Fractional excitations in the square lattice quantum antiferromagnet

The empty world - a view from the free volume concept and Eyring's rate process theory

The many-body problem is a common issue, irrespective of the scale of entities under consideration. From electrons to atoms, small molecules like simple inorganic or organic structures, large molecules like proteins or polymers, nanometer- or micrometer-sized particles, granular matter, and even galaxies, the precise determination or estimation of geometrical locations and momentum energy of individual entities, and interaction forces between these millions of entities, is impossible but unfortunately important for understanding the collective physical properties like mechanical and electrical characteristics of the whole system. Despite foreseeable difficulties and complexities, attempts to estimate "interparticle" forces have never stopped using traditional Newtonian models, quantum mechanical approaches, and density functional theory. In this review, a simple approach integrating the free volume and Eyring's rate process theory is summarized and its application across a wide range of scales from electrons to the universe is presented in a unified manner. The focus is on comparisons between theoretical predictions and experimental results.

Magnon interactions in a moderately correlated Mott insulator

Quantum fluctuations in low-dimensional systems and near quantum phase transitions have significant influences on material properties. Yet, it is difficult to experimentally gauge the strength and importance of quantum fluctuations. Here we provide a resonant inelastic x-ray scattering study of magnon excitations in Mott insulating cuprates. From the thin film of SrCuO2, single- and bi-magnon dispersions are derived. Using an effective Heisenberg Hamiltonian generated from the Hubbard model, we show that the single-magnon dispersion is only described satisfactorily when including significant quantum corrections stemming from magnon-magnon interactions. Comparative results on La2CuO4 indicate that quantum fluctuations are much stronger in SrCuO2 suggesting closer proximity to a magnetic quantum critical point. Monte Carlo calculations reveal that other magnetic orders may compete with the antiferromagnetic Néel order as the ground state. Our results indicate that SrCuO2-due to strong quantum fluctuations-is a unique starting point for the exploration of novel magnetic ground states.

Pressure-induced structural and magnetic ordering transitions in the J1-J2 square lattice antiferromagnets AMoOPO4Cl (A = K, Rb)

By means of ab initio density functional theory calculations taking into account electronic correlation and van der Waals force, we conducted comprehensive studies of the electronic and magnetic properties, as well as structural and magnetic ordering evolution under pressure of the square lattice antiferromagnets AMoOPO4Cl (A = K, Rb) containing Mo5+ ions with , theoretically predicted as the potential candidates for achieving quantum phases, existing in the boundary regimes for square lattice magnets. Our results indicate that the columnar antiferromagnetic ordering, experimentally determined, is the magnetic ground state of the ambient P4/nmm phase, stabilized by the predominant antiferromagnetic next nearest neighbor interaction J2 in the diagonal directions of the square lattice, regardless of the effective Hubbard amendment values. More importantly, the P4/n phase, involving the mutual twisting of the MoO5Cl and PO4 polyhedra, satisfactorily reproduces the experimentally observed structural transition and the subsequent magnetic ordering transition from columnar antiferromagnetic ordering to Néel antiferromagnetic one, identified to be the appropriate high pressure structure. Furthermore, the mechanism underlined responsible for the magnetic ordering transition at high pressure has been disclosed in terms of density of states and spin density isosurface analysis across the transition. The loss of mirror plane symmetry in the P4/n phase activates the P 3s orbitals to participate in the magnetic interaction, giving rise to a competitive ferromagnetic superexchange interaction, in addition to antiferromagnetic direct one, and consequently initiating the magnetic ordering transition. The insights revealed here not only deepen our understanding of the electronic properties and structural and magnetic ordering transitions under high pressure of square lattice antiferromagnets AMoOPO4Cl (A = K, Rb), but also push the boundaries of knowledge by recognizing the role of nonmagnetic ions P 3s in magnetic exchange coupling.

