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Open Access Publications from the University of California

Ordered States and Excitations of Frustrated Magnets

  • Author(s): Maksimov, Pavel
  • Advisor(s): Chernyshev, Alexander
  • et al.

Frustrated magnets gain a lot of interest due to promise of states with exotic properties, such as spinons in quantum spin liquids, emergent electrodynamics in quantum spin ices, and strong quantum effects in long-range ordered systems. Magnetic frustration is a situation where classical energy cannot be minimized for all interactions simultaneously, and different phases may be very competitive, or even degenerate. Such competition can either result in ordered states with significant quantum effects or it can completely destroy long-range order. Frustration in these systems can be induced either through geometry of the lattice or through anisotropic interactions.

Very often three-magnon interactions become allowed in frustrated magnets. Since magnons are bosons, as long as kinematic conditions are satisfied (energy and momentum conservation), magnons acquire finite lifetime from decaying into two magnons. There are two main ways to achieve three-magnon interaction: noncollinear ground state of isotropic model or anisotropic interactions.

We performed spin-wave theory calculations for easy-plane models, where frustration and magnon decays are induced with out-of-plane magnetic field. Thus, in easy-plane honeycomb and triangular antiferromagnets out-of-plane magnetic field makes the spins cant out of the plane, forming highly non-collinear structure, and affects magnon spectrum providing kinematic conditions for magnon decays.

We also studied a ferromagnet on kagome lattice with Dzyaloshinkii-Moriya interactions. As we found out, the anisotropic interactions do not affect the ground state, but they affect magnon spectrum and magnon interactions depending on the direction of the magnetic moment, which can be controlled externally. This system is of interest because magnons on kagome lattice are known to exhibit topological properties. Strong magnon interactions, however, put validity of quasiparticle picture in those systems to question.

As it turns out even finding ground states and excitations of anisotropic models is not a trivial task. In honeycomb system with bond-dependent interactions, so-called Kitaev-Heisenberg model, we were able to estimate magnon decay rate which matched numerics of my coauthors. We explored the same model on triangular lattice and found regions of quantum spin liquid and peculiarities of magnon spectrum, such as hidden accidental degeneracies and unexpectedly small quantum corrections to average magnetization.

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