Correlated Electrons in Transition-Metal Compounds:
New Challenges

Due to competition between lattice distortion and electronic correlations, rare earth nickelates exhibit a very rich structural, electronic and magnetic phase diagram. Rare-earth substitution can be used to tune the ground state but strain may also be an interesting option, especially on films. In the present study, we measured terahertz transmission, Far- and Mid-infrared reflectivity and visible light spectroscopic ellipsometry on LaNiO3 films grown on different substrates to investigate electronic properties. Film/substrate lattice mismatch begets tensile or compressive strain that induces strong structural and electronic perturbations. Through the redistribution of optical spectral weight as strain varies, we aim to disentangle the electron-lattice from the electron-electron interactions. Electronic and structural theoretical predictions allow us to deeper understand the evolution of the optical conductivity and spectral weight regarding combined effects of electron correlations, lattice distortion, bandwidth and orbital hybridization.

Materails with strong spin-orbit coupling exhibit large magnetic anisotropy and non-Heisenberg exchange interactions, that could lead to non-trivial magnetic states hosting topological excitations. Here we use Wannier tight-binding model derived from first-principles calculations to compute anisotropic magnetic exchange using a generalization of Lichtenstein formula. The calculations are performed for Sr2IrO4, GdMn2O5 and M3Mo2O8 compounds.

We explore the effects of disordered charged defects on the electronic excitations observed in the photoemission spectra of doped transition metal oxides in the Mott insulating regime by the example of the R1−xCaxVO3 perovskites, where R = La, . . . , Lu. A fundamental characteristic of these vanadium d2 compounds with partly filled t2g valence orbitals is the persistence of spin and orbital order up to high doping, in contrast to the loss of magnetic order in high-Tc cuprates at low defect concentration. We study the disordered electronic structure of such doped Mott-Hubbard insulators within the unrestricted Hartree-Fock approximation and, as a result, manage to explain the spectral features that occur in photoemission and inverse photoemission. In particular, (i) the atomic multiplet excitations in the inverse photoemission spectra and the various defect-related states and satellites are qualitatively well reproduced, (ii) a robust Mott gap survives up to large doping, and (iii) we show that the defect states inside the Mott gap develop a soft gap at the Fermi energy. The soft defect-states gap, which separates the highest occupied from the lowest unoccupied states, can be characterized by a shape and a scale parameter extracted from a Weibull statistical sampling of the density of states near the chemical potential. These parameters provide a criterion and a comprehensive schematization for the insulator-metal transition in disordered systems. Our results provide clear indications that doped holes are bound to charged defects and form small spin-orbital polarons whose internal kinetic energy is responsible for the opening of the soft defect-states gap. We show that this kinetic gap survives disorder fluctuations of defects and is amplified by the long-range electron-electron interactions, whereas we observe a Coulomb singularity in the atomic limit. The small size of spin-orbital polarons is inferred by an analysis of the inverse participation ratio and by means of a complementary many-body polaron theory, which yields a similar robust spin and orbital order as the Hartree-Fock approximation. Using realistic parameters for the vanadium perovskite $La_{1−x}Ca_xVO_3$, we show that its soft gap is reproduced as well as the marginal doping dependence of the position of the chemical potential relative to the center of the lower Hubbard band. The present theory uncovers also the reasons why the d1 → d0 satellite excitations, which directly probe the effect of the random defect fields on the polaron state, are not well resolved in the available experimental photoemission spectra for $La_{1−x}Ca_xVO_3$.

Quantum spin liquid is a state of matter with long-range entanglement between spins which prohibits a system to have any long-range magnetic order even at $T=0$ K. Here we have investigated two types of spin liquid candidates: one is a promising Kitaev material ($\alpha$-RuCl$_3$) and the other belongs to Kagome systems [Barlowite (Cu$_4$(OH)$-6$BrI) and Claringbullite (Cu$_4$(OH)$-6$ClI)]. First, we demonstrate clear evidence for a dimerized structure of $\alpha$-RuCl$_3$ at high pressure and observe the breakdown of the relativistic $j_{\rm eff}$ picture in this regime strongly affecting the electronic properties. A pressure-induced Kitaev quantum spin liquid cannot occur in this broken symmetry state. We shed light on the new phase of $\alpha$-RuCl$_{3}$ by results obtained from {\it ab initio} density functional theory calculations under hydrostatic pressure, along with experimental data from broad-band infrared spectroscopy. On the other hand, we show that Kagome systems barlowite and claringbullite show a dynamic Jahn-Teller (JT) distortion at room temperature, giving the Kagome lattice of Cu$^{2+}$ ions a perfect hexagonal symmetry. A transition from a dynamic to static JT distortion occurs at a higher temperature for barlowite than for Claringbullite. At this transition, the unit cell lowers the symmetry from P6$_3/mmc$ to $Cmcm$ and acquires a small unit cell distortion in the hexagonal $ab$-plane, slightly distorting the kagome lattice of Cu$^{2+}$ atoms. The energy barriers for these transitions are obtained by performing static DFT calculations.

Spin wave exchange mechanism of superconducting pairing in ferromagnet with conducting electrons and localized spins is considered by use of the microscopic Eliashberg-like theory for electrons and RPA approach to treat the system of localized spins. Magnon exchange mechanism results in the equal spin pairing described by two components of the order parameter $\Delta^{\uparrow}$ and $\Delta^{\downarrow}$. Coupling of these components is supported by radiation and absorption of spin waves by electrons of Cooper pair leading to transformation between state "both spin up" to state "both spin down" for Cooper pair. The processes of absorption and radiation of spin waves depend differently on the temperature with absorption being progressively suppressed as temperature drops. As a result, transition on heating from ferromagnetic normal phase to superconducting phase is characterized by descending dependence of low temperature critical temperature $T_{cl}$ on the coupling parameter of electron-localized spin exchange interaction. Transition back to normal state from triplet superconducting phase to normal phase on further heating occurs below the Curie temperature.

