Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session D15: Focus Session: Triangular Lattice Antiferromagnetism |
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Sponsoring Units: GMAG Chair: Oleg Tchernyshyov, The Johns Hopkins University Room: Colorado Convention Center Korbel 4E |
Monday, March 5, 2007 2:30PM - 3:06PM |
D15.00001: Spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice Invited Speaker: The Triangular lattice spin-1/2 Heisenberg AntiFerromagnet (TAF) is a prototypical model of frustrated quantum magnetism. While it is believed to exhibit long-range order in the isotropic limit, changes such as spatial anisotropy can alter the delicate balance amongst competing ground states. I will describe the static and dynamic properties of the spatially anisotropic TAF, with inter-chain diagonal exchange $J'$ much weaker than the intrachain exchange $J$. Treating $J'$ as a perturbation of decoupled Heisenberg spin-$1/2$ chains, I find that the ground state is spontaneously dimerized in a four-fold degenerate zig-zag pattern. This dimerization instability is driven by quantum fluctuations, which are dramatically enhanced here by the frustrated nature of inter-chain exchange. A magnetic field partially relieves frustration, by canting the spins along the field direction, and causes a quantum phase transition into a magnetically-ordered spin-density-wave phase. This is followed by cone and, finally, fully polarized (saturated) phases, as a function of increasing magnetic field. I show that many of these features are in fact observed in experiments on the celebrated material Cs$_2$CuCl$_4$ ($J'/J =1/3$). I will also discuss the significant modification of the phase diagram by symmetry-breaking anisotropic Dzyaloshinskii-Moriya (DM) interactions, present in this interesting magnet. In addition to static and thermodynamic properties, the proposed ``one-dimensional'' approach offers a compelling explanation of the unusual experimentally measured dynamical structure factor of Cs$_2$CuCl$_4$ in terms of descendants of one-dimensional spinons. Quite generally, I find characteristic features of a momentum-dependent spinon bound state and a dispersing incoherent excitation in the structure factor, in agreement with experiments. [Preview Abstract] |
Monday, March 5, 2007 3:06PM - 3:18PM |
D15.00002: Effective field theory with a $\theta$-vacua structure for 2d spin systems Akihiro Tanaka, Xiao Hu We derive a new 2+1d nonlinear sigma (NL$\sigma$) model description for coupled spin chains with competing AF-VBS orders, incorporating methods developed recently by ourselves and by Senthil and Fisher. The resulting 2+1d $O$(4) NL$\sigma$ model contains a topological $\theta$-term whose vacuum angle $\theta$ varies continuously with $\delta$, the bond-alternation strength of the interchain interaction. This implies that the $\theta$- vacua structure for this NL$\sigma$ model can be explored by tuning $\delta$ in a suitable 2+1d spin system, as in the case of the 1+1d AF spin chains with bond-alternation. We discuss the implications for frustrated spin systems. A. Tanaka and X. Hu, Phys. Rev. B{\bf 74}, 140407 (2006). [Preview Abstract] |
Monday, March 5, 2007 3:18PM - 3:30PM |
D15.00003: Spin Waves in Stacked Triangular Antiferromagnetic Thin Films E. Meloche, M. L. Plumer, C. M. Pinciuc A theory is presented for surface and bulk spin waves (SW) in stacked triangular antiferromagnetic thin films. The model uses a microscopic Heisenberg Hamiltonian which includes the dominant exchange interactions with either easy-plane [1] or easy-axis single-ion anisotropy. The equilibrium spin configurations in the frustrated thin films are obtained using a local field alignment approach. The effects of modified surface exchange and anisotropy parameters on the equilibrium spin configurations and the SW dispersion relations are discussed. Numerical results show that the presence of surfaces can give rise to several localized excitations that are characterized with decaying amplitudes into the bulk. The energy of the localized SW modes are found to be extremely sensitive to the boundary conditions. The spin-correlation functions are obtained using a Green's function formalism and used to evaluate the mean-squared amplitude of spin precession as a function of the distance away from the surfaces. Comparisons are made between the properties of SW excitations in frustrated magnetic systems that are quasi one- and two-dimensional in character. [1] E. Meloche, C. M. Pinciuc, M. L. Plumer, Phys. Rev. B \textbf{74} (2006) 94424. [Preview Abstract] |
Monday, March 5, 2007 3:30PM - 3:42PM |
