Correlated Electrons in Transition-Metal Compounds:
New Challenges

Orbital molecules are weakly bonded clusters of transition metal ions within an orbitally ordered solid. The importance of these quantum states has become apparent in recent years following the discovery of ‘trimeron’ orbital molecules in the ground state of magnetite (Fe3O4). Determination of the full superstructure below the famous Verwey transition at 125 K showed that Fe2+/Fe3+ charge ordering occurs with a pronounced orbital ordering of Fe2+ states that leads to localization of electrons in the linear, three-Fe trimerons. CaFe3O5 provides a new example of electronic phase separation driven by trimeron formation. Vanadium oxides also provide many examples of orbital molecule orders, associated with NTE (negative thermal expansion) in the orbital polymer material V2OPO4. Persistence of large orbital molecules to high temperatures is discovered in the spinels AlV2O4 and the new analog GaV2O4.

Vortices are among the simplest topological structures, and occur whenever a flow field `whirls' around a one-dimensional core. Although ubiquitous to many branches of physics, vortex formation in the crystalline state is rare, since it is generally hampered by long-range interactions. Here, we present the discovery of a novel form of crystalline vortices in \emph{antiferromagnetic} (AFM) hematite ($\alpha$-Fe$_2$O$_3$) epitaxial films, in which the primary whirling parameter is the non-ferroics staggered magnetisation. Remarkably, ferromagnetic (FM) topological objects known as half-skyrmions or \emph{merons} with the same vorticity and winding number of the $\alpha$-Fe$_2$O$_3$ vortices are imprinted onto an ultra-thin Co ferromagnetic over-layer by exchange proximity. Our data suggest that the vortex/meron pairs are relatively robust well beyond the Co coercive field, but can be manipulated by the application of a larger (H$_{\parallel}$~100mT) in-plane magnetic field H$_{\parallel}$, giving rise to large-scale vortex-antivortex annihilation.

There is a rapidly expanding field over the last few decades that deal with emergent properties at a variety of interfaces formed in heterostructured materials. Specifically, it has been shown that an atomically flat interface between two highly insulating oxide materials can exhibit properties not found in either of the bulk systems defining the interface, such properties covering realms of magnetic-nonmagnetic transitions, insulator-metal transitions, emergence of superconductivity, depending on specific systems and synthesis conditions. Interestingly, there are only few investigations to probe the nature of the charge carriers in such systems, arising from difficulties inherent in the problem. It is in general difficult to probe directly the nature of such interface states since these are typically buried under a depth and represent a very small volume fraction of the entire sample. Photoemission spectroscopy, capable of directly mapping out the electronic structure, has only been used in on-resonance condition to enhance the spectral intensity manifold, thereby making the signal visible. However, this has the potential problem of distorting spectral features in an uncontrolled manner, since the resonance condition itself depends on the energy state of the electron. We present layer-resolved electronic structures of two oxide heterostructures, namely the originally discovered LaAlO3-SrTiO3 as well as LaTiO3-SrTiO3, using non-resonant photoemission and contrast strikingly different behaviours between the two systems.

Topological insulators are seemingly ordinary insulators in the bulk, but have guaranteed surface states that are gapless and present the promise of unique functionalities, viz. next generation electronic devices with smaller dimension and much less use of power. If these materials break time-reversal symmetry, more specific properties emerge: a quantized anomalous Hall effect that takes strong advantage of the spin of the electron. We will discuss lessons learned from two types of systems, both of which incorporate Khomskii physics: the naturally occurring compound $BaFe_2(PO_4)_2$ (BFPO), and the designed system consisting of $Ru^{3+}$ on a honeycomb lattice (2LRO). Both systems contain Chern insulting phases in their multidimensional phase diagram. Both display competition between many energy scales including: Coulomb repulsion U, Hund's J, intersublattice hopping t, crystal subfield splitting $\Delta$ lattice distortion $\delta$t, spin-orbit coupling $\xi$, and strain, all accounted for within the rotationally invariant DFT+U approach. BFPO is a rare Ising ferromagnetic insulator that we find to be near, but not within, a Chern insulating phase in its ground state; its large Ising anisotropy and large orbital moment are reproduced correctly. While displaying related transitions between Chern and trivial insulator phases as the entire set of degrees of freedom are relaxed and practically all symmetries are broken, 2LRO (a [111] perovskite bilayer of $LaRuO_3$), unlike BFPO, settles down into a Chern insulator ground state with a calculated and potentially very useful gap of 130 meV. Crucial parts of both stories involve Khomskii physics ("blame it on Daniel"). We theorists have successfully written a grant for experimental testing of the predictions. Spoiler alert: the results of the (rather challenging) synthesis and characterization are not yet in.

We will review recent inelastic experiments in the triangular lattice $S=1/2$ Heisenberg antiferromagnet, Ba3CoSb2O9 [1-5], revealing large deviations from the dynamical spin structure factor obtained from non-linear spin wave theory (NSWT). We will see that, while NSWT works very well inside the magnetic field induced magnetization plateau (up-up-down phase) [5], it fails at zero magnetic field (120-degree ordering). This observation strongly suggests that the failure of a semiclassical treatment is due to strong quantum fluctuations, which are indeed expected for frustrated 2D antiferromagnets. In an attempt of finding alternative ways of modelling the of ordered low dimensional antiferromagnets, we will derive the zero temperature of the triangular lattice Heisenberg model using a Schwinger Boson approach that includes the Gaussian fluctuations ($1/N$ correction) around the saddle point solution [5]. While the ground state of this model exhibits a well-known 120 degree magnetic ordering, the excitation spectrum revealed by has a strong quantum character, which is not captured by low-order $1/S$expansions. The low-energy magnons consist of two-spinon bound states confined by the gauge fluctuations of the auxiliary fields. This composite nature of the magnons potentially leads to an internal structure of the magnon peaks. In addition, the continuum of high-energy spinon modes extends up to three times the single-magnon bandwidth. [1] Takuya Susuki, et al., Phys. Rev. Lett. 110, 267201 (2013). [2] Koutroulakis, G. et al., Phys. Rev. B 91, 024410 (2015). [3] Ma, J. et al., Phys. Rev. Lett. 116, 087201 (2016). [4] Ito, S. et al., Nat. Comm. 8, 235 (2017). [5] Y. Kamiya, et al., arxiv/1701.07971, Nat. Comm., in press. [6] E. A. Ghioldi, et al., arxiv/1802.06878.