The interplay of strong spin-orbit coupling, electron-electron correlation, and crystal-field splitting in 5-$d$ transition metal oxides have recently attracted much attention both theoretically and experimentally. Here we investigate the electronic and magnetic properties of $d^{3.5}$ iridate Ba$_3$LiIr$_2$O$_9$ using first-principles electronic structure calculations. The results of the calculations reveal that the system lies in an intermediate spin-orbit coupling (SOC) regime. There is strong covalency of Ir-5$d$ and O-2$p$ orbitals. SOC, together with covalency, conspires to reduce the magnetic moment at the Ir site. By calculating the hopping interactions and exchange interactions, it is found that there is strong antiferromagnetic intradimer coupling within an Ir$_2$O$_9$ unit and other antiferromagnetic interdimer interactions make the system frustrated. The anisotropic magnetic interactions are also calculated. The calculations reveal that the magnitude of the Dzyaloshinskii-Moriya interactions parameter is small for this system. The effects of small electron and hole doping on DM interactions are also investigated here. The magnetocrystalline anisotropy energy is significant for this system, and the easy axis lies on the $ab$ plane.

The compounds of heavy transition metals (with 4-$d$ and 5-$d$ electrons) have attracted considerable attention in recent years for their attractive properties due to the presence of strong spin-orbit coupling (SOC), which is comparable to their on-site Coulomb ($U$) and crystal field ($\Delta$) interactions. Such competitive interactions give rise to $J_{\text {eff}}$ =1/2 Mott state which was recently observed in layered iridates with Ir$^{\text{4+}}$ oxidation state. In these systems, a metallic behavior is expected due to the presence of partially filled $t_{2g}$ states. Insulating behavior can only be explained by including both spin-orbit coupling and electron-electron interactions. Due to strong crystal fields, 5d band states split off with, eg symmetry, whereas the remaining t2g bands form $J_{\text {eff}}$ =1/2 and $J_{\text {eff}}$=3/2 multiplets via strong SOC. The $J_{\text {eff}}$=3/2 band is lower in energy and filled, whereas $J_{\text {eff}}$=1/2 band is higher in energy and half filled. This $J_{\text {eff}}$= 1/2 band further splits into fully occupied lower Hubbard band and completely empty upper Hubbard band with a small inclusion of Hubbard $U$. On the other hand, iridates with pentavalent Ir$^{5+}$ (5-$d^4$) ions is expected to be nonmagnetic singlet ground state due to strong spin-orbit coupling. However, the strong crystal field, band structure effect, etc. are crucial to determine the ground state. Recently honeycomb iridate Sr$_3$CaIr$_2$O$_9$, where Ir is in 5+($d^4$) oxidation state was synthesized, and magnetic measurements show that it exhibits negligible magnetic susceptibility, implying the system is close proximity to either $S$=0 or $J$=0 state. We have investigated the electronic structure and magnetic properties of Sr$_3$CaIr$_2$O$_9$ in detail using first principle density functional theory calculations. Our calculations of various hopping interactions between Ir5+ ions show that there is strong intra-dimer interaction and also substantial inter dimer interactions. Although there is no net magnetization in the system, but each Ir site possesses weak magnetic moment. Calculations with spin-orbit coupling suggest that the adjacent Ir octahedra in a dimer prefer to be in a spin-orbital singlet state which should have eliminated any net magnetization from each dimer. The system is insulating within LDA+U+SOC calculations.

We consider the spin-1/2 isotropic Heisenberg antiferromagnet on several frustrated bilayer lattices (square, honeycomb, and triangular) to discuss the ground-state and low-temperature properties of the frustrated quantum spin systems. In the absence of an external magnetic field, the square-lattice bilayer has been discussed recently to illustrate a quantum critical end point [1]. We demonstrate that the ground-state phase diagram of this system (as well as of the honeycomb-lattice bilayer [2]) can be reproduced by a simple variational approach [3]. In the presence of an external magnetic field, one can utilize the concept of localized magnons to arrive at nontrivial classical lattice-gas models. As a result, the frustrated bilayer Heisenberg antiferromagnets may show interesting finite-temperature order-disorder phase transitions which belong either to the Ising-model or to the three-state Potts-model universality classes [4,5]. The recently synthesized magnetic compound Ba2CoSi2O6Cl2 seems to be an almost perfect candidate to observe the features of square-lattice frustrated bilayer in experiments [6]. We suggest new experiments to detect a field-driven phase transition in Ba2CoSi2O6Cl2 [4]. [1] J.Stapmanns et al., arXiv:1805.11017. [2] H.Zhang, C.A.Lamas, M.Arlego, and W.Brenig, Phys. Rev. B 93, 235150 (2016). [3] J.Richter and O.Derzhko, European Journal of Physics 38, 033002 (2017). [4] J.Richter et al., Phys. Rev. B 97, 024405 (2018). [5] J.Strecka, K.Karlova, V.Baliha, and O.Derzhko, arXiv:1807.08042. [6] H.Tanaka et al., J. Phys. Soc. Jpn. 83, 103701 (2014).

Understanding microscopic properties of LiNiO$_2$, a Li-ion battery cathode material with extraordinarily high reversible capacity, has remained a challenge for decades. Based on extensive electronic structure calculations, which reveal a large number of nearly degenerate phases involving local Jahn-Teller effect as well as bond and oxygen-based charge disproportionation, we propose that LiNiO$_2$ exists in an entropy-stabilized state at ambient temperatures, which freezes upon temperature lowering into a charge-glass-like state. Recognizing the glassy nature of LiNiO$_2$ does not only explain its key experimental features, but also opens a new path in designing entropy-stabilized battery cathodes with superb capacities.