D15.00004: Octupolar order in the multiple spin exchange model on a triangular lattice Tsutomu Momoi, Philippe Sindzingre, Nic Shannon We showed how a gapless spin liquid with hidden octupolar order arises in applied magnetic field, in a model applicable to thin films of solid $^3$He with competing ferromagnetic and antiferromagnetic (cyclic) exchange interactions. In this, dynamical effects lead to the formation of three-magnon bound states, which undergo Bose-Einstein condensation, giving rise to octupolar order. We confirmed its existence through the exact diagonalization of finite-size clusters. We also presented evidence for nematic -- i.e. quadrupolar -- correlations bordering on ferromagnetism in the absence of magnetic field. [Preview Abstract] |
Monday, March 5, 2007 3:42PM - 3:54PM |
D15.00005: Quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice Andreas L\"auchli, Fr\'ed\'eric Mila, Karlo Penc Using mean-field theory, exact diagonalizations and SU(3) flavour theory, we have precisely mapped out the phase diagram of the $S=1$ bilinear-biquadratic Heisenberg model on the triangular lattice in a magnetic field, with emphasis on the quadrupolar phases and their excitations. In particular, we show that ferroquadrupolar order can coexist with short-range helical magnetic order, and that the antiferroquadrupolar phase is characterized by a remarkable 2/3 magnetization plateau, in which one site per triangle retains quadrupolar order while the other two are polarized along the field. Implications for actual $S=1$ magnets, such as NiGa$_2$S$_4$, are discussed. [Preview Abstract] |
Monday, March 5, 2007 3:54PM - 4:06PM |
D15.00006: Flat spin wave dispersion in a triangular antiferromagnet Oleg Starykh, Andrey Chubukov, Alexander Abanov The excitation spectrum of a S=1/2 two-dimensional triangular quantum antiferromagnet is studied using 1/S expansion. Due to the non-collinearity of the classical ground state significant and non-trivial corrections to the spin wave spectrum appear already in the first order in 1/S in contrast to the square lattice antiferromagnet. The resulting magnon dispersion is almost flat in a substantial portion of the Brillouin zone. Our results are in quantitative agreement with recent series expansion studies by Zheng, Fj\ae restad, Singh, McKenzie, and Coldea [PRL {\bf 96}, 057201 (2006) and cond-mat/0608008]. [Preview Abstract] |
Monday, March 5, 2007 4:06PM - 4:18PM |
D15.00007: Frustrated antiferromagnet on generalized partial line graphs of a honeycomb lattice Shin Miyahara, Chisa Hotta, Kenn Kubo, Nobuo Furukawa Recently we have proposed generalized partial line graphs on which tight binding models of electronic energy bands realize flat bands [1]. We study Heisenberg antiferromagnets on these structures, which are frustrated and may realize novel ground states. In this report, we focus on a generalized partial line graph created on a honeycomb lattice. The model is a honeycomb lattice composed of A and B-sublattice, where a triangle cluster sits on a site of A-sublattice and a single spin exists on a site of the B-sublattice. We assume the two-types of exchange coupling: J inside the triangle cluster and J' between the cluster and B-sublattice. In the limit J $<<$ J' the model is equivalent to the spin-1 triangle model. We introduce an effective model for two limits J $>>$ J' and J $<<$ J'. The results of exact diagonalization will be reported and discussed. [1] S. Miyahara et al., J. Phys. Soc. Japan, 74 1918 (2005). [Preview Abstract] |
Monday, March 5, 2007 4:18PM - 4:30PM |
D15.00008: Excitation spectra of the spin-$1/2$ triangular-lattice Heisenberg antiferromagnet Rajiv R. P. Singh, Weihong Zheng, John Fj{\ae}restad, Ross McKenzie, Radu Coldea We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-$1/2$ triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a three-sublattice ordered ground state. Several striking features are observed compared to the classical (large-$S$) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find roton-like minima at special wave-vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order $1/S$ calculated recently by Starykh, Chubukov, and Abanov [cond-mat/0608002]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as $0.1J$ the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a non-linear sigma model description of the finite-temperature properties is only applicable at temperatures $\ll 0.1J$. [Preview Abstract] |
Monday, March 5, 2007 4:30PM - 4:42PM |