From the early days of the ``Renaissance'' of the Field of Multiferroics I have enjoyed enthusiastic and stimulating discussions with Daniel Khomskii, and benefited tremendously from his extensive knowledge of the Russian literature. After some years, our discussions evolved from his pointing out (very helpfully) that my favorite ideas had been studied already in Moscow in the '50s, as I progressed to ideas that had been discovered in St. Petersburg in the '70s. Recently, Daniel paid me the strongest possible compliment, when he commented that one of our projects was interesting enough to have been done in Moscow in the '50s but to his surprise it had not been. I will talk about this project -- our search for a magnetic monopole at a magnetoelectric surface -- today.

A prerequisite for a microscopic understanding of the physical properties of materials is the identification of quantum numbers that characterize, for example, the charge, spin, and orbital degrees of freedom of the atomic constituents. This is especially true for strongly correlated or narrow band systems. While invaluable insight has been obtained using a wide range of x-ray based spectroscopic techniques, most of these are based on dipolar electronic transitions and have as such limitations, e.g. asymmetries with higher than twofold rotational symmetry cannot be detected (unless it is accompanied by a sufficiently large energy difference). Here we utilize the opportunities provided by a new technique, namely non-resonant x-ray scattering (NIXS). This photon-in-photon-out technique with hard x-rays has become feasible thanks to the high brilliance of modern synchrotrons and advanced instrumentation. The available large momentum transfers allows for the study of excitations that are well beyond the dipole limit. While so far most of the NIXS studies were carried out on powder samples, it becomes very clear that the directional dependence of the momentum transfer observed in experiments on single crystals has the potential to give a very detailed insight into the ground-state symmetry of the ion of interest. It is this very aspect, i.e. the direction dependence of the scattering function beyond the dipole limit, that we utilize for our study of strongly correlated systems for which the orbital symmetry remained elusive so far [1-6]. The interpretation of the spectra is straightforward and quantitative, facilitated also by the fact the multipolar excitations are more excitonic than the dipole ones. Our excitement about NIXS is further enhanced by the fact that this element specific technique is also bulk sensitive, requires only tiny samples not larger than 0.1 mm, and allows for more demanding sample environments. We now have also the first results from our own Max Planck inelastic scattering beamline at PETRA III in Hamburg. *Work done in close collaboration with Martin Sundermann and Andrea Severing from the Physics Institute 2, University of Cologne, and with Maurits Haverkort, Institute for Theoretical Physics, Heidelberg University. [1] T. Willers, F. Strigari, N. Hiraoka, Y. Q. Cai, M.W. Haverkort, K.-D. Tsuei, Y. F. Liao, S. Seiro, C. Geibel, F. Steglich, L. H. Tjeng, and A. Severing, Phys. Rev. Lett. 109, 046401 (2012). [2] J.-P. Rueff, J.M. Ablett, F. Strigari, M. Deppe, M.W. Haverkort, L.H. Tjeng, and A. Severing, Phys. Rev. B 91, 201108(R) (2015). [3] M. Sundermann, F.Strigari, T. Willers, H. Winkler, A. Prokofiev, J.M. Ablett, J.-P. Rueff, D. Schmitz, E. Weschke, M. Moretti Sala, A. Al-Zein, A. Tanaka, M.W. Haverkort, D. Kasinathan, L.H. Tjeng, S. Paschen, and A. Severing, Sci. Rep. 5:17937 (2015). [4] M. Sundermann, M.W. Haverkort, S. Agrestini, A. Al-Zein, M. Moretti Sala, Y.K. Huang, M. Golden, A. deVisser, P. Thalmeier, L.H. Tjeng, and A. Severing, PNAS 113 (49), 13898 (2016) [5] M. Sundermann, K. Chen, H. Yavaç, H. Lee, Z. Fisk, M. W. Haverkort, L. H. Tjeng, and A. Severing, Europhys. Lett. 117 (2017) 17003. [6] M. Sundermann, H. Yavas, K. Chen, D. J. Kim, Z. Fisk, D. Kasinathan, M. W. Haverkort, P. Thalmeier, A. Severing and L. H. Tjeng, Phys. Rev. Lett. 120 (2018) 016402.

In high oxidation state oxides like the trivalent Nickel oxides, tetravalent Co and Fe oxides as well as the parent superconductors $BaBiO_3$ and $SrBiO_3$ and High Tc hole doped cuprates, the cation electron affinity in the formal valence could end up larger than the O2-ionization potential leading to a so called negative charge transfer gap. If the charge transfer energy is strongly negative, then we should really adopt starting electronic configurations such as Ni2+ rather than 3+ or Bi 3+ rather than 4+ with compensation holes in the O 2p valence band for charge neutrality. If in addition the lowest energy cation ionization states are strongly hybridized with the valence O 2p states the low energy scale electronic structure and be well described by a molecular orbital type of approach (1,2). This is a new approach to the Wannier function description (3) but with explicit inclusion of the O states which provides a natural path to inclusion of the electron phonon coupling, charge density wave formation, potential bipolaron formation and paring interactions in superconductors. We discuss recent developments in this approach and show that the effective electron phonon coupling involving these molecular like orbitals is much stronger than that estimated from density function approaches. We also show that this leads to Peierls like charge density wave like ground states and we describe how the electron phonon coupling involving the hopping integrals rather than the on-site energies evolves into a large effective attractive interaction between low energy scale electrons. I will also briefly describe how these effects lead to our coelution that the ion battery material $LiNiO_2$ should be viewed as an “entropy-stabilized charge- and bond-disproportionated glass”.

