Magnetoelectric behavior of breathing kagom\'{e} monolayers of $\mathrm{Nb}_3\mathrm{(Cl, Br, I)}_8$ from first-principles calculations

TL;DR

This study uses first-principles calculations to investigate the magnetoelectric properties of 2D Nb3(Cl,Br,I)8 monolayers, revealing complex magnetic orders and conditions under which magnetoelectric effects can occur.

Contribution

It provides the first detailed theoretical prediction of magnetic ground states and magnetoelectric behavior in Nb3(Cl,Br,I)8 monolayers based on density functional theory.

Findings

Nb3Cl8 has a 120° cycloid of trimerized spins as ground state.

Nb3Br8 and Nb3I8 exhibit long-period incommensurate helical order.

Magnetoelectric effects are suppressed by helical magnetic order in the ground state.

Abstract

We apply density functional theory to explore the magnetoelectric (ME) properties of two-dimensional $\mathrm{Nb}_3\mathrm{(Cl,Br,I)}_8$. These compounds have recently been proposed to exhibit coupled ferroelectric and ferromagnetic order leading to a switchable anomalous valley Hall effect (AVHE). Using both spin-spiral and self-consistent spin-orbit coupled calculations, we predict an in-plane $120^\circ$ cycloid of trimerized spins as the ground state for $\mathrm{Nb}_3\mathrm{Cl}_8$. For $\mathrm{Nb}_3\mathrm{Br}_8$ and $\mathrm{Nb}_3\mathrm{I}_8$ we find long period incommensurate helical order. We calculate a number of magnetic properties such as the exchange constants, orbital magnetization, and Weiss temperatures. It is then shown that, despite having both broken inversion and time-reversal symmetry, the proposed AVHE and linear ME response are forbidden by the presence of helical order in the ground state. In addition, the computed switching trajectory demonstrates that it is unlikely that the polar state of the monolayers can be switched with a homogeneous electric field due to an unusual equation of state of the out-of-plane dipole moment. Nevertheless, we highlight that in the presence of a strong electric field, the trimerized spins in $\mathrm{Nb}_3\mathrm{Cl}_8$ will exhibit a magnetic phase transition from the $120^\circ$ cycloid to out-of-plane ferromagnetic order, which restores the symmetry required for both AVHE and linear ME effects.