Implementation of a laser-neutron pump-probe capability for inelastic neutron scattering

Knowledge about nonequilibrium dynamics in spin systems is of great importance to both fundamental science and technological applications. Inelastic neutron scattering (INS) is an indispensable tool to study spin excitations in complex magnetic materials. However, conventional INS spectrometers currently only perform steady-state measurements and probe averaged properties over many collision events between spin excitations in thermodynamic equilibrium, while the exact picture of re-equilibration of these excitations remains unknown. In this paper, we report on the design and implementation of a time-resolved laser-neutron pump-probe capability at hybrid spectrometer (beamline 14-B) at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory. This capability allows us to excite out-of-equilibrium magnons with a nanosecond pulsed laser source and probe the resulting dynamics using INS. Here, we discussed technical aspects to implement such a capability in a neutron beamline, including choices of suitable neutron instrumentation and material systems, laser excitation scheme, experimental configurations, and relevant firmware and software development to allow for time-synchronized pump-probe measurements. We demonstrated that the laser-induced nonequilibrium structure factor is able to be resolved by INS in a quantum magnet. The method developed in this work will provide SNS with advanced capabilities for performing out-of-equilibrium measurements, opening up an entirely new research direction to study out-of-equilibrium phenomena using neutrons.

Quantum spin nematic phase in a square-lattice iridate

Spin nematic is a magnetic analogue of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid1,2. Particularly intriguing is a valence-bond spin nematic3-5, in which spins are quantum entangled to form a multipolar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here we establish a spin nematic phase in the square-lattice iridate Sr2IrO4, which approximately realizes a pseudospin one-half Heisenberg antiferromagnet in the strong spin-orbit coupling limit6-9. Upon cooling, the transition into the spin nematic phase at TC ≈ 263 K is marked by a divergence in the static spin quadrupole susceptibility extracted from our Raman spectra and concomitant emergence of a collective mode associated with the spontaneous breaking of rotational symmetries. The quadrupolar order persists in the antiferromagnetic phase below TN ≈ 230 K and becomes directly observable through its interference with the antiferromagnetic order in resonant X-ray diffraction, which allows us to uniquely determine its spatial structure. Further, we find using resonant inelastic X-ray scattering a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a many-body quantum entanglement in the antiferromagnetic state10,11. Taken together, our results reveal a quantum order underlying the Néel antiferromagnet that is widely believed to be intimately connected to the mechanism of high-temperature superconductivity12,13.

Real-Space Imaging of Triplon Excitations in Engineered Quantum Magnets

Quantum magnets provide a powerful platform to explore complex quantum many-body phenomena. One example is triplon excitations, exotic many-body modes emerging from propagating singlet-triplet transitions. We engineer a minimal quantum magnet from organic molecules and demonstrate the emergence of dispersive triplon modes in one- and two-dimensional assemblies probed with scanning tunneling microscopy and spectroscopy. Our results provide the first demonstration of dispersive triplon excitations from a real-space measurement.

A model of d-wave superconductivity, antiferromagnetism, and charge order on the square lattice

We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory of Nf = 2 massless Dirac fermions carrying fundamental gauge charges-this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice with π-flux per plaquette in the ℤ2 center of SU(2). This theory has an emergent SO(5)f global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion U at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in π ℤ2-flux. At half-filling, the low-energy theory of the Higgs sector has Nb = 2 relativistic bosons with a possible emergent SO(5)b global symmetry describing rotations between a d-wave superconductor, period-2 charge stripes, and the time-reversal breaking "d-density wave" state. We propose a conformal SU(2) gauge theory with Nf = 2 fundamental fermions, Nb = 2 fundamental bosons, and a SO(5)f×SO(5)b global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)f and a confining state which breaks SO(5)b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and d-wave superconductivity. A similar theory applies at nonzero doping and large U, with longer-range couplings of the chargons leading to charge order with longer periods.