Magnetic Weyl Semimetals! Claudia Felser1, Johannes Gooth1, Kaustuv Manna1, Enke Lui1 and Yan Sun1 1Max Planck Institute Chemical Physics of Solids, Dresden, Germany (e-mail: felser@cpfs.mpg.de) Topology a mathematical concept became recently a hot topic in condensed matter physics and materials science. One important criteria for the identification of the topological material is in the language of chemistry the inert pair effect of the s-electrons in heavy elements and the symmetry of the crystal structure [1]. Beside of Weyl and Dirac new fermions can be identified compounds via linear and quadratic 3-, 6- and 8- band crossings stabilized by space group symmetries [2]. Binary phoshides are the ideal material class for a systematic study of Dirac and Weyl physics. Weyl points, a new class of topological phases was also predicted in NbP, NbAs. TaP, MoP and WP2. [3-7]. In magnetic materials the Berry curvature and the classical AHE helps to identify interesting candidates. Magnetic Heusler compounds were already identified as Weyl semimetals such as Co2YZ [8-10], in Mn3Sn [11,12] and Co3Sn2S2 [13]. The Anomalous Hall angle helps to identify even materials in which a QAHE should be possible in thin films. Besides this k-space Berry curvature, Heusler compounds with non-collinear magnetic structures also possess real-space topological states in the form of magnetic antiskyrmions, which have not yet been observed in other materials [14]. [1] Bradlyn et al., Nature 547 298, (2017) arXiv:1703.02050 [2] Bradlyn, et al., Science 353, aaf5037A (2016). [3] Shekhar, et al., Nature Physics 11, 645 (2015) [4] Liu, et al., Nature Materials 15, 27 (2016) [5] Yang, et al., Nature Physics 11, 728 (2015) [6] Shekhar, et al. preprint arXiv:1703.03736 [7] Kumar, et al., Nature Com. , preprint arXiv:1703.04527 [8] Kübler and Felser, Europhys. Lett. 114, 47005 (2016) [9] Chang et al., Scientific Reports 6, 38839 (2016) [10] Kübler and Felser, EPL 108 (2014) 67001 (2014) [11] Nayak, et al., Science Advances 2 e1501870 (2016) [12] Nakatsuji, Kiyohara and Higo, Nature 527 212 (2015) [13] Liu, et al. preprint arXiv:1712.06722 [14] Nayak, et al., Nature 548, 561 (2017)

Triplet pairing in Sr$_{2}$RuO$_{4}$ was initially suggested based on the hypothesis of strong ferromagnetic spin fluctuations, but so far there is little evidence for these. Magnetic excitations are dominated by antiferromagnetic incommensurate excitations, but these do not change when entering into the superconducting state for energies well below twice the superconducting gap. This observation renders their dominant role in the superconducting pairing rather unlikely. Using polarized inelastic neutron scattering, we accurately determine the full spectrum of spin fluctuations in Sr$_{2}$RuO$_{4}$. Besides the well-studied incommensurate magnetic fluctuations we do find a sizeable quasiferromagnetic signal, quantitatively consistent with all macroscopic and microscopic probes. We use this result to address the possibility of magnetically-driven triplet superconductivity in Sr$_{2}$RuO$_{4}$. We conclude that, even though the quasiferromagnetic signal is stronger and sharper than previously anticipated, spin fluctuations alone are not enough to generate a triplet state strengthening the need for additional interactions. The quasiferromagnetic fluctuations in Sr$_{2}$RuO$_{4}$ considerably differ from the expectations for a nearly ferromagnetic material. In contrast SrRuO$_{3}$ exhibits ferromagnetic order and true ferromagnetic magnons, that show a strange temperature dependence for the anisotropy gap and for the stiffness constant possibly related to the impact of Weyl fermions.

Orbital degree of freedom is one of the least understood degrees of freedom compared with other threes: spin, charge, and lattice. Nonetheless, it has demonstrated itself that it is at the very heart of several intriguing problems of condensed matter physics, and hence has attracted significant attentions over the past decades or so. In this talk, I am going to highlight how the orbital degree of freedom plays an important role in the metal-insulator transition of several Ru compounds covering several aspects of its physics: Tl2Ru2O7 [1], Li2RuO3 [2, 3], SrRuO3 thin film [4]. [1] Seongsu Lee, et al., Nature Materials 5, 471-476 (2006). [2] J. Park, et al., Scientific Reports 6, 25238 (2016). [3] S. Yun, et al., to be submitted. [4] S. Kang, et al., to be submitted.

Correlatioin-driven metal-insulator transitions often involve orbital ordering, which couples strongly both to local (octahedral distortion) and long wavelength (strain) lattice distortions. I present a theory of the intertwined electronic and lattice transitions in Ca2RuO4 and show how it accounts for the dramatic variation of the metal-insulator transition on epitaxial strain and for the stripe patterns observed at the metal-insulator interface in materials under current flow. Generalizations to Ca3Ru2O7, to VO2, and to other correlated electron materials will also be presented.

I this talk I will review recent work deeply linked to collaborations with Daniel Khomskii on the electronic and magnetic properties of two-dimensional honeycomb-lattice materials ranging from Li$_2$RuO$_3$, Li$_2$RhO$_3$, Na$_2$IrO$_3$, $\alpha$-Li$_2$IrO$_3$ to RuCl$_3$ where dimers, quasi-moleculars orbitals, Kitaev physics and possible novel states of matter emerge. [1] Hermann et al. PRB 97, 020104(R) (2018). [2] Biesner et al. arXiv:1802.10060 [3] Winter et al. PRL 120, 077203 (2018). [4] Kimber et al. PRB 89, 081408(R) (2014). [5] Foyevtsova et al. PRB 88, 035107 (2013). [6] Mazin et al. PRL 109, 197201 (2012).

