as the magenta arrows shown in (h).
• Figure 3: $P_s$ vs $\gamma$ for different carrier density $n_0$ in the first row and the corresponding free energy in the second row and $m_N$ in the third rows. The parameters used are: $t=1$, $t^{'}/t=0.3$, $\delta=0.2$, $T/t=0.1$, and $\eta C^4t^3=0.25$.