Session H8: Focus Session: Frustrated Magnetism - Kagome I

Confinement transitions of Z2 spin liquids on the kagome lattice

Motivated by numerical evidence of a Z2 spin liquid ground state of the Heisenberg model on the kagome lattice and indications of a proximate valence bond solid (VBS) phase (see S. Yan et al, Science 332, 1173 (2011)), we study quantum phase transitions between Z2 spin liquids and VBS states, in which the space group of the kagome lattice is broken. These confinement transitions are driven by the condensation of elementary vortex excitations of the Z2 spin liquid, so called visons. In this talk I will show how a projective symmetry group (PSG) analysis of effective models for the visons can be used to construct quantum field theories for such confinement transitions, which in turn allow for a classification of the spatial symmetries of possible VBS states. Interestingly, the kagome lattice is unique in the sense that the critical properties at the confinement transition are seemingly not described by the Wilson-Fisher fixed point, as is the case for other lattice geometries.   

NMR study of the spin-1/2 near-kagome system Vesignieite

The spin-1/2 kagome lattice antiferromagnet is understood to be an ideal setting in which to find novel quantum spin liquid physics. Here, $^{51}$V NMR results are presented on the quantum spin system Vesignieite, which closely approximates such an antiferromagnetic kagome model, possessing a minute 0.7\% length difference between inequivalent Cu-Cu bonds. We obtain a measure of the intrinsic magnetic susceptibility of the near-kagome lattice, which shows commonalities with other kagome systems, in particular Herbertsmithite. Meanwhile, the system is found to undergo partial spin freezing at a surprisingly high temperature of $T_C = 9 K \simeq J/6$. Through a loss of NMR intensity and detailed analysis of the spectral linewidth, we infer a heterogeneous ground state in which 50\% of the spins are very weakly frozen, with a moment of $\sim 0.2$ $\mu_B$ and the remaining 50\% remain dynamic down to very low temperatures. These results are found to be highly consistent with $\mu$SR studies, which find a similar frozen fraction and small size of magnetic moment. We propose that the elevated transition temperature and weakly frozen ground state are explained by the Dzyaloshinskii-Moriya interaction and a proximity to the resulting quantum phase transition.   

Magnetization Process of Spatially Anisotropic Kagome Heisenberg Model

Motivated by recent experiments on volborthite, a typical spin-1/2 antiferromagnet with a kagome lattice structure, we study magnetization process of a Heisenberg model on a kagome lattice with a spatial anisotropy in applied magnetic fields. First, for the classical Heisenberg model, by using the Monte Carlo method, we find a magnetization step due to the anisotropy at low temperatures and low magnetic fields. The magnetization step signals a first-order transition, between two phases distinguished by distinct and well-developed short-range spin correlations, one characterized by a local $120^{\circ}$ structure and the other by a partially spin-flopped structure. These states are also evident in magnon dispersions based on a classical spin configuration for each phase. Then, to clarify how quantum fluctuations affect the magnetization process, we calculate the sublattice magnetization by using the exact diagonalization method. We find that the sublattice magnetization process of the quantum model looks qualitatively similar to that of the classical model, which indicates that the spin structure observed in the classical model also appears in the quantum model. Finally, we point out the relevance of our results to the magnetization steps observed in volborthite.   

Investigation of fermi-liquid-like specific heat and spin-density-wave signatures in the distorted kagome compound Volborthite, Cu$_3$V$_2$O$_7$(OH)$_2$$\cdot2$H$_2$O

The distorted kagome compound Volborthite shows signatures of spin-density-wave magnetic order and Fermi-liquid specific heat at low temperatures and magnetic fields. A recent density functional study [O. Janson {\it et al}., Phys. Rev. B {\bf{82}}, 104434 (2010)] suggests that Volborthite can be viewed as coupled frustrated Heisenberg spin chains, a model we approach using a slave-fermion representation of the spins. For a certain range of couplings, our mean-field theory finds a Fermi surface of spinons, a portion of which contains nesting. We investigate whether the coexistence of a U(1) spin liquid with a spinon Fermi surface, along with a spinon spin-density-wave, may describe the aforementioned features of the low-field phase. Furthermore, at higher fields, conventional magnetically ordered states are found. We examine if higher magnetic fields can lead to the destruction of the fermi surface, prompting a spinon confinement transition into such a conventionally magnetically ordered state.   

Experimental signatures of spin liquid physics on the S=1/2 kagom\'{e} lattice

I will describe our recent experimental progress on the quest to study novel ground states in frustrated magnets. New states of matter may be produced if quantum effects and frustration conspire to prevent the ground state from achieving classical order. Materials based on the kagom\'{e} lattice appear to be ideal hosts for the possibility of a quantum spin liquid ground state in two-dimensions. I will discuss our work which includes single crystal growth, bulk characterization, and neutron scattering measurements of the S=1/2 kagom\'{e} lattice material ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ (also known as herbertsmithite). Recent susceptibility measurements on single crystals yield valuable information on the additional terms in the spin Hamiltonian beyond nearest neighbor Heisenberg exchange, and anomalous x-ray diffraction yields detailed information on the presence of a small amount of atomic impurities. Most interestingly, inelastic neutron scattering measurements of the spin correlations in a single crystal sample reveal a continuum of spinon excitations in this two-dimensional insulating magnet. We will discuss our results in relation to recent theories for spin liquid physics on the S=1/2 kagom\'{e} lattice.   

