Observation of 4- and 6-Magnon Bound States in the Spin-Anisotropic Frustrated Antiferromagnet FeI_{2}.

We observe a wealth of multimagnon bound states in the strongly anisotropic spin-1 triangular antiferromagnet FeI_{2} using time-domain terahertz spectroscopy. These unconventional excitations can arise in ordered magnets due to attractive magnon-magnon interactions and alter their properties. We analyze the energy-magnetic field spectrum via an exact diagonalization method for a dilute gas of interacting magnons and detect up to 4- and 6-magnon bound states, hybridized with single magnons. This zoo of tunable interacting quasiparticles provides a unique platform to study decay and renormalization, reminiscent of the few-body problems found in cold-atom, nuclear, and particle physics.

Skyrmion Crystal from RKKY Interaction Mediated by 2D Electron Gas.

We consider a C_{6} invariant lattice of magnetic moments coupled via a Kondo exchange J with a 2D electron gas (2DEG). The effective Ruderman-Kittel-Kasuya-Yosida interaction between the moments stabilizes a magnetic skyrmion crystal in the presence of magnetic field and easy-axis anisotropy. An attractive aspect of this mechanism is that the magnitude of the magnetic ordering wave vectors, Q_{ν} (ν=1, 2, 3), is dictated by the Fermi wave number k_{F}: |Q_{ν}|=2k_{F}. Consequently, the topological contribution to the Hall conductivity of the 2DEG becomes of the order of the quantized value, e^{2}/h, when J is comparable to the Fermi energy ε_{F}.

Strain-Modulated Slater-Mott Crossover of Pseudospin-Half Square-Lattice in (SrIrO_{3})_{1}/(SrTiO_{3})_{1} Superlattices.

We report on the epitaxial strain-driven electronic and antiferromagnetic modulations of a pseudospin-half square-lattice realized in superlattices of (SrIrO_{3})_{1}/(SrTiO_{3})_{1}. With increasing compressive strain, we find the low-temperature insulating behavior to be strongly suppressed with a corresponding systematic reduction of both the Néel temperature and the staggered moment. However, despite such a suppression, the system remains weakly insulating above the Néel transition. The emergence of metallicity is observed under large compressive strain but only at temperatures far above the Néel transition. These behaviors are characteristics of the Slater-Mott crossover regime, providing a unique experimental model system of the spin-half Hubbard Hamiltonian with a tunable intermediate coupling strength.

Vison Crystals in an Extended Kitaev Model on the Honeycomb Lattice.

We introduce an extension of the Kitaev honeycomb model by including four-spin interactions that preserve the local gauge structure and, hence, the integrability of the original model. The extended model has a rich phase diagram containing five distinct vison crystals, as well as a symmetric π-flux spin liquid with a Fermi surface of Majorana fermions and a sequence of Lifshitz transitions. We discuss possible experimental signatures and, in particular, present finite-temperature Monte Carlo calculations of the specific heat and the static vison structure factor. We argue that our extended model emerges naturally from generic perturbations to the Kitaev honeycomb model.

Dynamics and Instabilities of the Shastry-Sutherland Model.

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, and plaquette order, two of which have been reported in previous studies.

Face Centered Cubic and Hexagonal Close Packed Skyrmion Crystals in Centrosymmetric Magnets.

Skyrmions are disklike objects that typically form triangular crystals in two-dimensional systems. This situation is analogous to the so-called pancake vortices of quasi-two-dimensional superconductors. The way in which Skyrmion disks or "pancake Skyrmions" pile up in layered centrosymmetric materials is dictated by the interlayer exchange. Unbiased Monte Carlo simulations and simple stabilization arguments reveal face centered cubic and hexagonal close packed Skyrmion crystals for different choices of the interlayer exchange, in addition to the conventional triangular crystal of Skyrmion lines. Moreover, an inhomogeneous current induces a sliding motion of pancake Skyrmions, indicating that they behave as effective mesoscale particles.

Principal Chiral Model in Correlated Electron Systems.

We discuss noncollinear magnetic phenomena whose local order parameter is characterized by more than one spin vector. By focusing on the simple cases of 2D triangular and 3D pyrochlore lattices, we demonstrate that their low-energy theories can be described by a one-parametric class of sigma models continuously interpolating between the classical Heisenberg model and the principal chiral model Tr(∂_{a}U∂_{a}U^{†}) for all U∈SU(2). The target space can be viewed as a U(1) fibration over the CP(1) space. The 3D version of our model is further generalized to break spatial and spin rotation symmetry SO(3)×SO(3)→SO(3).

Mott Transition in a Metallic Liquid: Gutzwiller Molecular Dynamics Simulations.

