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Register a new userMaterializing Rival Ground States in the Barlowite Family of Kagome Magnets: Quantum Spin Liquid, Spin Ordered, and Valence Bond Crystal States
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The spin-$frac{1}{2}$ kagome antiferromagnet is considered an ideal host for a quantum spin liquid ground state. We find that when the bonds of the kagome lattice are modulated with a periodic pattern, new quantum ground states emerge. Newly synthesized crystalline barlowite (Cu$_4$(OH)$_6$FBr) and Zn-substituted barlowite demonstrate the delicate interplay between singlet states and spin order on the spin-$frac{1}{2}$ kagome lattice. Comprehensive structural measurements demonstrate that our new variant of barlowite maintains hexagonal symmetry at low temperatures with an arrangement of distorted and undistorted kagome triangles, for which numerical simulations predict a pinwheel valence bond crystal (VBC) state instead of a quantum spin liquid (QSL). The presence of interlayer spins eventually leads to an interesting pinwheel $q=0$ magnetic order. Partially Zn-substituted barlowite (Cu$_{3.44}$Zn$_{0.56}$(OH)$_6$FBr) has an ideal kagome lattice and shows QSL behavior, indicating a surprising robustness of the QSL against interlayer impurities. The magnetic susceptibility is similar to that of herbertsmithite, even though the Cu$^{2+}$ impurities are above the percolation threshold for the interlayer lattice and they couple more strongly to the nearest kagome moment. This system is a unique playground displaying QSL, VBC, and spin order, furthering our understanding of these highly competitive quantum states.
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There is a growing family of rare-earth kagome materials with dominant nearest-neighbor interactions and strong spin orbit coupling. The low symmetry of these materials makes theoretical description complicated, with six distinct nearest-neighbor coupling parameters allowed. In this Article, we ask what kinds of classical, ordered, ground states can be expected to occur in these materials, assuming generic (i.e. non-fine-tuned) sets of exchange parameters. We use symmetry analysis to show that there are only five distinct classical ground state phases occurring for generic parameters. The five phases are: (i) a coplanar, 2-fold degenerate, state with vanishing magnetization (${sf A_1}$), (ii) a noncoplanar, 2-fold degenerate, state with magnetization perpendicular to the kagome plane (${sf A_2}$), (iii) a coplanar, 6-fold degenerate, state with magnetization lying within the kagome plane (${sf E}$-coplanar), (iv) a noncoplanar, 6-fold degenerate, state with magnetization lying within a mirror plane of the lattice (${sf E}$-noncoplanar$_{6}$), (v) a noncoplanar, 12-fold degenerate, state with magnetization in an arbitrary direction (${sf E}$-noncoplanar$_{12}$). All five are translation invariant (${bf q}=0$) states. Having found the set of possible ground states, the ground state phase diagram is obtained by comparing numerically optimized energies for each possibility as a function of the coupling parameters. The state ${sf E}$ noncoplanar$_{12}$ is extremely rare, occupying $<1%$ of the full phase diagram, so for practical purposes there are four main ordered states likely to occur in anisotropic kagome magnets with dominant nearest neighbor interactions. These results can aid in interpreting recent experiments on ``tripod kagome systems R$_3$A$_2$Sb$_3$O$_{14}$, as well as materials closer to the isotropic limit such as Cr- and Fe- jarosites.
The emergent behavior of spin liquids that are born out of geometrical frustration makes them an intriguing state of matter. We show that in the quantum kagome antiferromagnet ZnCu$_3$(OH)$_6$SO$_4$ several different correlated, yet fluctuating states exist. By combining complementary local-probe techniques with neutron scattering, we discover a crossover from a critical regime into a gapless spin-liquid phase with decreasing temperature. An additional unconventional instability of the latter phase leads to a second, distinct spin-liquid state that is stabilized at the lowest temperatures. We advance such complex behavior as a feature common to different frustrated quantum magnets.
This article is an introductory review of the physics of quantum spin liquid (QSL) states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semi-classical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semi-classical approaches fail once quantum mechanics become important and then describes the alternative approaches for addressing the problem. We discuss mainly spin $1/2$ systems, and we spend most of our time in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called $SU(2)$, $U(1)$ or $Z_2$ spin liquid states. We review the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin ($S>1/2$) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular lattice systems ($kappa$-(ET)$_{2}$Cu$_{2}$(CN)$_{3}$ and EtMe$_{3}$Sb[(Pd(dmit)$_{2}$]$_{2}$), kagome lattice systems (ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$) and hyperkagome lattice systems (Na$_{4}$Ir$_{3}$O$_{8}$), is reviewed and compared against the corresponding theories.
We present new magnetic heat capacity and neutron scattering results for two magnetically frustrated molybdate pyrochlores: $S=1$ oxide Lu$_2$Mo$_2$O$_7$ and $S={frac{1}{2}}$ oxynitride Lu$_2$Mo$_2$O$_5$N$_2$. Lu$_2$Mo$_2$O$_7$ undergoes a transition to an unconventional spin glass ground state at $T_f {sim} 16$ K. However, the preparation of the corresponding oxynitride tunes the nature of the ground state from spin glass to quantum spin liquid. The comparison of the static and dynamic spin correlations within the oxide and oxynitride phases presented here reveals the crucial role played by quantum fluctuations in the selection of a ground state. Furthermore, we estimate an upper limit for a gap in the spin excitation spectrum of the quantum spin liquid state of the oxynitride of ${Delta} {sim} 0.05$ meV or ${frac{Delta}{|theta|}}sim0.004$, in units of its antiferromagnetic Weiss constant ${theta} {sim}-121$ K.
A class of local SU(2)-invariant spin-1/2 Hamiltonians is studied that has ground states within the space of nearest neighbor valence bond states on the kagome lattice. Cases include generalized Klein models without obvious non-valence bond ground states, as well as a resonating-valence-bond Hamiltonian whose unique ground states within the nearest neighbor valence bond space are four topologically degenerate Sutherland-Rokhsar-Kivelson (SRK) type wavefunctions, which are expected to describe a gapped $mathbb{Z}_2$ spin liquid. The proof of this uniqueness is intimately related to the linear independence of the nearest neighbor valence bond states on quite general and arbitrarily large kagome lattices, which is also established in this work. It is argued that the SRK ground states are also unique within the entire Hilbert space, depending on properties of the generalized Klein models. Applications of the strategies developed in this work to other lattice types are also discussed.
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