A route to fully-compensated ferrimagnetic metal: electric-field annihilation of the bilayer bandgap

Abstract

Fully-compensated ferrimagnet has garnered widespread attention due to its zero-net total magnetic moment and non-relativistic global spin splitting. In general, for a fully-compensated ferrimagnet, at least one spin channel should be gapped to ensure a zero-net total magnetic moment, which would lead to a fully-compensated ferrimagnetic (FC-FIM) semiconductor or half-metal, and appears to limit the existence of an FC-FIM metal. Here we propose that an FC-FIM metal can be achieved by electrically closing the gap of a bilayer system. Using two-dimensional (2D) ferromagnetic (FM) semiconductor as building block, we examine both FM and antiferromagnetic (AFM) interlayer couplings and distinguish unipolar magnetic semiconductor (UMS) and bipolar magnetic semiconductor (BMS) monolayers. It is concluded that an electric field can annihilate the bilayer gap and realize the FC-FIM metal only when the interlayer coupling is AFM and the building block is a UMS. Our scheme for realizing an FC-FIM metal can be generalized to electrically tuned 2D spin-degenerate metal with spin-layer locking. Using first-principles calculations, we have validated our proposal by taking bilayer MnOF, bilayer $\mathrm{ScI_2}$ and monolayer $\mathrm{Hf_2S}$ as examples. Our work offers an alternative route to realize the originally forbidden FC-FIM metal, paving the way for further exploration of FC-FIM metal.

Figures (7)

• Figure 1: (Color online) (a): the fundamental building block of 2D FM semiconductor; (b): the bilayer system under an out-of-plane electric field; (c): the interlayer coupling types, including FM ($\alpha$, $\gamma$) and AFM ($\beta$, $\delta$) coupling; (d): the band types of the building block, including unipolar ($\alpha$, $\beta$) and bipolar ($\gamma$, $\delta$) ferromagnetic semiconductors; (e): after the electric field induces gap closure in the bilayer system, its band character spans: FM half-metal ($\alpha$), FC-FIM metal ($\beta$), FM metal ($\gamma$) and FC-FIM half-metal ($\delta$). In (a, c, d, e), the blue and red denote spin-up and spin-down, respectively. In (b), the green arrow represents an out-of-plane electric field. In (d, e), the black horizontal dashed lines indicate the Fermi level.
• Figure 2: (Color online)(a): the energy band structures of monolayer $\mathrm{MnOF}$; (b, c): the side and top views of bilayer $\mathrm{MnOF}$; (d): the total magnetic moment per unit cell as a function of electric field $E$ for bilayer MnOF with FM and AFM interlayer coupling. In (a), the blue and red lines denote spin-up and spin-down states, respectively.
• Figure 3: (Color online)For bilayer $\mathrm{MnOF}$, the band structures for interlayer FM (upper panel) and AFM (lower panel) couplings under electric fields of $E$=0.00 (a, f), 0.02 (b, g), 0.04 (c, h), 0.06 (d, i), 0.08 (e, j) $\mathrm{V/{\AA}}$. The blue and red lines denote spin-up and spin-down states, respectively.
• Figure 4: (Color online)(a): the energy band structures of monolayer $\mathrm{ScI_2}$; (b, c): the side and top views of bilayer $\mathrm{ScI_2}$; (d): the total magnetic moment per unit cell as a function of electric field $E$ for bilayer $\mathrm{ScI_2}$ with FM and AFM interlayer coupling. In (a), the blue and red lines denote spin-up and spin-down states, respectively.
• Figure 5: (Color online) For bilayer $\mathrm{ScI_2}$, the band structures for interlayer FM (upper panel) and AFM (lower panel) couplings under electric fields of $E$=0.00 (a, f), 0.10 (b, g), 0.20 (c, h), 0.30 (d, i), 0.40 (e, j) $\mathrm{V/{\AA}}$. The blue and red lines denote spin-up and spin-down states, respectively.