Relativistic Mott Research Articles

Direct visualization of spin-dependent orbital geometry on the Na2IrO3 surface with ultra-high resolution

The honeycomb iridate Na2IrO3, as a candidate for the Kitaev model, has drawn increasing attention in recent years. It is a rare example of a strongly correlated, topologically nontrivial band structure that may have protected quantum spin Hall states. The nature of its intriguing insulating phase and magnetic order is still under debate. In the present work, we combine low-temperature scanning tunneling microscopy/spectroscopy and density functional theory calculations to show that Na2IrO3 exhibits a band gap of 420 meV at 77 K, indicating a novel relativistic Mott insulator rather than Slater-like states. In addition, it is demonstrated that the Ir-O-Ir bonds and the subtle local density of states variation of Ir atoms induced by spin correlations can be imaged in real space in ultra-high resolution utilizing a spin-polarized oxygen-functionalized scanning tunneling microscopy tip. The direct observation of the zigzag Ir-O-Ir bonds at 77 K strongly dictates the zigzag magnetic ordering below T N ≈ 15 K because of the strong spin-orbit interactions that lock the lattice and magnetic moments.

Dynamical Anyon Generation in Kitaev Honeycomb Non-Abelian Spin Liquids.

Relativistic Mott insulators known as "Kitaev materials" potentially realize spin liquids hosting non-Abelian anyons. Motivated by fault-tolerant quantum-computing applications in this setting, we introduce a dynamical anyon-generation protocol that exploits universal edge physics. The setup features holes in the spin liquid, which define energetically cheap locations for non-Abelian anyons, connected by a narrow bridge that can be tuned between spin liquid and topologically trivial phases. We show that modulating the bridge from trivial to spin liquid over intermediate time scales-quantified by analytics and extensive simulations-deposits non-Abelian anyons into the holes with O(1) probability. The required bridge manipulations can be implemented by integrating the Kitaev material into magnetic tunnel junction arrays that engender locally tunable exchange fields. Combined with existing readout strategies, our protocol reveals a path to topological qubit experiments in Kitaev materials at zero applied magnetic field.

Advanced First-Principle Modeling of Relativistic Ruddlesden—Popper Strontium Iridates

In this review, we provide a survey of the application of advanced first-principle methods on the theoretical modeling and understanding of novel electronic, optical, and magnetic properties of the spin-orbit coupled Ruddlesden–Popper series of iridates Srn+1IrnO3n+1 (n = 1, 2, and ∞). After a brief description of the basic aspects of the adopted methods (noncollinear local spin density approximation plus an on-site Coulomb interaction (LSDA+U), constrained random phase approximation (cRPA), GW, and Bethe–Salpeter equation (BSE)), we present and discuss select results. We show that a detailed phase diagrams of the metal–insulator transition and magnetic phase transition can be constructed by inspecting the evolution of electronic and magnetic properties as a function of Hubbard U, spin–orbit coupling (SOC) strength, and dimensionality n, which provide clear evidence for the crucial role played by SOC and U in establishing a relativistic (Dirac) Mott–Hubbard insulating state in Sr2IrO4 and Sr3Ir2O7. To characterize the ground-state phases, we quantify the most relevant energy scales fully ab initio—crystal field energy, Hubbard U, and SOC constant of three compounds—and discuss the quasiparticle band structures in detail by comparing GW and LSDA+U data. We examine the different magnetic ground states of structurally similar n = 1 and n = 2 compounds and clarify that the origin of the in-plane canted antiferromagnetic (AFM) state of Sr2IrO4 arises from competition between isotropic exchange and Dzyaloshinskii–Moriya (DM) interactions whereas the collinear AFM state of Sr3Ir2O7 is due to strong interlayer magnetic coupling. Finally, we report the dimensionality controlled metal–insulator transition across the series by computing their optical transitions and conductivity spectra at the GW+BSE level from the the quasi two-dimensional insulating n = 1 and 2 phases to the three-dimensional metallic n=∞ phase.

