Session B5: Frustrated Magnetism: Low Dimensional Magnets I

Magnetic nanopantograph in the in SrCu$_2$(BO$_3$)$_2$ Shastry-Sutherland lattice

Magnetostriction experiments of the frustrated spin dimer compound SrCu$_2$(BO$_3$)$_2$ have shown that its macroscopic physical dimensions change with the applied magnetic field mimicking the complicated structures, with discreet jumps and plateaus, observed in the magnetization. Using Density Functional based methods we find that the driving force behind the magnetoelastic coupling is the Cu-O-Cu superexchange angle which, thanks to the orthogonal Cu$^{2+}$ dimers acting as pantographs, can shrink significantly (0.44\%) with minute (0.01\%) variations in the lattice parameters. Our calculations show that the consequence is a reduction of the order of $\sim$10\% in the antiferromagnetic intra-dimer exchange integral $J$, sufficient to compensate the elastic energy loss in the deformation. This reduction should impact our reading of existing predictions of the magnetization versus field phase diagram and the effect of hydrostatic pressures on the ground state. Finally, our prediction of the dimer shrinking under applied magnetic field should appear as a modification of the optical Raman active modes compatible with the pantograph effect.   

Hysteretic magnetoresistance and unconventional anomalous Hall effect in the frustrated magnet TmB4

We study TmB$_4$, a frustrated magnet on the Archimedean Shastry-Sutherland lattice, through magnetization and transport experiments. The lack of anisotropy in resistivity shows that TmB$_4$ is an electronically three-dimensional system. The magnetoresistance (MR) is hysteretic at low-temperature even though a corresponding hysteresis in magnetization is absent. The Hall resistivity shows unconventional anomalous Hall effect (AHE) and is linear above saturation despite a large MR. We suggest that both hysteretic MR and AHE arise from the formation of complex non-coplanar structures at magnetic domain walls.   

Spin-lattice coupling of $R_{\mathrm{1-x}}$Lu$_{\mathrm{x}}$B$_{\mathrm{4}}$ revealing anomalous weak ferromagnetism ($R=$Sm, Gd, Tb, Dy, Ho)

$R$B$_{\mathrm{4}}$ ($R=$rare-earth elements) compounds exhibits antiferromagnetic ordering at low temperature and are classified as the Shastry-Sutherland lattice, which is a geometrically frustrated system. In previous study, it was reported that Y substitution in TbB$_{\mathrm{4}}$ single crystals causes anomalous WF (weak ferromagnetism) even though Y$^{\mathrm{3+}}$ is non-magnetic. The disturbance of a delicate equilibrium in a frustrated system can lead to new electronic and magnetic states. In this study, single crystals of $R_{\mathrm{1-x}}$Lu$_{\mathrm{x}}$B$_{\mathrm{4}}$ ($R=$Sm, Gd, Tb, Dy, Ho), (x$=$0 \textasciitilde 0.8) were synthesized. WF is also observed. TbB$_{\mathrm{4}}$ went through orthorhombic distortion below N\'{e}el temperature. To investigate the existence of orthorhombic distortion in TbLu$_{\mathrm{x}}$B$_{\mathrm{4}}$ (x$=$0.1, 0.35), high resolution single crystal x-ray diffraction was performed at 5 K. It was confirmed that the distortion was vanished with Lu substitution. Interestingly, lattice constant $a$ was increased with decreasing temperature below the T$_{\mathrm{C}}$. The strong correlation between spin-lattice coupling and WF will be discussed in detail.   

Neutron Diffraction on NaNi2BiO6: Complex Interactions on a Honeycomb Lattice

Magnetic crystals with a honeycomb lattice can have a very high degree of frustration when next-nearest neighbor interactions are strong. Such complex interactions can lead to Kitaev model physics, including a proposed spin liquid phase. Using neutron scattering, we studied the magnetic properties of a new spin-1/2 honeycomb compound, NaNi$_{2}$BiO$_{6}$, which was known to have heat capacity peaks indicative of a phase transition at 5 K. The magnetic order indicates beyond nearest-neighbor exchange as well as significant inter-plane interaction, which allows for a study of rich and complex structure. In this talk I report the magnetic structure of the compound as found with neutron powder diffraction, and discuss the exchanges necessary to lead to such a complex order.   

Field-induced dynamical properties of the $XXZ$ model on a honeycomb lattice

We present a comprehensive $1/S$ study of the field-induced dynamical properties of the nearest-neighbor $XXZ$ antiferromagnet on a honeycomb lattice using the formalism of the nonlinear spin-wave theory developed for this model. External magnetic field controls spin frustration in the system and induces non-collinearity of the spin structure, which is essential for the two-magnon decay processes. Our results include an intriguing field-evolution of the regions of the Brillouin zone where decays of spin excitations are prominent, a thorough analysis of the singularities in the magnon spectra due to coupling to the two-magnon continuum, the asymptotic behavior of the decay rates near high-symmetry points, and inelastic neutron-scattering spin-spin structure factor obtained in the leading $1/S$ order.   

Featureless Quantum Insulator on the Honeycomb Lattice

We construct fully symmetric, gapped states without topological order on a spin-1/2's honeycomb lattice at half-filling in terms of projected entangled pair states (PEPS) Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, arXiv:1505.03171 (2015)]. Lack of topological degeneracy or other conventional form of symmetry breaking, and the existence of the energy gap in both wave functions are checked by numerical calculation of the entanglement entropy and various correlation functions.   

