We report a high-resolution neutron diffraction study on the orbitally-degenerate spin-1/2 hexagonal antiferromagnet AgNiO2. A structural transition to a tripled unit cell with expanded and contracted NiO6 octahedra indicates root(3) x root(3) charge order on the Ni triangular lattice. This suggests charge order as a possible mechanism of lifting the orbital degeneracy in the presence of charge fluctuations, as an alternative to Jahn-Teller distortions. A novel magnetic ground state is observed at base temperatures with the electron-rich S = 1 Ni sites arranged in alternating ferromagnetic rows on a triangular lattice, surrounded by a honeycomb network of non-magnetic and metallic Ni ions. We also report first-principles band-structure calculations that explain microscopically the origin of these phenomena.
We report the single-crystal growth and the fundamental magnetic and thermodynamic properties of a rare-earth triangular lattice antiferromagnet CeCd$_3$As$_3$. In this rare-earth antiferromagnet, the Ce local moments form a perfect triangular lattice. Due to the spin-orbital-entangled nature of the Ce local moments, the compound exhibits extremely anisotropic antiferromagnetic couplings along the c direction and in the ab plane respectively. We show that CeCd$_3$As$_3$ represents a {\it rare} experimental realization of an antiferromagnetic Ising model on a two dimensional triangular lattice …
We analyze the zero temperature phase diagrams of the spin S quantum antiferromagnet on square and triangular lattices with competing nearest and next-nearest exchange interactions as well as biquadratic couplings. We approach the problem from the large S limit. Our primary focus is on determining the extent to which the existence and character of any quantum disordered phases can be inferred from this approach.
Motivated by multiple possible physical realizations, we study the SU(4) quantum antiferromagnet with a fundamental representation on each site of the triangular lattice. We provide evidence for a gapless liquid ground state of this system with an emergent Fermi surface of fractionalized fermionic partons coupled with a U(1) gauge field. Our conclusions are based on numerical simulations using the density matrix renormalization group (DMRG) method, which we support with a field theory analysis.
We study the anomalous Hall effect on the antiferromagnetic coloring-triangular lattice with a coplanar magnetic configuration in presence of a spin-orbit interaction. The effect of the spin-orbit coupling is included at effective level as a rotation of the electronic spin as the electrons hop from site to site. Our result reveals that a finite Hall conductivity in the planar 120$^{\circ}$ structure takes place if a finite spin-orbit coupling is present. A quantized Hall conductivity occurs at global band gaps resulting from the topologically non-trivial band structure.
We elucidate the role of magnon interaction and spontaneous decays in the spin dynamics of the triangular-lattice Heisenberg antiferromagnet by calculating its dynamical structure factor within the spin-wave theory. Explicit theoretical results for neutron-scattering intensity are provided for spins S=1/2 and S=3/2. The dynamical structure factor exhibits unconventional features such as quasiparticle peaks broadened by decays, non-Lorentzian lineshapes, and significant spectral weight redistribution to the two-magnon continuum. This rich excitation spectrum illustrates the complexity of the tr…
Non-collinear triangular antiferromagnets with a coplanar spin arrangement and vanishing net magnetic moment can exhibit a large anomalous Hall effect owing to their non-vanishing momentum space Berry curvature. Here we show the existence of a large field induced topological Hall effect in the non-coplanar triangular antiferromagnetic geometry of Mn3Sn. A detailed magnetic and Hall effect measurements demonstrate the presence of three distinct Hall contributions; a high temperature anomalous Hall effect, a low temperature topological Hall effect and an intermediate temperature region with coex…
