Session A43: Spin Orbit Physics in Oxides I

Visualizing ferromagnetic domains in undoped and Fe-doped \textbf{${\mathrm{Sr}}_{\mathrm{4}}{\mathrm{Ru}}_{\mathrm{3}}\mathrm{O}_{\mathrm{10}}$}

Transition-metal oxides have proven to be a great source of interesting phenomena and new quantum phases of matter with high potential for developing exciting technologies. A remarkable sub-class of these materials with layer dependent properties is the ruthenium perovskites of the Ruddlesden-Popper series, specifically$\thinspace {\mathrm{Sr}}_{\mathrm{n+1}}{\mathrm{Ru}}_{\mathrm{n}}\mathrm{O}_{\mathrm{3n+1}}$, exhibiting a range of behavior from ferromagnetism and metamagnetic quantum criticality to p-wave superconductivity. The triple layered oxide ${\mathrm{Sr}}_{\mathrm{4}}{\mathrm{Ru}}_{\mathrm{3}}\mathrm{O}_{\mathrm{10}}$ exhibits coexistence of ferro- ($\mathrm{T}_{\mathrm{C}}<$ 105 K) and meta- ($\mathrm{T}_{\mathrm{M}}\thinspace <$ 50 K) magnetism with strong anisotropy. Despite many studies on bulk magnetic properties of this material, the microscopic nature of the magnetic phase is still unclear. What is lacking is the real space imaging of magnetic domains. To this end, we report our variable temperature magnetic force microscopy studies on floating-zone grown undoped and Fe-doped${\mathrm{\thinspace Sr}}_{\mathrm{4}}{\mathrm{Ru}}_{\mathrm{3}}\mathrm{O}_{\mathrm{10}}$ single crystals. Various stripe and branch-like domain patterns were observed below   

The realization of Majorana fermions in Kitaev Quantum Spin Lattice

The Kitaev honeycomb lattice is envisioned as an ideal host for Majorana fermions that are created out of the spin liquid background. Combining specific heat and neutron scattering experiments with theoretical calculations, here, we establish a hitherto unparalleled spin fractionalization to two species of Majorana fermions in the Kitaev material $\alpha $-RuCl$_{\mathrm{3}}$. The specific heat data unveil a two-stage release of magnetic entropy by (R/2)ln2 and the $T$-linear dependence at intermediate temperatures. Our inelastic neutron scattering measurements further corroborate two distinct characters of fractionalized excitations: an Y-like, dispersive, magnetic continuum at higher energies and a dispersionless excitation at low energies around the Brillouin zone center. These dual features are well described by a Ferromagnetic Kitaev model, providing a smoking gun proof of the itinerant and localized Majorana fermions emergent in Kitaev magnets.   

Low Energy Spectrum of Proximate Kitaev Spin Liquid $\alpha$ -RuCl$_{3}$ by Terahertz Spectroscopy

A Quantum Spin Liquid (QSL) is an ultra-quantum state of matter with no ordered ground state. Recently, a route to a QSL identified by Kitaev has received a great deal of attention. The compound $\alpha$ -RuCl$_{3}$, in which Ru atoms form a honeycomb lattice, has been shown to possess Kitaev exchange interactions, although a smaller Heisenberg interaction exists and leads to a zig-zag antiferromagnetic state below 7 K. Because of proximity to the exactly-solvable Kitaev spin-liquid model, this material is considered a potential host for Majorana-like modes. In this work, we use time-domain terahertz (THz) Spectroscopy to probe the low-energy excitations of $\alpha$ -RuCl$_{3}$. We observe the emergence of a sharp magnetic spin-wave absorption peak below the AFM ordering temperature at 7 K— on top of a broad continuum that persists up to room temperature. Additionally we report the polarization dependence of the THz absorption, which reveals optical birefringence, indicating the presence of large monoclinic domains.   

Iridates and RuCl$_3$ - from Heisenberg antiferromagnets to potential Kitaev spin-liquids

The observed richness of topological states on the single-electron level prompts the question what kind of topological phases can develop in more strongly correlated, many-body electron systems. Correlation effects, in particular intra- and inter-orbital electron-electron interactions, are very substantial in $3d$ transition-metal compounds such as the copper oxides, but the spin-orbit coupling (SOC) is weak. In $5d$ transition-metal compounds such as iridates, the interesting situation arises that the SOC and Coulomb interactions meet on the same energy scale. The electronic structure of iridates thus depends on a strong competition between the electronic hopping amplitudes, local energy-level splittings, electron-electron interaction strengths, and the SOC of the Ir 5d electrons. The interplay of these ingredients offers the potential to stabilise relatively well-understood states such as a 2D Heisenberg-like antiferromagnet in Sr$_2$IrO$_4$, but in principle also far more exotic ones, such a topological Kitaev quantum spin liquid, in (hyper)honeycomb iridates. I will discuss the microscopic electronic structures of these iridates, their proximity to idealized Heisenberg and Kitaev models and our contributions to establishing the physical factors that appear to have preempted the realization of quantum spin liquid phases so far and include a discussion on the 4d transition metal chloride RuCl$_3$.   

