Session L8: Focus Session: Frustrated Magnetism - 1D

Magnon pairing in Quantum Spin Nematic

The phenomenon of the Bose-Einstein condensation is inherent not only to superfluid He-4 and cold atomic gases but also describes in a unified way a variety of field-induced transitions in quantum magnets. In this talk we discuss a novel example of the Bose-Einstein condensation of bound magnon pairs. The binding mechanism is based on a competition between ferro- and antiferromagnetic exchange bonds in a frustrated quantum spin system. As a result bound magnon pairs are formed in the fully polarized magnetic state at high fields. Upon decreasing field magnon pairs undergo a condensation into a state which is bosonic analog of a BCS superconductor [1]. The magnon-pair condensate lacks a conventional transverse magnetic order and is described instead by a quadrupolar or spin-nematic order parameter. We consider in detail magnon-pairing mechanism for two spin models: frustrated chains weakly coupled by interchain interactions and frustrated square-lattice antiferromagnet, which exhibit high-field spin-nematic states. Our theory predicts existence of the long-range spin-nematic phase in the frustrated chain material LiCuVO4. We also review recent experimental evidences, which support presence of a new phase in this material. Work done in collaboration with H. Tsunetsugu (ISSP, University of Tokyo) \\[4pt] [1] M. E. Zhitomirsky and H. Tsunetsugu, Europhys. Lett. 92, 37001 (2010).   

Competition between Spin Nematic and Spin Density Wave Orders in Spatially Anisotropic Frustrated Magnets in Magnetic Fields

Magnetic multipolar order including spin nematic order is one of the current topics in frustrated magnetism. Recently, frustrated spin chains with ferromagnetic nearest-neighbor coupling J1 and antiferromagnetic next-nearest-neighbor one J2 have been theoretically shown to exhibit multipolar quasi long-range orders in the wide region of J1/J2 as an external magnetic field is applied. In addition, it is known that several kinds of quasi one-dimensional cuprates can be described by this J1-J2 spin chain. Particularly, a recent experiment shows that LiCuVO4, one of the cuprates, possesses a new phase near saturation and it is expected to be a spin nematic ordered phase. Motivated by these results, we have completed the field-temperature phase diagram for spatially anisotropic magnets consisting of weakly coupled J1-J2 spin chains, by making use of accurate results of the single J1-J2 spin chain. The phase diagram contains spin nematic and spin-density-wave ordered phases, and these two orders compete with each other. We will discuss some universal features of the phase diagram and the relevance of our result to LiCuVO4.   

Unusual interchain coupling effects in frustrated edge-shared chain cuprates with ferromagnetic NN in-chain coupling

We consider the effect of weak antiferromagnetic interchain coupling (AFM IC) on the saturation field, the magnetization curve, the phase diagram of multipolar phases at high magnetic fields, the dynamical magnetic structure factor, as well as the pitch angle at ambient fields applying the DMRG-technique to clusters of coupled long chains and the hard-core boson method to quasi-1D spin nematics at T=0 The critical AFM IC couplings for various multipolar phases and types of IC are determined. The results are applied to Li$_{2}$CuO$_{2}$, LiVCuO$_{4}$, Ca$_{2}$Y$_{2}$Cu$_{5}$O$_{10}$, as well as to linarite. The multipolar phases can be stabilized by easy-axis spin anisotropy. Linarite and LiVCuO$_{4}$, are found to be good candidates for the detection of mulipolar phases. Microscopic considerations based on the extended five-band Hubbard model and L(S)DA+$U $calculations provide exchange integrals which support the empirically found values for the main exchange integrals. We discuss the applicability of spin-wave theory and the role of quantum fluctuations for a correct description of magnetic excitations. Cases when a weak IC coupling dominates solely or predominantly the saturation field and/or the pitch angle are emphasized.   

Frustrated 1D Spin-S chain Below Saturation Magnetization

Ground states of frustrated spin-S chains in strong magnetic field in the immediate vicinity of saturation are mapped out. For ferromagnetic nearest-neighbor and frustrating antiferromagnetic next-nearest-neighbor exchange interactions generic feature is metamagnetic behavior under the influence of an external magnetic field for small S, in the form of a first-order transition to the fully polarized state. The magnetization jump increases gradually starting from an S-dependent critical value of exchange couplings and takes a maximum in the vicinity of a ferromagnetic Lifshitz point. The metamagnetism results from resonances in the dilute magnon gas caused by an interplay between quantum fluctuations and frustration. For antiferromagnetic nearest neighbour interactions generic feature is emergence of two-component Luttinger liquid phase and series of phase transitions between that phase and chiral phase.   

