Session Y15: Focus Session: Kagome Materials and Experiments

Detection of low energy spin loop excitations in rare earth kagom\'{e} systems

Collective spin excitation spectra in frustrated antiferromagnets have been detected using high field electron magnetic resonance (EMR). At low temperatures the langasite kagom\'{e} systems R$_{3}$Ga$_{5}$SiO$_{14}$(R = Pr and Nd) exhibit short range spin correlation effects. Neutron scattering has shown that these systems do not exhibit long-range magnetic order at temperatures down to 30 mK. Field-sweep EMR measurements made on single crystals of Pr$_{3}$Ga$_{5}$SiO$_{14}$ and Nd$_{3}$Ga$_{5}$SiO$_{14}$ in the temperature range 1.3 - 20 K, and in fields up to 22 T, give a series of absorption peaks which are quite different to conventional EMR spectra. The resonances are interpreted using a model which involves spin-wave excitations in short range antiferromagnetically correlated spin loops or clusters.   

Oxygen Defect Structure in the Geometrically Frustrated Kagom\'{e} System YBaCo$_4$O$_{7+\delta}$: Impact on Structure and Magnetic Properties

The $R$BaCo4O7 family ``$R$-114''(where $R =$ rare earth, Y or Ca) have been a model system due to their high oxygen affinity, significant electrochemical properties and geometric frustration, in which face-sharing tetrahedra of Co ions link to form trigonal bipyramids on a Kagom\'{e} lattice. Here we report quantitative thermogravimetric analysis (TGA), \textit{in-situ} x-ray diffraction (XRD), high resolution synchrotron x-ray and neutron diffraction data characterizing the oxygen uptake/release phenomenon and its impacts on structure and magnetic properties of YBaCo$_4$O$_{7+\delta}$. We show that YBaCo$_4$O$_{7+\delta}$ reaches an equilibrium state with $\delta \sim$0.1 when heated slightly above 350 $^{\mathrm{o}}$C. When heated slightly below 350 $^{\mathrm{o}}$C, it absorbs significantly more oxygen ($\delta = 1 \sim$1.1) and shows the orthorhombic \textit{Pbc}2$_1$ symmetry previously reported [O. Chmaissem et al. J. Solid State Chem. 181, 664 (2008)]. We also detected the existence of a miscibility gap that separates the $\delta =$ 0 and $\delta =$0.1 phases. In samples $\delta$ $\geq$ 0.1, excess oxygen suppresses the structural transition however, there are strong short range magnetic correlations below 100 K despite the preserved Kagom\'{e} structure.   

Neutron Scattering Studies of a Flat Mode in an S=$\frac{1}{2}$ Kagome Ferromagnet

Systems with flat bands provide macroscopic degeneracy that allows for the emergence of interesting strongly correlated phenomena such as the fractional quantum Hall effect. Hopping models on geometrically frustrated lattices with spin-orbit interactions predict the existence of flat, topologically nontrivial bands. Experimental realizations of these systems have proved challenging, as the flat band is often distorted by additional interactions. Cu(1,3-bdc) is a hybrid organometallic compound featuring S=$\frac{1}{2}$ Cu$^{2+}$ ions on a kagome lattice. The magnetic moments order ferromagnetically below T=1.8K. We present neutron scattering measurements of Cu(1,3-bdc) and note the emergence of a flat magnon band in the ordered phase. The presence of a small Dzaloshinsky-Moriya interaction along with an applied magnetic field perpendicular to the kagome plane creates a gap between the flat band and lower energy dispersive band.   

Kapellasite: a kagome quantum spin liquid with competing interactions

In recent years, the search for an experimental quantum spin liquid in two dimensions has attracted much interest in the community. Magnetic frustration and quantum fluctuations are believed to be key ingredients to stabilize such a spin liquid ground state in 2D. The $S=\frac{1}{2}$ kagome lattice combines these two ingredients. Among the materials available with this geometry, herbertsmithite has proven to be a very promising candidate. There, the antiferromagnetic nearest neighbor coupling $J_1$ is dominant. In this talk, I will explore the effect of frustration generated by competing interactions on the quantum kagome lattice, based on experiments performed on kapellasite Cu$_3$Zn(OH)$_6$Cl$_2$, a polymorph to herbertsmithite. The system Hamiltonian, determined from a fit of a high-temperature series expansion to magnetic susceptibility and specific heat data, points to competing interactions with a ferromagnetic nearest neighbor exchange $J_1$ and an ``across-hexagon'' antiferromagnetic one $J_d$, with a ratio $\vert J_d / J_1 \vert \simeq 0.85$. Local probes ($\mu$SR, $^{35}$Cl-NMR) and inelastic neutron scattering (INS) experiments evidence a gapless spin-liquid state down to 20 mK, showing unusual dynamic short-range correlations characteristic of a 12 spin sublattices antiferromagnetic state called Cuboc2. We further investigate the spin dynamics at different timescales by NMR, $\mu$SR and INS measurements and discuss our results within the context of theoretical calculations using the Schwinger-Boson mean field approach.   

