We study the classical Heisenberg model on the geometrically frustrated Shastry-Sutherland (SS) lattice with additional Dzyaloshinskii-Moriya (DM) interaction in the presence of an external magnetic field. We show that several noncollinear and noncoplanar magnetic phases, such as the flux, all-in/all-out, 3in-1out/3out-1in, and canted-flux phases are stabilized over wide ranges of parameters in the presence of the DM interaction. We discuss the role of DM interaction in stabilizing these complex magnetic phases. When coupled to these noncoplanar magnetic phases, itinerant electrons experience a finite Berry phase, which manifests in the form of topological Hall effect, whereby a non-zero transverse conductivity is observed even in the absence of a magnetic field. We study this anomalous magneto-transport by calculating the electron band structure and transverse conductivity for a wide range of parameter values, and demonstrate the existence of topological Hall effect in the SS lattice. We explore the role of the strength of itinerant electron-local moment coupling on electron transport and show that the topological Hall features evolve significantly from strong to intermediate values of the coupling strength, and are accompanied by the appearance of a finite spin Hall conductivity.
Motivated by recent experiments on TmB4 (arXiv:0712.1537), we examine the phase diagram of the Shastry-Sutherland antiferromagnet in an applied magnetic field in the limit of strong Ising anisotropy. In classical Ising limit, we demonstrate that the only fractional magnetization plateau is at 1/3 of the saturated magnetization. We study the perturbative influence of transverse quantum spin fluctuations, and present evidence that they can stabilize a narrow 1/2 magnetization plateau.
We study the Kondo lattice model on the geometrically frustrated Shastry-Sutherland lattice focusing on the quantum phase transition between the valence bond solid and the heavy fermion liquid phase. By explicitly including spinon pairing of local moments at the mean-field level, we establish the emergence of a unique heavy fermion superconducting phase induced by dimer ordering of the local moments coexisting with Kondo hybridization. Furthermore, we demonstrate that for suitable choices of parameters, a partial Kondo-screening phase, where some of the valence bonds are broken, precedes the a…
We study the excitation spectrum in the dimer phase of the Shastry-Sutherland model by using an unbiased variational method that works in the thermodynamic limit. The method outputs dynamical correlation functions in all possible channels. This output is exploited to identify the order parameters with the highest susceptibility (single or multitriplon condensation in a specific channel) upon approaching a quantum phase transition in the magnetic field versus the $J'/J$ phase diagram. We find four different instabilities: antiferro spin nematic, plaquette spin nematic, stripe magnetic order, an…
Controlled doping of SrCu$_2$(BO$_3$)$_2$, a faithful realization of the Heisenberg spin-1/2 antiferromagnet on the Shastry-Sutherland lattice, with non-magnetic impurities generates bound-states below the spin gap. These bound-states and their symmetry properties are investigated by exact diagonalisation of small clusters and within a simple effective model describing a spinon submitted to an attractive extended potential. It is shown that Raman spectroscopy is a unique technique to probe these bound-states. Quantitative theoretical Raman spectra are numerically obtained.