D15.00009: Excitation spectrum of an ordered Heisenberg antiferromagnet on a triangular lattice Sasha Chernyshev, Michael Zhitomirsky We have shown that magnon decays must be prominent in a wide class of noncollinear antiferromagnets. We calculated the decay rate in the spin-1/2 triangular lattice antiferromagnet within the spin-wave theory. In the long-wavelength limit, the life-time of low-energy excitations is predicted to exhibit a non-trivial scaling. For the short-wavelength magnons, the decay rate is large, $2\Im{\rm m}\{\tilde\varepsilon_{\bf k}\} \sim 0.4\Re{\rm e}\{\tilde\varepsilon_{\bf k}\}$, in a substantial part of the Brillouin zone. Topological transitions of the decay surface also lead to strong singularities in the spectrum that remain essential even for large values of spin. Therefore, excitations in ordered, spin-$S$, AFs may not necessarily be well-defined for all wave-vectors.\newline \newline [1] A. L. Chernyshev and M. E. Zhitomirsky, Phys. Rev. Lett. {\bf 87}, 207202 (2006). [Preview Abstract] |
Monday, March 5, 2007 4:42PM - 4:54PM |
D15.00010: Spinon excitation in spatially anisotropic frustrated Heisenberg models Masanori Kohno, Leon Balents, Oleg Starykh We investigate the elementary excitations of spin-1/2 antiferromagnetic Heisenberg models with spatially anisotropic frustrated couplings. By projecting the Hamiltonian into a subspace of exact spinon eigenstates of the one-dimensional chains, we obtain and solve an effective Schr\"odinger equation. We argue this weak interchain-coupling approach has a broad regime of validity for frustrated models. As a general feature, we find a bound state of spinons and incoherent excitations depending on the momentum. Various experimental features observed in Cs$_{2}$CuCl$_{4}$ such as asymmetry of the dispersion relation and large tail at $k_x$=$\pi$\footnote{R. Coldea, D. A. Tennant, and Z. Tylczynski, Phys. Rev. B 68, 134424 (2003).} are consistently explained within the framework of the present approach with few adjustable parameters. Our results suggest that the spectral features in Cs$_{2}$CuCl$_{4}$ should be interpreted as descendents of one-dimensional spinons, which persist more strongly at some momenta in spatially anisotropic frustrated systems even with finite interchain couplings. [Preview Abstract] |
Monday, March 5, 2007 4:54PM - 5:06PM |
D15.00011: Competition between charge and spin orders on a frustrated system: The triangular lattice. B. Davoudi, S.R. Hassan, A.-M.S. Tremblay We study the properties of the extended Hubbard model on a triangular lattice by means of generalized two-particle self consistent approach(GTPSC). We present the structure functions over a wide range of physical parameters. Rapid increase in the charge and spin response functions indicates crossover towards various types of charge and spin orders. The competition between the on-, off-site interaction and the frustration leads to a very rich density dependent phase diagram. We also evaluate the one-particle spectral function in various ranges of physical parameters and find that the pseudo-gap can also appear in the regime where the charge density wave is dominant. [Preview Abstract] |
Monday, March 5, 2007 5:06PM - 5:18PM |
D15.00012: Anisotropic interactions in a Quantum Antiferromagnet Cs$_2$CuCl$_4$ as revealed by NMR. Marc-Andre Vachon, Georgios Koutroulakis, Vesna F. Mitrovic, Arneil P. Reyes, Philip L. Kuhns, Radu Coldea We report nuclear magnetic resonance (NMR) measurements on the 2D frustrated quantum antiferromagnet Cs$_2$CuCl$_4$. $^{133}$Cs spectra at temperatures down to $60$\,mK and in external magnetic field up to $16$\,T are presented. We discuss the details of the destruction of the 3D long range ordered phases in this compound. The effects of temperature and the applied field are contrasted, that is, the details of the nature of the phase transition will be discussed. Furthermore, we will address the influence of anisotropic interactions on these phase transitions. [Preview Abstract] |
Monday, March 5, 2007 5:18PM - 5:30PM |
D15.00013: Spin Order by Frustration in Triangular Lattice NaCrO$_2$ : A Neutron Scattering Study D. Hsieh, D. Qian, R.F. Berger, B. Ueland, P. Schiffer, R.J. Cava, J.W. Lynn, Q. Huang, M.Z. Hasan We report high resolution neutron scattering measurements on the triangular lattice antiferromagnet NaCrO$_2$. In contrast to the host compound of the 2D cobaltate superconductor Na$_x$CoO$_2$, no magnetic long-range order is observed down to 1.5K. For $T >$ 40K purely 2D quasi-static 120$^{\circ}$ spin correlations extend to a maximum of 20 lattice constants. For $T <$ 30K, a small in-plane incommensuration develops together with short-range $c$-axis correlations. Our observation of strong spin fluctuations over an extended temperature range and a long wave-length incommensurate modulation strongly suggest an out-of-plane frustration as the mechanism for stabilizing this rare 2D correlated phase in NaCrO$_2$. [Preview Abstract] |
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