Session J27: Focus Session: Triangular Lattice

Mean filed study of disordered spin-$1\over 2$ antiferromagnetic systems

We present a mean filed theory picture of disordered spin-$1\over 2$ antiferromagnetic system as a function of the degree of disorder, in connection to the insulating doped semiconductors. The system is a resonant valence bond (RVB) liquid state at zero disorder, and a possible RVB glass state when the disorder is finite but weak. For a highly disordered system, we show that the essential physics is the formation and decimation of strongly coupled bonds, and the thermodynamics shows an effective power-law singularity, in qualitative agreement with renormalization group result of Bhatt and Lee.   

Dynamical properties of spatially anisotropic frustrated Heisenberg models in a magnetic field

We investigate spectral features of spatially anisotropic spin-1/2 frustrated antiferromagnets in a magnetic field in terms of fractional excitations. Restricting the Hilbert space to that spanned by the eigenstates of the Heisenberg chain [1], we calculate dynamical structure factor $S$(\textbf{\textit{k}},$\omega )$ in the two-dimensional momentum space. We obtain sharp peaks and broad continuum depending on the momentum. We interpret the sharp peaks as signatures of bound states of psinons and antipsinons, fractional excitations in a magnetic field. We compare these spectral features with available experimental results on Cs$_{2}$CuCl$_{4}$ [2], and make detailed predictions on momentum- and field-dependence of peak structures and line shapes of $S$(\textbf{\textit{k}},$\omega )$ for Cs$_{2}$CuCl$_{4}$ in a magnetic field. [1] M. Kohno, O. A. Starykh, and L. Balents, Nature Phys. \textbf{3}, 790 (2007). [2] R. Coldea, \textit{et al}., Phys. Rev. Lett. \textbf{79}, 151 (1997).   

Quantum Order by Disorder in Frustrated Diamond Spinel Antiferromagnets

We study the effect of quantum fluctuations on the frustrated diamond lattice antiferromagnet where frustration arises from the presence of second neighbor interactions. Such an antiferromagnet describes the magnetic properties of spinel AB$_2$X$_4$ where magnetic ions are located on A-sites. We compare the resulting phase diagram of the quantum model and that of its classical counterpart, and discuss the difference/similarity between the quantum and thermal order by disorder phenomena. Implications for experiments on CoRh$_2$O$_4$, Co$_3$O$_4$ and MnSc$_2$S$_4$ will be discussed.   

Random Fields and the Partially Paramagnetic State of CsCo$_{0.83}$Mg$_{0.17}$Br$_{3}$

Partially paramagnetic Neel states are among the exotic magnet states known to exist in nature as a consequence of geometrical frustration. This unusual magnetic structure occurs in the stacked triangular lattice antiferromagnets such as CsCoBr$_{3}$ and CsCoCl$_{3}$. CsCoBr$_{3}$ displays at least 2 magnetic phase transitions. The first, T$_{n1}\sim $28K where the system enters a 3-sublattice state in which on of the sublattices remains disordered and the second, T$_{n2}\sim $13K where the remaining disordered sublattice orders[1]. Critical neutron scattering measurements were performed on the doped system CsCo$_{(1-x)}$Mg$_{(x)}$Br$_{3}$ with x =0.17. We will discuss the evolution of the observed two component scattering below T$_{n1}$ in terms of a Random Field Ising model in both zero applied magnetic field and an applied magnetic field of 2.6T along the c-axis. [1] M.Mao et al. Phys. Rev. B 66, 184432 (2002).   

New ordered phases of the spin-1/2 triangular-lattice antiferromagnet Cs$_{2}$CuBr$_{4}$

Quantum fluctuations and geometric frustration are theoretically expected to produce a gapped, collinear 'up-up-down' phase in spin-1/2 Heisenberg and XY antiferromagnets on a triangular lattice. Experimentally, this phase should manifest itself as a magnetization plateau at 1/3 of the saturation value. Despite being a fundamental theoretical property of such systems, this behavior has to date only been observed in one triangular lattice antiferromagnet: Cs$_{2}$CuBr$_{4}$. We have investigated the magnetic phase diagram of this compound by means of specific-heat, magnetocaloric-effect, and magnetic-torque measurements in magnetic fields up to the saturation field of about 30 T, finding a cascade of new ordered phases adjacent to the up-up-down phase. The evolution of these phases as a function of the field orientation with respect to the crystallographic bc plane suggests that they arise from the competition between the scalar exchange interaction and the symmetry-breaking Dzyaloshinskii-Moriya interaction.   