Quasi-one-dimensional antiferromagnetism and multiferroicity in CuCrO$_4$

The bulk magnetic properties of the new quasi-one-dimensional Heisenberg antiferromagnet, CuCrO$_4$, were characterized by magnetic susceptibility, heat capacity, optical spectroscopy, EPR and dielectric capacitance measurements and density functional evaluations of the intra- and interchain spin exchange interactions. We found type-II multiferroicity below the N\'{e}el temperature of 8.2(5)~K, arising from competing antiferromagnetic nearest-neighbor ($J_{\rm nn}$) and next-nearest-neighbor ($J_{\rm nnn}$) intra-chain spin exchange interactions. Experimental and theoretical results indicate that the ratio $J_{\rm nn}$/$J_{\rm nnn}$ is close to 2, putting CuCrO$_4$ in the vicinity of the Majumdar-Ghosh point. First low-temperature neutron powder diffraction data are consistent with a canted magnetic structure below $\sim$8 K.   

Magnetic field induced ferroelectric transition of quantum spin chain system Rb$_{2}$Cu$_{2}$Mo$_{3}$O$_{12}$

Dielectric and magnetic properties have been studied for Rb$_{2}$Cu$_{2}$Mo$_{3}$O$_{12}$, which includes quasi one-dimensional spin $1/2$ chains formed of edge-sharing CuO$_{4}$ square planes called CuO$_{2}$ ribbon chains. The system does not exhibit a magnetic transition above temperature $T>2$K owing to quantum fluctuation and low dimensionality. We have observed anomalous increase of dielectric constant $\varepsilon$ with decreasing $T$ below $\sim 50$ K, which is originated from growing a short range ordering of a helical magnetic structure. For an external magnetic field $H>0.5$T, a peak structure is observed in the $\varepsilon -T$ curves at $T_{c} \sim 8$K and the ferroelectric polarization has been observed below $T_{c}$. However, the magnetic susceptibility and specific heat do not have anomaly at $T_{c}$ for $H>0.5$T. The anomalous increase of $\varepsilon$ and field-induced ferroelectric transition are found to be suppressed by impurity doping such as Zn and Ni atoms to the Cu sites. These results indicate that the ferroelectric transition is found to be induced by applying field without magnetic transition which strongly suggests a new type of ferroelectric transition triggered by the magnetism of frustrated quantum spin systems.   

On the onset of incommensurate behavior in the $J_1$-$J_2$-chain with an odd number of sites

The anti-ferromagnetic spin-$1/2$-$J_1$-$J_2$-chain is one of the most researched spin-systems. For a chain with an even number of sites the ground-state is analytically known at $J_2/J_1 = 0.5$ and at $J_2/J_1 > 0.5$ spin-spin-correlations become incommensurate. Very little is known about how this incommensurability is manifested in chains with an odd number of sites. In this presentation we show results of variational calculations for $J_1$-$J_2$-chains with an odd number of sites and open boundary conditions in this incommensurate regime. The results indicate that the system becomes gapless at $J_2/J_1 \approx 0.53$. We show results for the on-site magnetization, the entanglement as well as correlation functions and discuss how the incommensurability dramatically affects them. In particular we show how the usual well defined single soliton excitation breaks up at $J_2/J_1 \approx 0.53$.   

Broken vector spin chirality in biatomic Fe chains on Ir(001)

We investigate from {\em ab initio} the magnetism of biatomic Fe chains, which form due to self-organization on the (5$\times$1)-reconstructed Ir(001) surface [1,2]. Using the {\tt FLEUR} code [3], we calculate the magnetic properties and exchange interactions in this system, finding a very small Heisenberg exchange along the chain of the order of 10 meV/Fe-atom. Upon including spin-orbit coupling we obtain the contribution from the Dzyaloshinskii-Moriya interaction and find that it leads to a 120$^{\circ}$ spin-spiral ground state of the Fe chains with a unique rotational sense. The results of the Monte-Carlo simulations based on the parameters from {\it ab initio} are in a very good agreement to STM experiments on the system. Moreover, simulations indicate a robustness of the spin chiral order parameter, which decays with temperature much slower than the scalar spin correlation, in analogy to a vector spin chiral liquid state. We discuss possible applications of the magnetism in these chains with respect to the transfer of information on the nanoscale.\newline [1] L. Hammer {\it et al.}, Phys. Rev. B {\bf 67}, 125422 (2003). [2] Y. Mokrousov \textit{et al.}, Phys. Rev. B \textbf{80}, 195420 (2009). [3] www.flapw.de   

Highly frustrated quantum magnetism in the mineral azurite: multi-step approach from first-principles computations to experimental data