We study an anisotropic Heisenberg antiferromagnet with ferromagnetic transverse spin exchange using exact quantum Monte Carlo methods. Such a model is relevant to a class of rare earth tetraboride materials that display a range of magnetization plateaus under applied magnetic field. The layered arrangement of magnetic ions in these materials is topologically equivalent to the Shastry-Sutherland lattice. In this frustrated geometry, we study the interplay of next-nearest neighbor interactions in stabilizing a plateau at half the saturation magnetization (or 1/2 plateau). We also show hysteresi…
Thermodynamics of Shastry-Sutherland Model under Magnetic Field
The University of Hong Kong（香港大学）；HK Institute of Quantum Science & Technology, The University of Hong Kong（香港大学量子科学研究所）；State Key Laboratory of Optical Quantum Materials, The University of Hong Kong（香港大学光学量子材料国家重点实验室）
We study the Kondo lattice Shastry-Sutherland model with additional Dzyaloshinskii-Moriya(DM) interactions, exploring the possible magnetic phases in its multi-dimensional parameter space. Treating the local moments as classical spins and using a variational ansatz, we identify the parameter ranges over which various common magnetic orderings are potentially stabilized. Our results reveal that the competing interactions result in a heightened susceptibility towards a wide range of spin configurations including longitudinal ferromagnetic and antiferromagnetic order, coplanar flux configurations…
Exact Demonstration of Magnetization Pleateaus and First Order Dimer-Néel Phase Transitions in a Modified Shastry-Sutherland Model for SrCu$_2$(BO$_3$)$_2$
The Shastry-Sutherland lattice, one of the simplest systems with geometric frustration, which has an exact eigenstate by putting singlets on diagonal bonds, can be realized in a group of layered compounds and rises both theoretical and experimental interest. Most of the previous studies on the Shastry-Sutherland lattice are focusing on the Heisenberg model. Here we opt for the Hubbard model to calculate phase diagrams over a wide range of interaction parameters, and show the competing effects of interaction, frustration and temperature. At low temperature, frustration is shown to favor a param…
The 1/8 fractional plateau phase (1/8-FPP) in Shastry-Sutherland Lattice (SSL) spin systems has been viewed an exemplar of emergence on an Archimedean lattice. Here we explore this phase in the Ising magnet TmB4 using high-resolution specific heat (C) and magnetization (M) in the field-temperature plane. We show that the 1/8-FPP is smoothly connected to the antiferromagnetic (AF) phase on ramping the field from H= 0. Thus, the 1/8-FPP is not a distinct ground state of TmB4. The implication of these results for Heisenberg spins on the SSL is discussed.
The fermionic Shastry-Sutherland model has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin-1 Weyl fermion. Berry phases defined by the one-dimensional momentum as a parameter are quantized into 0 or pi due to the inversion symmetry combined with the time reversal, or existence of the glide plane, which also protects the massless Dirac cones with continuous parameters. This is the symmetry protected Z2 quantization. We have further demonstrated the Z2 Berry phases generically determine the existence of edge states in various…
Shastry-Sutherland lattice was observed as alternative ground state in Rare Earth intermetallic with Mo$_2$B$_2$Fe and U$_2$Pt$_2$Sn anisotropic structures where magnetic frustration is favored. In the case of Ce$_2$Pd$_2$Sn, it was shown that such phase can be suppressed by the application of magnetic field and, in this work, its stability is studied as a function of the electronic concentration by doping the Sn(4+) lattice with In(3+) atoms. Magnetic and specific heat measurements show that around 50\% substitution the Shastry Sutherland lattice vanishes in a critical point. This result conf…
Considerable recent theoretical and experimental efforts have been devoted to the study of quantum criticality and novel phases of antiferromagnetic heavy-fermion metals. In particular, quantum phase transitions have been discovered in the compound Yb$_2$Pt$_2$Pb. These developments have motivated us to study the competition between the RKKY and Kondo interactions on the Shastry-Sutherland lattice. We determine the zero-temperature phase diagram as a function of magnetic frustration and Kondo coupling within a slave-fermion approach. Pertinent phases include the Shastry-Sutherland valence bond…