Antiferromagnetic Phase Induced by Nitrogen Doping in 2D Cr2S3

Exploration for the new members of air-stable 2D antiferromagnetic magnets to widen the magnetic families has drawn great attention due to its potential applications in spintronic devices. In addition to seeking the intrinsic antiferromagnets, externally introducing antiferromagnetic ordering in existing 2D materials, such as structural regulation and phase engineering, may be a promising way to modulate antiferromagnetism in the 2D limit. In this work, the in situ nitrogen doping growth of ultrathin 2D Cr2S3 nanoflakes has been achieved. Antiferromagnetic ordering in 2D Cr2S3 nanoflakes can be triggered by nitrogen doping induced new phase (space group P3¯1c). This work provides a new route to realize antiferromagnetism in atomically thin 2D magnets and greatly extend applications of 2D magnets in valleytronics and spintronics.

Thermal Properties and Instability of a U(1) Spin Liquid on the Triangular Lattice

We study the effect of Dzyaloshinskii-Moriya (DM) interaction on the triangular lattice U(1) quantum spin liquid (QSL) which is stabilized by ring-exchange interactions. A weak DM interaction introduces a staggered flux to the U(1) QSL state and changes the density of states at the spinon Fermi surface. If the DM vector contains in-plane components, then the spinons gain nonzero Berry phase. The resultant thermal conductances κ_{xx} and κ_{xy} qualitatively agree with the experimental results on the material EtMe_{3}Sb[Pd(dmit)_{2}]_{2}. Furthermore, owing to perfect nesting of the Fermi surface, a spin density wave state is triggered by larger DM interactions. On the other hand, when the ring-exchange interaction decreases, another antiferromagnetic (AFM) phase with 120° order shows up which is proximate to a U(1) Dirac QSL. We discuss the difference of the two AFM phases from their static structure factors and excitation spectra.

Supermagnonic Propagation in Two-Dimensional Antiferromagnets

We investigate the propagation of magnons after ultrashort perturbations of the exchange interaction in the prototype two-dimensional Heisenberg antiferromagnet. Using the recently proposed neural quantum states, we predict highly anisotropic spreading in space constrained by the symmetry of the perturbation. Interestingly, the propagation speed at the shortest length scale and timescale is up to 40% higher than the highest magnon velocity. We argue that the enhancement stems from extraordinary strong magnon-magnon interactions, suggesting new avenues for manipulating information transfer on ultrashort length scales and timescales.

Quantifying and Controlling Entanglement in the Quantum Magnet Cs_{2}CoCl_{4}

The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.

Why the Schwinger boson mean field theory fails to describe the spin dynamics of the triangular lattice antiferromagnetic Heisenberg model?

We find that the Schwinger boson mean field theory (SBMFT) supplemented with Gutzwiller projection provides an exceedingly accurate description for the ground state of the spin-12triangular lattice antiferromagnetic Heisenberg model (spin-12TLHAF). However, we find the SBMFT fails even qualitatively in the description of the dynamical behavior of the system. In particular, the SBMFT fails to predict the Goldstone mode in the magnetic ordered phase. We show that the coherent peak in the two-spinon continuum in the presence of spinon condensate should not be interpreted as a magnon mode. The SBMFT also predicts incorrectly a gapless longitudinal spin fluctuation mode in the magnetic ordered phase. We show that these failures are related to the following facts: (1) spinon condensation fails to provide a consistent description of the order parameter manifold of the 120 degree ordered phase. (2) There lacks in the SBMFT the coupling between the uncondensed spinon and the spinon condensate, which breaks both the spin rotational and the translational symmetry. (3) There lacks in the SBMFT the rigidity that is related to the no double occupancy constraint on the spinon system. We show that such failures of the SBMFT is neither restricted to the spin-12TLHAF nor to the magnetic ordered phase. We proposed a generalized SBMFT to resolve the first two issues and a new formalism to address the third issue.

Probing resonating valence bond states in artificial quantum magnets

Designing and characterizing the many-body behaviors of quantum materials represents a prominent challenge for understanding strongly correlated physics and quantum information processing. We constructed artificial quantum magnets on a surface by using spin-1/2 atoms in a scanning tunneling microscope (STM). These coupled spins feature strong quantum fluctuations due to antiferromagnetic exchange interactions between neighboring atoms. To characterize the resulting collective magnetic states and their energy levels, we performed electron spin resonance on individual atoms within each quantum magnet. This gives atomic-scale access to properties of the exotic quantum many-body states, such as a finite-size realization of a resonating valence bond state. The tunable atomic-scale magnetic field from the STM tip allows us to further characterize and engineer the quantum states. These results open a new avenue to designing and exploring quantum magnets at the atomic scale for applications in spintronics and quantum simulations.