With the development of ultrafast X-ray probes of quantum matter, it is now possible to ask questions about how different aspects of order behave in the non-equilibrium realm. With systems such as strongly correlated electron systems, the system can simultaneously possess different types of electronic and magnetic order. However, a fundamental question is which orders are driving the physics and which are following. To answer this question, we have explored the non-equilibrium response of perovskite nickelates, which undergo an metal insulator transition (MIT) associated with charge and magnetic order. Using X-ray based probes at the Linac Coherent Light Source together with optical probes, we have been able to track the magnetic and electronic order separately at sub-psec timescales. We find that they possess different timescales of collapse in this regime and have formulated a model to understand the process. Together with wavelength dependent pumping above and below the bandgap of 0.1 eV, we are creating a better understanding of how to efficiently control order parameters with optical excitation. This science is funded by by the Department of Energy grant DE-SC0012375. Work at Argonne is supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357 and use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, which is a DOE Office of Science User Facility, under Contract No. DE-AC02-76SF00515.

Momentum-resolved Electron Energy Loss Spectroscopy (M-EELS) is a newly developed experimental technique that can directly probe collective excitations (and their momentum-dependence) in materials. Performing such a measurement on 1T-TiSe$_2$ near the charge density wave (CDW) transition temperature shows a plasmonic mode go soft at the nesting vector momentum. This is strong evidence for the involvement of excitons in the transition, and makes TiSe$_2$ the first material shown to host an exciton condensate - a new phase of matter! We also show that the fact that M-EELS can see the excitonic mode indicates the CDWs in TiSe$_2$ must be chiral in nature, something that has long been debated in the literature. Next, M-EELS was performed on Cu$_x$TiSe$_2$ to test the doping-dependence of the excitonic transition. Surprisingly, it appears the excitonic mode softening is much more quickly suppressed than the CDW transition as determined by X-ray diffraction and resistance measurements. Furthermore, the (q=0) plasmon frequency shows an anomalous temperature dependence.

Kitaev's honeycomb model is a remarkable exactly solvable spin-1/2 model, consisting of bond dependent Ising interactions, and with a gapless quantum spin liquid ground state. Even more remarkably such interactions are actually realized in a number of spin-orbit entangled Mott insulators, alongside other more conventional interactions. Here, motivated by the recent surge in interest in the behaviour of these materials in a magnetic field, we map out the complete phase diagram of the pure Kitaev model in tilted magnetic fields. Besides the expected gapped quantum spin liquid at low fields and the trivial polarized state at high fields we report the emergence of a distinct gapless quantum spin liquid at intermediate field strengths. Analyzing a number of static, dynamical, and finite temperature quantities using numerical exact diagonalization techniques, we find strong evidence that this phase exhibits gapless fermions coupled to a massless gauge field resulting in a dense continuum of low-energy states. We discuss its stability in the presence of perturbations, Heisenberg and off-diagonal symmetric exchange interactions, that naturally arise in spin-orbit entangled Mott insulators alongside Kitaev interactions.

Quantum effect is expected to dictate the behaviour of physical systems at low temperature. For quantum magnets with geometrical frustration, quantum fluctuation lifts the macroscopic classical degeneracy, and exotic quantum states emerge. However, how different types of quantum processes entangle wave functions in a constrained Hilbert space is not well understood. Here, we study the topological entanglement entropy the thermal entropy of a quantum ice model on a geometrically frustrated kagome lattice. We find that the system does not show a Z2 topological order down to extremely low temperatures, yet continues to behave like a classical kagome ice with finite residual entropy. Our theoretical analysis indicates that an intricate competition of off-diagonal and diagonal quantum tunneling processes leading to a suppression of the quantum energy scale. This new paradigm suggests quantum spin ice materials can be engineered to study the novel quantum-classical transition.

We investigate the quantum Heisenberg model on the pyrochlore lattice for a generic spin-S in the presence of nearest-neighbor J1 and second-nearest-neighbor J2 exchange interactions. By employing the pseudofermion functional renormalization group (PFFRG) method, we find, for S=1/2 and S=1, an extended quantum spin liquid phase centered around J2=0, which is shown to be robust against the introduction of breathing anisotropy. The effects of temperature, quantum fluctuations, breathing anisotropies, and a J2 coupling on the nature of the scattering profile, in particular, the pinch points are studied. For the magnetic phases of the J1-J2 model, quantum fluctuations are shown to strongly renormalize phase boundaries compared to the classical model and shift the ordering wave vectors of spiral magnetic states, however, no new magnetic orders are found to be stabilized. arXiv: 1802.09546 (2018), Yasir Iqbal, Tobias Müller, Pratyay Ghosh, Michel J. P. Gingras, Harald O. Jeschke, Stephan Rachel, Johannes Reuther, Ronny Thomale

Experiments on optical and STM injection of carriers in layered $\mathrm{MX_2}$ materials revealed the formation of nanoscale patterns with networks and globules of domain walls. This is thought to be responsible for the metallization transition of the Mott insulator and for stabilization of a ``hidden'' state. In response, here we present studies of the classical charged lattice gas model emulating the superlattice of polarons ubiquitous to the material of choice $1T-\mathrm{TaS_2}$. The injection pulse was simulated by introducing a small concentration of voids which subsequent evolution was followed by means of Monte Carlo cooling. Below the detected phase transition, the voids gradually coalesce into domain walls forming locally connected globules and then the global network leading to a mosaic fragmentation into domains with different degenerate ground states. The obtained patterns closely resemble the experimental STM visualizations. The surprising aggregation of charged voids is understood by fractionalization of their charges across the walls' lines.

We report experimental results of the static magnetization, ESR and NMR spectroscopic measurements of the Ni-hybrid compound NiCl$_3$C$_6$H$_5$CH$_2$CH$_2$NH$_3$. In this material NiCl$_3$ octahedra are structurally arranged in chains along the crystallographic $a$-axis. According to the static susceptibility and ESR data Ni$^{2+}$ spins $S = 1$ are isotropic and are coupled antiferromagnetically (AFM) along the chain with the exchange constant $J = 25.5$\,K. These are important prerequisites for the realization of the Haldane spin-1 chain with the spin-singlet ground state and a quantum spin gap. However, experimental results evidence AFM order at $T_{\rm N} \approx 10$\,K presumably due to small interchain couplings. Interestingly, frequency-, magnetic field-, and temperature-dependent ESR measurements, as well as the NMR data, reveal signatures of an inhomogeneous ground state with co-existent mesoscopically spatially separated AFM ordered and spin-singlet state regions similar to the situation observed before in some spin-diluted Haldane magnets.