Kitaev's honeycomb-lattice spin-1/2 model has become a paradigmatic example for $Z_2$ quantum spin liquids, both gapped and gapless. Here we study the fate of these spin-liquid phases in differently stacked bilayer versions of the Kitaev model. Increasing the ratio between the inter-layer Heisenberg coupling $J_\perp$ and the intra-layer Kitaev couplings $K_{x,y,z}$ destroys the topological spin liquid in favor of a paramagnetic dimer phase. We study phase diagrams as a function of $J_\perp/K$ and Kitaev coupling anisotropies using Majorana-fermion mean-field theory, series expansions, and effective models. We find that the phase diagrams depend sensitively on the nature of the stacking and anisotropy strength. While in some stackings and at strong anisotropies we find a single transition between the Kitaev and dimer phases, other stackings are more involved: Most importantly, we prove the existence of two novel macro-spin phases which can be understood in terms of Ising chains which can be either coupled ferromagnetically, or remain degenerate, thus realizing a classical spin liquid. In addition, our results suggest the existence of a flux phase with spontaneous inter-layer coherence.

The recent observation [1] of a half-integer quantized thermal Hall effect in $\alpha$-RuCl$_3$ is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. In the talk we will discuss why it is possible to observe an approximately quantized Hall effect in the presence of phonons [2]. In the experiment phonons carry 99.9\% of the heat and the coupling to phonons destroys ballistic transport at the edge channels. Nevertheless, the thermal Hall conductivity remains approximately quantized and we argue, that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The coupling to phonons activates a gravitational anomaly which pumps heat in transversal direction into the phonon system. Furthermore, we calculate the intrinsic Hall effect of acoustic phonons in a spin liquid and argue that it gives only a tiny correction to the quantized thermal Hall effect. [1] Y. Kasahara et al., Nature 559, 227-231 (2018) [2] Y. Vinkler-Aviv, A. Rosch, Phys. Rev. X 8, 031032 (2018)

Requirements to "good multiferroics" are tough. They are supposed to have a spontaneous magnetization and polarization, preferably parallel to each other, with a strong magnetoelectric coupling between them. Inevitably, this leads to a multiferroic state that is described by a very complex set of order parameters – complex enough to provide the symmetry degrees of freedom to fulfil so many requirements at once. With the focus on electric-field-controlled magnetic order, it goes unnoticed that these degrees of freedom will permit many functionalities other than a refined magnetoelectric coupling. In my talk, I will describe the quest for such functionalities in our group. Here are some examples for the cases I may discuss: (i) For the multiferroic hexagonal manganites I will show that amplitude and phase of the order parameter may exhibit different coherence length. Taking this into account, we resolve the long-standing controversial question of how exactly the topological ferroelectric state in this system arises. (ii) The emergence of a magnetic bulk phase transition out of the spin structure in the domain walls is shown for (Tb,Dy)FeO$_3$. (iii) Inversion of a ferroelectric and a ferromagnetic multi-domain state in homogeneous external fields is demonstrated: In each domain, the direction of the order parameter is reversed but the domain pattern as such is left untouched.

Due to the presence of sizable nearest-neighbor bond-dependent Ising interactions between effective spin-1/2 local moments, hexagonal 4d and 5d metal oxides have been intensively scrutinized as candidates for the realization of the Kitaev model, although deviation from ideal bond symmetry and presence of additional exchange interactions drive these materials away from the Kitaev limit. We discuss recent hydrostatic pressure experiments on \alpha- and \beta-Li2IrO3 [1,2], which indicate much richer physics, including by off-diagonal exchange induced classical spin liquid behavior, as well as structural dimerization. [1] V. Hermann, M. Altmeyer, J. Ebad-Allah, F. Freund, A. Jesche, A.A. Tsirlin, M. Hanfland, P. Gegenwart, I.I. Mazin, D.I. Khomskii, R. Valentí, C.A. Kuntscher, Phys. Rev. B 97, 020104(R) (2018). 2] M. Majumder, R.S. Manna, G. Simutis, J.C. Orain, T. Dey, F. Freund, A. Jesche, R. Khasanov, P.K. Biswas, E. Bykova, N. Dubrovinskaia, L.S. Dubrovinsky, R. Yadav, L. Hozoi, S. Nishimoto, A.A. Tsirlin, P. Gegenwart, arXiv:1802.06819, Phys. Rev. Lett, in press.

This talk offers a brief review of current experimental studies of iridates [1] and emphasize discrepancies between experimental confirmation and theoretical proposals that address superconducting, topological and quantum spin liquid phases. It then reports our recent study on electrical-current controlled behavior in iridates [2]. Electrical control of structural and physical properties is a long-sought, but elusive goal of contemporary science and technology. This work demonstrates that a combination of strong spin-orbit interactions and a canted antiferromagnetic Mott state is sufficient to attain that goal and points the way to novel possibilities for functional materials and devices [2]. References: 1. “The Challenge of Spin-Orbit-Tuned Ground-States in the Iridates: A Key Issues Review”, Gang Cao and P. Schlottmann, Reports on Progress in Physics 81 042502 (2018); https://doi.org/10.1088/1361-6633/aaa979 2. “Electrical Control of Structural and Physical Properties via Spin-Orbit Interactions in Sr2IrO4”, G. Cao, J. Terzic, H. D. Zhao, H. Zheng, Peter Riseborough, L. E. DeLong, Phys. Rev. Lett. 120, 017201 (2018); https://doi.org/10.1103/PhysRevLett.120.017201; Editor’s Suggestion

For the past decade, condensed matter physics has witnessed a tremendous shift from the understanding of materials based on bands and bonds towards non-trivial geometric properties of the symmetry protected bands where Dirac or Weyl equations govern electrons. In parallel, a new paradigm of quantum topology (QT) has emerged. This QT framework encompasses Majorana and Haldane states, various quantum spin liquids, FQHE and all that characterized by topological order. From the materials standpoint, however, the fundamental challenge is to discover broad materials architectures which can host these exotic phases. In this talk, I will present a recently developed approach collectively known as the geometrical lattice engineering and illustrate how potential quantum spin liquid and QAHE can be realized in practice.