Signature of a Spin Liquid State in the Low-Frequency Optical Conductivity of the S $=$ 1/2 Kagome Antiferromagnet Herbertsmithite

Herbertsmithite (ZnCu$_{\mathrm{3}}$(OH)$_{\mathrm{6}}$Cl$_{\mathrm{2}})$ is an antiferromagnetic Mott insulator composed of a planar kagome arrangement of S $=$ 1/2 copper atoms separated by nonmagnetic zinc atoms. It has recently emerged as one of the best candidates for exhibiting a quantum spin liquid state, showing no magnetic order down to 50 mK despite an exchange energy of 200 K. Here we report a signature of a spin liquid state in the terahertz optical conductivity of Herbertsmithite, measured via Terahertz Time-Domain Spectroscopy. A power-law dependence on frequency with exponent $\sim$ 1.4 is observed in the in-plane conductivity at low frequency, which increases in magnitude as temperature is decreased. This contribution to the conductivity is notably absent in the out-of-plane direction. Theory has predicted that the existence of a Dirac spin liquid with a gauge field serving to couple the spin and charge degrees of freedom would give rise to a power-law conductivity with exponent $\sim$ 2 inside the Mott gap. We discuss this prediction as well as other possible sources of the observed behavior.   

Thermodynamic analysis of a kagome spin liquid candidate

Herbertsmithite ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$--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, 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 phase. Additional analysis of the thermodynamic measurements on single crystal samples lends further hints on the intrinsic spin liquid physics.   

High field magnetic studies of S=1/2 Kagome lattice single crystalline Herbertsmithite

Herbertsmithite ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ is a promising system to study frustrated magnetism on S=1/2 kagome lattice. A continuum of spinon excitations has been revealed by recent neutron scattering measurements on single crystals. Interesting questions arise on the fate of this spinon excitation under intense external magnetic field. We report field-driven transitions in the high field magnetization of single crystalline ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$. These transitions appear below 1 K, and the transition field values are almost independent of the magnetic field orientation. We further discuss methods to separate the magnetic contribution from the impurity to repeal the intrinsic response of the kagome lattice.   

Fermion mediated state selection in the Kagome lattice and antiferromagnetism in FeCrAs

We study classical spins on a kagome lattice with weak Hund's coupling $J_{H}$ to hopping electrons. For each filling, the effective RKKY interactions at all distances are extracted both by fits of the total electronic energy to a database of random spin configurations, as well as second order perturbation theory in $J_{H}$. We apply this to model the Cr antiferromagnetic order found below 125K in FeCrAs [2], in which one Cr d band split by the crystal field plays the role of the itinerant fermions; the observed $\sqrt3 \times \sqrt3$ type order is indeed, close to half filling, the optimum state according to our model (out of the commonly considered alternatives) . In contrast, the limit of strong $J_{H}$ favors the cuboc1[1] state over the $\sqrt3 \times \sqrt3$ state[3], giving a bound on the possible value of the $J_{H}$ in FeCrAs. Additionally, for weak $J_{H}$, cuboc1[1] is selected instead of $\sqrt3 \times \sqrt3$ close to 5/12 filling. The complete phase diagram as a function of filling can be found using Monte Carlo (MC) minimization with the RKKY Hamiltonian. [1] Messio et al PRB 83, 184401 (2011) [2] W. Wu et al EPL 85, 17009 (2009) [3] Shivam Ghosh, Contributed talk, March Meeting 2013   

Double Exchange, Berry fluxes, and fermion mediated state selection in frustrated lattices

