Augmented and quenched local moments in a van der Waals itinerant moiré ferromagnet

Twisted two-dimensional (2D) van der Waals (vdW) quantum materials are renowned for their uncanny features like unconventional superconductivity, metal insulator transition (Mott transition), spin liquid phase etc., offering a rich landscape for strong electron correlations. Such electronic correlations also account for unusual magnetism in twisted crystals. However, advancement in the field of 2D twisted magnetism has been constrained, owing to lack of ideal materials as well as proper ways to design moiré magnets correlating their emergent magnetic and electronic properties. Here, we design a vdW moiré magnet and demonstrate that the simple act of rotating two monolayers i.e., $\mathrm{1T}\text{−}{\mathrm{NbSe}}_2$ and $\mathrm{1T}\text{−}{\mathrm{VSe}}_2$ at various twist angles, produces an inhomogeneous mixture of augmented and quenched localized magnetic moments per transition metal vanadium (V) and niobium (Nb) atoms. Precisely, twist angle affects the induced local magnetic moments of each constituent layers. Notable flat bands and itinerant ferromagnetism emerge in vdW moiré superlattice, the latter satisfying Stoner criterion. These features result from orbital rehybridization at atomic lattice sites instead of interlayer coupling between layers. Moreover, orbital magnetism is identified in untwisted heterobilayer system. The results present an effective strategy for designing moiré magnets with insights into new quantum-mechanical phenomenon of twist regulated on-site magnetism.

Figure 1

Portrayal of atomic configurations for optimized vdW moiré magnets. (a) Upper view of extended AA stacked 1T-${\mathrm{NbSe}}_2$ and 1T-${\mathrm{VSe}}_2\mathrm{vdW}$ heterobilayers; (b) lateral view of bilayer heterostructure, top view of twisted unit cells at (c) $\theta =13.17{}^{\circ }$, (d) $\theta =21.79{}^{\circ }$, and (d) $\theta =27.80{}^{\circ }$ (Blue, green, and light pink spheres represent vanadium, niobium, and selenium atoms, respectively).

Figure 2

Density overlap region and charge density difference (CDD) analysis of moiré magnets. First row (a)–(d) displays contour plot of density overlap regions at the interface along with a lateral view of CDD plots (e)–(h) in the second row for vdW ${\mathrm{NbSe}}_2\text{−}{\mathrm{VSe}}_2$ hybrid systems with isosurface value of 0.0004 electron/Å. Blue and Red lobes represent net charge accumulation and dissipations across the layers and at atomic sites, respectively. (Color box shows maximum and minimum density overlap regions indicated by blue and red color).

Figure 3

Illustration of spin populations under spin polarized density of states (DOS) (a)–(d) and energy spectrum diagrams (e)–(h) for spin up channel at twist $\mathrm{angle}\theta =0{}^{\circ },13.17{}^{\circ },21.79{}^{\circ }\text{,}\text{and}27.80{}^{\circ }$. The black arrows in the DOS plot correspond to shuffle of density peaks for spin up (blue arrow) and down channels (orange arrow) toward valance band (VB) and conduction band (CB) regions with respect to Fermi energy under spin polarization. Here, $\langle ▵E\rangle$ corresponds to average exchange splitting energy in the energy range of $-1$ eV to 1 eV.

Figure 4

Representation of projected DOS (PDOS) (a)–(d) and orbital resolved band diagrams (e)–(h) of $1{\mathrm{TNbSe}}_2\text{−}1{\mathrm{TVSe}}_2$ vdW heterostructure along $\mathrm{\Gamma }-M-K-\mathrm{\Gamma }$ directions at $\theta =0^{\circ }13.17{}^{\circ },21.{79}^{\circ }$, and $27.{80}^{\circ }$ geometrical configurations. Each color in the PDOS plot corresponds to a specific orbital belonging to constituent atoms.

Figure 5

Display of twist modified inhomogeneous local magnetization, average magnetic moment per atom, and orbital magnetism in studied systems. (a), (b) variation of localized magnetic moments per vanadium (V) atoms and niobium (Nb) atoms as a function of twist angles, (c), (d) average magnetic moment (${\mathrm{M}}_{\text{average}}$) per atom with respect to twist angles and (e), (f) electronic motion as well as orbital magnetism spread along the $\mathrm{\Gamma }-M-K-\mathrm{\Gamma }$ path of twist free unit cell in the Brillouin zone. The color boxes correspond to induced local moments at twist angle $0^{{}^{\circ }},{13.17}^{{}^{\circ }},{21.79}^{{}^{\circ }},{27.80}^{{}^{\circ }},{32.20}^{{}^{\circ }},\text{and}{\text{42.11}}^{{}^{\circ }}$, respectively.