We report the crystal structure of Ba$_2$La$_2$CoTe$_2$O$_{12}$ determined by Rietveld analysis using X-ray powder diffraction data. It was found from magnetic measurements that Ba$_2$La$_2$CoTe$_2$O$_{12}$ can be described as a spin-1\2 triangular-lattice antiferromagnet with easy-plane anisotropy at low temperatures. This compound undergoes a magnetic phase transition at $T_{\rm N}\,{=}\,3.26$ K to an ordered state with the $120^{\circ}$ structure. The magnetization curve exhibits the one-third plateau characteristic of triangular-lattice quantum antiferromagnets. The antiferromagnetic excha…
We present a detailed magnetic study of the triangular antiferromagnet ErMgGaO$_4$. A point charge calculation under the single ion approximation reveals a crystal field ground state doublet with a strong Ising-like behavior of the Er$^{3+}$ moment along the c axis. Magnetic susceptibility and specific heat measurements indicate no presence of magnetic transitions above 0.5~K and no evidence of residual entropy as temperature approaching zero. Zero field (ZF) $μ$SR measurements shows no sign of static uniform or random field and longitudinal field (LF) $μ$SR measurements exhibit persistent spi…
Muon spin relaxation and rotation ($μ$SR) experiments on single crystals of the structurally perfect triangular antiferromagnet YbMgGaO$_4$ indicate the absence of both static long-range magnetic order and spin freezing down to 0.048 K in zero field. Below 0.4 K, the $μ^{+}$ spin relaxation rates, which are proportional to the dynamic correlation function of the Yb$^{3+}$ spins,exhibit temperature-independent plateaus. Same behavior is revealed by temperature-independent local susceptibilities extracted from the Knight shifts of the $μ^{+}$ spin rotation frequencies under a transverse field of…
We study the quantum phase transition of an $S=1/2$ anisotropic $α$ $(\equiv J_z/J_{xy})$ Heisenberg antiferromagnet on a triangular lattice. We calculate the sublattice magnetization and the long-range helical order-parameter and their Binder ratios on finite systems with $N \leq 36$ sites. The $N$ dependence of the Binder ratios reveals that the classical 120$^{\circ}$ Néel state occurs for $α\lesssim 0.55$, whereas a critical collinear state occurs for $1/α\lesssim 0.6$. This result is at odds with a widely-held belief that the ground state of a Heisenberg antiferromagnet is the 120$^{\circ…
CeCd$_3$As$_3$ is a rare-earth triangular-lattice antiferromagnet with large inter-layer separation. Our field-dependent heat capacity measurements at dilution fridge temperatures allow us to trace the field-evolution of the spin-excitation gaps throughout the antiferromagnetic and paramagnetic regions. The distinct gap evolution places strong constraints on the microscopic pseudo-spin model, which, in return, yields a close {\it quantitative} description of the gap behavior. This analysis provides crucial insights into the nature of the magnetic state of CeCd$_3$As$_3$, with a certainty regar…
The $1/4$-filled organic compound, $δ$-(EDT-TTF-CONMe$_{2}$)$_{2}$AsF$_6$ is a frustrated two-dimensional triangular magnetic system as shown by high-frequency (111.2 and 222.4 GHz) electron spin resonance (ESR) and structural data in the literature. The material gradually orders antiferromagnetically below 40~K but some magnetically disordered domains persist down to 4 K. We propose that in defect free regions frustration prevents true magnetic order down to at least 4 K in spite of the large first- and second-neighbor exchange interactions along chains and between chains, respectively. The a…
Elementary quasiparticles in solids such as phonons and magnons occasionally have nontrivial interactions between them, as well as among themselves. As a result, their energy eigenvalues are renormalized, the quasiparticles spontaneously decay into a multi-particle continuum state, or they are hybridized with each other when their energies are close. As discussed in this review, such anomalous features can appear dominantly in quantum magnets but are not, a priori, negligible for magnetic systems with larger spin values and noncollinear magnetic structures. We review the unconventional magneti…
We study the magnetization process of the spin-1/2 antiferromagnetic Heisenberg model on a layered triangular lattice by means of a numerical cluster mean-field method with a scaling scheme (CMF+S). It has been known that antiferromagnetic spins on a two-dimensional (2D) triangular lattice with quantum fluctuations exhibit a one-third magnetization plateau in the magnetization curve under magnetic field. We demonstrate that the CMF+S quantitatively reproduces the magnetization curve including the stabilization of the plateau. {We also discuss the effects of a finite interlayer coupling, which …