Novel quantum phases of matter arising in heavy transition metal compounds due to the strong relativistic spin-orbit coupling have attracted a lot of interest recently. Current experiments on the molybdenum [1-3] and osmium [4-6] based double perovskites, suggest that unusual ordered and disorder quantum states are hosted by these materials. We formulate and study a microscopic spin-orbital model for a family of cubic double perovskites with $d^1$ ions occupying frustrated fcc sublattice. Relying on variational approaches and a complimentary analytical analysis, we find a rich variety of phases, emerging from the interplay of Hund’s coupling and spin-orbit interaction. The phase digram contains non-collinear ordered states, with or without net moments, and, remarkably, a large window of magnetically disordered spin-orbit dimer phase [7]. We discuss the physical origin of the unusual amorphous valence bond state experimentally suggested for Ba$_2${\it B}MoO$_6$ ({\it B}=Y,Lu), and predict possible ordered patterns in Ba$_2${\it B}OsO$_6$ ({\it B}=Na,Li) compounds. Additionally, we provide a theoretical background for the available experimental observation in these materials [7]. The proposed physical picture applies to a broad family of heavy transition metal compounds and helps uncovering the origins of magnetism in spin-orbit assisted Mott insulators. [1] T. Aharen, et al, Phys. Rev. B, 81, 224409 (2010). [2] M. de Vries, et al, Phys. Rev. Lett., 104, 177202 (2010). [3] M. de Vries, et al, New Journal of Physics, 15, 043024 (2013). [4] K. Stitzer, et al, Solid State Sciences, 4, 311 (2002). [5] A. Erickson, et al, Phys. Rev. Lett., 99, 016404 (2007). [6] A. Steele, et al, Phys. Rev. B 84, 144416 (2011). [7] J.Romhanyi, L. Balents, and G. Jackeli Phys. Rev. Lett. 118, 217202 (2017).

Spin-orbit (SO) Mott insulators are regarded as a new paradigm of magnetic materials, whose properties are largely influenced by the SO coupling and featured by highly anisotropic bond-dependent exchange interactions between the spin-orbital entangled Kramers doublets, as manifested in 5d iridates and 4d ruthenates. I will show that a very similar situation can be realized in cuprates, when the Cu$^{2+}$ ions reside in a tetrahedral environment, like in spinel compounds. A special attention will be paid to CuAl$_2$O$_4$, which was experimentally found to retain cubic structure and does not show any long-range magnetic ordering down to very temperatures (0.5 K). We argue that these are the strong Coulomb correlations and the spin-orbit coupling, which conspire to suppress the Jahn-Teller distortions in CuAl$_2$O$_4$. The spin-orbit-entangled $j_{eff}$=1/2 state is then naturally realizes in the situation of $t_{2g}^5$ configuration and degenerate $t_{2g}$ subshell. This in turn explains unusual magnetic properties of CuAl$_2$O$_4$. Using first-principles electronic structure calculations, we construct a realistic model for the diamond lattice of the Cu$^{2+}$ ions in CuAl$_2$O$_4$ and show that the magnetic properties of this compound are largely controlled by anisotropic compass-type exchange interactions that dramatically modify the magnetic ground state by lifting the spiral spin-liquid degeneracy and stabilizing a commensurate single-q spiral.

I will review some of the new approaches we have developed in spin and time-resolved ARPES, and their application to unconventional superconductors and Dirac materials.

Fusion of strong correlation and quantum topology may provide a new arena for materials physics toward emerging quantum technology. Here, we target the Ir-oxides with orthodox structures of perovskite ({\it A}IrO$_{3}$) and pyrochlore ({\it R}$_{2}$Ir$_{2}$O$_{7}$), which are both characterized by strong electron correlation and large spin-orbit coupling. In those compounds, intriguing magneto-transport properties emerge in the proximity of the Mott transition, such as unusually high electron mobility, large thermoelectric effect, large topological Hall response, and large magnetoresistance in the symmetry-protected Dirac semimetal states of {\it A}IrO$_{3}$ and the magnetic-order-induced multiple Weyl semimetal states of {\it R}$_{2}$Ir$_{2}$O$_{7}$.

Topology induces remarkable new phases of electronic matter with emergent types of particles such as Weyl and Majorana fermions. To *observe* these particles is trickier! I will discuss some recent work showing some ways they can be revealed in transport, and give connections to recent experiments on topological semimetals and quantum spin liquids. I may also discuss topological effects in twisted bilayer graphene, and their relation to flat band correlation physics.

The electron-phonon interaction in solids is considered to be mainly related to the charge degrees of freedom. However, spin-phonon interaction is also relevant to variety of phenomena in magnets. Especially, the modulation of spin-orbit interaction by phonons recently turns to be strong both experimentally and theoretically. I this talk, I will discuss the interplay between magnetism and phonon in several situations of interests including the phonon-Hall effect and orbital magnetism, nonreciprocal spin-phonon propagation, and ultrasonic attenuation in magnetic monopole system.

