## What is/are Kagome Antiferromagnet?

Kagome Antiferromagnet - We uncover qualitatively different behaviours on different timescales, and argue that the ground state of Ca10Cr7O28 is born out of a slowly-fluctuating “spiral spin liquid”, while faster fluctuations echo the U(1) spin liquid found in the kagome antiferromagnet.^{[1]}Only combined contributions of dual J3 couplings with anisotropic Dzyaloshinskii-Moriya interactions are capable to suppress frustration of kagome antiferromagnetics.

^{[2]}We predict a mechanism to controllably manipulate domain walls in kagome antiferromagnets via a single linearly polarized spin-wave source.

^{[3]}We report an experimental study of the static magnetization $M(H,T)$ and high-field electron spin resonance (ESR) of polycrystalline Mg$_{2}$Gd$_{3}$Sb$_{3}$O$_{14}$, a representative member of the newly discovered class of the so-called tripod-kagome antiferromagnets where the isotropic Gd$^{3+}$ spins ($S = 7/2$) form a two-dimensional (2D) kagome spin-frustrated lattice.

^{[4]}The 2D kag-CrPc framework is an ideal candidate for $S$ = kagome antiferromagnet with RT3 magnetic order.

^{[5]}We apply the formalism to a kagome antiferromagnet which is augmented by general in-plane and out-of-plane Dzyaloshinskii-Moriya (DM) interactions, as argued to be present in the spin liquid candidate material herbertsmithite.

^{[6]}

## spin 1 2

The discovery of ideal spin-1/2 kagome antiferromagnets Herbertsmithite and Zn-doped Barlowite represents a breakthrough in the quest for quantum spin liquids (QSLs), and nuclear magnetic resonance (NMR) spectroscopy plays a prominent role in revealing the quantum paramagnetism in these compounds.^{[1]}As a working example we investigate the possible ordering of nuclear spins that interact through an underlying lattice of the two-dimensional spin-1/2 kagome antiferromagnet (KHAF), although the treatment remains general and can be extended to other spin liquids and dimensions.

^{[2]}The ground state of the spin-1/2 kagome antiferromagnet remains uncertain despite decades of active research.

^{[3]}A spin-1/2 lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration.

^{[4]}

## quantum spin liquid

Realization of the Kagome antiferromagnetic (KAF) lattice is of high interest because the geometric frustration in the Kagome lattice is expected to give rise to highly degenerated ground states that may host exotic phases such as quantum spin liquid.^{[1]}These models can be realized in any lattice that can be tiled by triangles, such as the triangular or kagome lattices, and have been shown to have close connections to the physics of quantum spin liquids in the Heisenberg kagome antiferromagnet.

^{[2]}We identify a metal-insulator transition around U ∼ Uc1 and four distinct phases as a function of U/t on narrower cylinders, including a metallic phase at U < Uc1, two insulating intermediate phases: a translational symmetry breaking phase at Uc1 < U < Uc2 and a quantum spin liquid phase at Uc2 < U < Uc3, and the kagome antiferromagnetic phase at U > Uc3.

^{[3]}

## Quantum Kagome Antiferromagnet

Here, we perform the Raman scattering on single crystals of two quantum kagome antiferromagnets, of which one is the kagome QSL candidate Cu3Zn(OH)6FBr, and another is an antiferromagnetically ordered compound EuCu3(OH)6Cl3.^{[1]}The quantum kagome antiferromagnets YCu3(OH)6OxCl3-x (x=0,1/3) are produced using a unified solid state synthesis route for polycrystalline samples.

^{[2]}In this context, the quantum kagome antiferromagnets YCu$_3$(OH)$_6$Cl$_3$, which has been recently reported as the first geometrically perfect realization of the kagome lattice with negligible magnetic/non-magnetic intersite mixing and a possible quantum-spin-liquid ground state, is of particular interest.

^{[3]}The magnetic ground state of the ideal quantum kagome antiferromagnet (QKA) has been a long-standing puzzle, mainly because perturbations to the nearest-neighbor isotropic Heisenberg Hamiltonian can lead to various fundamentally different ground states.

^{[4]}

## Distorted Kagome Antiferromagnet

The magnetic properties of the S = 1/2 distorted kagome antiferromagnet CdCu3(OH)6Cl2 have been studied by magnetic susceptibility, heat capacity, and high-field magnetization measurements.^{[1]}High-resolution time-of-flight powder neutron diffraction and high-field magnetization were measured to investigate the magnetic structure and existence of a field-induced magnetic phase transition in the distorted kagome antiferromagnet Cs$_2$Cu$_3$SnF$_{12}$.

^{[2]}Employing a combination of all electron density functional theory and numerical diagonalization techniques, we establish the Heisenberg Hamiltonians for the distorted kagome antiferromagnets Rb2NaTi3F12, Cs2NaTi3F12 and Cs2KTi3F12.

^{[3]}

## 2 Kagome Antiferromagnet

The discovery of ideal spin-1/2 kagome antiferromagnets Herbertsmithite and Zn-doped Barlowite represents a breakthrough in the quest for quantum spin liquids (QSLs), and nuclear magnetic resonance (NMR) spectroscopy plays a prominent role in revealing the quantum paramagnetism in these compounds.^{[1]}As a working example we investigate the possible ordering of nuclear spins that interact through an underlying lattice of the two-dimensional spin-1/2 kagome antiferromagnet (KHAF), although the treatment remains general and can be extended to other spin liquids and dimensions.

^{[2]}The ground state of the spin-1/2 kagome antiferromagnet remains uncertain despite decades of active research.

^{[3]}

## Heisenberg Kagome Antiferromagnet

We investigate the low temperature magnetic properties of a S=5/2 Heisenberg kagome antiferromagnet, the layered monodiphosphate Li_{9}Fe_{3}(P_{2}O_{7})_{3}(PO_{4})_{2}, using magnetization measurements and ^{31}P nuclear magnetic resonance.^{[1]}These models can be realized in any lattice that can be tiled by triangles, such as the triangular or kagome lattices, and have been shown to have close connections to the physics of quantum spin liquids in the Heisenberg kagome antiferromagnet.

^{[2]}A spin-1/2 lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration.

^{[3]}