The natural mineral azurite Cu$_3$(CO$_3$)$_2$(OH)$_2$ is a frustrated magnet displaying unusual and controversially discussed magnetic behavior. We perform a theoretical study based on density functional theory as well as state-of-the-art numerical many-body calculations [1]. We propose an effective generalized spin-1/2 diamond chain model which provides a consistent description of experiments: low-temperature magnetization, inelastic neutron scattering, nuclear magnetic resonance measurements, magnetic susceptibility as well as new specific heat measurements. With this study we demonstrate that the balanced combination of first principles with powerful many-body methods successfully describes the behavior of this frustrated material. \newline [1] H. O. Jeschke {\it et al.}, Phys. Rev. Lett. {\bf 106}, 217201 (2011)   

Magnetic anisotropy in the frustrated spin-ladder system BiCu$_{2}$PO$_{6}$ from magnetostriction in pulsed fields

The spin interactions in BiCu$_{2}$PO$_{6}$ have been studied by inelastic neutron scattering, magnetic susceptibility, and numerical calculation. There is strong frustration between magnetic interactions along the ladder leg, $J_{Leg}$ and $J_{NNN}$, and it has been pointed out that a spin gap persists in this frustrated system. Both $J_{leg}$ and $J_{NNN}$ are intra-ladder and two-leg ladder is always gapped. Longitudinal magnetostriction (MS) measurements were performed using a fiber optic strain gauge in a 60 T pulsed magnet [1] . Specific heat ($C_{p})$ and magnetocaloric effect (MCE) measurements were performed in a 35 T DC magnet. $C_{p}$ vs $T$ was obtained using both a thermal relaxation time and dual slope techniques. We have in this way determined the (H,T) phase diagram of BiCu$_{2}$PO$_{6}$ up to 45 T. The 3D character of phase transitions is suggested by the observation of sharp anomalies in CM and \textit{$\Delta $}L/L. Our MCE and MS data provides direct evidence of first-order phase transitions for H//c, while phase transitions for H//a and H//b are characterized as second-order phase transitions. The anisotropic and complex phase boundaries will be discussed. \\[4pt] [1] Daou R et al., \textit{Rev. Sci. Instrum}. \textbf{81}, 033909 (2010).   

Magnetism of a Frustrated Four-Spin-Tube

We report on the magnetism of a frustrated four-leg spin-$1/2$ tube (FFST) [1]. Using a combination of series expansion, based on the continuous unitary transformation method and density-matrix renormalization group we analyze the ground-state correlations, and the one-, and the two-particle excitations in the regime of strong rung-coupling. We find that frustration destabilizes the spin-gapped quadrumer singlet-phase of the FFST, leading to first order quantum phase transitions. Apart from the well-know triplon branch of two-leg spin-ladders, the FFST is shown to sustain additional elementary excitations, including a singlon, and additional triplons. Finally, in the two-particle sector the FFST exhibits several collective (anti)bound states. Frustration has significant impact on the FFST leading to a flattening of the ground-state energy landscape, a mass-enhancement of the excitations, and a relative enhancement of the (anti)binding strength.\\[4pt] [1] Marcelo Arlego and Wolfram Brenig Phys. Rev. B {\bf 84}, 134426 (2011).   

Pursuit of a spin Bose-metal phase in Hubbard-type models on the two-leg triangular strip

Motivated by recent experiments on the organic materials $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$ and EtMe$_3$Sb[Pd(dmit)$_2$]$_2$, we numerically investigate the Mott metal-insulator transition in a system of interacting, itinerant electrons at half-filling on the two-leg triangular strip (i.e., zigzag chain). Previous work [1] has revealed that an exotic ``spin Bose-metal'' (SBM) phase with three gapless modes is stabilized on the zigzag strip in a pure spin model of Heisenberg exchange supplemented with four-site cyclic ring exchange, a model appropriate for describing weak Mott insulators near the Mott transition. Indeed, a physically appealing picture of the realized SBM phase is to view it as a particular Mott insulating instability out of a two-band metal of interacting electrons. Guided by this idea, we perform large-scale DMRG calculations across the Mott transition in various Hubbard-type models (e.g., with on-site repulsion, longer-ranged repulsion, and/or explicit spin exchange terms). We focus on the successes and failures of describing the insulating phase near the transition within the SBM framework. Finally, the implications of our findings to the full 2D triangular lattice will be discussed.\\[4pt] [1] D. N. Sheng \emph{et al.}, PRB {\bf 79}, 250112 (2009).   

Symmetry protected topological phases for 1-dimensional spin-1 antiferromagnets

Symmetry protected topological phases for 1-dimensional S=1 antiferromagnets respecting D2+T symmetry (D2 is a point group and T is the time reversal symmetry) are studied. There are 15 different nontrivial topological phases, all of them are non-symmetry-breaking. One of these phases is the usual Haldane phase, and the others are new. We find that four of the nontrivial SPT phases can be realized in spin-1 chains and the rest can be realized in spin-1 ladders. We propose experimental methods to distinguish all of these phases.