Microscopic origin of magnetism in monolayer 3d transition metal dihalides

Atomic‐Scale Visualization of Multiferroicity in Monolayer NiI2

“…[ 33,34 ] DFT calculations have determined that the q vector characterizing the spin spiral order in bulk is a consequence of the competition between magnetic exchange interactions between Ni atoms. [ 31,36,37 ] In particular, ferromagnetic intralayer first‐neighbor J 1 , antiferromagnetic intralayer third‐neighbor J 3 , and antiferromagnetic interlayer second‐neighbor $$\tilde{J}_2$$ magnetic exchange interactions are the most relevant. These interactions lead to a q vector in bulk whose in‐plane component lies on the $$\overline{\Gamma M}$$ segment in reciprocal space, and whose value can be modified by external parameters, such as pressure, that change the ratio between the different magnetic exchanges.…”

“…These interactions lead to a q vector in bulk whose in‐plane component lies on the $$\overline{\Gamma M}$$ segment in reciprocal space, and whose value can be modified by external parameters, such as pressure, that change the ratio between the different magnetic exchanges. [ 36,38 ] In the monolayer limit, there are no interlayer interactions, hence the q vector is determined by the competition between J 1 and J 3 ( Figure b). DFT calculations have predicted that in this scenario the q vector lies on the $$\overline{\Gamma K}$$ segment in reciprocal space, corresponding to the third‐neighbor bond direction.…”

Delving into the anisotropic interlayer exchange in bilayer CrI3

“…The superexchange mechanisms leading to anisotropic exchange interactions are therefore different from those discussed in the seminal Moriya's paper [22], where it was assumed that the spin of the magnetic atom couples to its own orbital moment. On the other hand, the microscopic mechanisms at play are analogous to those analysed for related transition-metal dihalides, with trihalides similar local bonding environments and strong magnetic anisotropies [59,60] To examine the influence of a stacking sequence we gradually translated the upper layer along the a 2 lattice vector, starting from the LT and ending with the HT structure (figure 3(c)). The different behavior of D and K with stacking alteration demonstrates the importance of angles in the Cr-I-I-Cr bonds for hopping processes that are governing the interlayer interaction.…”

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

“…The cases of FeX2, CoCl2 and CoBr2 are half metals, which enforces integer magnetic moment despite the metallic ground state. The * indicate ferromagnets where full spinorbit coupling was included and the angles then refer to the direction of the spins rather that the spiral plane normal vector ligands in agreement with the conclusion of [46]. The magnetic moments are calculated as the total moment in the unit cell using the ferromagnetic configurations without spinorbit interaction and thus yields an integer number of Bohr magnetons for insulators and half metals.…”

“…The sensitivity to Hubbard corrections in Mn halides is conjectured to be due to the small band width of the spin spirals as it indicates weak exchange interactions in agreement with the findings of Re. [46]. The 120 • order is expected if nearest neighbour anti-ferromagnetic interactions dominate.…”