The resonating valence bond state is a spin-liquid state where spins continuously alter their singlet partners. Here Yang et al. use spin-1/2 atoms precision-placed by a scanning tunnelling microscope to create artificial quantum magnets exhibiting the resonating valence bond state.

Nonclassical Spin Transfer Effects in an Antiferromagnet

We simulate scattering of electrons by a chain of antiferromagnetically coupled quantum Heisenberg spins, to analyze spin-transfer effects not described by the classical models of magnetism. Our simulations demonstrate efficient excitation of dynamical states that would be forbidden by the semiclassical symmetries, such as generation of multiple magnetic excitation quanta by a single electron. Furthermore, quantum interference of spin wave functions enables generation of magnetization dynamics with amplitudes exceeding the transferred magnetic moment. The efficiency of excitation is almost independent of the electron spin polarization, and is governed mainly by the transfer of energy. Nonclassical spin transfer may thus enable efficient electronic control of antiferromagnets not limited by the classical constraints.

Dominant Fifth-Order Correlations in Doped Quantum Antiferromagnets

Traditionally, one- and two-point correlation functions are used to characterize many-body systems. In strongly correlated quantum materials, such as the doped 2D Fermi-Hubbard system, these may no longer be sufficient, because higher-order correlations are crucial to understanding the character of the many-body system and can be numerically dominant. Experimentally, such higher-order correlations have recently become accessible in ultracold atom systems. Here, we reveal strong non-Gaussian correlations in doped quantum antiferromagnets and show that higher-order correlations dominate over lower-order terms. We study a single mobile hole in the t-J model using the density matrix renormalization group and reveal genuine fifth-order correlations which are directly related to the mobility of the dopant. We contrast our results to predictions using models based on doped quantum spin liquids which feature significantly reduced higher-order correlations. Our predictions can be tested at the lowest currently accessible temperatures in quantum simulators of the 2D Fermi-Hubbard model. Finally, we propose to experimentally study the same fifth-order spin-charge correlations as a function of doping. This will help to reveal the microscopic nature of charge carriers in the most debated regime of the Hubbard model, relevant for understanding high-T_{c} superconductivity.

Van Hove singularity in the magnon spectrum of the antiferromagnetic quantum honeycomb lattice

In quantum magnets, magnetic moments fluctuate heavily and are strongly entangled with each other, a fundamental distinction from classical magnetism. Here, with inelastic neutron scattering measurements, we probe the spin correlations of the honeycomb lattice quantum magnet YbCl₃. A linear spin wave theory with a single Heisenberg interaction on the honeycomb lattice, including both transverse and longitudinal channels of the neutron response, reproduces all of the key features in the spectrum. In particular, we identify a Van Hove singularity, a clearly observable sharp feature within a continuum response. The demonstration of such a Van Hove singularity in a two-magnon continuum is important as a confirmation of broadly held notions of continua in quantum magnetism and additionally because analogous features in two-spinon continua could be used to distinguish quantum spin liquids from merely disordered systems. These results establish YbCl₃ as a benchmark material for quantum magnetism on the honeycomb lattice.

Temperature dependence of the(π,0)anomaly in the excitation spectrum of the 2D quantum Heisenberg antiferromagnet