Pressure-induced structural transition in SrRu$_{\mathrm{2}}$O$_{\mathrm{6}}$

SrRu$_{\mathrm{2}}$O$_{\mathrm{6}}$ crystallizes into a quasi-two-dimensional structure with layers of edge-sharing RuO$_{\mathrm{6}}$ octahedra separated by nonmagnetic Sr layers. Despite this quasi-two-dimensional structure, SrRu$_{\mathrm{2}}$O$_{\mathrm{6}}$ was found to order magnetically at an usually high Neel temperature of 565 K. As part of the effort understanding the underlying mechanisms driving the high Neel temperature, we studied the effect of high pressure on the structure, magnetism, and physical properties of SrRu$_{\mathrm{2}}$O$_{\mathrm{6}}$. The results from our density functional calculations will also be presented.   

Mott transition controlled by lattice-orbital coupling in double layer ruthenates

We have investigated unusual phase transitions triggered by chemical doping in Ca$_{\mathrm{3}}$Ru$_{\mathrm{2}}$O$_{\mathrm{7}}$. Our experiments show a few percent doping of Mn (\textgreater 4{\%}) can switch the quasi-two-dimensional metallic state with the antiferromagnetic order (AFM-b) comprised of ferromagnetic (FM) bilayers of Ca$_{\mathrm{3}}$Ru$_{\mathrm{2}}$O$_{\mathrm{7}}$ to a Mott insulating state with the nearest-neighbor antiferromagnetic order (G-AFM), while Fe doping cannot realize such a Mott transition, but leads to a localized state with the AFM-b order. Combined with first-principles calculations, we find that the lattice-orbital coupling (LOC) plays a critical role in driving the Mott transition caused by Mn doping and the Mott transition temperature $T_{\mathrm{MIT}}$ is strikingly dependent on the structural parameter $c/a$ at the temperatures far above $T_{\mathrm{MIT}}$. Such LOC-assisted Mott transition mechanism, which also accounts for the previously-reported Mott transition induced by Ti doping in Ca$_{\mathrm{3}}$Ru$_{\mathrm{2}}$O$_{\mathrm{7}}$, forms a clear contrast with the Mott transition mechanism controlled by band filling in 3$d$ strongly correlated systems. Our findings advance the understanding of how exotic properties of 4$d$ correlated systems are governed by the complex interplay between charge, spin, lattice and orbital degrees of freedom.   

Itinerant antiferromagnetism in RuO$_{2}$

Bulk rutile RuO$_{2}$ has long been considered a Pauli paramagnet. Here we report that RuO$_{2}$ exhibits a hitherto undetected lattice distortion below approximately 900 K. The distortion is accompanied by antiferromagnetic order up to at least 300 K with a small room temperature magnetic moment of approximately 0.05 $\mu$ B as evidenced by polarized neutron diffraction. Density functional theory plus U (DFT$+$U) calculations indicate that antiferromagnetism is favored even for small values of the Hubbard U of the order of 1 eV. The antiferromagnetism may be traced to a Fermi surface instability, lifting the band degeneracy imposed by the rutile crystal field. The combination of high N\'{e}el temperature and small itinerant moments make RuO$_{2}$ unique among ruthenate compounds and among oxide materials in general.   

The Consequences of Spin-Orbit Coupling on the 5d$^{\mathrm{3}}$ Electronic Configuration

