Biquadratic exchange interactions in two-dimensional magnets

Abstract

Magnetism in recently discovered van der Waals materials has opened several avenues in the study of fundamental spin interactions in truly two-dimensions. A paramount question is what effect higher-order interactions beyond bilinear Heisenberg exchange have on the magnetic properties of few-atom thick compounds. Here we demonstrate that biquadratic exchange interactions, which is the simplest and most natural form of non-Heisenberg coupling, assume a key role in the magnetic properties of layered magnets. Using a combination of nonperturbative analytical techniques, non-collinear first-principles methods and classical Monte Carlo calculations that incorporate higher-order exchange, we show that several quantities including magnetic anisotropies, spin-wave gaps and topological spin-excitations are intrinsically renormalized leading to further thermal stability of the layers. We develop a spin Hamiltonian that also contains antisymmetric exchanges (e.g., Dzyaloshinskii–Moriya interactions) to successfully rationalize numerous observations, such as the non-Ising character of several compounds despite a strong magnetic anisotropy, peculiarities of the magnon spectrum of 2D magnets, and the discrepancy between measured and calculated Curie temperatures. Our results provide a theoretical framework for the exploration of different physical phenomena in 2D magnets where biquadratic exchange interactions have an important contribution.

Properties and dynamics of meron topological spin textures in the two-dimensional magnet CrCl3

“…The fourth term in Eq. (1) represents the biquadratic (BQ) exchange, which involves the hopping of two or more electrons between two adjacent sites 15,16 . Its strength is given by the constant K ij , which is the simplest and most natural form of non-Heisenberg coupling.…”

“…Its strength is given by the constant K ij , which is the simplest and most natural form of non-Heisenberg coupling. We recently found that several 2D magnets develop substantial BQ exchange in their magnetic properties, which is critical to quantitatively describe important features such as Curie temperatures, thermal stability, and magnon spectra 16 . The magnitude of K ij for CrCl 3 is 0.22 meV, which is slightly smaller than the BL exchange for the first-nearest neighbors J 1 = 1.28 meV but too large to be ignored.…”

“…(1) are extracted from non-collinear ab initio simulations including spin-orbit coupling to determine the different components of J ij , λ ij , and K ij (ij = xx, yy, zz) as described in ref. 16 . For atomistic spin dynamics, we calculate the effective magnetic field B i arising from the BQ exchange interactions with components:…”

“…S6). We can understand this type of magnetic frustration in terms of the competing exchange interactions between the different nearest neighbors (1st, 2nd, 3rd) in CrCl 3 16 . In terms of the isotropic exchange (J 1st , J 2nd , J 3rd ), we observe that the frustration takes places due to the third-nearest-neighbor, which has an anti-ferromagnetic exchange (J 3rd = −0.025 meV) relative to the first-(J 1st = 1.28 meV) and the second-nearest neighbors (J 2nd = 0.072 meV).…”

Electron correlation effects on exchange interactions and spin excitations in 2D van der Waals materials

“…Using the energy-mapping method, exchange and SW energy increase with U, worsening the agreement between theory and INS measurements. This suggests that non-Heisenberg interactions, such as biquadratic exchange or multisite exchange interactions [56][57][58][59][60] , might be important in this system, especially when additional electron correlations are taken into account. By analogy with transition-metal oxide systems 57 one can assume that the induced magnetic polarization on iodine ligands can play a decisive role in this non-Heisenberg behavior.…”