It is well established that in the low-temperature limit, the two-dimensional quantum Heisenberg antiferromagnet on a square lattice (2DQHAFSL) exhibits an anomaly in its spectrum at short-wavelengths on the zone-boundary. In the vicinity of thepoint the pole in the one-magnon response exhibits a downward dispersion, is heavily damped and attenuated, giving way to an isotropic continuum of excitations extending to high energies. The origin of the anomaly and the presence of the continuum are of current theoretical interest, with suggestions focused around the idea that the latter evidences the existence of spinons in a two-dimensional system. Here we present the results of neutron inelastic scattering experiments and Quantum Monte Carlo calculations on the metallo-organic compound Cu(DCOO)D2O (CFTD), an excellent physical realisation of the 2DQHAFSL, designed to investigate how the anomaly atevolves up to finite temperatures. Our data reveal that on warming the anomaly survives the loss of long-range, three-dimensional order, and that it is thus a robust feature of the two-dimensional system. With further increase of temperature the zone-boundary response gradually softens and broadens, washing out theanomaly. This is confirmed by a comparison of our data with the results of finite-temperature Quantum Monte Carlo simulations where the two are found to be in good accord. In the vicinity of the antiferromagnetic zone centre, there was no significant softening of the magnetic excitations over the range of temperatures investigated.

Spin liquids in geometrically perfect triangular antiferromagnets

The cradle of quantum spin liquids, triangular antiferromagnets show strong proclivity to magnetic order and require deliberate tuning to stabilize a spin-liquid state. In this brief review, we juxtapose recent theoretical developments that trace the parameter regime of the spin-liquid phase, with experimental results for Co-based and Yb-based triangular antiferromagnets. Unconventional spin dynamics arising from both ordered and disordered ground states are discussed, and the notion of a geometrically perfect triangular system is scrutinized to demonstrate non-trivial imperfections that may assist magnetic frustration in stabilizing dynamic spin states with peculiar excitations.

Upgrade to the MAPS neutron time-of-flight chopper spectrometer

The MAPS direct geometry time-of-flight chopper spectrometer at the ISIS pulsed neutron and muon source has been in operation since 1999, and its novel use of a large array of position-sensitive neutron detectors paved the way for a later generations of chopper spectrometers around the world. Almost two decades of experience of user operations on MAPS, together with lessons learned from the operation of new generation instruments, led to a decision to perform three parallel upgrades to the instrument. These were to replace the primary beamline collimation with supermirror neutron guides, to install a disk chopper, and to modify the geometry of the poisoning in the water moderator viewed by MAPS. Together, these upgrades were expected to increase the neutron flux substantially, to allow more flexible use of repetition rate multiplication and to reduce some sources of background. Here, we report the details of these upgrades and compare the performance of the instrument before and after their installation as well as to Monte Carlo simulations. These illustrate that the instrument is performing in line with, and in some respects in excess of, expectations. It is anticipated that the improvement in performance will have a significant impact on the capabilities of the instrument. A few examples of scientific commissioning are presented to illustrate some of the possibilities.

Interplay of Spin and Spatial Anisotropy in Low-Dimensional Quantum Magnets with Spin 1/2

Quantum Heisenberg chain and square lattices are important paradigms of a low-dimensional magnetism. Their ground states are determined by the strength of quantum fluctuations. Correspondingly, the ground state of a rectangular lattice interpolates between the spin liquid and the ordered collinear Néel state with the partially reduced order parameter. The diversity of additional exchange interactions offers variety of quantum models derived from the aforementioned paradigms. Besides the spatial anisotropy of the exchange coupling, controlling the lattice dimensionality and ground-state properties, the spin anisotropy (intrinsic or induced by the magnetic field) represents another important effect disturbing a rotational symmetry of the spin system. The S = 1/2 easy-axis and easy-plane XXZ models on the square lattice even for extremely weak spin anisotropies undergo Heisenberg-Ising and Heisenberg-XY crossovers, respectively, acting as precursors to the onset of the finite-temperature phase transitions within the two-dimensional Ising universality class (for the easy axis anisotropy) and a topological Berezinskii–Kosterlitz–Thouless phase transition (for the easy-plane anisotropy). Experimental realizations of the S = 1/2 two-dimensional XXZ models in bulk quantum magnets appeared only recently. Partial solutions of the problems associated with their experimental identifications are discussed and some possibilities of future investigations in quantum magnets on the square and rectangular lattice are outlined.