Interplay of electronic correlations and spin-orbit interactions in Ir4+ and Ir5+ oxides results in insulating Jeff = 1/2 and Jeff = 0 ground states, respectively. By now, this has been well understood theoretically and established experimentally [1,2]. Excitingly, such spin-orbit coupled ground states are predicted to host exotic phenomena such as the Kitaev-type anisotropic magnetic interactions [3] that produce a quantum spin-liquid state [4] and excitonic magnetism [5]. However, in compounds where the dimerisation of Ir4+ and Ir5+ ions is structurally more favourable, the microscopic understanding of the local electronic structure is lacking. For example, a direct overlap of the Ir d-orbitals within the dimers may lead to significant bonding—antibonding splittings, which in principle diminishes the role of spin-orbit mixing, considerably modifying the local electronic picture compared to that of isolated Ir ion compounds. With Ba5AlIr2O11 as an example, we show that the direct d-d hybridisation effects are relatively weak in iridium dimer compounds while electronic correlations (configuration mixing) and spin-orbit coupling play a dominant role. Using a combination of ab initio many-body wave function quantum chemistry calculations and resonant inelastic X-ray scattering experiments, we elucidate the electronic structure of Ba5AlIr2O11. Our investigation shows that the two Ir ions (Ir4+ and Ir5+) in Ir2O9 dimer units preserve their local Jeff ground states close to 1/2 and 0, respectively. Bibliography [1] B. J. Kim, H. Ohsumi, T. Komesu, S. Sakai, T. Morita, H. Takagi, and T. Arima, Phase-Sensitive Observation of a Spin-Orbital Mott State in Sr2IrO4, Science 323, 1329–1332 (2009). [2] M. Kusch, V. M. Katukuri, N. A. Bogdanov, B. Bu ̈chner, T. Dey, D. V. Efremov, J. E. Hamann-Borrero, B. H. Kim, M. Krisch, A. Maljuk, M. Moretti Sala, S. Wurmehl, G. Aslan-Cansever, M. Sturza, L. Hozoi, J. van den Brink, and J. Geck, “Observation of heavy spin-orbit excitons propagating in a nonmagnetic back- ground: The case of (Ba,Sr)2YIrO6,” Phys. Rev. B 97, 064421 (2018). [3] J. Chaloupka, G. Jackeli, G. Khaliullin, Kitaev-Heisenberg Model on a Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides A2IrO3, Phys. Rev. Lett. 105, 027204 (2010). [4] S. Hwan Chun, J.-W. Kim, J. Kim, H. Zheng, Constantinos C. Stoumpos, C.D. Malliakas, J.F. Mitchell, K. Mehlawat, Y. Singh, Y. Choi, T. Gog, A. Al-Zein, M.M. Sala, M. Krisch, J. Chaloupka, G. Jackeli, G. Khaliullin, B.J. Kim, Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3, Nature Physics 11, 462 (2015). [5] G. Khaliullin, Excitonic Magnetism in Van Vleck--type d4 Mott Insulators, Phys. Rev. Lett. 111,197201 (2013).

In the present work we address a long standing problem of the magnetic ground state and magnetic excitations in underdoped cuprates. Modelling cuprates by the extended t−J model we show that there is a hidden dimensionless parameter λ which drives magnetic criticality at low doping x. Hence we derive the zero temperature λ−x phase diagram of the model. It is argued that all underdoped cuprates are close to the quantum tricritical point x=0, λ=1. The three phases "meet" at the tricritical point: (i) N\'eel antiferromagnet, (ii) spin spiral with antinodal direction of the spiral wave vector, (iii) algebraic spin liquid. We argue that underdoped cuprates belong either to the spin liquid phase or they are on the borderline between the spin liquid and the spin spiral. We calculate the energy position Ecross of the inelastic neutron scattering response maximum at ${\bf q}=(\pi,\pi)$ and compare our results with experiments. We also explain softening of magnons in the intermediate regime observed in inelastic neutron scattering.

Systematic XRD, STEM, EPR and PPMS measurements of structural and magnetic properties are performed for different sizes copper nanoparticles embedded in carbon matrix synthesized by solid phase pyrolysis of polycrystalline phthalocyanine (CuPc, Pc= C$_{32}$N$_8$H$_{16}$). Our results on magnetization carried out by vibrational magnetometer for average sizes of copper nanoparticles in range of 2-6 nm provide a strong evidence for coexistence of ferromagnetism and giant paramagnetism in wide range of temperature and magnetic field. At low temperatures we observe a giant paramagnetism, apparently due to the (ballistic) conduction electron (large orbital magnetism). The X-ray diffraction data and HRTEM images show the face-centered cubic structure of Cu nanocrystallites and their uniform distribution in the carbon matrix. The temperature and field dependencies of the magnetization in all studied samples reveal both ferromagnetic and giant-paramagnetic properties in the measured temperature range of 10-300 K. The saturation magnetization of ferromagnetic nanoparticles in the studied samples falls in the range 0.2-1.5 emu/ g and show weak depends on the temperature from helium up to the room temperatures. The paramagnetic magnetizations in Cu@C nanocomposites at H = 50 kOe and T = 10 K are practically an order of magnitude higher in all the samples than the ferromagnetic saturation magnetizations. The paramagnetic susceptibilities of the Cu@C nanocomposites at T=10 K are of the order (0.3-1) x $10^{-4}$ emu/ gCuOe, which is two orders of magnitude higher than the specific paramagnetic susceptibility of the carbon matrix.

We have investigated the Kitaev candidate material RuCl3 using Raman scattering. We detect a low energy scattering continuum which has previously been claimed to be of Majorana Fermion origin. A careful analysis of the spectra allows us to extract the continuum spectral weight and determine its temperature dependence, in order to compare to theoretical predictions. We also investigated the temperature, polarization and wavelength dependence of higher energy excitations. Furthermore, we present the evolution of the spectra in magnetic fields up to 30 T, revealing the opening of an excitation gap and the formation of complex magnetic excitation features above 7 T.