The fundamental electronic structure of transition-metal oxides (TMOs) is characterized by on-site Coulomb interaction $U$ between d electrons and the charge-transfer energy $\Delta$ from the oxygen 2p to transition-metal d orbitals [1]. In TMOs with small or negative $\Delta$, the effect of oxygen 2p orbitals becomes relevant for understanding of their physical properties. The exotic electronic structure of such TMOs can be investigated due to combination of advanced crystal growth and x-ray spectroscopy techniques. In the present work, we focus on the effect of oxygen holes in novel perovskite-type TMOs in which both A-site and B-site metals are electronically active. In BiNiO$_3$ and PbCoO$_3$, valence instability of Bi or Pb is coupled with spin-charge-orbital orderings of Ni or Co 3d electrons, and provides giant negative thermal expansion [2,3]. Recent x-ray photoemission measurements indicate that the unique valence states of BiNiO$_3$ and PbCoO$_3$ are stabilized by O 2p hole transfer between the Ni-O or Co-O bond and the Bi-O or Pb-O bond. In a similar manner, A-site ordered perovskites such as CaCu$_3$Co$_4$O$_{12}$ exhibit charge transfer between A-site and B-site transition-metal ions which is mediated by O 2p holes involved in the A-O and B-O bond formations [4,5]. The effect of oxygen 2p holes on the various valence and magnetic transitions in TMOs will be discussed in details based on the results of x-ray spectroscopy measurements and model calculations. The authors would like to thank Prof. M. Azuma, Prof. Y. Shimakawa, Prof. M. Takano, Prof. A. Fujimori, Prof. D. I. Khomskii, Prof. G. A. Sawatzky for the long term collaborations and Mr. K. Murota, Mr. K. Yamamoto, and Mr. J. Komiyama for the contributions to the recent works. [1] D. I. Khomskii, Transition Metal Compounds (Cambridge University Press, 2014). [2] M. Azuma et al., Nat. Commun. 2, 347 (2011). [3] Y. Sakai et al., J. Am. Chem. Soc., 139, 4574 (2017). [4] T. Mizokawa et al., Phys. Rev. B 80, 125105 (2009). [5] M. Mizumaki et al., Phys. Rev. B 84, 094418 (2011).

Oxides vs peroxides D.I.Khomski II.Physikalisches Institut, Universitaet zu Koeln, Germany In this talk I will discuss some effects occurring in transition metal compounds with small or negative charge transfer gap and with large contribution of ligand (e.g. oxygen) holes. In this case, when a lot of holes are transferred to oxygens (or in general to ligands, e.g. S, Se, Te) one of the options is that instead of the usual oxides, like say Ti4+(O2-)2 one could form peroxides, e.g. with pyrite structure, such as for example Mg2+(O2)2- or Fe2+(S2)2-. This is a very interesting class of compounds, having nontrivial magnetic and sometimes orbital properties. Specifically we consider the recently synthesized material FeO2 [1], which, according to our theoretical calculations [2], is a system “in between” the usual dioxides like TiO2, VO2, and peroxides M2+(O2)2- : in FeO2 the valence of Fe is neither 4+ as in dioxides nor 2+ as in pyrite, but 3+. This specific material can play a very important role in the physics of the deep Earths mantle, especially at the early stages of the Earths history. Peroxides can also be important ingredients in the attempts to make better cathode materials for rechargeable batteries, and in many other applications. [1] Hu, Q. et al. ‘’FeO2 and FeOOH under deep lower-mantle conditions and Earth’s oxygen–hydrogen cycles’’, Nature 534, 241–244 (2016). [2] S.V. Streltsov, A.O. Shorikov, S.L. Skornyakov, A.I. Poteryaev, D.I. Khomskii, ‘’ Unexpected 3+ valence of iron in FeO2 , a geologically important material lying "in between" oxides and peroxides ‘’, Sci. Rep. 7, 13005 (2017)

When the motion of an object in one direction is different from that in the opposite direction is called non-reciprocal directional dichroism (or simply a non-reciprocal effect). The object can be electron, phonon (lattice wave), magnon (spin wave), or light in crystalline solids, and the best known example is non-reciprocal charge transport (i.e. diode) effects in p-n junctions, where a built-in electric field (E) breaks the directional symmetry. In addition to p-n junctions, numerous technological devices such as optical isolators or spin current diodes can utilize non-reciprocal effects. We, fist, insource the concept of symmetry-Operational Equivalence (SOE). Then, we will discuss how non-reciprocal effects can be understood in terms of SOE. Furthermore, we will demonstrate that the SOE approach can readily explain various mechanisms for multiferroicity with magnetism-induced electric polarization.

TANTALIZING SRONTIUM TITANATE A. Stucky, Willem Rischau, Dorota Pulmannova, G. Scheerer, Z. Ren, D. Jaccard, J.-M. Poumirol, C. Barreteau, E. Giannini and D. van der Marel* University of Geneva, SWITZERLAND * Presenting Author, E-mail: dirk.vandermarel@unige.ch SrTiO3 in its’ pristine state is a band insulator. Doping with 1 electron per 10'000 formula units suffices to render the material superconducting. The maximum Tc of 0.5 Kelvin occurs for about 1 percent doping. The doped electrons are coupled to the lattice parameters, and from a wealth of experiments it is known that this causes a factor of two mass enhancement, corresponding to the limit of large -and highly mobile-polarons [1]. The pairing interaction in this limit has significant momentum and energy dependence, a state of affairs which is appropriately captured by the Kirznits-Maksimov-Khomskii formalism [2]. The insulating parent compound can be made ferroelectric by substitution 18O on the oxygen sites [3,4]. Recently it has been suggested that superconductivity may be mediated by coupling to fluctuations of the ferro-electric order parameter, and that this results in an anomalous isotope effect [5]. Inspired by this prediction we carried out studies where we substituted 18O for 16O in SrTiO3, and observed a very strong enhancement of Tc [6,7]. The observed isotope effect is more than a factor 20 stronger than the BCS prediction and, even more tantalizing, it is of opposite sign. While this observation is in agreement with Ref. [5], the 18O-induced Tc enhancement is also a consequence of polaronic band narrowing [6,8]. Clearly the last word hasn’t been said on the puzzle of superconductivity in doped SrTiO3. References 1. For a review see D. van der Marel et al., Phys. Rev. B 84, 251 11 (2011). 2. D. A. Kirzhnits, E. G. Maksimov and D. I. Khomskii, J. Low Temp. Phys. 10, 79 (1973). 3. K. A. Mueller, H. Burkard, Phys. Rev. B, 19, 3593-3602 (1979). 4. S. E. Rowley et al., Nat. Phys. 10, 367-372 (2014). 5. J. M. Edge et al., Phys. Rev. Lett. 115, 247002 (2016). 6. A. Stucky et al.; Scientific Reports 6, 37582 (2016). 7. W. Rischau et al.; to be published (2018). 8. A. S. Alexandrov, Phys. Rev. B 46, 14932 (1992).