The range of non-Kitaev terms and fractional particles in \u03b1-RuCl3

Significant efforts have focused on the magnetic excitations of relativistic Mott insulators, predicted to realize the Kitaev quantum spin liquid (QSL). This exactly solvable model involves a highly entangled state resulting from bond-dependent Ising interactions that produce excitations which are non-local in terms of spin flips. A key challenge in real materials is identifying the relative size of the non-Kitaev terms and their role in the emergence or suppression of fractional excitations. Here, we identify the energy and temperature boundaries of non-Kitaev interactions by direct comparison of the Raman susceptibility of α-RuCl3 with quantum Monte Carlo (QMC) results for the Kitaev QSL. Moreover, we further confirm the fractional nature of the magnetic excitations, which is given by creating a pair of fermionic quasiparticles. Interestingly, this fermionic response remains valid in the non-Kitaev range. Our results and focus on the use of the Raman susceptibility provide a stringent new test for future theoretical and experimental studies of QSLs.

Crossover between Mott and Efros-Shklovskii variable-range hopping in Sr2IrO4 epitaxial thin films by misfit strain and isovalent doping

We report three-dimensional Mott variable-range hopping (3D Mott-VRH) transport of Sr2IrO4 epitaxial thin films, with a transition to Efros-Shklovskii variable-range hopping (ES-VRH) with increased misfit strain or isovalent doping. We have observed that the characteristic temperature of 3D Mott-VRH transport decreases under increased misfit strain, implying that the density of states near the Fermi energy is reconstructed. With further increased misfit strain (or doping with Ca or Ba ions), a crossover from the 3D Mott-VRH to ES-VRH transport takes place due to increased carrier localization by disorder, opening a Coulomb gap by increasing the effective electron-correlation. The results of magnetoresistance measurements also confirm that the disorder caused by misfit strain or isovalent doping plays an important role in the electronic transport of these Sr2IrO4 thin films. Our experimental observations propose that subtle external stimuli such as structural modifications can modulate the electronic properties of the relativistic Mott insulator, suggesting an unprecedented pathway for electronic device applications.

Atomic-scale fragmentation and collapse of antiferromagnetic order in a doped Mott insulator

Disentangling the relationship between the insulating state with a charge gap and the magnetic order in an antiferromagnetic (AF) Mott insulator remains difficult due to inherent phase separation as the Mott state is perturbed. Measuring magnetic and electronic properties at the atomic length scales would provide crucial insight, but this is yet to be experimentally achieved. Here we use spectroscopic-imaging spin-polarized scanning tunneling microscopy (SP-STM) to visualize periodic spin-resolved modulations originating from the AF order in a relativistic Mott insulator Sr2IrO4, and study these as a function of doping. We find that near insulator-to-metal transition (IMT), the long-range AF order melts into a fragmented state with short-range AF correlations. Crucially, we discover that the short-range AF order is locally uncorrelated with the observed spectral gap magnitude. This strongly suggests that short range AF correlations are unlikely to be the culprit behind inhomogeneous gap closing and the emergence of pseudogap regions near IMT. Our work establishes SP-STM as a powerful tool for revealing atomic-scale magnetic information in complex oxides.

Theoretical evidence of spin-orbital-entangled Jeff=12 state in the 3d transition metal oxide CuAl2O4

Transition metal oxides exhibit various competing phases and exotic phenomena depending on how their reaction to the rich degeneracy of the $d$-orbital. Large spin-orbit coupling (SOC) reduces this degeneracy in a unique way by providing a spin-orbital-entangled ground state for 4$d$ and 5$d$ transition metal compounds. In particular, the spin-orbital-entangled Kramers doublet, known as the $J_{\mathbf{eff}}$=1/2 pseudospin, appears in layered iridates and $\alpha$-RuCl$_3$, manifesting a relativistic Mott insulating phase. Such entanglement, however, seems barely attainable in 3$d$ transition metal oxides, where the SOC is small and the orbital angular momentum is easily quenched. From experimental and theoretical evidence, here we report on the CuAl$_2$O$_4$ spinel as the first example of a $J_{\mathbf{eff}}$=1/2 Mott insulator in 3$d$ transition metal compounds. Based on the experimental study, including synthesis of the cubic CuAl$_2$O$_4$ single crystal, density functional theory and dynamical mean field theory calculations reveal that the $J_{\mathbf{eff}}$=1/2 state survives the competition with an orbital-momentum-quenched $S$=1/2 state. The electron-addition spectra probing unoccupied states are well described by the $j_{\mathbf{eff}}$=1/2 hole state, whereas electron-removal spectra have a rich multiplet structure. The fully relativistic entity found in CuAl$_2$O$_4$ provides new insight into the untapped regime where the spin-orbital-entangled Kramers pair coexists with strong electron correlation.