We consider a Kagome or Pyrochlore magnet with local moments (treated as classical) as well as noninteracting electrons with hopping $t$ at metallic filling, in the ``Double Exchange'' (DE) limit of infinitely strong Hund's rule coupling $J_{H}$. Whereas a DE-dominated model always has a ferromagnetic ground state, we make the problem nontrivial by including a dominant separate antiferromagnetic exchange $J >> t$, so the DE is a perturbation selecting within the highly degenerate ground states of J [1]. We derive this in two stages (i) spin directions define a set of Berry fluxes for each loop in the lattice (ii) we fit an effective Hamiltonian in terms of these fluxes. The same method can be applied to the energy landscape of competing spin-liquid-like states within large-N mean field theories. Depending on filling, the stable state on the Kagome is coplanar or the non-coplanar ``cuboc1'' [2] phase.\\[4pt] [1] Motome and Furukawa, PRL 104, 106407(2010).\\[0pt] [2] Messio, Lhuillier, and Misguich, PRB 83, 184401 (2011).   

Neutron scattering study of the dimerized spin 1/2 AFM kagome lattice in $Rb_2Cu_3SnF_{12}$

The deformed AFM kagome lattice $Rb_2Cu_3SnF_{12}$ is the first realization of 'pinwheel' valence bond solid (VBS) ground state system [1]. Using inelastic neutron scattering technique, we mapped out the spin excitation spectrum up to 12 meV. The singlet to triplet transition is split by a substantial Dzyaloshinskii-Moriya (DM) interaction, with the energy gap at 2.4 meV ($S_z$= $\pm$ 1) and 6.9 meV ($S_z$ = 0), respectively. While both excitations are non-dispersive to within 1.0 meV for wave vectors, $q_z$, perpendicular to the kagome like plane, the intensity varies differently with $q_z$ for the two modes. This difference can be explained by the different polarization factor for $S_z$= $\pm$ 1 and $S_z$ = 0 excitations. Under a magnetic field along the c-axis, the low energy gap persist near 1 meV for the fields between 9 T and 15 T. Our findings emphasize the important role of DM interaction in this material.\\[4pt] [1] K. Matan, T. Ono, Y. Fukumoto, T. J. Sato, J. Yamaura, M. Yano, K. Morita, and H. Tanaka, Nature Physics 10 (2010).   

Electronic structure of the kagome lattice Cu$_4$(OH)$_6$FBr

We investigate the electronic and magnetic properties of Cu$_4$(OH)$_6$FBr in the framework of ab initio density functional theory calculations and model considerations. This system, similarly to the well known Herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, consists of stacked layers of Cu$^{2+}$ ions arranged in a Kagome pattern. We will discuss in terms of microscopic models the resemblances and differences between these two systems.   

Spin configurations in the frustrated spin system YBaCo$_{4}$O$_{7}$ by $^{59}$Co NMR

The frustrated spin system YBaCo$_{4}$O$_{7}$ has both kagom\'{e} and triangular planes of cobalt ions alternating with each other. The cobalt spins in the triangular layers order antiferromagnetically below the N\'{e}el temperature at 106 K. The configurations of the cobalt spins have been studied by both neutron scattering\footnote{D. D. Khalyavin, P. Manuel, J. F. Mitchell, and L. C. Chapon, Phys Rev B \textbf{82,} 094401 (2010).} and zero applied field $^{59}$Co NMR. While the triangular spin orientations are in agreement for the two approaches, this is not the case for the kagom\'{e} layers. The present in-field sample rotation NMR experiments confirm our previous finding that the triangular spins are aligned perpendicular to the [110] crystallographic direction and provide strong evidence that the spins in the kagom\'{e} layers are orthogonal those in the triangular layers in what may be described as an internal-field-induced spin-flop configuration.   

NIR Optical Studies of the Warped-Kagome Frustrated Magnet Neodymium Langasite

We investigate the anti-ferromagnetic-to-spin liquid phase transition of Neodymium (Nd) Langasite, a warped Kagome lattice, using static fluorescence spectroscopy as a function of temperature. Nd3$+$ is excited at 808 nm and the fluorescence of the ground state to first excited transition is measured, the spectrum of which is a multiplet centered on 890 nm. We measure this spectrum at temperatures ranging between room temperature (295K) and 5K. The individual transitions comprising the spectrum are then fit by Lorentzians to determine the center wavelength ($\lambda _{\mathrm{c}}$) of each transition. Plots of $\lambda_{\mathrm{c}}$ versus temperature show zeros in the first derivative near 52 K, the Neel temperature, and second derivative near 33K, the anti-ferromagentic-to-spin liquid transition temperature. We attribute this to the phase transitions affecting the Zeeman energy of these levels.