We study the ground-state and thermodynamic properties of an $S = 1$ Kitaev model. We first clarify the existence of global parity symmetry in addition to the local symmetry on each plaquette, which enables us to perform large-scale calculations on up to 24 sites. It is found that the ground state should be singlet, and its energy is estimated as $E/N ∼ −0.65J$, where $J$ is the Kitaev exchange coupling. We find that the lowest excited state belongs to the same subspace as the ground state, and that the gap decreases monotonically with increasing system size, which suggests that the ground state of the S = 1 Kitaev model is gapless. Using the thermal pure quantum states, we clarify the finite temperature properties characteristic of the Kitaev models with $S\leq 2$.

We discuss the appearance of the Kondo effect in the framework of a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons and derive scaling equation to the second order for such a model. The approach is applied to the spin-anisotropic Kondo model generalized for the case of the power law DOS for itinerant electrons, and solved analytically in terms of elliptic functions. We also introduce the anisotropic Coqblin--Schrieffer model, apply the general method to derive scaling equation for that model for the power law DOS, and integrate the derived equation analytically.

According to Ref. [1], low-temperature crystal structure of spinel AlV$_2$O$_4$ is characterized by formation of V clusters (heptamers). A very different picture has recently been suggested in Ref. [2]. These heptamers were experimentally found to be unstable and decay into pairs of V$_3^{9+}$ trimers and V$_4^{8+}$ tetramers. Starting with high-temperature cubic structure of AlV$_2$O$_4$ we performed lattice dynamics calculations [3] and found this stucture to be unstable. Corresponding structural distortion of the lattice is in a good agreement with the presence of both trimers and tetramers. For this purpose DFT within generalized gradient approximation GGA [4] calculations were performed in the Vienna ab initio simulation package (VASP) [5-8]. 1. Y. Horibe et al. Spontaneous Formation of Vanadium "Molecules" in a Geometrically Frustrated Crystal: AlV$_2$O$_4$. Phys. Rev. Letters 96:086406, 2006. 2. Alexander J. Browne et al. Persistent three- and four-atom orbital molecules in the spinel AlV$_2$O$_4$. Phys. Rev. Materials 1:052003(R), 2017. 3. A. Togo and I. Tanaka. First principles phonon calculations in materials science. Scr. Mater., 108, 1-5 (2015) 4. J.P. Perdew, K. Burke, and M. Ernzerhof. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77:3865, 1996. 5. G. Kresse and J. Hafner. Ab initio molecular dynamics for liquid metals. Phys. Rev. B, 47:558, 1993. 6. G. Kresse and J. Hafner. Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium. Phys. Rev. B, 49:14251, 1994. 7. G. Kresse and J. Furthmüller. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mat. Sci., 6:15, 1996. 8. G. Kresse and J. Furthmüller. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B, 54:11169, 1996.

The curvature of the magnetic film is a source of new physical phenomena. In particular, it results in a number of new properties of magnetic skyrmions if the curvature radius is comparable with the size of the skyrmion. Ferromagnetic skyrmions can be stabilized due to the curvature effects only without intrinsic chiral magnetic interactions [1]. In presence of the intrinsic chiral interaction, skyrmion can be pinned on a localized curvilinear defect. Moreover, ferromagnetic skyrmion pinned on a curvilinear defect demonstrates a discrete set of equilibrium states [2]. Transitions between different states can be controlled by an external magnetic field. Thus, the periodically arranged curvilinear defects can result in a reconfigurable skyrmion lattice. This opens new perspectives on processing and storing of the information. We also predict the reversal effect -- a skyrmion induced deformation of a flexible magnetic film. [1] V.P. Kravchuk, U. Rößler, O. Volkov et al., Phys. Rev. B, 94, 144402 (2016). [2] V.P. Kravchuk, D.D. Sheka, A. Kakay. et al., Phys. Rev. Lett. 120, 067201 (2018).

Half-metals are rather unusual and promising materials. The Fermi surface of a half-metal is completely spin-polarized. Namely, electronic states with only one spin projection value reach the Fermi energy. States with the other spin projection are pushed away from the Fermi level. This makes half-metals useful for spintronics. Typically, half-metallicity arises in strongly correlated electron systems, or when localized magnetic moments are present. Here, we demonstrate that doping a density-wave insulator even in the weak-coupling limit may stabilize new types of half-metallic states, such as spin-valley half-metal and charge-density wave (CDW) half-metal [1]. Our analysis is based on a simple model Hamiltonia describing charge carriers belonging to two bands: electron band $a$ and hole band $b$. Both bands have the parabolic dispersion law and spherical Fermi surface pockets (or valleys). When the Fermi surface valleys nest well (that is, the Fermi momentum of electrons $a$ equals to the Fermi momentum of holes $b$), the electron-electron repulsion generates spin- or charge-density wave state. This ordered mean-field ground state is unique up to symmetry transformations, for example, spin rotations. If charge is added or removed from such a system, the situation becomes less clear-cut: it is believed that at finite doping level, several states with close energies compete against each other to become a true ground state. Several possibilities are discussed in the theoretical literature: incommensurate density wave, electronic phase separation, stripes, etc. We demonstrate that yet another type of many-body state is available. In the doped system, the two-valley Fermi surface emerges. One valley is electron-like. It is composed mostly of states of band a with spin projection $\sigma$. Another valley is hole-like, composed predominantly of states of band $b$ with spin $\sigma'$. These Fermi surface valleys have half-metallic character: the states in band $a$ with spin $sigma$, as well as states in band $b$ with spin $-\sigma'$, do not reach the Fermi level and have no Fermi surface. Depending on the parameters, the spin polarizations of the electron-like valley and hole-like valley may be parallel ($\sigma = -\sigma'$) or antiparallel ($\sigma = -\sigma'$). The former case is similar to the usual half-metal: quasiparticles at the Fermi surface are completely spin-polarized. In addition, the system exhibits a finite CDW order parameter. For this reason, we refer to such a state as the CDW half-metal. When $\sigma = -\sigma'$, the total spin polarization averages to zero. It is proven, however, that in this situation, the so-called spin-valley polarization is nonzero. Thus, the state is called the spin-valley half-metal. The specific features of these half-metallic states are discussed. 1. A.V. Rozhkov, A.L. Rakhmanov, A.O. Sboychakov, K.I. Kugel, and F. Nori, "Spin-valley half-metal as a prospective material for spin valleytronics", Phys. Rev. Lett. 119, 107601 (2017).