Quantum theory of spin waves for helical ground states in a hollandite lattice

We perform spin-wave analysis of classical ground states of a model Hamiltonian proposed earlier (Mandal et al 2014 Phys. Rev. B 90 104420) for [Formula: see text] compounds. It is known that the phase diagram of the hollandite lattice (lattice of [Formula: see text] compounds) consists of four different helical phases (FH, A2H, C2H, CH phase) in the space of model parameters [Formula: see text]. The spin wave dispersion shows presence of gapless mode which interpolates between quadratic to linear depending on phases and values of J _i . In most cases, the second lowest mode shows the existence of a roton-like minima mainly from [Formula: see text] to [Formula: see text] and [Formula: see text] to [Formula: see text] path and it appears at the value of [Formula: see text] for constant [Formula: see text]. Few higher modes also show similar minima. Each helical phase has its characteristic traits which can be used to determine the phases itself. The analytical expressions of eigenmodes at high symmetry points are obtained which can be utilized to extract the values of J _i . Density of states, specific heat and susceptibilities at low temperature have been studied within spin-wave approximation. The specific heat shows departure from T ^1.5(3) dependence found in three-dimensional unfrustrated ferromagnetic(anti-ferromagnetic) system which seems to be the signature of incommensurate helical phase. The parallel susceptibility is maximum for FH phase and minimum for CH phase at low temperature. The perpendicular susceptibility is found to be independent of temperature at very low temperature. Our study can be used to compare experiments on magnon spectrum, elastic neutron scattering, and finite temperature properties mentioned above for clean [Formula: see text] system as well as determining the values of J _i .

Anharmonic Magnon Excitations in Noncollinear and Charge-Ordered RbFe^{2+}Fe^{3+}F_{6}

RbFe^{2+}Fe^{3+}F_{6} is an example of a charge ordered antiferromagnet where iron sites, with differing valences, are structurally separated into two interpenetrating sublattices. The low temperature magnetically ordered Fe^{2+} (S=2) and Fe^{3+} (S=5/2) moments form a noncollinear orthogonal structure with the Fe^{3+} site displaying a reduced static ordered moment. Neutron spectroscopy on single crystals finds two distinct spin wave branches with a dominant coupling along the Fe^{3+} chain axis (b axis). High resolution spectroscopic measurements find an intense energy and momentum broadened magnetic band of scattering bracketing a momentum-energy region where two magnon processes are kinematically allowed. These anharmonic excitations are enhanced in this noncollinear magnet owing to the orthogonal spin arrangement.

The nature of spin excitations in the one-third magnetization plateau phase of Ba3CoSb2O9

Magnetization plateaus in quantum magnets—where bosonic quasiparticles crystallize into emergent spin superlattices—are spectacular yet simple examples of collective quantum phenomena escaping classical description. While magnetization plateaus have been observed in a number of spin-1/2 antiferromagnets, the description of their magnetic excitations remains an open theoretical and experimental challenge. Here, we investigate the dynamical properties of the triangular-lattice spin-1/2 antiferromagnet Ba₃CoSb₂O₉ in its one-third magnetization plateau phase using a combination of nonlinear spin-wave theory and neutron scattering measurements. The agreement between our theoretical treatment and the experimental data demonstrates that magnons behave semiclassically in the plateau in spite of the purely quantum origin of the underlying magnetic structure. This allows for a quantitative determination of Ba₃CoSb₂O₉ exchange parameters. We discuss the implication of our results to the deviations from semiclassical behavior observed in zero-field spin dynamics of the same material and conclude they must have an intrinsic origin.

Frustrated magnetic materials attract significant interest because their properties can become dominated by quantum fluctuations. Here the authors show that excitations in the plateau phase of a quantum magnet can be understood semiclassically even though the ground state involves strong quantum effects.

