Session A24: 2D Frustrated Spin Systems: Shastry Sutherland and Bipartite Lattices

Mapping the Phase Diagram of Frustrated Quantum Magnets Using Magnetic Field, Pressure and Chemical Doping

The interactions that define how spins arrange themselves in a material play a fundamental role in a wide variety of physical phenomena. Frustrated quantum magnets are systems in which the exchange interactions governing the interacting spins cannot be simultaneously satisfied, leading to a highly degenerate ground state and exotic states of matter. In this talk I will discuss how chemical doping, hydrostatic pressure and application of magnetic field regulates the underlying electronic and magnetic interactions in two-dimensional geometrically frustrated systems, ultimately driving the ground state across the phase diagram and leading to emergent quantum critical phenomena. I will present our results for magnetometry, x-ray and neutron scattering experiments performed under extreme sample environments on Shastry-Sutherland model systems and rare-earth triangular antiferromagnets.   

High Magnetic Field, High Pressure Studies of Emergent Bound States in Chemically Doped Shastry-Sutherland System

The orthogonal-dimer antiferromagnet SrCu₂(BO3)₂ (SCBO) is an experimental realization of the two-dimensional Shastry-Sutherland (SSL) model, which represents one of the very few topologies where the ground state of a frustrated lattice could be exactly solved. The delicate competition between the intra-dimer and inter-dimer exchange interactions in SCBO enables tuning of its ground state by a variety of experimental parameters, such as magnetic field, pressure, and chemical doping. While pure SCBO has been well studied, less is known about the doping effect on the SSL system. In this talk we present our recent high-pressure, high-magnetic field neutron scattering and megnetometry results performed on chemically doped SCBO single crystals, where magnetic Cu²⁺ has been substituted with nonmagnetic isoelectronic Mg²⁺. We discuss the interplay between the induced disorder and external tuning parameters, and explain how such correspondence results in stabilizing the emergent new bound states in SSL systems.   

Raman Scattering and Dilatometry of Frustrated Spin Dimer Compound SrCu2(BO3)2 in High Magnetic Fields to 45T

SrCu₂(BO₃)₂ is a quasi-two dimensional orthogonal spin dimer system with a spin singlet ground state. It is a realization of the Shastry Sutherland model, and exhibits a sequence of magnetization plateaux at magnetic fields in excess of 20 T, i.e. high enough to close the low temperature spin gap [1]. The unique behavior of this quantum spin liquid results from the interplay between geometrical frustration and strong quantum fluctuations. We will discuss the origin and characteristics of the strong spin-lattice coupling in SrCu₂(BO₃)₂, as learned from experimetal studies of Raman scattering, thermal expansion, and magnetostriction performed in high DC magnetic fields to 45T. The interpretation of experimental results is supported by a theoretical analysis and prediction of active Raman modes that include the so-called panthograph mode [2].
[1] M. Jaime, et al. Proc. Natl. Acad. Sci. 109, 12407 (2012).
[2] G. Radtke et al., Proc. Natl. Acad. Sci. 112, 1971 (2015).   

Thermal Transport Measurements of a Shastry-Sutherland Magnet with Capacitive Thermometry

The Shastry-Sutherland magnet SrCu₂(BO₃)₂ has been predicted to host excitations known as triplons which give rise to a thermal Hall conductivity. Measurements of the thermal Hall effect are challenging to make since they require sensitive thermometry at low temperatures and in intense magnetic fields. Most standard methods of measuring temperature are either not sensitive enough or have significant magnetic field induced deviations. We have developed a technique using Oxygen-18 doped Strontium Titanate to make capacitive thermometers which are sensitive at the required temperature range while also not being affected by magnetic fields. By combining this method with more traditional methods of thermometry, we have been able to observe field-dependent thermal properties in SrCu₂(BO₃)₂, including a strongly varying thermal conductivity as well as our exploration of the predicted thermal Hall conductivity.   