We propose the concept of hybridization-switching induced Mott transition which is relevant to a broad class of $ABO_3$ perovskite materials including $BiNiO_3$ and $PbCrO_3$ which feature extended 6s orbitals on the A-site cation (Bi or Pb). Using ab initio electronic structure and slave rotor theory calculations, we show that such systems exhibit a breathing phonon driven A-site to oxygen hybridization-wave instability which conspires with strong correlations on the B-site transition metal ion (Ni or Cr) to induce a Mott insulator. In contrast to perovskites with passive A-site cations, these Mott insulators with active A-site orbitals are shown to undergo a pressure induced insulator to metal transition accompanied by a colossal volume collapse due to ligand hybridization switching. Work carried out in collaboration with Atanu Paul, Anamitra Mukherjee, Indra Dasgupta, Arun Paramekanti

The undoped cuprates display a Mott insulating antiferromagnetically ordered ground state whose excitations to first order can be described by simple spin-wave theory. I will present 3 extensions to this picture: i) a quantum effect around the $(0,\pi)$ zone boundary point, which indicates spinon-deconfinement or strong spin-wave interaction; ii) deriving the spin-wave dispersion by projecting an effective one-band Hubbard model allow quantitative comparison of hopping in different cuprate families; iii) Finally we point out that inserting the thermal and zero-point ionic motion into expressions for distance and angle dependence of $t$ and $J$ lead to significant modulations, posing the question as to whether lattice effects need to be included when describing magnetism of cuprates.

Mott insulators with competing Heisenberg exchange interactions form a new class of materials where topological magnetic defects, such as skyrmions, can exist in absence of inversion symmetry breaking [1-4]. Skyrmions in centrosymmetric materials have more degrees of freedom and show more complex dynamics than skyrmions in chiral magnets. In addition, the electric polarization induced by non-collinear spin textures couples the topological magnetic defects to an applied electric field [5]. This magnetoelectric coupling allows for an electric control of skyrmions in Mott insulators accompanied by low energy losses. In my talk I will discuss stability, dynamics and ferroelectric properties of skyrmions and merons in frustrated magnets. I will also discuss materials that can host these topological defects. [1] T. Okubo, S. Chung and H. Kawamura, Phys. Rev. Lett. 108, 017206 (2012). [2] A. O. Leonov and M. Mostovoy, Nature Commun. 6, 8275 (2015); 8, 14394 (2017). [3] S. Hayami, S.-Z. Lin, and C. D. Batista, Phys. Rev. B 93, 184413 (2016). [4] Y. A. Kharkov, O. P. Sushkov and M. Mostovoy, Phys. Rev. Lett. 119, 207201 (2017). [5] S-W. Cheong and M. Mostovoy, Nature Materials 6, 13 (2007).

With DK and other co-workers, we have been co-authoring 10 papers (decathlon). Starting from our common results, obtained mostly on manganites and cobaltites, including spin blockade [1], quantum tunnelling of the magnetization [2] or magnetothermopower [3], recent results will be shown. First, cobaltites and sulphides, crystallizing in structures derived from delafossite, will be chosen: 2D metals (Fig.1), bad metals and multiferroics [4]. Second, ferrites containing Jahn-Teller $Fe^{2+}$ as the "429" $Fe_4(Nb/Ta)_2O_9$ phases [5] or the $Fe^{2+}:Fe^{3+}$ containing $Fe_3BO_5$ vonsenite [6] will be taken as examples to illustrate the ferrites richness for multiferroic or magnetoelectric properties. Most of the common work with DK was made possible through several EU projects including OXSEN, SCOOTMO and SOPRANO. [1] A Maignan et al, Phys Rev Lett 93, 026401 (2004) [2] A Maignan et al, J Mater Chem 14, 1231 (2004) [3] A Maignan et al, J Phys : Cond Matter 15, 2711 (2003) [4] R. Daou et al, Sc Techn of Adv Mater, 18, 919 (2017) [5] A Maignan and C Martin, Phys Rev B 97, 161106(R) (2018) ; Phys Rev Mater (2018) [6] A. Maignan et al., J. of Solid State Chem., 246 209 (2017)

The physics of oxide heterostructures is often governed by electronic correlations, implying that charge, orbital and spin degrees of freedom are simultaneously present. The combination of density functional theory and dynamical mean-field theory, DFT+DMFT, is a state-of-the-art method to address such complicated cases [1]. Recently, (111) heterostructures came into the focus as prospective correlated analogs of graphene: perovskite bilayers grown in the [111] direction form a buckled honeycomb lattice. Here, we apply DFT+DMFT to explore the electronic, magnetic and topological properties of two different (111) heterostructures: i) bilayers of $SrRuO_3$ (a $t_{2g}$ system) in $SrTiO_3$ and ii) bilayers of $LaNiO_3$ (an $e_g$ system) in $LaAlO_3$. For (111) $SrRuO_3$ bilayers, we find half-metallic ferromagnetism with a remarkably high Curie temperature of 500K and the ordered magnetic moment of 2 $\mus_B/Ru$ [2]. This resilient ferromagnetism is attributed to the orbital degeneracy of $t_{2g}$ electrons, which is largely preserved in (111) layers, in contrast to conventional (001) heterostructures. Moreover, the topologically nontrivial quantum anomalous Hall (QAH) state can be induced by doping [2]. The strength of interaction parameters in nickelates is under debate. Hence for (111) $LaNiO_3$ in $LaAlO_3$, we study a wide range of interaction parameters, and find a involved phase diagram comprising four phases: a ferromagnetic metal, a paramagnetic metal, an antiferro-orbitally-ordered insulator, and a paramagnetic insulator [3]. Interestingly, breathing distortions of $NiO_6$ octahedra have only a minor impact on the phase diagram. By comparing with the experimental data and earlier model DMFT studies, we argue that (111) $LaNiO_3$ bilayers are close to the metal-insulator transition and may exhibit a high magnetoresistance at low temperatures [3]. [1] O. Janson, Z. Zhong, G. Sangiovanni, and K. Held, Dynamical mean field theory for oxide heterostructures, in Spectroscopy of Complex Oxide Interfaces, Springer Series in Materials Science 266, eds. C. Cancellieri and V. Strocov (Springer International Publishing, Basel, 2018), pp. 215-243. [2] L. Si, O. Janson, G. Li, Z. Zhong, Z. Liao, G. Koster, and K. Held, Phys. Rev. Lett. 119, 026402 (2017). [3] O. Janson and K. Held, Phys. Rev. B 98, 115118 (2018).