Quasi-2D Heisenberg Antiferromagnets [CuX(pyz)2](BF4) with X = Cl and Br

Two Cu²⁺ coordination polymers [CuCl(pyz)₂](BF₄) 1 and [CuBr(pyz)₂](BF₄) 2 (pyz = pyrazine) were synthesized in the family of quasi two-dimensional (2D) [Cu(pyz)₂]²⁺ magnetic networks. The layer connectivity by monatomic halide ligands results in significantly shorter interlayer distances. Structures were determined by single-crystal X-ray diffraction. Temperature-dependent X-ray diffraction of 1 revealed rigid [Cu(pyz)₂]²⁺ layers that do not expand between 5 K and room temperature, whereas the expansion along the c-axis amounts to 2%. The magnetic susceptibility of 1 and 2 shows a broad maximum at ∼8 K, indicating antiferromagnetic interactions within the [Cu(pyz)₂]²⁺ layers. 2D Heisenberg model fits result in J_∥ = 9.4(1) K for 1 and 8.9(1) K for 2. The interlayer coupling is much weaker with | J_⊥| = 0.31(6) K for 1 and 0.52(9) K for 2. The electron density, experimentally determined and calculated by density functional theory, confirms the location of the singly occupied orbital (the magnetic orbital) in the tetragonal plane. The analysis of the spin density reveals a mainly σ-type exchange through pyrazine. Kinks in the magnetic susceptibility indicate the onset of long-range three-dimensional magnetic order below 4 K. The magnetic structures were determined by neutron diffraction. Magnetic Bragg peaks occur below T_N = 3.9(1) K for 1 and 3.8(1) K for 2. The magnetic unit cell is doubled along the c-axis ( k = 0, 0, 0.5). The ordered magnetic moments are located in the tetragonal plane and amount to 0.76(8) μ_B/Cu²⁺ for 1 and 0.6(1) μ_B/Cu²⁺ for 2 at 1.5 K. The moments are coupled antiferromagnetically both in the ab plane and along the c-axis. The Cu²⁺ g-tensor was determined from electron spin resonance spectra as g _x = 2.060(1), g _z = 2.275(1) for 1 and g _x = 2.057(1), g _z = 2.272(1) for 2 at room temperature.

Engineering the Eigenstates of Coupled Spin-1/2 Atoms on a Surface

Quantum spin networks having engineered geometries and interactions are eagerly pursued for quantum simulation and access to emergent quantum phenomena such as spin liquids. Spin-1/2 centers are particularly desirable, because they readily manifest coherent quantum fluctuations. Here we introduce a controllable spin-1/2 architecture consisting of titanium atoms on a magnesium oxide surface. We tailor the spin interactions by atomic-precision positioning using a scanning tunneling microscope (STM) and subsequently perform electron spin resonance on individual atoms to drive transitions into and out of quantum eigenstates of the coupled-spin system. Interactions between the atoms are mapped over a range of distances extending from highly anisotropic dipole coupling to strong exchange coupling. The local magnetic field of the magnetic STM tip serves to precisely tune the superposition states of a pair of spins. The precise control of the spin-spin interactions and ability to probe the states of the coupled-spin network by addressing individual spins will enable the exploration of quantum many-body systems based on networks of spin-1/2 atoms on surfaces.

Dynamics of the Kitaev-Heisenberg Model

We introduce a matrix-product state based method to efficiently obtain dynamical response functions for two-dimensional microscopic Hamiltonians. We apply this method to different phases of the Kitaev-Heisenberg model and identify characteristic dynamical features. In the ordered phases proximate to the spin liquid, we find significant broad high-energy features beyond spin-wave theory, which resemble those of the Kitaev model. This establishes the concept of a proximate spin liquid, which was recently invoked in the context of inelastic neutron scattering experiments on α-RuCl_{3}. Our results provide an example of a natural path for proximate spin liquid features to arise at high energies above a conventionally ordered state, as the diffuse remnants of spin-wave bands intersect to yield a broad peak at the Brillouin zone center.

Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data

A data-science approach to solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred real-frequency spectra. By means of a modern regularization technique, we eliminate redundant degrees of freedom that essentially carry the noise, leaving only relevant information unaffected by the noise. The resultant spectrum is represented with minimal bases and thus a stable analytical continuation is achieved. This framework further provides a tool for analyzing to what extent the Monte Carlo data need to be accurate to resolve details of an expected spectral function.

