Session H37: Spin Dimers in a Frustrated Lattice and Other Systems

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

We investigate the minus-sign problem that afflicts quantum Monte Carlo (QMC) simulations of frustrated quantum spin systems, focusing on spin S=1/2, two spatial dimensions, and the extended Shastry-Sutherland model. We show that formulating the Hamiltonian in the diagonal dimer basis leads to a sign problem that becomes negligible at low temperatures for small and intermediate values of the ratio of the inter- and intra-dimer couplings. This is a consequence of the fact that the product state of dimer singlets is the exact ground state both of the extended Shastry-Sutherland model and of a corresponding sign-problem-free model. We map the sign problem throughout the extended parameter space from the Shastry-Sutherland to the fully frustrated bilayer model and compare it with the phase diagram computed by tensor-network methods. We use QMC to compute with high accuracy the temperature dependence of the magnetic specific heat and susceptibility of the Shastry-Sutherland model for large systems up to a coupling ratio of 0.526(1) and down to low temperature.   

Thermal Critical Points and Quantum Critical End Point in the Frustrated Bilayer Heisenberg Antiferromagnet

We present a quantum Monte Carlo scheme for the simulation of frustrated quantum magnets that allows us to reduce or even eliminate the spin-problem for several dimerized quantum spin systems. We discuss in particular its application to the thermal properties of the spin-1/2 Heisenberg model on a frustrated square lattice bilayer. At zero temperature for the later model, a discontinuous quantum phase transition separates an interlayer singlet phase from an antiferromagnetic ground state formed by interlayer triplets. We show that this discontinuous transition extends up to finite temperatures and terminates in a quantum critical point. We identify this critical point as belonging to the Ising universality class, alert long-range order being absent at finite temperatures. We furthermore trace the discontinuous quantum phase transitions between the fully frustrated and the unfrustrated bilayer model using iPEPS tensor network methods. In particular, we identify a quantum critical end point that terminates the quantum critical line originating from the critical point of the unfrustrated bilayer system on the discontinuous transition line.   

Dimers on the checkerboard: model, partition sum, and correlations

We present analytic results on a special dimer model on the {\em non-bipartite} checkerboard that does not allow for parallel dimers surrounding diagonal links. We report exact results on the enumeration of closed packed dimer coverings on finite checkerboard lattices under periodic boundary conditions. Further, we comment on the behavior of the dimer-dimer correlations and find that the correlations between any two dimers vanishes identically if the distance between them is larger than two unit cells.   

Semiclassical Analysis of Quantum Dimer Models

We use the slave boson approach to develop the semiclassical description of the Rokshar Kivelson square lattice quantum dimer model, which allows a 1/S expansion. The action reproduces a generalized height representation. We extend these results to the dimer model on the cubic lattice, where we obtain emergent quantum electrodynamics description. The estimated speed of light: c = S/2*Sqrt[(J−V)J]. We confirm aspects of the height mapping such as the correlation between the sign of the terms in the height action and the sign of the potential term in the RK Hamiltonian. In dimensions D = 2, 3 the QED emerges at wave vectors (π,π) and (π,π,π) respectively. Our estimate of the RK parameter is 1/16 which is within a 20 to 30 percent of the exact value of 1/4π. We extend our analysis to the hexagonal and diamond lattices, and we find that the speed of light for the diamond lattice is given by c^2 = S^4*[(J − V )J]/64.   

Quantum Order-By-Disorder in Frustrated Spin Nanotube Models

Thermally driven order-by-disorder has been extensively studied in two-dimesional frustrated Heisenberg magnets where it gives rise to long-range discrete order. Here we discuss the quantum analogue in frustrated magnets wrapped around one-dimensional nanotubes that we call "wrapped magnets". We show that as a function of the ratio of the frustrated bond couplings, wrapped magnets develop quantum phase transitions into states with nematic spin orders. For the simplest J1-J2 wrapped magnet, the emergent order parameter has Z2 symmetry and thus can undergo a transition from disordered to ordered at T=0 (D = 1+ 1). The quantum critical point is in the Ising universality class, and has gapless Ising excitations. In more complex models, such as the wrapped windmill model, there is the interesting possibility of an intermediate spin Luttinger liquid phase.   