Spin cluster operator theory for the kagome lattice antiferromagnet

The spin-1/2 quantum antiferromagnet on the kagome lattice provides a quintessential example in the strongly correlated electron physics where both effects of geometric frustration and quantum fluctuation are pushed to their limit. Among possible non-magnetic ground states, the valence bond solid (VBS) with a 36-site unit cell is one of the most promising candidates. Improving the bond operator theory, we propose a new approach dubbed as the spin cluster operator theory in which extended clusters of spin are treated as fundamental building blocks of the system. As a result, it is shown that the lowest spin excitation has a gap much lower than the previous value obtained by the bond operator theory, narrowing the difference against exact diagonalization results.   

Low Energy Spectrum and Correlation Functions of the $S=1/2$ Kagome Antiferromagnet

We report a large scale Exact Diagonalization study of the $S=1/2$ Heisenberg antiferromagnet on samples of up to 48 sites. The singlet spectrum at low energies involves only energy levels at the Gamma point, indicating the probable absence of spontaneous translation symmetry breaking in the thermodynamic limit. The spin-spin correlations are short ranged as expected, and the dimer-dimer correlation functions reveal traces of diamond-like resonances. We discuss the compatibility of our results with different theoretical proposals for the ground state of the Kagome antiferromagnet   

Valence bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: Symmetry classification and projected wave function study

We present a hierarchical group theoretical classification and representation of Valence bond crystal (VBC) phases on the kagome lattice. Starting from the most symmetric parent VBC, we enumerate and give the ansatz for all 6, 12, and 36-site unit cell VBC's in order of increasing number of broken point group symmetry elements. We treat the VBC's within the class of Gutzwiller projected fermonic variational wave functions, which are optimized using a sophisticated implementation of the stochastic reconfiguration method. In particular, for the spin-1/2 quantum Heisenberg antiferromagnetic model, we show that the U(1) Dirac spin liquid is remarkably stable (locally and globally) with respect to all possible VBC patterns enumerated. However, upon addition of a small ferromagnetic next-nearest-neighbor coupling we find that the lowest energy state is a non-trivial generalized 36-site VBC, which can be regarded as being continuously connected to a uniform RVB spin liquid. We also communicate the ground state energy on the kagome 48 site cluster for the nearest-neighbor spin-1/2 quantum Heisenberg antiferromagnetic model, using the technique of application of a few Lanczos steps (within a variational Monte carlo scheme) on the U(1) Dirac spin liquid and the uniform RVB wave function.   

Neutron Scattering and Thermodynamic Studies of Low Spin Kagome Magnets

Materials containing low quantum number spins arranged on a kagome lattice are some of the most promising candidates to display spin liquid ground states due to the high degree of geometric frustration. Cu(1,3-bdc) is a hybrid organometallic compound featuring antiferromagnetically coupled S=$\frac{1}{2}$ Cu$^{2+}$ ions on a kagome lattice. Below T=1.8 K the magnetic moments enter a quasi-static phase with no long range magnetic order but extremely slow spin fluctuations. Application of a magnetic field quickly leads to a competing magnetic phase, with a 1 Tesla field able to completely polarize the magnetization below T=2 K. We present inelastic neutron scattering measurements of Cu(1,3-bdc) and note the emergence of low-energy modes in the quasi-static phase. We also present new thermodynamic data on the compound BaNi$_{3}$(OH)$_{2}$(VO$_{4}$)$_{2}$, recently synthesized by our group, which features S=1 Ni$^{2+}$ ions on a kagome lattice.   

Magnetic studies of S=1/2 kagom\'e lattice single crystals

Herbertsmithite ZnCu3(OH)6Cl2--one of the most promising quantum spin liquid candidates--presents a promising system for studies of frustrated magnetism on an S=1/2 kagom\'e lattice. Following our recent success in crystal growth, we have measured anisotropies in the magnetic susceptibility and specific heat. The implication on the Hamiltonian will be discussed. Specific heat has been measured at dilution fridge temperatures up to 18 T on a single crystal sample which gives further information on the low temperature phases. In addition, inelastic neutron scattering has been performed and the broad continuum observed is consistent with deconfined 2D spinons which lends further support of herbertsmithite's quantum spin liquid candidacy.   

Single Crystal NMR Study of Frustrated Spin-Liquid in S = 1/2 Kagome Lattice $ZnCu_{3}(OD)_{6}Cl_{2}$

Herbertsmithite $ZnCu_{3}(OD)_{6}Cl_{2}$ is one of the most promising examples for a quantum spin liquid state. Despite the remarkable absence of long range magnetic order down to at least 50mK, understanding the magnetic properties of $ZnCu_{3}(OD)_{6}Cl_{2}$ remains a challenge. This is mainly due to the difficulty in locating the defects, and in understanding the possible role of defects in the physical properties of this material. We have investigated the local magnetic and lattice environment of $ZnCu_{3}(OD)_{6}Cl_{2}$ single crystals\footnote{T. H. Han \textit{et al}., Phys. Rev. B {\bf 83}, 100402(R) (2011)} using NMR techniques\footnote{T. Imai \textit{et al}., Phys. Rev. B {\bf 84}, 020411(R) (2011); see also Phys. Rev. Lett. {\bf 100}, 077203 (2008)}. With successful identification of $^{2}D$ NMR signals arising from the nearest neighbors of $Cu^{2+}$ defects substituting Zn, we find that $14(2)\%$ of Zn sites are occupied by these weakly interacting $Cu^{2+}$ defect spins, which contribute to the large Curie-Weiss enhancement of bulk susceptibility at low temperatures. We then discuss the key aspects of nuclear spin-lattice relaxation rate $1/T_{1}$ measured near the defect and intrinsic sites.