Mechanism of Type-II Multiferroicity in Pure and Al-Doped CuFeO${}_2$

Abstract

Type-II multiferroicity, where electric polarization is induced by specific spin patterns, is crucial in fundamental physics and advanced spintronics. However, the spin model and magnetoelectric coupling mechanisms in prototypical type-II multiferroic CuFeO${}_2$ and Al-doped CuFeO${}_2$ remain unclear. Here, by considering both spin and alloy degrees of freedom, we develop a magnetic cluster expansion method, which considers all symmetry allowed interactions. Applying such method, we not only obtain realistic spin model that can correctly reproduce observations for both CuFeO${}_2$ and CuFe${}_{1-x}$Al${}_x$O${}_2$, but also revisit well-known theories of the original spin-current (SC) model and $p$-$d$ hybridization model. Specifically, we find that (i) a previously overlooked biquadratic interaction is critical to reproduce the $\uparrow \uparrow \downarrow \downarrow$ ground state and excited states of CuFeO${}_2$; (ii) the combination of absent biquadratic interaction and increased magnetic frustration around Al dopants stabilizes the proper screw state; and (iii) it is the generalized spin-current (GSC) model that can correctly characterize the multiferroicity of CuFeO${}_2$. These findings have broader implications for understanding novel magnetoelectric couplings in, e.g., monolayer multiferroic NiI${}_2$.