Abstract
We determine magnon spectra of an atomic bilayer magnet with ferromagnetic intra- and both ferro- and anti- ferromagnetic interlayer coupling. Analytic expressions for the full magnon band of the latter case reveal that both exchange interactions govern the fundamental magnon gap. The inter and intralayer magnetic ordering are not independent: the intralayer ferromagnetism stabilizes antiferromagnetic inter-layer order. The topology of these exchange-anisotropy spin models without spin-orbit interaction turns out to be trivial.
Highlights
Two-dimensional van der Waals magnets (2DvdWM) [1] are a unique platform to study magnetism in 2 + ε dimensions [2,3,4]
Analytic expressions for the full magnon band of the latter case reveal that both exchange interactions govern the fundamental magnon gap
Two-dimensional order is associated with strong intrinsic thermal fluctuations [3,5] and characteristic quantum phases [3], offering a possible test bed for competing interactions, such as Heisenberg and anisotropic exchange [6] with different range, Dzyaloshinskii-Moriya interaction (DMI) [7,8] and other spin-orbit couplings [9,10], and magnetodipolar interactions [11,12] in a rich variety of elements and crystal structures
Summary
Two-dimensional van der Waals magnets (2DvdWM) [1] are a unique platform to study magnetism in 2 + ε dimensions [2,3,4]. For compounds with a hexagonal lattice such as CrI3 and CrBr3 [23] as considered here, we may expect a magnon dispersion relation similar to that of the π -electron bands of graphene—a minimum at k = 0 and two degenerate Dirac points per unit cell at an intermediate energy This was confirmed by an analytic expression for a 2DvdWM with ferromagnetic (FM) exchange interactions [24,25,26].
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