Dynamics of the Spin Liquid Phase of Cs$_2$CuCl$_4$

The dynamics of a spin-liquid phase of an antiferromagnet on the anisotropic triangular lattice and in a magnetic field are studied with a combination of Gutzwiller-projected wavefunctions and mean-field theory. Candidate ground states that support fermionic gapless spinon excitations include four different U(1) spin liquids\footnote{Y. Zhou, X. G. Wen, cond-mat/0210662 (2003).}. The lattice and the states interpolate between limiting cases of 1D decoupled chains ($J/J^{\prime} = 0$) and the isotropic 2D square lattice ($J/J^{\prime}= \infty$). Parameters of the mean field theory are chosen to minimize the ground state energy of the corresponding Gutzwiller-projected wavefunction. The spin-lattice relaxation rate $1/T_1$, calculated within the mean-field approximation, is compared to NMR measurements\footnote{M. A. Vachon, O. Ma, J. B. Marston, V. F. Mitrovi{\'c}, unpublished (2007).} in the spin liquid phase of Cs$_2$CuCl$_4$\footnote{Y. Tokiwa, T. Radu, R. Coldea, H. Wilhelm, Z. Tylczynski, F. Steglich, PRB 73, 134414 (2006).}.   

Photoemission study of triangular lattices in NiGa$_2$S$_4$, FeGa$_2$S$_4$, and Fe$_2$Ga$_2$S$_5$

The newly-discovered NiGa$_2$S$_4$ (Ni$^{2+}$, $S$=1) and FeGa$_2$S$_4$ (Fe$^{2+}$, $S$=2) form frozen spin-disordered states within the triangular lattice [1,2]. The spins of both compounds have no long range order even at lowest temperature. We have performed photoemission spectroscopy of NiGa$_2$S$_4$, FeGa$_2$S$_4$, and Fe$_2$Ga$_2$S$_5$. The photoemission results and subsequent model calculations indicate that the ground state of NiGa$_2$S$_4$ has the $d^9L$ character ($L$ is a S 3$p$ hole) and that the strong S 3$p$ hole character of the ground state provides the enhanced superexchange interaction between the third nearest neighbor sites. In contrast, the ground state of FeGa$_2$S$_4$ is dominated by the $d^6$ configuration and the superexchange interactions between the second and third neighbor sites are less important. [1] S. Nakatsuji, {\it et al}., Science 309, 1697 (2005). [2] S. Nakatsuji, {\it et al}., Phys. Rev. Lett. 99, 157203 (2007).   

The origin of anomalous 3rd neighbor exchange in 2D triangular magnets (NiGa2S4 and others)

2D magnetic materials with triangular lattices have been attracting much interest. Among them one finds the parent compound of an exotic superconductor, Na$_x$CoO$_2\cdot y$H$_2$O, A-type antiferromagnets like NaNiO$_2$, in-plane antiferromagnetism (LiCrO$2$), spin-liquid type materials (NiGa$_2$S$_4$), charge-order (AgNiO$_2$). The main structural motif in all of them is the AB$_2$ plane, where A is a transition metal and B is oxygen or sulfur. Experiments and calculations inevitably find anomalously strong 3rd neighbor exchange coupling in all these triangular planes, despite different band fillings and different magnetic ground states. I will explain why this happens, why this effect is so universal, and why it can be understood entirely on a one-electron level. I will use as an example NiGa$_2$S$_4$, with a reference to Na$_x$CoO$_2$ as well.   

Elementary excitations in the spin liquid phase of Cs$_2$CuCl$_4$ as revealed by $^{133}$Cs NMR spin-lattice relaxation rate measurements.

We present $^{133}$Cs NMR spin-lattice relaxation rate measurements in the spin liquid phase of Cs$_2$CuCl$_4$ as a function of temperature and external magnetic field. At fixed temperature, we found that the rate increases with increasing field, reaching a maximum at the phase boundary of the spin liquid state. The results are compared with the calculated NMR rates in different proposed spin liquid states. The implications of the results on determining the fermionic or bosonic nature of the elementary excitations in the spin liquid phase will be discussed.   

Spin-1/2 Heisenberg Antiferromagnet on the Spatially Anisotropic Kagome Lattice

We study the quasi-one-dimensional limit of the Spin-1/2 quantum antiferromagnet on the Kagome lattice, a model Hamiltonian that might be of relevance for the mineral volborthite [1,2]. The lattice is divided into antiferromagnetic spin-chains (exchange $J$) that are weakly coupled via intermediate ``dangling'' spins (exchange $J'$). Using bosonization, renormalization group methods, and current algebra techniques we determine the ground state as a function of $J'/J$. The case of a strictly one-dimensional Kagome strip is also discussed. \newline \newline [1] Z.~Hiroi, M.~Hanawa, N.~Kobayashi, M.~Nohara, Hidenori~Takagi, Y.~Kato, and M.~Takigawa, J. Phys. Soc. Japan \textbf{70}, 3377 (2001). \newline [2] F.~Bert, D.~Bono, P.~Mendels, F.~Ladieu, F.~Duc, J.-C.~Trumbe, and P.~Millet, Phys.~Rev.~Lett.~\textbf{95}, 087203 (2005).   

