Electric-Field-induced Two-Dimensional Fully Compensated Ferrimagnetism and Emergent Transport Phenomena

Abstract

The recent discovery of altermagnetism has demonstrated that spin-split electronic band structures can emerge in magnetic systems with zero net magnetization. In contrast, fully compensated ferrimagnetic (fFIM) systems remain far less explored, despite exhibiting similar characteristics such as vanishing magnetization and spin-split bands. Here, based on first-principles calculations combined with theoretical analysis, we demonstrate that monolayer CoS and CoSe can be driven into fFIM states by an external electric field. These materials possess collinear antiferromagnetic ground states with out-of-plane Néel vectors, and their electronic bands are spin degenerate due to $\mathcal{PT}$ symmetry. When an out-of-plane electric field is applied, $\mathcal{PT}$ symmetry is broken, inducing fFIM states with pronounced spin splitting. Moreover, we show that the resulting fFIM states host fully spin-polarized currents, anomalous Hall effects, and magneto-optical Kerr and Faraday effects. Our results establish monolayer CoS and CoSe as promising platforms for electric-field-controlled fFIM states and spintronic applications.

Figures (6)

• Figure 1: Four typical types of collinear magnetic order. (a) Ferromagnetism (FM) exhibits a finite net magnetization and spin-split bands. (b) Conventional antiferromagnetism (AFM) features magnetic sublattices related by $[\mathcal{C}_2 \parallel \mathcal{P}]$ or $[\mathcal{C}_2 \parallel \tau]$, resulting in zero net magnetization and spin-degenerate bands. (c) Altermagnetism (AM) has magnetic sublattices connected by $[\mathcal{C}_2 \parallel \mathcal{O}]$, where $\mathcal{O}$ denotes a rotation or mirror symmetry, leading to zero net magnetization with anisotropic spin splitting. (d) Fully compensated ferrimagnetism (fFIM) lacks symmetry relations between magnetic sublattices and exhibits zero net magnetization with isotropic spin splitting. Red and blue denote spin-up and spin-down sublattices or bands, respectively.
• Figure 2: (a) Top, (b) side, and (c) perspective views of monolayer Co$X$ ($X$ = S, Se) crystal structure. (d) Corresponding BZ with high-symmetry points labeled. Calculated phonon spectra of monolayer (e) CoS and (f) CoSe. Ab initio molecular dynamics results of monolayer (g) CoS and (h) CoSe.
• Figure 3: Band structures and projected density of states of monolayer (a) CoS and (b)CoSe in the absence of SOC. Band structures of monolayer CoS under out-of-plane electric fields of (c) $E = 0.1$ V/Å and (d) $E = -0.1$ V/Å, and (e) the corresponding spin splitting of the top valence band at $\Gamma$, K, and M. Band structures of monolayer CoSe under out-of-plane electric fields of (f) $E = 0.1$ V/Å and (g) $E = -0.1$ V/Å, and (h) the corresponding spin splitting of the top valence band at $\Gamma$, K, and M.
• Figure 4: Band structures of monolayer (a) CoS and (c) CoSe under an out-of-plane electric field of $E = 0.3$ V/Å. Spin-resolved longitudinal conductivity $\sigma_{xx}$ of monolayer (b) CoS and (d) CoSe. Band structures of monolayer (e) CoS and (g) CoSe under an out-of-plane electric field of $E = -0.3$ V/Å. Corresponding spin-resolved longitudinal conductivity $\sigma_{xx}$ for monolayer (f) CoS and (h) CoSe.
• Figure 5: Electronic band structures with SOC of monolayer (a) CoS and (b) CoSe. Insets show a small band gap at the valence band maximum at the $\Gamma$ point and the lifting of valley degeneracy at the $K$ and $K'$ points. Band structures with spin projection $s_z$ of monolayer (c) CoS and (d) CoSe under an out-of-plane electric field of $E = 0.1$ V/Å. Berry curvature distribution summed over all valence bands of (e) CoS and (f) CoSe under an out-of-plane electric field of $E = 0.1$ V/Å. Anomalous Hall conductivity of monolayer (g) CoS and (h) CoSe under the same electric field.