  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, ultra-compact 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 NiX2 (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 NiCl2 single layers cannot be explained by
means of 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.