Visualizing Magnetic Domains at Fractional Magnetization Plateaus in a Metallic Shastry-Sutherland Ising-type Rare Earth Tetraboride

Recently, unconventional magnetic and electronic effects born out of lattice geometric frustration have been observed in metallic frustrated systems. The rare earth tertraboride TmB₄ is one such system with both lattice frustration and itinerant electronic behavior exhibiting complex magnetic phenomena. The Tm ions form a sublattice topologically equivalent to the Shastry-Sutherland lattice in the ab-plane which enters an antiferromagnetic ground state below 11.8 K. Interestingly, the system enters a field-induced ferrimagnetic state at high field, with strong c-axis anisotropy, eventually reaching a field-induced paramagnetic state, exhibiting hysteretic fractional magnetization plateaus along the way, induced by frustration and complex spin flip processes.² Magnetic hysteresis indicates domain formation and the coexistence of fractional magnetization phases. To this end, we report our variable temperature magnetic force microscopy studies on refined floating zone grown TmB₄ single crystals. Various multi-domain patterns were observed at different saturation magnetization plateaus below T_N. The evolution of these magnetic domains at various temperatures and magnetic fields will be presented.   

Frustrated Ground State in the metallic Ising 2D Anti-ferromagnet Nd2Ni2In

Nd₂Ni₂In is a 2D Ising anti-ferromagnet (T_N = 8 K) with a crystal structure equivalent to the Shastry-Sutherland (SS) lattice, leading to magnetic frustration. This system is well known for its high Hydrogen absorption capabilities, but recently its magnetic properties have been investigated revealing some very interesting anomalies. The magnetization curve in the ordered state obtained on the Nd₂Ni₂In polycrystal is not qualitatively different from a very narrow hysteresis loop of a ferromagnet. Nevertheless, neutron measurements indicate an anti-ferromagnetic structure with Ising Nd moments oriented mutually perpendicular along the direction of the [110] type, i.e. Nd moments in the basal plane.
Data collected at SEQUOIA and CNCS have been used to analyze the crystal field of Nd₂Ni₂In in zero field to shed light on its ground state. The results point towards a structure with Ising spins oriented along the local [110] direction with a magnetic moment of 2.59(13) μ_B/Nd, in excellent agreement with previous measurements. Moreover the analysis on the two magnetic Bragg peaks (2,0,0), (2,1,0) gave an order parameter ß=0.13, which is very close to the critical exponent for the 2D Ising model exactly solved by Onsager ß=1/8.   

Dynamical responses and instabilities of the Shastry-Sutherland model

The Shastry-Sutherland model (SSM) is famous for holding an exact ground state solution for inter-dimer exchange J'/J≤0.7. In this exact ground state, spins form singlets on the dimers. Single triplon excitations have a rather flat dispersion that renders perturbative treatments of the triplon-triplon interactions simply inadequate. In addition, the multiple competing length scales of this model also limits the applicability of finite size numerical simulations.
We introduce an unbiased variational method to study static and dynamic T=0 properties of the SSM in the thermodynamic limit. The variational basis is generated by dressing up the triplon excitations via a systematic inclusion of quantum fluctuations. The accuracy of this method is controlled by the number of iterations, which controls the size of the variational space. By solving the model in the thermodynamic limit, we can obtain dynamical responses (relevant to neutron, Raman and inelastic X-ray scattering) with high momentum resolution. Moreover, we can unbiasedly predict instabilities near the exact dimer phase, induced by single or multi-triplon condensation. We will discuss several competing orders (magnetic and nematic) next to the dimer phase and reveal the resulting phase diagram.   

Entanglement Studies of Resonating Valence Bonds on the Frustrated Square Lattice

We study a short-range resonating valence bond (RVB) wave function with diagonal links on the square lattice that permits sign-problem free wave function Monte-Carlo studies. Special attention is given to entanglement properties, in particular, the study of minimum entropy states (MES) according to the method of Zhang et. al. We provide evidence that the MES associated with the RVB wave functions can be lifted from an associated quantum dimer picture of these wave functions, where MES states are certain linear combinations of eigenstates of a 't Hooft ``magnetic loop''-type operator. From this identification, we calculate a value consistent with $\ln(2)$ for the topological entanglement entropy directly for the RVB states via wave function Monte-Carlo. This corroborates the $\mathbb{Z}_{2}$ nature of the RVB states. We furthermore extract information about the modular $\mathcal{S}$- and $\mathcal{U}$-matrices. Aspects of a related classical dimer partition function will also be discussed.   

