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Register a new userCorrelated impurities and intrinsic spin liquid physics in the kagome material Herbertsmithite
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Low energy inelastic neutron scattering on single crystals of the kagome spin liquid compound ZnCu3(OD)6Cl2 (Herbertsmithite) reveals antiferromagnetic correlations between impurity spins for energy transfers E < 0.8 meV (~J/20). The momentum dependence differs significantly from higher energy scattering which arises from the intrinsic kagome spins. The low energy fluctuations are characterized by diffuse scattering near wavevectors (1 0 0) and (0 0 3/2), which is consistent with antiferromagnetic correlations between pairs of nearest neighbor Cu impurities on adjacent triangular (Zn) interlayers. The corresponding impurity lattice resembles a simple cubic lattice in the dilute limit below the percolation threshold. Such an impurity model can describe prior neutron, NMR, and specific heat data. The low energy neutron data are consistent with the presence of a small spin-gap (Delta ~ 0.7 meV) in the kagome layers, similar to that recently observed by NMR. The ability to distinguish the scattering due to Cu impurities from that of the planar kagome Cu spins provides a new avenue for probing intrinsic spin liquid physics.
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Quantum spin liquids form a novel class of matter where, despite the existence of strong exchange interactions, spins do not order down to the lowest measured temperature. Typically, these occur in lattices that act to frustrate the appearance of magnetism. In two dimensions, the classic example is the kagome lattice composed of corner sharing triangles. There are a variety of minerals whose transition metal ions form such a lattice. Hence, a number of them have been studied, and were then subsequently synthesized in order to obtain more pristine samples. Of particular note was the report in 2005 by Dan Noceras group of the synthesis of herbertsmithite, composed of a lattice of copper ions sitting on a kagome lattice, which indeed does not order down to the lowest measured temperature despite the existence of a large exchange interaction of 17 meV. Over the past decade, this material has been extensively studied, yielding a number of intriguing surprises that have in turn motivated a resurgence of interest in the theoretical study of the spin 1/2 Heisenberg model on a kagome lattice. In this colloquium article, I will review these developments, and then discuss potential future directions, both experimental and theoretical, as well as the challenge of doping these materials with the hope that this could lead to the discovery of novel topological and superconducting phases.
Employing complementary torque magnetometry and electron spin resonance on single crystals of herbertsmithite, the closest realization to date of a quantum kagome antiferromagnet featuring a spin-liquid ground state, we provide novel insight into different contributions to its magnetism. At low temperatures, two distinct types of defects with different magnetic couplings to the kagome spins are found. Surprisingly, their magnetic response contradicts the three-fold symmetry of the ideal kagome lattice, suggesting the presence of a global structural distortion that may be related to the establishment of the spin-liquid ground state.
We analyze optical conductivity with the goal to demonstrate experimental manifestation of a new state of matter, the so-called fermion condensate. Fermion condensates are realized in quantum spin liquids, exhibiting typical behavior of heavy fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite provide important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of strongly correlated quantum spin liquid located near the fermion condensation phase transition. Our theoretical analysis of the optical conductivity allows us to expose the physical mechanism of its temperature dependence. We also predict a dependence of the optical conductivity on a magnetic field. We consider an experimental manifestation (optical conductivity) of a new state of matter (so-called fermion condensate) realized in quantum spin liquids, for, in many ways, they exhibit typical behavior of heavy-fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite produce important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of strongly correlated quantum spin liquid located near the fermion condensation phase transition. Our theoretical analysis of the optical conductivity allows us to reveal the physical mechanism of its temperature dependence. We also predict a dependence of the optical conductivity on a magnetic field.
Arguably the most favorable situation for spins to enter the long-sought quantum spin liquid (QSL) state is when they sit on a kagome lattice. No consensus has been reached in theory regarding the true ground state of this promising platform. The experimental efforts, relying mostly on one archetypal material ZnCu$_3$(OH)$_6$Cl$_2$, have also led to diverse possibilities. Apart from subtle interactions in the Hamiltonian, there is the additional degree of complexity associated with disorder in the real material ZnCu$_3$(OH)$_6$Cl$_2$ that haunts most experimental probes. Here we resort to heat transport measurement, a cleaner probe in which instead of contributing directly, the disorder only impacts the signal from the kagome spins. For ZnCu$_3$(OH)$_6$Cl$_2$ and a related QSL candidate Cu$_3$Zn(OH)$_6$FBr, we observed no contribution by any spin excitation nor any field-induced change to the thermal conductivity. These results impose different constraints on various scenarios about the ground state of these two kagome compounds: while a gapped QSL, or certain quantum paramagnetic state other than a QSL, is compatible with our results, a gapless QSL must be dramatically modified by the disorder so that gapless spin excitations are localized.
Optical conductivity measurements are combined with density functional theory calculations in order to understand the electrodynamic response of the frustrated Mott insulators Herbertsmithite $mathrm{ZnCu_{3}(OH)_{6}Cl_{2}}$ and the closely-related kagome-lattice compound $mathrm{Y_{3}Cu_{9}(OH)_{19}Cl_{8}}$. We identify these materials as charge-transfer rather than Mott-Hubbard insulators, similar to the high-$T_c$ cuprate parent compounds. The band edge is at 3.3 and 3.6 eV, respectively, establishing the insulating nature of these compounds. Inside the gap, we observe dipole-forbidden local electronic transitions between the Cu $3d$ orbitals in the range 1--2 eV. With the help of textit{ab initio} calculations we demonstrate that the electrodynamic response in these systems is directly related to the role of on-site Coulomb repulsion: while charge-transfer processes have their origin on transitions between the ligand band and the Cu $3d$ upper Hubbard band, textit{local} $d$-$d$ excitations remain rather unaffected by correlations.
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