Interface-engineered hole doping in Sr2IrO4/LaNiO3 heterostructure

The relativistic Mott insulator Sr2IrO4 driven by large spin–orbit interaction is known for the antiferromagnetic state which closely resembles the electronic structure of parent compounds of superconducting cuprates. Here, we report the realization of hole-doped Sr2IrO4 by means of interfacial charge transfer in Sr2IrO4/LaNiO3 heterostructures. X-ray photoelectron spectroscopy on Ir 4f edge along with the x-ray absorption spectroscopy at Ni L2 edge confirmed that 5d electrons from Ir sites are transferred onto Ni sites, leading to markedly electronic reconstruction at the interface. Although the Sr2IrO4/LaNiO3 heterostructure remains non-metallic, we reveal that the transport behavior is no longer described by the Mott variable range hopping mode, but by the Efros–Shklovskii model. These findings highlight a powerful utility of interfaces to realize emerging electronic states of the Ruddlesden–Popper phases of Ir-based oxides.

Sr3Ir2O7F2 : Topochemical conversion of a relativistic Mott state into a spin-orbit driven band insulator

The topochemical transformation of single crystals of Sr$_3$Ir$_2$O$_7$ into Sr$_3$Ir$_2$O$_7$F$_2$ is reported via fluorine insertion. Characterization of the newly formed Sr$_3$Ir$_2$O$_7$F$_2$ phase shows a nearly complete oxidation of Ir$^{4+}$ cations into Ir$^{5+}$ that in turn drives the system from an antiferromagnetic Mott insulator with a half-filled J$_{eff}=1/2$ band into a nonmagnetic $J=0$ band insulator. First principles calculations reveal a remarkably flat insertion energy that locally drives the fluorination process to completion. Band structure calculations support the formation of a band insulator whose charge gap relies on the strong spin-orbit coupling inherent to the Ir metal ions of this compound.

Spectroscopic Studies on the Metal-Insulator Transition Mechanism in Correlated Materials.

The metal-insulator transition (MIT) in correlated materials is a novel phenomenon that accompanies a large change in resistivity, often many orders of magnitude. It is important in its own right but its switching behavior in resistivity can be useful for device applications. From the material physics point of view, the starting point of the research on the MIT should be to understand the microscopic mechanism. Here, an overview of recent efforts to unravel the microscopic mechanisms for various types of MITs in correlated materials is provided. Research has focused on transition metal oxides (TMOs), but transition metal chalcogenides have also been studied. Along the way, a new class of MIT materials is discovered, the so-called relativistic Mott insulators in 5d TMOs. Distortions in the MO6 (M = transition metal) octahedron are found to have a large and peculiar effect on the band structure in an orbital dependent way, possibly paving a way to the orbital selective Mott transition. In the final section, the character of the materials suitable for applications is summarized, followed by a brief discussion of some of the efforts to control MITs in correlated materials, including a dynamical approach using light.

Electron and hole doping in the relativistic Mott insulator Sr2IrO4 : A first-principles study using band unfolding technique

We study the effects of dilute La and Rh substitutional doping on the electronic structure of the relativistic Mott insulator ${{\mathrm{Sr}}_{2}\mathrm{IrO}}_{4}$ using fully relativistic and magnetically noncollinear density functional theory with the inclusion of an on-site Hubbard $U$. To model doping effects, we have adopted the supercell approach, that allows for a realistic treatment of structural relaxations and electronic effects beyond a purely rigid band approach. By means of the band unfolding technique we have computed the spectral function and constructed the effective band structure and Fermi surface (FS) in the primitive cell, which are readily comparable with available experimental data. Our calculations clearly indicate that La and Rh doping can be interpreted as effective electron and (fractional) hole doping, respectively. We found that both electron and hole doping induce an insulating-to-metal transition (IMT) but with different characteristics. In ${\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{IrO}}_{4}$ the IMT is accompanied by a moderate renormalization of the electronic correlation substantiated by a reduction of the effective on-site Coulomb repulsion $U\ensuremath{-}J$ from 1.6 eV $(x=0)$ to 1.4 eV (metallic regime of $x=12.5%$). The progressive closing of the relativistic Mott gap leads to the emergence of connected elliptical electron pockets at $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ and less intense features at $X$ on the Fermi surface. The average ordered magnetic moment is slightly reduced upon doping, but the canted antiferromagnetic state is perturbed on the Ir-O planes located near the La atoms. The substitution of Ir with the nominally isovalent Rh is accompanied by a substantial hole transfer from the Rh site to the nearest-neighbor Ir sites. This shifts down the chemical potential, creates almost circular disconnected hole pockets in the FS, and establishes the emergence of a two-dimensional metallic state formed by conducting Rh planes intercalated by insulating Ir planes. Finally, our data indicate that hole doping causes a flipping of the in-plane net ferromagnetic moment on the Rh plane and induces a magnetic transition from the antiferromagnetic (AF)-I to the AF-II ordering.

