Type II multiferroic order in two-dimensional transition metal halides from first principles spin-spiral calculations

Abstract

We present a computational search for spin spiral ground states in two-dimensional transition metal halides that are experimentally known as van der Waals bonded bulk materials. Such spin spirals break the rotational symmetry of the lattice and lead to polar ground states where the axis of polarization is strongly coupled to the magnetic order (type II multiferroics). We apply the generalized Bloch theorem in conjunction with non-collinear density functional theory calculations to find the spiralling vector that minimizes the energy and then include spin-orbit coupling to calculate the preferred orientation of the spin plane with respect to the spiral vector. We find a wide variety of magnetic orders ranging from ferromagnetic, stripy anti-ferromagnetic, 120° non-collinear structures and incommensurate spin spirals. The latter two introduce polar axes and are found in the majority of materials considered here. The spontaneous polarization is calculated for the incommensurate spin spirals by performing full supercell relaxation including spinorbit coupling and the induced polarization is shown to be strongly dependent on the orientation of the spiral planes. We also test the effect of Hubbard corrections on the results and find that for most materials LDA+U results agree qualitatively with LDA. An exception is the Mn halides, which are found to exhibit incommensurate spin spiral ground states if Hubbard corrections are included whereas bare LDA yields a 120° non-collinear ground state.

Atomic‐Scale Visualization of Multiferroicity in Monolayer NiI2

“…[47] However, based on the phase diagrams obtained in that work, the different q vector that we have measured in the monolayer should lie in the regime dominated by the J 1 and J 3 parameters, in agreement with recent theoretical works. [39] Other spin-orbit coupling interactions such as Dzyaloshinskii-Moriya interaction may compete with Kitaev interactions, due to the explicit breaking of mirror symmetry in our system. Finally, the diffuse peaks around the M points are associated with the defect seen in the scan.…”

“…This could explain why "ab initio" calculations predict a spin spiral for NiCl 2 while the observed ground state is ferromagnetic. [39] Nevertheless, the effect of the substrate on the multiferroic order of NiI 2 should be further analyzed to reconcile the different experimental and theoretical works.…”

“…DFT calculations have predicted that in this scenario the q vector lies on the ΓK segment in reciprocal space, corresponding to the third-neighbor bond direction. [39] The classical Heisenberg model solution predicts that q = (q, q, 0), with q in units of the reciprocal lattice of the structural single-unit cell with lattice vector a, is determined by the J 1 /J 3 ratio. [40,41] Apart from the magnetic order, theoretical analyses have shown that monolayer NiI 2 develops a ferroelectric polarization ).…”

“…A comparison of the experimental q vector based on our experiments with previous theoretical predictions for free-standing monolayer NiI 2 , could point out that DFT tends to overestimate the |J 3 /J 1 | ratio. [38,39] This could be rationalized by the typical limitations of the different DFT functionals to deal with electronic correlations and electronic localization, thus introducing an overestimation of the long-range magnetic exchanges. This could explain why "ab initio" calculations predict a spin spiral for NiCl 2 while the observed ground state is ferromagnetic.…”

Antiferromagnetism in two-dimensional materials: progress and computational challenges

“…Planar spin spirals (including non-collinear commensurate order) allow for a similar classification in terms of 2D prototypes [27]. SOC determines the orientation of the spiral plane with respect to the lattice and the limiting cases are the proper helix (spiral plane orthogonal to Q), the in-plane cycloid (spiral plane coincides with atomic plane) and the out-ofplane cycloid (spiral plane spanned by Q and normal vector to atomic plane).…”