Magnetic Order and Spin Fluctuations in the Spin-1/2 Three-Dimensional Frustrated Magnet Clinoatacamite, Cu$_{2}$(OH)$_{3}$Cl

We have performed thermodynamic and neutron scattering measurements on the S=1/2 three-dimensional antiferromagnet clinoatacamite, Cu$_{2}$(OH)$_{3}$Cl. The crystal lattice feature Cu$^{2+}$ ions arranged on a distorted kagom\'{e} lattice with weak magnetic coupling between adjacent planes. Long range magnetic order with a weak ferromagnetic moment emerges at the N\'{e}el ordering temperature, T$_{N}$ = 6.2 K. The value of $\Theta_{CW}$ is roughly 30 times larger than T$_{N}$, demonstrating that the material is highly frustrated. Magnetic Bragg peaks are not observed above background for temperatures between 6.2 and 18 K, even though previous $\mu$SR measurements observed muon oscillations in this temperature range. We present a possible model of the magnetic transitions and analyze the inelastic spectrum of the ordered state, taking into account anisotropic terms in the spin Hamiltonian.   

Magnetic Properties of Yb$_{2}$Pt$_{2}$Pb with the Shastry-Sutherland Lattice

We have synthesized single crystals of Yb$_{2}$Pt$_{2}$Pb, which crystallize in the tetragonal U$_{2}$Pt$_{2}$Sn-type structure. Comparison of the crystal structure with that of other compounds reveals a structure dependent Yb valence state of Yb$_{2}$T$_{2}$M (T=transition metal; M=Cd, In, Sn, and Pb). The magnetic susceptibility $\chi$ of Yb$_{2}$Pt$_{2}$Pb is highly anisotropic. The $\chi_{\lbrack100\rbrack}$ for $B$$\parallel$$\lbrack100\rbrack$ is thirty times larger than $\chi_{\lbrack001\rbrack}$ for $B$$\parallel$$\lbrack001\rbrack$ at the lowest temperatures. A broad maximum in $\chi_{\lbrack100 \rbrack}$ is found around 3 K just above magnetic transition temperature 2.07 K. In agreement, the electrical resistivity shows a broad maximum around 5 K and the specific heat shows a long tail up to 8 K, due to the magnetic frustration originating from antiferromagnetic exchange interaction between Yb ions arranged in the network of the Shastry-Sutherland lattice.   

Dynamic Frustration in PrAu$_2$(Si$_{1-x}$Ge$_x$)$_2$

We have recently proposed that frustration is dynamically induced in the spin glass, PrAu$_2$Si$_2$, a singlet ground state system, in which the interionic exchange is just sufficient to induce a magnetic moment. The degree of static disorder is far too small to produce spin glass freezing but dynamic fluctuations can destabilize the induced moments and frustrate the long-range magnetic correlations. We have studied the crystal field excitations in PrAu$_2$(Si$_{1-x}$Ge$_x$)$_2$, for which long-range order is stabilized at $x\approx12$\%. The excitation energy is independent of $x$ but inhomogeneous broadening increases linearly for $x<0.2$, \textit{i.e.}, long-range order is stabilized even though static disorder is increasing. Tuning the dynamic frustration with concentration or pressure could provide a test of the concept of ``avoided criticality'' in glassy systems.   

KTi(SO$_{4}$)$_{2}$ .H$_{2}$O - a possible candidate for a new spin-Pierles system

Recently a large number of compounds belonging to the family of J$_{1}$-J$_{2}$ chain models with competing ferromagnetic (FM) and antiferromag- netic (AFM) interactions have been discovered. In most cases, FM-J$_{1}$ and AFM-J$_{2}$ is observed, leading to helical order with no spin gap (for frustration ratio $\alpha$ = $\frac{J_{1}}{J_{2}}$ $\geq$ -0.25). Systems with both J$_{1}$ and J$_{2}$ being AFM causing a spin gap are rather rare. The thermodynamic data of the recently prepared KTi(SO$_{4}$)$_{2}$.H$_{2}$O reveal that this system is a quasi 1D spin 1/2 chain compound with both J$_{1}$ and J$_{2}$ being AFM, and a frustration ratio $\alpha$ $\approx$ 0.29. Here we report the results of electronic structure calculations within the LSDA+$U$ method along with tight-binding models. Our calculations confirm that both J$_{1}$ and J$_{2}$ are AFM. In contrast to the experiments we obtain a larger $\alpha$, slightly depending on the choice of the Coulomb repulsion $U$ . Therefore KTi(SO$_{4}$)$_{2}$.H$_{2}$O might be a new candidate for a spin-Pierles ground state. A brief comparison with other systems belonging to the class of frustrated chain materials is given with respect to their position in the general phase diagram of the 1D J$_{1}$ - J$_{2}$ model.   

Valence bond solid phases in the spin-1 XXZ model on the kagome lattice

We study the spin-1 XXZ model on the kagome lattice using quantum Monte Carlo simulations. We find a rich phase diagram including two different valence bond solids and other quantum paramagnetic phases. We also characterize the nature of quantum phase transitions between those phases. These results are compared with various effective field theory approaches.