Tracking local magnetic dynamics via high-energy charge excitations in a relativistic Mott insulator

We use time- and energy-resolved optical spectroscopy to investigate the coupling of electron-hole excitations to the magnetic environment in the relativistic Mott insulator Na$_2$IrO$_3$. We show that, on the picosecond timescale, the photoinjected electron-hole pairs delocalize on the hexagons of the Ir lattice via the formation of quasi-molecular orbital (QMO) excitations and the exchange of energy with the short-range-ordered zig-zag magnetic background. The possibility of mapping the magnetic dynamics, which is characterized by typical frequencies in the THz range, onto high-energy (1-2 eV) charge excitations provides a new platform to investigate, and possibly control, the dynamics of magnetic interactions in correlated materials with strong spin-orbit coupling, even in the presence of complex magnetic phases.

From a Quasimolecular Band Insulator to a Relativistic Mott Insulator in t_{2g}^{5} Systems with a Honeycomb Lattice Structure.

The t_{2g} orbitals of an edge-shared transition-metal oxide with a honeycomb lattice structure form dispersionless electronic bands when only hopping mediated by the edge-sharing oxygens is accessible. This is due to the formation of isolated quasimolecular orbitals (QMOs) in each hexagon, introduced recently by Mazin etal. [Phys. Rev. Lett. 109, 197201 (2012)], which stabilizes a band insulating phase for t_{2g}^{5} systems. However, with the help of the exact diagonalization method to treat the electron kinetics and correlations on an equal footing, we find that the QMOs are fragile against not only the spin-orbit coupling (SOC) but also the Coulomb repulsion. We show that the electronic phase of t_{2g}^{5} systems can vary from a quasimolecular band insulator to a relativistic J_{eff}=1/2 Mott insulator with increasing the SOC as well as the Coulomb repulsion. The different electronic phases manifest themselves in electronic excitations observed in optical conductivity and resonant inelastic x-ray scattering. Based on our calculations, we assert that the currently known Ru^{3+} and Ir^{4+} based honeycomb systems are far from the quasimolecular band insulator but rather the relativistic Mott insulator.

Li2RhO3: A spin-glassy relativistic Mott insulator

Motivated by the rich interplay among electronic correlation, spin-orbit coupling (SOC), crystal-field splitting, and geometric frustrations in the honeycomb-like lattice, we systematically investigated the electronic and magnetic properties of Li$_2$RhO$_3$. The material is semiconducting with a narrow band gap of $\Delta\sim$78 meV, and its temperature dependence of resistivity conforms to 3D variable range hopping mechanism. No long-range magnetic ordering was found down to 0.5 K, due to the geometric frustrations. Instead, single atomic spin-glass behavior below the spin-freezing temperature ($\sim$6 K) was observed and its spin dynamics obeys the universal critical slowing down scaling law. First principle calculations suggested it to be a relativistic Mott insulator mediated by both electronic correlation and SOC. With moderate strength of electronic correlation and SOC, our results shed new light to the research of Heisenberg-Kitaev model in realistic materials.

Relativistic Mott criticality in graphene

We formulate the effective Gross-Neveu-Yukawa theory of the semimetal-insulator transitions on the honeycomb lattice and compute its quantum critical behavior near three (spatial) dimensions. We find that at the critical point Dirac fermions do not survive as coherent excitations and that the $\ensuremath{\sim}1/r$ tail of the weak Coulomb interaction is an irrelevant coupling. The emergent Lorentz invariance near criticality implies a universal ratio of the low-temperature specific heats of the metallic and the rotational-symmetry-broken insulating phase.

