Giant Biquadratic Exchange in 2D Magnets and Its Role in Stabilizing Ferromagnetism of NiCl_{2} Monolayers

Two-dimensional (2D) van der Waals (vdW) magnets provide an ideal platform for exploring, on the fundamental side, new microscopic mechanisms and for developing, on the technological side, ultracompact spintronic applications. So far, bilinear spin Hamiltonians have been commonly adopted to investigate the magnetic properties of 2D magnets, neglecting higher order magnetic interactions. However, we here provide quantitative evidence of giant biquadratic exchange interactions in monolayer NiX_{2} (X=Cl, Br and I), by combining first-principles calculations and the newly developed machine learning method for constructing Hamiltonian. Interestingly, we show that the ferromagnetic ground state within NiCl_{2} single layers cannot be explained by means of the bilinear Heisenberg Hamiltonian; rather, the nearest-neighbor biquadratic interaction is found to be crucial. Furthermore, using a three-orbitals Hubbard model, we propose that the giant biquadratic exchange interaction originates from large hopping between unoccupied and occupied orbitals on neighboring magnetic ions. On a general framework, our work suggests biquadratic exchange interactions to be important in 2D magnets with edge-shared octahedra.