The phase diagram of spin-1/2 square J1-J2 Heisenberg model: U(1)-symmetric infinite PEPS study

The tensor-network states have shown to be quite promising in studying the frustrated systems. Specifically, infinite projected entangled-pair state (iPEPS) anstaz, a generalization of powerful DMRG, could efficiently address the low-lying excited states of such systems and provide quite competitive variational energy. In this talk, we aim to introduce an "improved" U(1)-symmetric iPEPS anstaz and study phase diagram of the canonical spin-1/2 square J₁-J₂ Heisenberg model. We discuss a simple strategy to selects automatically relevant symmetric sectors without losing accuracy and also discuss an improved optimization method. We show variational ground-state energies of the model set better upper bound on the true energy, improving previous tensor-network-based results. By studying magnetization parameter and correlation functions, we find a direct Néel-to-VBS transition at J₂=0.53. The estimated critical anomalous exponents η_s=0.65(5) and η_d=1.9(1) show strong deviation from those of the well-known J-Q models, suggesting possibly different universality class. We compare our results with earlier DMRG and PEPS studies and suggest future directions for resolving remaining issues.   

Fermionic spinon theory of square lattice spin liquids near the Néel state

Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a CP¹ theory of bosonic spinons coupled to a U(1) gauge field with a global SU(2) spin rotation symmetry. Such a theory also has a confining phase with valence bond solid (VBS) order and deconfined phases with Z₂ topological order. We present dual theories of these phases starting from a mean-field theory of fermionic spinons with a π-flux in each plaquette. Fluctuations about this π-flux state are described by 2+1 dimensional quantum chromodynamics (QCD₃) with a SU(2) gauge group and N_f= 2 flavors of massless Dirac fermions. It has recently been argued by Wang et al. (arXiv:1703.02426) that this theory describes the Néel-VBS phase transition. We introduce adjoint Higgs fields in QCD₃, and obtain fermionic descriptions of both the VBS phase and the topologically ordered phases obtained earlier using the bosonic theory. The global phase diagram of these phases contains multi-critical points, and our results imply new boson-fermion dualities.   

Longitudinal (Higgs) Modes of Spin Fluctuations in Iron-based Superconductors

Iron-based superconductors can exhibit different magnetic orders and are in a critical magnetic region where frustrated magnetic interactions strongly compete with each other. The order parameters can fluctuate transversely as gapless Goldstone modes and longitudinally as gapped Higgs modes. Here we investigate the Higgs modes of spin fluctuations in the unified effective J₁-J₂-J₃-K model for iron-based superconductors. In this work, the Higgs modes are viewed as two-magnon resonance from the linear spin wave approach for the local spin exchange model. We focus on the collinear antiferromagnetic order and calculate the longitudinal modes when different phase boundaries are approached. We compare it with the observed longitudinal gap in CaFe₂As₂, which was looked as the support for the itinerant picture. This is a systematic method to explore the longitudinal excitations in the local spin exchange model and we can easily extend it in three dimensions.   

Entanglement Negativity and Sudden Death in the Toric Code at Finite Temperature

We study the fate of quantum correlations at finite temperature in the two dimensional toric code using the logarithmic entanglement negativity. We are able to obtain exact results that give us insight into how thermal excitations affect quantum entanglement. We show that an $O(1)$ density of the lower energy defect is required to degrade the zero-temperature entanglement between two subsystems in contact with one another. However, one type of excitation alone is not sufficient to kill all quantum correlations, and an $O(1)$ density of the higher energy defect is required to cause the so-called sudden death of the negativity. Interestingly, if the energy cost of one of the excitations is taken to infinity, quantum correlations survive up to arbitrarily high temperatures, a feature that is likely shared with other quantum spin liquids and frustrated systems in general, when projected down to their low energy states. We further observe that the negativity per boundary degree of freedom at a given temperature increases (parametrically) with the size of the boundary, and that quantum correlations between subsystems with extended boundaries are more robust to thermal fluctuations.   

Z2 Topological Quantum Paramagnet on a honeycomb bilayer

Topological quantum paramagnets are exotic states of matter with trivial paramagnetic ground states hosting topological excitations. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts a Z₂ topological quantum paramagnet in the presence of spin-orbit coupling. The Z₂ invariant is the same as that in the case of the fermionic quantum spin Hall state. We further show that upon making one of the Heisenberg couplings stronger the system undergoes a topological quantum phase transition, where the Z₂ invariant vanishes, to a different topological quantum paramagnet. In this case the edge states are disconnected from the bulk excitations. This phase is characterized by a different topological invariant. This physics is amenable to experiments, where an anisotropic coupling can be induced under pressure.