Magnetization Process of the Triangular- and Kagome-Lattice Antiferromagnets

The S = 1/2 kagome- and triangular-lattice Heisenberg antiferromagnets are investigated under a magnetic field using the numerical-diagonalization method[1]. A procedure is proposed to extract data points with very small finite-size deviations using the numerical-diagonalization results for capturing the magnetization curve. For the triangular-lattice antiferromagnet, the plateau edges at one-third the height of the saturation and the saturation field are successfully estimated. This study additionally presents results of magnetization process for a 45-site cluster of the kagome-lattice antiferromagnet; the present analysis suggests that the plateau does not open at one-ninth the height of the saturation.In addition the quantum phase transition of the triangular-lattice antiferromagnet at the 1/3 magnetization with respect to the next-nearest-neighbor interaction[2].
[1]H. Nakano and T. Sakai, J. Phys. Soc. Jpn. 87 (2018) 063706
[2]H. Nakano and T. Sakai, J. Phys. Soc. Jpn. 86 (2017) 114705   

Uncovering anisotropic magnetic phases via fast dimensionality analysis

A quantitative geometric predictor for the dimensionality of magnetic interactions is presented. This predictor is based on networks of superexchange interactions and can be quickly calculated for crystalline compounds of arbitrary chemistry, occupancy, or symmetry. The resulting data are useful for classifying structural families of magnetic compounds. We have examined compounds from a demonstration set of 42 520 materials with 3d transition metal cations. The predictor reveals trends in magnetic interactions that are often not apparent from the space group of the compounds, such as triclinic or monoclinic compounds that are strongly 2D. It can be used to identify quantum spin liquids, cuprate superconductors and other quasi-dimensional systems. We present specific cases where the predictor identifies compounds that should exhibit competition between 1D and 2D interactions, and how the predictor can be used to identify sparsely populated regions of chemical space with as-yet-unexplored topologies of specific 3d magnetic cations.¹
1. Karigerasi, Manohar; et.al. Phys. Rev. Materials 2, 094403   

Antiferromagnetic Stripe Order in NaFe1-xCuxAs Single Crystals

We present our ²³Na and ⁷⁵As NMR study of the over-doped pnictide NaFe_1-xCu_xAs, which has been demonstrated to be a possible Mott insulator near x ≈ 0.5 [1,2]. Our NMR spectral-weight and linewidth analysis of the ²³Na quadrupolar spectrum reveals inequivalent Na sites and indicates a progressive formation of real space Cu and Fe stripe ordering as the Cu concentration approaches 0.5. Our spin-lattice relaxation data shows an antiferromagnetic transition at 190 K for x = 0.48. At lower Cu concentration there is a spin-glass transition evident from both susceptibility and spin-lattice relaxation data that appears at 80 K for x = 0.39. We have performed numerical simulation of our ⁷⁵As lineshape by testing a Cu-induced staggered magnetization model and discuss these in the context of the ²³Na NMR data. [1] Song, Yu, et al., Nat. Commun. 7, 13879 (2016). [2] C.E. Matt et al.Phys. Rev. Lett. 117, 097001 (2016)




  

Tuning Magnetic Order with Iron Intercalation in Transition Metal Dichalcogenides

The transition metal dichalcogenides are a class of two-dimensional materials currently under intense research due to their attractive electronic properties. Through the process of intercalation, magnetic atoms can be inserted between the layers of these materials to introduce long range magnetic order, enabling the exploration of magnetism in these systems. I will present magnetization and thermodynamic measurements that indicate precise control of this introduced magnetic order in iron intercalated NbS₂, with antiferromagnetic order being established at iron intercalation values above x = 1/3 in Fe_xNbS₂. In addition, I will discuss evidence of a new frustrated magnetic order emerging below critical intercalation values.   

Magnetization plateaus in Tb2SrFe2O7

Discovery of emergent magnetic states has drawn a lot of interest in studying geometrically frustrated magnets. We recently studied magnetization plateaus in a layered perovskite Tb₂SrFe₂O₇. Tb₂SrFe₂O₇ has a bilayer perovskite structure (A₃B₂O₇) with Tb and Sr both at A-sites alternately ordered along the c-axis. Different from the multiferroic Ca₂SrFe₂O₇ that hosts the polar crystal structure and the magnetic ordered state with canted Fe moments, Tb₂SrFe₂O₇ has the non-polar structure symmetry of P42/mnm and the antiferromagnetic structure for the Fe-sublattice below 600 K. The magnetization plateaus were observed below the second transition at 15 K. With the field applied along c-axis, three plateaus were observed. Single crystal neutron diffraction revealed that the magnetic transition at 15 K is from magnetic order of Tb-sublattice accompanied with the spin reorientation of Fe-sublattice. It was also proved that the order of 2-in-2-out spin structure is due to magnetic coupling with the Fe-sublattice. In this presentation, I will show the evolution of the spin structure with temperature and magnetic field and disclose the nature of the magnetization plateaus in Tb₂SrFe₂O₇.