We present a formulation of quantum molecular dynamics that includes electron correlation effects via the Gutzwiller method. Our new scheme enables the study of the dynamical behavior of atoms and molecules with strong electron interactions. The Gutzwiller approach goes beyond the conventional mean-field treatment of the intra-atomic electron repulsion and captures crucial correlation effects such as band narrowing and electron localization. We use Gutzwiller quantum molecular dynamics to investigate the Mott transition in the liquid phase of a single-band metal and uncover intriguing structural and transport properties of the atoms.

Frustration and chiral orderings in correlated electron systems.

The term frustration refers to lattice systems whose ground state cannot simultaneously satisfy all the interactions. Frustration is an important property of correlated electron systems, which stems from the sign of loop products (similar to Wilson products) of interactions on a lattice. It was early recognized that geometric frustration can produce rather exotic physical behaviors, such as macroscopic ground state degeneracy and helimagnetism. The interest in frustrated systems was renewed two decades later in the context of spin glasses and the emergence of magnetic superstructures. In particular, Phil Anderson's proposal of a quantum spin liquid ground state for a two-dimensional lattice S = 1/2 Heisenberg magnet generated a very active line of research that still continues. As a result of these early discoveries and conjectures, the study of frustrated models and materials exploded over the last two decades. Besides the large efforts triggered by the search of quantum spin liquids, it was also recognized that frustration plays a crucial role in a vast spectrum of physical phenomena arising from correlated electron materials. Here we review some of these phenomena with particular emphasis on the stabilization of chiral liquids and non-coplanar magnetic orderings. In particular, we focus on the ubiquitous interplay between magnetic and charge degrees of freedom in frustrated correlated electron systems and on the role of anisotropy. We demonstrate that these basic ingredients lead to exotic phenomena, such as, charge effects in Mott insulators, the stabilization of single magnetic vortices, as well as vortex and skyrmion crystals, and the emergence of different types of chiral liquids. In particular, these orderings appear more naturally in itinerant magnets with the potential of inducing a very large anomalous Hall effect.

Magnetic Vortex Induced by Nonmagnetic Impurity in Frustrated Magnets.

We study the effect of a nonmagnetic impurity inserted in a two-dimensional frustrated ferromagnet above its saturation magnetic field H_{sat} for arbitrary spin S. We demonstrate that the ground state includes a magnetic vortex that is nucleated around the impurity over a finite range of magnetic field H_{sat}≤H≤H_{sat}^{I}. Upon approaching the quantum critical point at H=H_{sat}, the radius of the magnetic vortex diverges as the magnetic correlation length: ξ∝1/sqrt[H-H_{sat}]. These results are derived both for the lattice and in the continuum limit.

Resistivity Minimum in Highly Frustrated Itinerant Magnets.

We study the transport properties of frustrated itinerant magnets comprising localized classical moments, which interact via exchange with the conduction electrons. Strong frustration stabilizes a liquidlike spin state, which extends down to temperatures well below the effective Ruderman-Kittel-Kasuya-Yosida interaction scale. The crossover into this state is characterized by spin structure factor enhancement at wave vectors smaller than twice the Fermi wave vector magnitude. The corresponding enhancement of electron scattering generates a resistivity upturn at decreasing temperatures.

Three-Dimensional Crystallization of Vortex Strings in Frustrated Quantum Magnets.

We demonstrate that frustrated exchange interactions can produce exotic 3D crystals of vortex strings near the saturation field (H=H(sat)) of body- and face-centered cubic Mott insulators. The combination of cubic symmetry and frustration leads to a magnon spectrum of the fully polarized spin state (H>H(sat)) with degenerate minima at multiple noncoplanar Q vectors. This spectrum becomes gapless at the quantum critical point H=H(sat) and the magnetic ordering below H(sat) can be formally described as a condensate of a dilute gas of bosons. By expanding in the lattice gas parameter, we find that different vortex crystals span sizable regions of the phase diagrams for isotropic exchange and are further stabilized by symmetric exchange anisotropy.

Anyonic liquids in nearly saturated spin chains.

Most Heisenberg-like spin chains flow to a universal free-fermion fixed point near the magnetic-field induced saturation point. Here, we show that an exotic fixed point, characterized by two species of low-energy excitations with mutual anyonic statistics, may also emerge in such spin chains if the dispersion relation has two minima. By using bosonization, two-magnon exact calculations, and numerical density-matrix-renormalization-group calculations, we demonstrate the existence of this anyonic-liquid fixed point in an xxz spin chain with up to second-neighbor interactions. We also identify a range of microscopic parameters, which support this phase.

ac current generation in chiral magnetic insulators and Skyrmion motion induced by the spin Seebeck effect.