Possible spin liquid behavior in Sc$_2$Ga$_2$CuO$_7$

The title compound crystallizes in a hexagonal structure (space group P63/mmc) containing edge-shared triangular planes as also triangular bi-planes. Our work establishes that the single triangular layers mainly have $S = 0$ Ga$^{3+}$(85\% Ga, 15\% Cu), while the bi-layers contain 43\% Cu$^{2+}$ and 57\% Ga$^{3+}$, as far as the cations are concerned. Our $\chi(T)$ data shows no spin-freezing or magnetic long-range order (LRO) down to 1.8 K. We infer an effective moment of 1.79 $\mu_B$ and a $\theta_{CW}$ of about -50 K, suggesting AF interactions. In our specific heat data, no anomalies were found down to 0.35 K, in the field range 0-140 kOe. The magnetic specific heat has a nearly $T^2$ power-law behavior at low-$T$ (for $H > 90$ kOe). The $^{71}$Ga nuclear magnetic resonance (NMR) shift $K(T)$ displays a broad maximum at $T \sim 50$ K. The $^{71}$Ga spin lattice relaxation rate 1/$T_1$ displays a $T^{3.2}$ power-law increase from 0.1 K to 2 K, then remains nearly unchanged up to 10 K, and increases thereafter. Once again, down to 100 mK there is no indication of LRO which is usually manifested as an anomaly in the $T$-dependence of $K$ and 1/$T_1$. Our data suggest the formation of a quantum spin liquid in the $S=1/2$ system Sc$_2$Ga$_2$CuO$_7$.   

Phase diagram of weakly coupled Heisenberg spin chains subject to a uniform Dzyaloshinskii-Moriya interaction

Motivated by recent experiments on spin chain materials K$_2$CuSO$_4$Cl$_2$ and K$_2$CuSO$_4$Br$_2$, we theoretically investigate the problem of weakly coupled spin chains (chain exchange $J$, interchain $J'$) subject to a {\em staggered between chains}, but {\em uniform} within a given chain, Dzyaloshinskii-Moriya interaction (DMI) of magnitude $D$. In the experimentally relevant limit $J' \ll D \ll J$ of strong DMI the spins on the neighboring chains are forced to rotate in opposite directions, effectively resulting in a cancelation of the interchain interaction between components of spins in the plane normal to the vector ${\bf D}$. This has the effect of promoting two-dimensional collinear spin density wave (SDW) state, which preserves U(1) symmetry of rotations about the $D$-axis. We also investigate response of this interesting system to an external magnetic field $h$ and obtain the $h-D$ phase diagrams for the two important configurations, $h \parallel D$ and $h \perp D$. The transitions between various SDW-like phases are found to be of either a commensurate-incommensurate or a spin-flop kind.   

Spin Liquid in the Triangular Lattice Heisenberg Model

We report the results of a large-scale numerical study of the spin-1/2 Heisenberg model on the triangular lattice, with nearest- and next-nearest neighbor interactions. Using SU(2)-invariant iDMRG for infinite cylinders, we focus on the YC12 structure (with a circumference of 12 sites), and obtain 4 candidate groundstates, corresponding to even/odd spinon sectors, each with linear and projective representations of the cylinder geometry. The momentum-resolved entanglement spectrum reveals the structure of the low-lying spinon excitations. Contrary to some recent works, we find no evidence for chiral symmetry breaking.   

Anisotropic thermal conductivity of proton fluctuation-induced quantum spin liquid $\kappa $-H$_{\mathrm{3}}$(Cat-EDT-TTF)$_{\mathrm{2}}$

We report the thermal transport properties of a quantum spin liquid candidate $\kappa $-H$_{\mathrm{3}}$(Cat-EDT-TTF)$_{\mathrm{2}}$ (H-CAT) with a two-dimensional nearly isotropic triangular lattice. Above 1.0 K, thermal conductivity of H-CAT is substantially smaller than that of a deuterated non-magnetic sample (D-CAT) despite no spin thermal conductivity in D-CAT. In the zero-temperature limit, a finite $T$-linear term of the thermal conductivity of H-CAT is clearly observed when the heat current is parallel to $c$-axis, while it is almost zero when the heat current is parallel to $b$-axis. These features would be attributed to anisotropic proton fluctuations present in H-CAT.   

Theory of triplon dynamics in the quantum magnet BiCu$_{\mathrm{2}}$PO$_{\mathrm{6}}$

We provide a theory of triplon dynamics in the valence bond solid ground state of the coupled spin-ladders modeled for BiCu$_{\mathrm{2}}$PO$_{\mathrm{6}}$. Utilizing the recent neutron scattering experimental data as guides and a theory of interacting triplons via the bond operator formulation, we determine a minimal spin Hamiltonian for this system. It is shown that the splitting of the low energy triplon modes and the peculiar magnetic field dependence of the triplon dispersions can be explained by including substantial Dzyaloshinskii-Moriya and symmetric anisotropic spin interactions. Taking into account the interactions between triplons and the decay of the triplons to the two-triplon continuum via anisotropic spin interactions, we provide a theoretical picture that can be used to understand the main features of the recent neutron scattering experimental data.   

Multi-Magnon Bound States in J1-J2 Model on a Triangular Lattice

Competing exchange interactions in spin systems often give rise to unusual magnetic behavior, such as spiral orders and nematic orders in spin chains. Also, on classical triangular Heisenberg models, recent studies found skyrmion lattice phases in an applied magnetic field. Motivated by these studies, we investigate the magnetic phase diagram of a quantum J1-J2 XXZ model on a triangular lattice. In order to study the quantum phases close to the saturation field, we calculate the low energy excitation spectrum near the saturation field, and find the instability toward condensation of multi-magnon bound states, namely, multipolar order. A similar behavior is confirmed in the exact diagonalization of finite size clusters. We also discuss the relationship between the obtained quantum phases and the skyrmion lattice phase which is found in the classical counterpart of our model.