We report high-resolution inelastic neutron scattering measurements of the spin dynamics as a function of applied magnetic field in the frustrated quantum pyrochlore magnets Yb2Ti2O7 and Er2Ti2O7, which show persistent zero-point quantum fluctuations in their magnetically ordered ground states. In Yb2Ti2O7 we observe directly how magnons become unstable to decay into a continuum of multi-particle excitations upon decreasing magnetic field and we attribute this to anomalously strong quantum fluctuations due to proximity to a phase boundary between ferromagnetic and antiferromagnetic orders for a Kitaev-Gamma Hamiltonian. Er2Ti2O7 is located well inside an antiferromagnetic XY phase and here magnons remain well-defined throughout most of the spectrum, but we find strong field-dependent quantum renormalizations of their dispersion relations and magnon decay effects at high energies. [1] J.D. Thompson, P.A. McClarty, D. Prabhakaran, I. Cabrera, T. Guidi, D. Voneshen and R. Coldea, Phys. Rev. Lett. 119, 057203 (2017).

In systems with competing interactions frustration can create complex ground states with exotic excitations. Spin-ice is a solid manifestation of such a degenerate ground state in which magnetic degrees of freedom carry zero point entropy (in analogy to water ice) and for which the corresponding excitations behave like magnetic monopoles1. The density of these monopoles is a function of temperature and external magnetic field and the corresponding phase diagram exhibits a phase transition into a “monopole-ordered” state (again resembling the gas-liquid transition in water). Accordingly, there exists a critical end-point for the monopole condensation1. It had been postulated by Daniel Khomskii that the emergent magnetic monopoles in addition carry electric dipole moments2. Using dielectric and magnetic spectroscopy we demonstrate the existence of such an electric dipole moment coupled to magnetic monopole excitations in $Dy_2Ti_2O_7$. Furthermore we are able to examine the monopole dynamics via this magnetoelectric coupling. We can track the relaxation time of the electrically dipolar contribution down to low temperatures in the mK-range as a function of an external magnetic field along the crystalline [111] direction and are able to identify different contributions to the response function. Analyzing the dynamics at temperatures above the critical end-point we see the crossover from the conventional slowing down of the fluctuation dynamics to an critical speeding up. [1] C. Castelnovo, R. Moessner, and S. L. Sondhi, Nature 451, 42 (2008) [2] D. I. Khomskii, Nature Communications 3, 1 (2012) [3] C.P. Grams, M. Valldor, M. Garst, and J. Hemberger, Nature Communications 5:4853 (2014)

Orbitally degenerate magnetic compounds are known to often develop nonmagnetic ground states with a spin gap. I will discuss a possible theory behind this phenomenon. I argue that the orbital degrees of freedom induce a spontaneous dimerization of spins and drive them into highly degenerate nonmagnetic manifold spanned by hard-core dimer (spin-singlet) coverings of the lattice. Two possible mechanisms of lifting this extensive degeneracy will be discussed: (i) by order-out-of-disorder due to the virtual triplet fluctuations and (ii) by magneto-elastic interaction. They lead to dimer condensation into a valence bond crystal pattern and provide an explanation for dimerized superstructures seen experimentally.

In insulating states of transition metal oxides with orbital degeneracy effective interactions are described in terms of spin-orbital superexchange [1]. Consequently, the resulting models are often inherently frustrated and the quasi-empirical Goodenough-Kanamori rules may be violated leading to (intersite) spin-orbital entanglement which excludes the use of mean field procedure separating spin and orbital degrees of freedom [2]. Here we present a brief overview of the earlier study of the one-dimensional (1D) SU(2)$\otimes$SU(2) symmetric models that show entangled spin-orbital bound states and enhanced spin-orbital fluctuations, both for antiferromagnetic and ferromagnetic exchange [3], and analyze the respective phase diagrams. We show that in general spin-orbital fluctuations are enhanced near the highly symmetric SU(4) model. Next, we concentrate on a 1D spin-orbital model with lower symmetry that is able to describe a wider class of transition metal oxides [4]. It turns out that, even though such a model exhibits a more complex spin-orbital entanglement, amazingly it can under some circumstances be reduced to an exactly solvable free fermion model. This property gives more insights into the nature of spin-orbital correlations. \\ \scriptsize{\hspace{-2mm} %%%%insert bibliographic reference here. if needed %%%%use the format: [numb] %%%%%multiple references separated by semicolons %\noindent [1] A. M. Ole\'s, J. Phys.: Condensed Matter \textbf{24}, 313201 (2012).\hfill\break [2] A. M. Ole\'s, P. Horsch, L. F. Feiner, and G. Khaliullin, Phys. Rev. Lett. \textbf{96}, 147205 (2006).\hfill\break [3] W.-L. You, P. Horsch, and A. M. Ole\'s, Phys. Rev. B \textbf{92}, 054423 (2015).\hfill\break [4] D. Gotfryd, E. Paerschke, K. Wohlfeld et al., in preparation (2018).