Effects of the electron's anomaly in relativistic laser-assisted Mott scattering

We investigate the influence of the electron's anomalous magnetic moment on the process of relativistic Mott scattering in a powerful electromagnetic plane wave for which the ponderomotive energy is of the order of the magnitude of the electron's rest mass. For this purpose, we use the Coulomb–Dirac–Volkov and the Dirac–Volkov functions with the electron's anomaly to describe the initial and final states respectively. First-order Born differential cross-sections of induced and inverse bremsstrahlung are obtained for linearly polarized laser light. Numerical calculations are carried out for various parameters values (i.e. scattering angle, the nucleus charge, photon energy, electrical field) and are compared with results obtained by Li et al 2004 (J. Phys. B: At. Mol. Opt. Phys. 37 653). It is found that for parameters used in the present work, incorporating the anomaly of the electron in the initial and final states yields cross-sections which are strongly modified whatever the scattering geometry as compared to the outcome of the previous treatment.

Investigation of the passage of 100–1000-MeV/nucleon superheavy ions through homogeneous media

This work is a continuation of the experimental and theoretical investigations of the effect of the Z 1 3 correction to the stopping power of ions on the passage of heavy ions 40Ar, 56Fe, 197Au, 131Xe, and 238U with energies of about 1 GeV/nucleon through a homogeneous medium. The previously observed systematic deviations of the calculations based on the first Born approximation to the scattering of a particle by the atomic electrons in the medium from the experimental values of the total ionization ranges of the nuclei and their stopping powers is confirmed. The discrepancy increases with the atomic number of the projectile nucleus. It is shown that the Z 1 3 correction in the form proposed by Jackson and McCarthy eliminates, especially for ions with Z1>50, the systematic discrepancy between the computed and experimental values. For the experimental energy range relativistic Mott scattering of a particle by the atomic electrons in the target makes the dominant contribution to the observed Z 1 3 effect.

Attenuation of electrons in non-crystalline solids

A comparison of the attenuation of electrons in non-crystalline solids as described by the transport theory (TT), using the transport length as obtained in a quasiclassical approach, and by Monte Carlo (MC) calculations based on relativistic Mott cross sections for elastic scattering is presented. Both approaches yield an exponential law for the electron escape probability for particles generated at great depths. An exact expression has been obtained by transport theory for the characteristic length of this exponential function, the so called attenuation parameter (AP). It has been shown that the AP depends only on two quantities: the inelastic and the transport mean free path. According to the MC results, this AP governs the electron attenuation over the entire depth range, but with a non-exponential law at small depths. The AP values have been calculated for 45 elements (ranging from Be to Au) at different energies in the 250–1500 eV range. Excellent agreement between the TT and the MC results has been found.

An improved electron multiple-scattering distribution for Monte Carlo transport simulation.

An improved electron multiple-scattering distribution is presented in the form of a composite function which combines three expressions valid over different scattering angle regions: a modified relativistic Mott single-scattering term for large angle scattering, a modified Moliere Gaussian term for small angle scattering, and an exponential term for the intermediate angle scattering region. The exponential term has two adjustable parameters which make possible the smooth transition from the large to the small scattering angle regions. The proposed distribution exhibits better agreement with experiment than other multiple-scattering distributions commonly used in Monte Carlo electron transport codes, is amenable to direct sampling over a continuous range of electron energies and step sizes, can be used for elements of any atomic number, and is particularly suitable for use on small memory computers.

High Energy Electron-Electron Scattering

Eradicated electron sensitive nuclear emulsions were exposed to 200-Mev electrons at the Berkeley synchrotron. In scanning the electron tracks 427 events were observed in which the scattered electron of lower energy, or knock-on electron, had an energy greater than 30 kev. The observed differential cross section was found to agree in absolute value with M\o{}ller's theoretical cross section, although an insufficient number of high energy knock-on electrons were observed to distinguish between the M\o{}ller, relativistic Mott, and relativistic Rutherford formulas. Two pairs initiated by primary electrons and two cases in which primary electrons vanished in the emulsion were also observed in 102.6 cm of track. No heavy particle events were seen.