The impact of spin-orbit coupling on collective properties of matter is of considerable interest. The most intensively investigated materials in this regard are Iridium-based transition metal oxides which exhibit a host of interesting ground states that originate from a 5d$^{\mathrm{5}}$ J$_{\mathrm{eff}}=$1/2 electronic configuration. Moving beyond the J$_{\mathrm{eff}}=$1/2 paradigm to other electronic configurations where spin-orbit coupling plays a prominent role is a key objective of ongoing research. Here we focus on several Osmium-based transition metal oxides such as NaOsO$_{\mathrm{3}}$, Cd$_{\mathrm{2}}$Os$_{\mathrm{2}}$O$_{\mathrm{7}}$, Ca$_{\mathrm{3}}$LiOsO$_{\mathrm{6}}$, Sr$_{\mathrm{2}}$ScOsO$_{\mathrm{6}}$, Ba$_{\mathrm{2}}$YOsO$_{\mathrm{6}}$, and Sr$_{\mathrm{2}}$FeOsO$_{\mathrm{6}}$, which are nominally in the 5d$^{\mathrm{3}}$ electronic configuration. Within the LS coupling picture and a strong octahedral crystal field, the 5d$^{\mathrm{3}}$ configuration is expected to be an orbital singlet and spin-orbit effects should be minimal. Nevertheless, our neutron and x-ray scattering investigations of these materials as well as investigations by other groups show dramatic effects of spin-orbit coupling including reduced moment magnetic order, enhanced spin-phonon coupling, and large spin gaps. In particular, the anisotropy induced by spin-orbit coupling tips the balance of the frustrated interactions and drives the selection of particular magnetic ground states. To understand the mechanism driving the spin-orbit effects, we have explored the ground state t$_{\mathrm{2g}}$ manifold with resonant inelastic x-ray scattering and observe a spectrum inexplicable by an LS coupling picture. On the other hand, an intermediate coupling approach reveals that the ground state wave function is a J$=$3/2 configuration which answers the question of how strong spin-orbit coupling effects arise in 5d$^{\mathrm{3}}$ systems.   

Terahertz Spectroscopy of Sr$_{2-x}$Ca$_{x}$CoOsO$_{6}$ Double Perovskites

The osmate double perovskite family of materials Sr$_{2-x}$Ca$_{x}$CoOsO$_{6}$ displays a rich phase diagram as a function of temperature and Ca substitution. Using time-domain terahertz (THz) spectroscopy, we observe that a phonon centered at a frequency of 1.4 THz disappears between x=0 and x=0.1. However, this phonon seems to be decoupled from the magnetic and structural phase transitions that occur as a function of temperature. In addition, the THz conductivities of the compacted powders below 1 THz can be interpreted either as variable range hopping conductivity, or understood within the framework of universality of disordered systems (Jonscher Law). We will also report a study of absorptions and spin-phonon coupling in the infrared using Fourier transform infrared spectroscopy.   

Ba$_{\mathrm{2}}$NiOsO$_{\mathrm{6}}$: a Dirac-Mott insulator with ferromagnetism near 100 K

The ferromagnetic semiconductor Ba$_{\mathrm{2}}$NiOsO$_{\mathrm{6}}$ ($T_{\mathrm{mag}}$\textasciitilde 100 K) was synthesized at 6 GPa and 1500 $^{\circ}$ C. It crystallizes into a double perovskite structure [\textit{Fm}-3$m$; $a \quad =$ 8.0428(1) Å], where the Ni$^{\mathrm{2+}}$ and Os$^{\mathrm{6+}}$ ions are perfectly ordered at the perovskite B-site. We show that the spin-orbit coupling of Os$^{\mathrm{6+}}$ plays an essential role in opening the charge gap. The magnetic state was investigated by density functional theory calculations and powder neutron diffraction. The latter revealed a collinear ferromagnetic order in a \textit{\textgreater }21-kOe magnetic field at 5 K. The ferromagnetic gapped state is fundamentally different from that of known dilute magnetic semiconductors such as (Ga,Mn)As and (Cd,Mn)Te ($T_{\mathrm{mag}}$\textless 180 K), the spin-gapless semiconductor Mn$_{\mathrm{2}}$CoAl ($T_{\mathrm{mag}}$\textasciitilde 720 K), and the ferromagnetic insulators EuO ($T_{\mathrm{mag}}$\textasciitilde 70 K) and Bi$_{\mathrm{3}}$Cr$_{\mathrm{3}}$O$_{\mathrm{11}}$ ($T_{\mathrm{mag}}$\textasciitilde 220 K). It is also qualitatively different from known ferrimagnetic insulator/semiconductors, which are characterized by an antiparallel spin arrangement. Our report of cubic Ba$_{\mathrm{2}}$NiOsO$_{\mathrm{6}}$ heralds a new class of FM insulator oxides, which may be useful in developing a practical magnetic semiconductor that can be employed in spintronic and quantum magnetic devices.   

Resonant X-ray Magnetic Diffraction of all-in-all-out antiferromagnetic order in Cd2Os2O7 Under Pressure

The pyrochlore structured Cd$_{2}$Os$_{2}$O$_{7}$ orders magnetically with spins on each Os tetrahedron arranged in either all-in or all-out geometries. Simultaneously, the system manifests a continuous metal-insulator transition at the N\'{e}el temperature of 227 K at ambient pressure. In an attempt to better understand the relationship between magnetism and electron localization, we explore the evolution of the antiferromagnetic order using pressure as the tuning technique and~resonant x-ray magnetic diffraction as the direct probe.~ Our diffraction results indicate that while the antiferromagnetic state is stable to above 30 GPa at T $=$ 4 K with a gradually suppressed intensity, the crystal lattice and its symmetry evolve.~