The stability of a magnetic skyrmion crystal in a centrosymmetric orthorhombic lattice system is numerically investigated. By performing the simulated annealing for an effective spin model with the momentum-resolved interaction on a uniaxially distorted triangular lattice, we find that the skyrmion crystal is robustly realized when dominant interaction channels consist of the double-$Q$ structure in momentum space. Moreover, we show that an anti-type skyrmion crystal with the opposite skyrmion number is obtained by tuning the sign of the bond-dependent anisotropic exchange interaction that ori…
We investigate non-equilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp crossover) at the same temperature $T_{\rm u}=0.282 J$ as for static properties due to unbinding of $\mathbb{Z}_2$-vortices. We show that starting from the high-temperature initial state, due to presence of $\mathbb{Z}_2$-vortices in the considering system, in a broad temperature range $T<T_{\rm u}$ the dynamic properties in the intermediate time range are s…
We report an excellent realization of the highly non-classical incommensurate spin-density wave (SDW) state in the quantum frustrated antiferromagnetic insulator Cs$_2$CoBr$_4$. In contrast to the well-known Ising spin chain case, here the SDW is stabilized by virtue of competing planar in-chain anisotropies and frustrated interchain exchange. Adjacent to the SDW phase is a broad $m = 1/3$ magnetization plateau that can be seen as a commensurate locking of the SDW state into the up-up-down (UUD) spin structure. This represents the first example of long-sought SDW-UUD transition in triangular-t…
Yb-based triangular magnets have recently attracted attention as promising candidates to explore frustrated quantum magnetism. However, some candidates have turned out to have significant amounts of site disorder, which significantly affects the low-temperature magnetic behavior. To overcome this issue, Yb-based frustrated systems without structural disorder are required. In this paper, we report physical properties of two Yb-based triangular magnets Ba3YbB3O9 and Ba3YbB9O18, without structural disorder. Via magnetic susceptibility, magnetization, and muon spin rotation measurements, we verifi…
We show that the mesoscopic incommensurate $\mathbb{Z}_2$ vortex crystals proposed for layered triangular anisotropic magnets can be most saliently identified by two distinctive signatures in dynamical spin response experiments: The presence of pseudo-Goldstone `phonon' modes at low frequencies $ω$, associated with the collective vibrations of the vortex cores, and a characteristic multi-scattered intensity profile at higher $ω$, arising from a large number of Bragg reflections and magnon bandgaps. These are direct fingerprints of the large vortex sizes and magnetic unit cells and the solitoni…
We study the spin liquid candidate of the spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet on the triangular lattice by means of density matrix renormalization group (DMRG) simulations. By applying an external Aharonov-Bohm flux insertion in an infinitely long cylinder, we find unambiguous evidence for gapless $U(1)$ Dirac spin liquid behavior. The flux insertion overcomes the finite size restriction for energy gaps and clearly shows gapless behavior at the expected wave-vectors. Using the DMRG transfer matrix, the low-lying excitation spectrum can be extracted, which shows characteristic Dir…
We present single-crystal neutron scattering measurements of the spin-1/2 equilateral triangular lattice antiferromagnet Ba$_3$CoSb$_2$O$_9$. Besides confirming that the Co$^{2+}$ magnetic moments lie in the ab plane for zero magnetic field, we determine all the exchange parameters of the minimal quasi-2D spin Hamiltonian, which confirms that Ba$_3$CoSb$_2$O$_9$ is an almost perfect realization of the paradigmatic model of frustrated quantum magnetism. A comparison with linear and nonlinear spin-wave theory reveals that quantum fluctuations induce a strong downward renormalization of the magno…