We study topological properties of one-triplon bands in an extended Shastry-Sutherland model relevant for the frustrated quantum magnet SrCu_2(BO_3)_2. To this end perturbative continuous unitary transformations are applied about the isolated dimer limit allowing to calculate the one-triplon dispersion up to high order in various couplings including intra and inter Dzyaloshinskii-Moriya interactions and a general uniform magnetic field. We determine the Berry curvature and the Chern number of the different one-triplon bands. We demonstrate the occurance of Chern numbers $\pm 1$ and $\pm 2$ for…
The temperature dependence of the gapped triplet excitations (triplons) in the 2D Shastry-Sutherland quantum magnet SrCu$_2$(BO$_3$)$_2$ is studied by means of inelastic neutron scattering. The excitation amplitude rapidly decreases as a function of temperature while the integrated spectral weight can be explained by an isolated dimer model up to 10~K. Analyzing this anomalous spectral line-shape in terms of damped harmonic oscillators shows that the observed damping is due to a two-component process: one component remains sharp and resolution limited while the second broadens. We explain the …
Magnetization Plateaus in the Shastry-Sutherland Model for SrCu_2(BO_3)_2: Results of Fourth-Order Perturbation Expansion with a Low-Density Approximation
Motivated by the intriguing properties of the Shastry-Sutherland compound SrCu2(BO3)2 under pressure, with a still debated intermediate plaquette phase appearing at around 20 kbar and a possible deconfined critical point at higher pressure upon entering the antiferromagnetic phase, we have investigated its high-field properties in this pressure range using tunnel diode oscillator (TDO) measurements. The two main new phases revealed by these measurements are fully consistent with those identified by infinite Projected Entangled Pair states (iPEPS) calculations of the Shastry-Sutherland model, a…
We simulate the Shastry-Sutherland model in two dimensions by means of infinite projected entangled-pair states (iPEPS) - a variational tensor network method where the accuracy can be systematically controlled by the so-called bond dimension. Besides the well established dimer and Néel phase iPEPS confirms the presence of an intermediate phase with plaquette long-range order, and we determine its phase boundaries with high accuracy. The first order phase transition for $J=0.675(2)$ between dimer and plaquette phase is compatible with previous series expansion results. iPEPS predicts a weak fir…
It is known that for a topologically ordered state the area law for the entanglement entropy shows a negative universal additive constant contribution, $-γ$, called the topological entanglement entropy. We theoretically study the entanglement entropy of the two-dimensional Shastry-Sutherland quantum antiferromagnet using exact diagonalization on clusters of 16 and 24 spins. By utilizing the Kitaev-Preskill construction [A. Kitaev and J. Preskill, Phys. Rev. Lett. {\bf 96}, 110404 (2006)] we extract a finite topological term, $-γ$, in the region of bond-strength parameter space corresponding to…
The small-cluster exact-diagonalization calculations and the projector quantum Monte Carlo method are used to examine the competing effects of geometrical frustration and interaction on ferromagnetism in the Hubbard model on the Shastry-Sutherland lattice. It is shown that the geometrical frustration stabilizes the ferromagnetic state at high electron concentrations ($n \gtrsim 7/4$), where strong correlations between ferromagnetism and the shape of the noninteracting density of states are observed. In particular, it is found that ferromagnetism is stabilized only for these values of frustrati…
We study magnetic properties of the $S=1/2$ Ising-like XXZ model on the Shastry-Sutherland lattices with long-range interactions, using the quantum Monte Carlo method. This model shows magnetization plateau phases at one-half and one-third of the saturation magnetization when additional couplings are considered. We investigate the finite temperature transition to one-half and one-third plateau phases. The obtained results suggest that the former case is of the first order and the latter case is of the second order. We also find that the system undergoes two successive transitions with the 2D I…
The minimal effective model for the magnetisation plateaus below 1/2 in the Shastry-Sutherland model is derived to be an Ising model of certain unit-cell hard-core bosons with anisotropic repulsive interactions on isosceles triangular lattice. It unambiguously gives the prominent plateaus at 1/8, 1/6, 1/4, 1/3 and an additional one at 3/8, related through a particle-hole (p-h) transformation. The Dzyaloshinsky-Moriya (DM) interaction dresses it up with an inhomogeneous transverse field that also causes p-h asymmetry due to an in-plane component of the inter-dimer DM vector. This explains the a…