We show that a temperature gradient induces an ac electric current in multiferroic insulators when the sample is embedded in a circuit. We also show that a thermal gradient can be used to move magnetic Skyrmions in insulating chiral magnets: the induced magnon flow from the hot to the cold region drives the Skyrmions in the opposite direction via a magnonic spin transfer torque. Both results are combined to compute the effect of Skyrmion motion on the ac current generation and demonstrate that Skyrmions in insulators are a promising route for spin caloritronics applications.

Stiffness from disorder in triangular-lattice Ising thin films.

We study the triangular lattice Ising model with a finite number of vertically stacked layers and demonstrate a low temperature reentrance of two Berezinskii-Kosterlitz-Thouless transitions, which results in an extended disordered regime down to T=0. Numerical results are complemented with the derivation of an effective low-temperature dimer theory. Contrary to order by disorder, we present a new scenario for fluctuation-induced ordering in frustrated spin systems. While short-range spin-spin correlations are enhanced by fluctuations, quasi-long-range ordering is precluded at low enough temperatures by proliferation of topological defects.

Orbital magnetism induced by heat currents in Mott insulators.

We derive the effective heat current density operator for the strong-coupling regime of Mott insulators. Similarly to the case of the electric current density, the leading contribution to this effective operator is proportional to the local scalar spin chirality χ(jkl)=S(l)·(S(j)×S(k)). This common form of the effective heat and electric current density operators leads to a novel cross response in Mott insulators. A heat current induces a distribution of orbital magnetic moments in systems containing loops of an odd number of hopping terms. The relative orientation of the orbital moments depends on the particular lattice of magnetic ions. This subtle effect arises from the symmetries that the heat and electric currents have in common.

Driven Skyrmions and dynamical transitions in chiral magnets.

We study the dynamics of Skyrmions in chiral magnets in the presence of a spin polarized current. The motion of Skyrmions in the ferromagnetic background excites spin waves and contributes to additional damping. At a large current, the spin wave spectrum becomes gapless and Skyrmions are created dynamically from the ferromagnetic state. At an even higher current, these Skyrmions are strongly deformed due to the damping and become unstable at a threshold current, leading to a chiral liquid. We show how Skyrmions can be created by increasing the current in the magnetic spiral state. We then construct a dynamic phase diagram for a chiral magnet with a current. The instability transitions between different states can be observed as experimentally clear signatures in the transport measurements, such as jumps and hysteresis.

CP2 skyrmions and skyrmion crystals in realistic quantum magnets.

Magnetic skyrmions are nanoscale topological textures that have been recently observed in different families of quantum magnets. These objects are called CP1 skyrmions because they are built from dipoles-the target manifold is the 1D complex projective space, CP1 ≅ S2. Here we report the emergence of magnetic CP2 skyrmions in a realistic spin-1 model, which includes both dipole and quadrupole moments. Unlike CP1 skyrmions, CP2 skyrmions can also arise as metastable textures of quantum paramagnets, opening a new road to discover emergent topological solitons in non-magnetic materials. The quantum phase diagram of the spin-1 model also includes magnetic field-induced CP2 skyrmion crystals that can be detected with regular momentum- (diffraction) and real-space (Lorentz transmission electron microscopy) experimental techniques.

Flexible class of exact Hubbard-Stratonovich transformations.

We consider a class of Hubbard-Stratonovich transformations suitable for treating Hubbard interactions in the context of quantum Monte Carlo simulations. A tunable parameter p allows us to continuously vary from a discrete Ising auxiliary field (p=∞) to a compact auxiliary field that couples to electrons sinusoidally (p=0). In tests on the single-band square and triangular Hubbard models, we find that the severity of the sign problem decreases systematically with increasing p. Selecting p finite, however, enables continuous sampling methods such as the Langevin or Hamiltonian Monte Carlo methods. We explore the tradeoffs between various simulation methods through numerical benchmarks.

Instabilities of heavy magnons in an anisotropic magnet.

The search for new elementary particles is one of the most basic pursuits in physics, spanning from subatomic physics to quantum materials. Magnons are the ubiquitous elementary quasiparticle to describe the excitations of fully-ordered magnetic systems. But other possibilities exist, including fractional and multipolar excitations. Here, we demonstrate that strong quantum interactions exist between three flavors of elementary quasiparticles in the uniaxial spin-one magnet FeI2. Using neutron scattering in an applied magnetic field, we observe spontaneous decay between conventional and heavy magnons and the recombination of these quasiparticles into a super-heavy bound-state. Akin to other contemporary problems in quantum materials, the microscopic origin for unusual physics in FeI2 is the quasi-flat nature of excitation bands and the presence of Kitaev anisotropic magnetic exchange interactions.