Magnetic Excitations and Electronic Interactions in Sr_{2}CuTeO_{6}: A Spin-1/2 Square Lattice Heisenberg Antiferromagnet

Sr_{2}CuTeO_{6} presents an opportunity for exploring low-dimensional magnetism on a square lattice of S=1/2  Cu^{2+} ions. We employ ab initio multireference configuration interaction calculations to unravel the Cu^{2+} electronic structure and to evaluate exchange interactions in Sr_{2}CuTeO_{6}. The latter results are validated by inelastic neutron scattering using linear spin-wave theory and series-expansion corrections for quantum effects to extract true coupling parameters. Using this methodology, which is quite general, we demonstrate that Sr_{2}CuTeO_{6} is an almost ideal realization of a nearest-neighbor Heisenberg antiferromagnet but with relatively weak coupling of 7.18(5) meV.

Persistent Paramagnons Deep in the Metallic Phase of Sr_{2-x}La_{x}IrO_{4}

We have studied the magnetic excitations of electron-doped Sr_{2-x}La_{x}IrO_{4} (0≤x≤0.10) using resonant inelastic x-ray scattering at the Ir L_{3} edge. The long-range magnetic order is rapidly lost with increasing x, but two-dimensional short-range order (SRO) and dispersive magnon excitations with nearly undiminished spectral weight persist well into the metallic part of the phase diagram. The magnons in the SRO phase are heavily damped and exhibit anisotropic softening. Their dispersions are well described by a pseudospin-1/2 Heisenberg model with exchange interactions whose spatial range increases with doping. We also find a doping-independent high-energy magnetic continuum, which is not described by this model. The spin-orbit excitons arising from the pseudospin-3/2 manifold of the Ir ions broaden substantially in the SRO phase, but remain largely separated from the low-energy magnons. Pseudospin-1/2 models are therefore a good starting point for the theoretical description of the low-energy magnetic dynamics of doped iridates.

Magnetic Fluctuations in Pair-Density-Wave Superconductors

Pair-density-wave superconductivity constitutes a novel electronic condensate proposed to be realized in certain unconventional superconductors. Establishing its potential existence is important for our fundamental understanding of superconductivity in correlated materials. Here we compute the dynamical magnetic susceptibility in the presence of a pair-density-wave ordered state and study its fingerprints on the spin-wave spectrum including the neutron resonance. In contrast to the standard case of d-wave superconductivity, we show that the pair-density-wave phase exhibits neither a spin gap nor a magnetic resonance peak, in agreement with a recent neutron scattering experiment on underdoped La_{1.905}Ba_{0.095}CuO_{4} [Z. Xu et al., Phys. Rev. Lett. 113, 177002 (2014)].

CAMEA--A novel multiplexing analyzer for neutron spectroscopy

The analyzer detector system continuous angle multiple energy analysis will be installed on the cold-neutron triple-axis spectrometer RITA-2 at SINQ, PSI. CAMEA is optimized for efficiency in the horizontal scattering plane enabling rapid and detailed mapping of excitations. As a novelty the design employs a series of several sequential upward scattering analyzer arcs. Each arc is set to a different, fixed, final energy and scatters neutrons towards position sensitive detectors. Thus, neutrons with different final energies are recorded simultaneously over a large angular range. In a single data-acquisition many entire constant-energy lines in the horizontal scattering plane are recorded for a quasi-continuous angular coverage of about 60°. With a large combined coverage in energy and momentum, this will result in a very efficient spectrometer, which will be particularly suited for parametric studies under extreme conditions with restrictive sample environments (high field magnets or pressure cells) and for small samples of novel materials. In this paper we outline the concept and the specifications of the instrument currently under construction.

Roton Minimum as a Fingerprint of Magnon-Higgs Scattering in Ordered Quantum Antiferromagnets

A quantitative description of magnons in long-range ordered quantum antiferromagnets is presented which is consistent from low to high energies. It is illustrated for the generic S=1/2 Heisenberg model on the square lattice. The approach is based on a continuous similarity transformation in momentum space using the scaling dimension as the truncation criterion. Evidence is found for significant magnon-magnon attraction inducing a Higgs resonance. The high-energy roton minimum in the magnon dispersion appears to be induced by strong magnon-Higgs scattering.