Using inelastic neutron scattering, x-ray, neutron diffraction, and the first-principle calculation techniques, we show that the crystal structure of the two-dimensional quantum spin system (CuCl)LaNb$_2$O$_7$ is orthorhombic with $Pbam$ symmetry in which CuCl$_4$O$_2$ octahedra are tilted from their high symmetry positions and the Cu$^{2+} (s = 1/2)$ ions form a distorted square lattice. The dominant magnetic interactions are the fourth nearest neighbor antiferromagnetic interactions with a Cu-Cl--Cl-Cu exchange path, which lead to the formation of spin singlets. The two strongest interaction…
Insulator-metal transition is investigated self-consistently on the frustrated Shastry-Sutherland lattice in the framework of Slave-Boson mean-field theory. Due to the presence of quasi-flat band structure characteristic, the system displays a spin-density-wave (SDW) insulating phase at the weak doping levels, which is robust against frustration, and it will be transited into an SDW metallic phase at high doping levels. As further increasing the doping, the temperature or the frustration on the diagonal linking bonds, the magnetic order $m$ will be monotonically suppressed, resulting in the ap…
We look into the quantum phase diagram of a spin-$\frac{1}{2}$ antiferromagnet on the square lattice with degenerate Shastry-Sutherland ground states, for which only a schematic phase diagram is known so far. Many exotic phases were proposed in the schematic phase diagram by the use of exact diagonalization on very small system sizes. In our present work, an important extension of this antiferromagnet is introduced and investigated in the thermodynamic limit using triplon mean-field theory. Remarkably, this antiferromagnet shows a stable plaquette spin-gapped phase like the original Shastry-Su…
Using infinite projected entangled-pair states (iPEPS), we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and {\it not} to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu$_2$(BO$_3$)$_2$, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confin…
We investigate the physical properties of the Shastry-Sutherland lattice material BaNd$_2$ZnO$_5$. Neutron diffraction, magnetic susceptibility, and specific heat measurements reveal antiferromagnetic order below 1.65 K. The magnetic order is found to be a 2-$\boldsymbol{Q}$ magnetic structure with the magnetic moments lying in the Shastry-Sutherland lattice planes comprising the tetragonal crystal structure of BaNd$_2$ZnO$_5$. The ordered moment for this structure is 1.9(1) $μ_B$ per Nd ion. Inelastic neutron scattering measurements reveal that the crystal field ground state doublet is well s…
The magnetic phase diagram of Ce$_2$Pd$_2$Sn is investigated through the field dependence of thermal, transport and magnetic measurements performed at low temperature. The upper transition, $T_M=4.8$ K is practically not affected by magnetic field up to B=1 T, whereas the lower one $T_C(B)$ rapidly increases from 2.1 K joining $T_M$ in a critical point at $T_{cr}=(4.2\pm 0.3$)K for $B_{cr}=(0.12\pm 0.03)$ T. At that point the intermediate phase, previously described as an unstable Shastry-Sutherland phase, is suppressed. A detailed analysis around the critical point reveals a structure in the …
Anomalous thermal broadening in the Shastry-Sutherland model and SrCu$_2($BO$_3)_2$
University of Munich（慕尼黑大学）；Arnold Sommerfeld Center for Theoretical Physics, University of Munich（慕尼黑大学阿诺德·索末菲尔德理论物理中心）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Laboratoire Léon Brillouin, CEA, CNRS, Université Paris-Saclay（巴黎萨克雷大学CEA-CNRS莱昂·布里渊实验室）；Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université（CY塞吉巴黎大学CNRS 8089号理论与建模物理实验室）
Motivated by intertwined crystal symmetries and topological phases, we study the possible realization of topological insulator in nonsymmorphic crystals at integer fillings. In particular, we consider spin orbit coupled electronic systems of two-dimensional crystal Shastry-Sutherland lattice at integer filling where the gapless line degeneracy is protected by glide reflection symmetry. Based on a simple tight-binding model, we investigate how the topological insulating phase is stabilized by breaking nonsymmorphic symmetries but in the presence of time reversal symmetry and inversion symmetry.…
