Spin liquids on triangular and kagome lattices

7 problems

• Has a Dirac spin liquid been realized in a material?

  Contested

  In a Dirac spin liquid the spinons have energies growing linearly with momentum near a few points, so the neutron signal rises linearly with energy and forms cones. Candidates have been reported in kagome and triangular compounds, but confirmation in independent materials is lacking.

• Does herbertsmithite have an intrinsic spin gap?

  Contested

  Herbertsmithite, ZnCu3(OH)6Cl2, is the best-studied kagome spin-liquid material, but some copper and zinc atoms swap places. Nuclear magnetic resonance experiments disagree with each other on whether there is a small energy gap, and the defects make the data hard to interpret.

• Ground state of the spin-$1/2$ kagome Heisenberg antiferromagnet

  Contested

  The simplest model of spins on the kagome lattice still has no agreed ground state. The two main candidates are a spin liquid with a small energy gap and one with no gap and Dirac-cone excitations (energy growing linearly with momentum).

• Nature of the $1/9$ magnetization plateau of kagome antiferromagnets

  Contested

  In a strong field the magnetization of a kagome antiferromagnet can stay fixed at one ninth of its maximum over a range of fields. Calculations disagree on whether this plateau state is a spin liquid with topological order or a regular crystal of spin pairs, and a 2024 experiment observed the plateau in a real compound.

• Is $\kappa$-(BEDT-TTF)2Cu2(CN)3 a spin liquid or a gapped valence-bond state?

  Contested

  This organic salt was the first proposed triangular-lattice spin liquid. Later experiments suggest a spin gap opens near 6 K, which would mean the spins pair into singlets instead.

• Does any insulator host a spinon Fermi surface?

  Open

  A spinon Fermi surface would make an electrical insulator behave like a metal for spin and heat. Candidates include organic triangular-lattice salts and the layered compound 1T-TaS2, but no measurement has established it.

• Nature of the spin liquid in the triangular $J1-J2$ Heisenberg model

  Contested

  Adding a weak second-neighbor coupling to the triangular-lattice Heisenberg model destroys its 120-degree magnetic order and produces a nonmagnetic phase. Whether this phase is a gapless Dirac spin liquid, a gapped spin liquid or a chiral state is unsettled.