Selected delafossite materials such as PdCoO$_2$ or PdCrO$_2$ display extraordinary metallic conductivity despite the fact that they harbor transition-metal oxide layers, which are in principle prone to strong electronic correlations. First principles many-body theory may account for several intriguing features of these systems. In this presentation, the physics of Mott-insulating CrO$_2$ layers in PdCrO$_2$ as well as the more subtle effects of electronic correlations in PdCoO$_2$ will be discussed. Furthermore, the issue of doping these challenging materials will be addressed by theoretical means.

The complexity and counterintuitive sequence of phase transitions in elemental calcium has attracted a keen interest recently. This is partly due to the fact that the DFT method does not allow us to completely describe the experimentally observed phase diagram with increasing pressure. In this paper, we propose the importance of taking into account the Coulomb interactions on molecular orbitals formed from the interstitial site centered electronic and Ca-d states. The DFT+DMFT calculations completely confirm this idea and correctly reproduce the corresponding structural phase transitions, and also allow to interpret the nature underlying them.

Transition metal oxide interfaces exhibit a variety of functional properties that are not available in the respective bulk compounds and open possibilities for applications in future electronics and spintronics devices. An intriguing example are honeycomb lattices of transition metal ions confined in the perovskite or corundum structure, i.e. $(LaXO_3)_2/(LaAlO_3)_4(11)$ [1-3] or $(X_2O_3)_1/(Al_2O_3)_5(0001)$ [4]. Density functional theory calculations with an on-site Hubbard term indicate the formation of unanticipated charge, spin and orbital reconstructions, leading to a rich set of Mott and even topologically nontrivial phases. While the systems with $X = 3d$ cations tend towards trivial Mott symmetry broken insulating ground states, the ferromagnetic solutions of $X$ = Ti, Mn, Co and Ni with constrained symmetry of the two sublattices exhibit a characteristic set of four bands associated with the single occupation of $e^'_g$ (Ti) and $e_g$ (Mn, Co, Ni) orbitals. The Dirac point, formed by two of the bands, can be tuned to the Fermi level by strain and a finite anomalous Hall conductivity arises when spin-orbit coupling (SOC) is switched on. Suppressing the tendency towards Jahn-Teller distortion, $(LaMnO_3)_2/(LaAlO_3)_4(111)$ emerges as a Chern insulator [1]. Moreover, a strong SOC effect is identified for $X = Ti$ at $\alphaAl_2O_3 = 4.81 \AA$ accompanied by an unusually high orbital moment of $-0.88 \muB$ nearly quenching the spin moment of $1.01 \muB$. [4] Collaboration with Okan Köksal, David Doennig, S. Baidya, Warren E. Pickett is gratefully acknowledged, as well as support by the DFG within collaborative research ceter TRR80, project G3 and a computational grant at the Leibniz Rechenzentrum. [1] D. Doennig, S. Baidya, W. E. Pickett and R. Pentcheva, Phys. Rev. B 93, 165145 (2016). [2] D. Doennig, W. E. Pickett, and R. Pentcheva, Phys. Rev. B 89, 121110 (R) (2014). [3] S. Middey et al., Phys. Rev. Lett. 116 056801 (2016). [4] O. Köksal, S. Baidya and R. Pentcheva, Phys. Rev. B 97, 035126 (2018).

The binary compound FeSe is a multiband superconductor with fascinating properties. An orbitally selective electron pairing has been recently discovered in this material [1]. Unlike Fe-pnictides, a structural transition from tetragonal (P4/nmm) to the orthorhombic (Cmme) low-temperature lattice structure is not accompanied by a long-range magnetic order at ambient pressure [2]. The order parameter of this phase transition is considered to be of nematic (electronic) origin. Here, using scanning tunneling microscopy/spectroscopy (STM/S) and heat capacity measurements, we show that the superconducting gaps are anisotropic [3]. The spectroscopic response to a non-magnetic defect suggests a sign changing pairing-state in this material [4]. The quasiparticle interference (QPI) measured at 1.8 K and for the bias voltages larger than the superconducting gap displays a strong unidirectional intra-band scattering, which suggests a one-dimensional behavior. In addition, we show several experimental indications for an incipient ordering mode with a local symmetry reduction below 20 K. This mode also appears to suppress the local density of states in the tunneling spectra measured by STM [5, 6]. We propose a scenario in which this incipient mode competes with superconductivity and introduces the superconducting gap anisotropy in FeSe. [1] Sprau et al., Science, 357, 75 (2017). [2] McQueen et al., Phys. Rev. Lett. 102, 057002 (2009). [2] Jiao et al., Sci. Rep. 7, 44024 (2017). [3] Jiao et al., Phys. Rev. B 96, 094504 (2017). [4] Rößler et al., Phys. Rev. B 92, 060505(R) (2015). [5] Rößler et al., Phys. Rev. B 97, 094503 (2018).

