Spin liquids in geometrically perfect triangular antiferromagnets

Static and dynamic magnetic properties of the spin-52triangle lattice antiferromagnet Na3Fe(PO4)2studied by31P NMR

³¹P nuclear magnetic resonance (NMR) measurements have been carried out to investigate the magnetic properties and spin dynamics of Fe³⁺(S= 5/2) spins in the two-dimensional triangular lattice (TL) compound Na₃Fe(PO₄)₂. The temperature (T) dependence of nuclear spin-lattice relaxation rates (1/T1) shows a clear peak around Néel temperature,TN=10.9K, corresponding to an antiferromagnetic (AFM) transition. From the temperature dependence of NMR shift (K) aboveTN, an exchange coupling between Fe³⁺spins was estimated to beJ/kB≃1.9K using the spin-5/2 Heisenberg isotropic-TL model. The temperature dependence of1/T1Tdivided by the magnetic susceptibility (χ),1/T1Tχ, aboveTNproves the AFM nature of spin fluctuations below∼50 Kin the paramagnetic state. In the magnetically ordered state belowTN, the characteristic rectangular shape of the NMR spectra is observed, indicative of a commensurate AFM state in its ground state. The strong temperature dependence of 1/T₁in the AFM state is well explained by the two-magnon (Raman) process of the spin waves in a 3D antiferromagnet with a spin-anisotropy energy gap of 5.7 K. The temperature dependence of sublattice magnetization is also well reproduced by the spin waves. Those results indicate that the magnetically ordered state of Na₃Fe(PO₄)₂is a conventional 3D AFM state, and no obvious spin frustration effects were detected in its ground state.

Stripe-yzmagnetic order in the triangular-lattice antiferromagnet KCeS2

Yb- and Ce-based delafossites were recently identified as effective spin-1/2 antiferromagnets on the triangular lattice. Several Yb-based systems, such as NaYbO₂, NaYbS₂, and NaYbSe₂, exhibit no long-range order down to the lowest measured temperatures and therefore serve as putative candidates for the realization of a quantum spin liquid. However, their isostructural Ce-based counterpart KCeS₂exhibits magnetic order belowT_N= 400 mK, which was so far identified only in thermodynamic measurements. Here we reveal the magnetic structure of this long-range ordered phase using magnetic neutron diffraction. We show that it represents the so-called 'stripe-yz' type of antiferromagnetic order with spins lying approximately in the triangular-lattice planes orthogonal to the nearest-neighbor Ce-Ce bonds. No structural lattice distortions are revealed belowT_N, indicating that the triangular lattice of Ce³⁺ions remains geometrically perfect down to the lowest temperatures. We propose an effective Hamiltonian for KCeS₂, based on a fit to the results ofab initiocalculations, and demonstrate that its magnetic ground state matches the experimental spin structure.