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*When the energy eigenvalues of two coupled quantum states approach each other in a certain parameter space, their energy levels repel each other and level crossing is avoided 1 . Such level repulsion, or avoided level crossing, is commonly used to describe the dispersion relation of quasiparticles in solids 2 . However, little is known about the level repulsion when more than two quasiparticles are present; for example, in a strongly interacting quantum system where a quasiparticle can spontaneously decay into a many-particle continuum [3][4][5] . Here we show that even in this case level repulsion exists between a long-lived quasiparticle state and a continuum. In our fine-resolution neutron spectroscopy study of magnetic quasiparticles in the frustrated quantum magnet BiCu 2 PO 6 , we observe a renormalization of the quasiparticle dispersion relation due to the presence of the continuum of multi-quasiparticle states.A fundamental concept in condensed matter physics is the idea that strongly interacting atomic systems can be treated as a collection of weakly interacting and long-lived quasiparticles. Within a quasiparticle picture, complex collective excited states in a many-body system are described in terms of effective elementary excitations. The quanta of these excitations carry a definite momentum and energy, and are termed quasiparticles. Magnetic insulators containing localized S = 1/2 magnetic moments and having valence-bond solid ground states are ideal systems in which to study bosonic quasiparticles in an interacting quantum many-body system 6 . The elementary magnetic excitations in these materials are triply degenerate S = 1 quasiparticles called triplons, and their momentum-and energy-resolved dynamics can be probed directly though inelastic neutron scattering (INS) measurements.In particular, when the system's Hamiltonian has an interaction term coupling single-particle and multi-particle states, the single quasiparticles may decay into the continuum of multi-particle states 3,4 . In such a system, the Hamiltonian for the single quasiparticles is non-Hermitian and the energy eigenvalues are in general complex. The single-particle decay typically occurs in two ways. Often the single-particle mode stays as a resonance inside the continuum, but the lifetime becomes short and the mode is highly damped 3 . Sometimes the single quasiparticle simply ceases to exist, and the dispersion abruptly terminates when it crosses the continuum boundary 5 . However, there is a third possibility, in which the single-quasiparticle dispersion is significantly renormalized to avoid the multi-particle continuum. This is analogous to the wellknown avoided level crossing behaviour of coupled modes, but in the complex plane of energy eigenvalues 7 . Despite broad interest in strongly interacting quantum systems, experimentally realizing an ideal condition to study the interaction between a quasiparticle and a multi-particle continuum turns out to be extremely difficult. One realization occurs in semiconducting quantum do...

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Spin-orbit coupling (SOC), the interaction between the electron spin and the orbital angular momentum, can unlock rich phenomena at interfaces, in particular interconverting spin and charge currents. Conventional heavy metals have been extensively explored due to their strong SOC of conduction electrons. However, spin-orbit effects in classes of materials such as epitaxial 5d-electron transition-metal complex oxides, which also host strong SOC, remain largely unreported. In addition to strong SOC, these complex oxides can also provide the additional tuning knob of epitaxy to control the electronic structure and the engineering of spin-to-charge conversion by crystalline symmetry. Here, we demonstrate room-temperature generation of spin-orbit torque on a ferromagnet with extremely high efficiency via the spin-Hall effect in epitaxial metastable perovskite SrIrO3. We first predict a large intrinsic spin-Hall conductivity in orthorhombic bulk SrIrO3 arising from the Berry curvature in the electronic band structure. By manipulating the intricate interplay between SOC and crystalline symmetry, we control the spin-Hall torque ratio by engineering the tilt of the corner-sharing oxygen octahedra in perovskite SrIrO3 through epitaxial strain. This allows the presence of an anisotropic spin-Hall effect due to a characteristic structural anisotropy in SrIrO3 with orthorhombic symmetry. Our experimental findings demonstrate the heteroepitaxial symmetry design approach to engineer spin-orbit effects. We therefore anticipate that these epitaxial 5d transition-metal oxide thin films can be an ideal building block for low-power spintronics.

The exactly-solvable Kitaev model of twodimensional honeycome magnet leads to a quantum spin liquid (QSL) characterized by Majorana fermions, relevant for fault-tolerant topological quantum computations. In the high-field paramagnetic state of α-RuCl 3 , half-integer quantization of thermal Hall conductivity has been reported as a signature of Majorana fermions, but the bulk nature of this state remains elusive. Here, from high-resolution heat capacity measurements under in-plane field rotation, we find strongly angle-dependent low-energy excitations in the bulk of α-RuCl 3 . The excitation gap has a sextuple node structure, and the gap amplitude increases with field, exactly as expected for itinerant Majorana fermions in the Kitaev model. Our thermodynamic results are fully linked with the transport quantization properties, providing the first demonstration of the bulk-edge correspondence in a Kitaev QSL.Quantum spin liquids (QSLs) are enigmatic states of matter, in which quantum fluctuations and frustrations prevent spin configurations in a lattice from any solid-like ordered alignments [1,2]. In the exactly solvable model of two-dimensional honeycome lattice proposed by Kitaev [3], the bond-dependent Ising interactions act as an exchange frustration, leading to a QSL ground state with characteristic excitations of Majorana fermions. These Majorana excitations are important to make non-abelian anyons that are useful for fault-tolerant topological quantum computations. Realizing this intriguing QSL state in real materials is therefore quite important, and there are tremendous efforts to search the QSL states in Mott insulators with strong spin-orbit coupling [4][5][6].In the Kitaev model [3], each S = 1/2 spin at the honeycome site can be converted to two kinds of Majorana fermions, itinerant and localized ones, the latter of which form the so-called Z 2 flux (which may also be called as vison) per hexagon plaquette. By this representation the quantum many-body problem of spins can

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We theoretically investigate the mechanism to generate large intrinsic spin Hall effect in iridates or more broadly in 5d transition metal oxides with strong spin-orbit coupling. We demonstrate such a possibility by taking the example of orthorhombic perovskite iridate with nonsymmorphic lattice symmetry, SrIrO3, which is a three-dimensional semimetal with nodal line spectrum. It is shown that large intrinsic spin Hall effect arises in this system via the spin-Berry curvature originating from the nearly degenerate electronic spectra surrounding the nodal line. This effect exists even when the nodal line is gently gapped out, due to the persistent nearly degenerate electronic structure. The magnitude of the spin Hall conductivity is shown to be comparable to the best known example such as doped topological insulators and the biggest in any transition metal oxides. To gain further insight, we compute the intrinsic spin Hall conductivity in both bulk and thin film systems. We find that the geometric confinement in thin films leads to significant modifications of the electronic states, leading to even bigger spin Hall conductivity in certain cases. We compare our findings with the recent experimental report on the discovery of large spin Hall effect in SrIrO3 thin films.