Eliashberg -- McMillan theory of superconductivity is essentially based on the adiabatic approximation. Small parameter of perturbation theory is given by $\lambda\frac{\Omega_0}{E_F}\ll 1$, where $\lambda$ is the dimensionless electron -- phonon coupling constant, $\Omega_0$ is characteristic phonon frequency, while $E_F$ is Fermi energy of electrons. Here we present an attempt to describe electron -- phonon interaction within Eliashberg -- McMillan approach in situation, when characteristic phonon frequency $\Omega_0$ becomes large enough (comparable or exceeding the Fermi energy $E_F$). We consider the general definition of electron -- phonon pairing coupling constant $\lambda$, taking into account the finite value of phonon frequency. Also we obtain the simple expression for the generalized coupling constant $\tilde\lambda$, which determines the mass renormalization, with the account of finite width of conduction band, and describing the smooth transition from the adiabatic regime to the region of strong nonadiabaticity. In the case of strong nonadiabaticity, when $\Omega_0\gg E_F$, the new small parameter appears $\lambda\frac{E_F}{\Omega_0}\sim\lambda\frac{D}{\Omega_0}\ll 1$ ($D$ is conduction band half -- width), and corrections to electronic spectrum become irrelevant. At the same time, the temperature of superconducting transition $T_c$ in antiadiabatic limit is still determined by Eliashberg -- McMillan coupling constant $\lambda$, while the preexponential factor in the expression for $T_c$, conserving the form typical of weak -- coupling theory, is determined by the bandwidth (Fermi energy). For the case of interaction with a single optical phonon we derive the single expression for $T_c$, valid both in adiabatic and antiadiabatic regimes and describing the continuous transition between these two limiting cases. The results obtained are discussed in the context of superconductivity in FeSe/STO.

We will present the power of non-resonant inelastic x-ray scattering (NIXS) at the example of the f-electron materials $SmB_6$ and $URu_2Si_2$, and the text-book d-electron material NiO. NIXS is a photon-in photon-out technique where inelastically scattered photons excite a core-level. Higher than dipole terms of the transition operator will contribute to the double differential cross-section when performing such a scattering experiment at large momentum transfers of the order of 10Å$^{-1}$. We explore these core-level scattering intensities in the beyond-the-dipole-limit and obtain unprecedented insight into which orbital is active in forming the ground state in the solid. NIXS yields information that is not accessible with dipole methods like e.g. x-ray absorption or EELS. 1) Direct imaging of orbital wave functions in quantum materials Hasan Yavaş, Martin Sundermann, Kai Chen, Andrea Amorese, Andrea Severing, Hlynur Gretarsson, Maurits W. Haverkort, Liu Hao Tjeng, submitted 2) 4f Crystal Field Ground State of the Strongly Correlated Topological Insulator $SmB_6$ M. Sundermann, H. Yavaş, K. Chen, D. J. Kim, Z. Fisk, D. Kasinathan, M. W. Haverkort, P. Thalmeier, A. Severing, L. H. Tjeng, Phys. Rev. Lett. 120, 016402 (2018). 3) Direct bulk sensitive probe of 5f symmetry in $URu_2Si_2$ M. Sunderman, M. W. Haverkort, S. Agrestini, A. Al-Zein, M. Moretti Sala, Y. Huang, M. Golden, A. de Visser, P. Thalmeier, L. H. Tjeng, A. Severing, Proc. Nat. Acad. Sci. 113 (49), 13989 (2016).

Helices of increased electron density can spontaneously form in materials containing multiple, interacting density waves. Although a macroscopic order parameter theory describing this behaviour has been proposed and experimentally tested, a detailed microscopic understanding of spiral electronic order in any particular material is still lacking. Here, we present the elemental chalcogens Selenium and Tellurium as model materials for the development of chiral charge and orbital order. We formulate minimal models capturing the formation of spiral structures both in terms of a macroscopic Landau theory and a microscopic Hamiltonian. Both reproduce the known chiral crystal structure and are consistent with its observed thermal evolution and behaviour under applied pressure. The combination of microscopic and macroscopic frameworks allows us to distil the essential ingredients in the emergence of helical charge order, and may serve as a guide to understanding spontaneous chirality both in other specific materials and throughout materials classes.

In this poster, the selected examples from our recent neutron scattering studies of emergent transition-metal compounds with frustrated pyrochlore, honeycomb and triangular lattices will be presented.

We propose an effective model for $\alpha$-RuCl$_3$ that includes a strong ferromagnetic Kitaev coupling [1]. We show that this model quantitatively reproduces both the inelastic-neutron-scattering experiments [2,3] and the heat-capacity measurements [3,4]. We further calculate the field dependence of the polarized terahertz spectra using a numerical exact-diagonalization method. The obtained result well explains the experiments [5]. From the result, we point out that the low-energy excitation in the magnetic field is governed mainly by the off-diagonal interactions and the Heisenberg interaction. [1] T. Suzuki and S. Suga, PRB 97, 134424 (2018). [2] A. Banerjee, et al, Science 356, 1055 (2017). [3] S.-H. Do, et al., Nat. Phys. 13, 1079 (2017). [4] Y. Kubota, et al., PRB 91, 094422 (2015). [5] Z. Wang, et al., PRL 119, 227202 (2017).

We investigate quantized excitation spectra in quasi-one-dimensional (q1D) S=1 antiferromagnetic (AF) spin-chain systems below the Ne\’eel temperature [1]. We calculate dynamical spin-structure factors of the q1D S=1 antiferromagnetic systems with single-ion anisotropy and bond alternation by using infinite-time-evolving-block-decimation method. The excitation continuum originating from magnon excitations appears in the low-energy excitation of the system. We find that, when the single-ion anisotropy is easy-axis type, the magnon continuum shows quantization by the inter-chain couplings. The excitation energies of the quantized spectra are well-explained by the negative zeros of the Airy function (NZAF), when the easy-axis anisotropy is strong. We further find that, when the system is located far from the singlet-dimer phase, the quantized spectra appears, although the excitation energies of the quantized spectra deviate from NZAF. We discuss the origin of the quantization of the magnon continuum. [1] T. Suzuki and S. Suga, arXiv:1808.06270.

We investigate a bilayer Kitaev model in which two honeycomb layers are coupled by the Heisenberg interactions to discuss the effects of interlayer coupling on Kitaev quantum spin liquids (QSLs). Using the exact diagonalization, we study ground-state properties in the system. The obtained results suggest the existence of a quantum phase transition between the Kitaev QSL and dimer-singlet states~[1]. To examine finite-temperature properties, we make use of the thermal pure quantum state approach. We clarify that the double-peak structure in the specific heat inherent in the Kitaev QSL is maintained even above the quantum phase transition. The present results suggest that the Kitaev QSL is stable against the interlayer interference. [1] H. Tomishige, J. Nasu, and A. Koga, Phys. Rev. B 97, 094403 (2018).

Crystal and electronic structures, as well as magnetic properties of the Ir$^{4+}$ hexahalides K$_2$IrCl$_6$ and K$_2$IrBr$_6$ will be presented. These compounds serve as rare experimental realizations of the ideal, undistorted IrX$_6$ octahedra and, consequently, reveal the $J_{\rm eff}=\frac12$ electronic state of Ir$^{4+}$. We show that K$_2$IrCl$_6$ retains its cubic symmetry down to low temperatures, whereas K$_2$IrBr$_6$ undergoes a sequence of symmetry-lowering structural phase transitions. Both compounds show signatures of frustrated magnetism driven by the fcc-lattice of the Ir$^{4+}$ ions. The relevant microscopic parameters and the role of Kitaev interactions in these compounds will be discussed.

Recent experiments [portnichenko2016] and quantum calculations [janson2014] have established tetrahedral Cu$_4$ spin triplet (S=1) clusters as the relevant spin entity in the formation of long-range chiral magnetic order in the charge-transfer insulator Cu$_2$OSeO$_3$. [seki2012,versteeg2016] This peculiar spin ordering leads to a rich spin excitation spectrum, consisting of spin excitations with inter- and intra-cluster character. [portnichenko2016] Here, we use time-resolved spontaneous Raman spectroscopy [versteeg2018] to simultaneously probe lattice and intra-cluster spin excitation dynamics in the helimagnetically ordered phase of Cu$_2$OSeO$_3$. As such, we obtain a picture of the photo-induced non-equilibrium dynamics which goes beyond the time-evolution of the average magnetic order parameter in Cu$_2$OSeO$_3$. The Raman-active spin excitations within the Cu$_4$ spin clusters soften on a time-scale of 200ps. The lattice thermalization, probed by the phonon Stokes intensity, takes place on a substantially faster time-scale of 50ps. The dissimilar time-scales points to a spin-lattice relaxation process predominantly taking place through low-energy inter-cluster excitations, while the high-energy intra-cluster excitations form a bottleneck for the long-term equilibration dynamics. On the 1.5ps time-scale we find an evidence of efficient coupling between optical phonons and the intra-cluster excitations, in agreement with the findings reported by Langner et al.[langner2017] Our results provide a new viewpoint of the non-equilibrium magnetization dynamics in the chiral magnet Cu$_2$OSeO$_3$, and demonstrate a novel method to measure net-zero magnetization dynamics in, for instance, helimagnets, cycloidal ordered magnets, and antiferromagnets. References: 1. Portnichenko et al., Nat. Commun 7, 10725 (2016) 2. Janson et al, Nat. Commun 5, 5376 (2014) 3. Seki et al. Science 336, 198 (2012) 4. Versteeg et al. Phys. Rev. B 94, 094409 (2016) 5. Versteeg et al. Struct. Dyn. 5 044301 (2018) 6. Langner et al. Phys. Rev. Lett. 119 107204 (2017)

We motivate torque magnetometry as key experimental probe for studying unconventional magnetic states in various quantum spin liquid (QSL) and Kitaev candidate materials. The magnetic torque is related to the angular derivative of the energy in a magnetic field, and therefore may serve as a direct probe of any order parameter that couples anisotropically to the field. For the triangular lattice organic QSL materials, we show that this allows torque to probe a variety of proposed scenarios[1], including proximity to states with antiferromagnetic or spin-chiral order. However, our analysis of recently reported experimental data[2] conclusively rules out these scenarios. Instead, we present a scaling approach for disorder-induced effects, and find that the predicted behaviour accounts for all features of the observed response, indicating an inhomogeneous valence bond glass ground state. For Jeff = 1/2 "Kitaev" materials, we highlight the varying effects of magnetic couplings arising at different orders, including g-anisotropies, Kitaev and related exchange interactions, and higher order ring-exchange terms[3]. We show how the relative strength of such terms may be distinguished by torque measurements, and provide some explanation of the ubiquitous saw-tooth angle dependencies recently noted[4] in such materials. [1] K. Riedl, et al. arXiv:1808.03868 (2018). [2] T. Isono, et al. Nature Comm. 7, 13494 (2016). [3] K. Riedl, et al. arXiv:1809.03943 (2018). [4] K. A. Modic, et al. arXiv:1807.06637 (2018).

Recently, Tanaka and Sato [1] discovered a series of manganese oxides $A$Mg4Mn6O15 ($A$ = K, Rb, Cs), which are ferromagnetic insulators with a cubic crystal structure. The Mn ions are fully spin-polarized in the ground state with a ferromagnetic transition temperature of about 170 K. The electric resistivity shows an insulating behavior in the entire temperature range observed. In our presentation, we show that a mechanism of insulating ferromagnetism similar to that of K$_2$Cr$_8$O$_{16}$ [2] also applies in this manganese series. Namely, using the density-functional-theory based electronic structure calculations, we demonstrate that the electronic state near the Fermi level may simply be described as a three-dimensional arrangement of the one-dimensional chains of O 2$p$ orbital and Mn 3$d$ orbital. These chains are ferromagnetic due to the double-exchange mechanism, and are distorted by the Peierls instability [3]. We thus conclude that these manganese oxides belong to a novel series of ferromagnetic Peierls insulators [4]. Refecences [1] T. Tanaka and H. Sato, J. Solid State Chem. 248, 150156 (2017). [2] T. Toriyama et al., Phys. Rev. Lett. 107, 266402 (2011). [3] S. Nishimoto and Y. Ohta, Phys. Rev. Lett. 109, 076401 (2012). [4] T. Yamaguchi et al., Phys. Rev. B 97, 161103(R) (2018).