Band topology, or global wave-function structure that enforces novel properties in the bulk and on the surface of crystalline materials, is currently under intense investigations for both fundamental interest and its technological promises [1-4]. While band crossing of non-trivial topological nature was first studied in three dimensions for electrons [4-10], the underlying physical idea is not restricted to fermionic excitations [11-15]. In fact, experiments have confirmed the possibility to have topological band crossing of electromagnetic waves in artificial structures [16]. Fundamental bosonic excitations in real crystals, however, have not been observed to exhibit the counterpart under ambient pressure and magnetic field, where the difficulty is in part because natural materials cannot be precisely engineered like artificial structures. Here, we use inelastic neutron scattering to reveal the presence of topological spin excitations (magnons) in a three-dimensional antiferromagnet, Cu3TeO6, which features a unique lattice of magnetic spin-1/2 Cu 2+ ions [17]. Beyond previous understanding [17,18], we find that the material's spin lattice possesses a variety of exchange interactions, with the interaction between the ninth-nearest neighbours being as strong as that between the nearest neighbours. Although theoretical analysis indicates that the presence of topological magnon band crossing is independent of model details [15], Cu3TeO6 turns out to be highly favourable for the experimental observation, as its optical magnons are spectrally sharp and intense due

Abstractα-RuCl3 is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of α-RuCl3 by a resonant inelastic x-ray scattering study at the Ru L3 absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilized by competing ferromagnetic correlations. The classical ground state of the experimentally determined Hamiltonian is actually ferromagnetic. The zigzag state is stabilized by quantum fluctuations, leaving ferromagnetism – along with the Kitaev spin liquid – as energetically proximate metastable states. The three closely competing states and their collective excitations hold the key to the theoretical understanding of the unusual properties of α-RuCl3 in magnetic fields.

We report an inelastic neutron scattering study of single crystals of (Li0.8Fe0.2)ODFeSe. Temperature-dependent low-energy spin excitations are observed near Q = (0.5, 0.27, 0.5) and equivalent wave vectors symmetrically surrounding Q = (0.5, 0.5, 0.5) in the 1-Fe Brillouin zone, consistent with a Fermi-surface-nesting description. The excitations are broadly distributed in energy, ranging from 16 to 35 meV. Upon cooling below the superconducting critical temperature (Tc), magnetic response below twice the superconducting gap 2∆SC exhibits an abrupt enhancement, consistent with the notion of spin resonance, whereas the response at higher energies increases more gradually with only a weak anomaly at Tc. Our results suggest that (Li0.8Fe0.2)ODFeSe might be on the verge of a crossover between different Cooper-pairing channels with distinct symmetries.A pivotal issue concerning the Cooper-pairing mechanism in the Fe-based superconductors (FeSCs) is the pairing symmetry, which is commonly regarded as an important thread for distinguishing among different theoretical proposals. Pairing mediated by electron-phonon interactions [1] and/or orbital fluctuations [2] is expected to occur in the plain s-wave (s ++ ) channel, whereas pairing mediated by spin fluctuations [3] is expected to have sign-reversal behaviors in the gap function and occur in the extended s-wave (s +− ) or the d-wave channel [4][5][6][7]. When hole pockets are present at the Γ point, it has been reasonably well established that the predominant pairing symmetry is s +− [8,9], which favors the unconventional pairing mechanism associated with spin fluctuations. But because the FeSCs are multi-orbital systems with multiple magnetic exchange interactions that are comparable in strength [10], the preference on one pairing channel over another may further depend on the Fermi-surface (FS) topology [5,11]. Therefore, the assumption that a universal pairing mechanism applies to all FeSCs requires a more stringent test, namely, pairing symmetry needs to be determined and compared with theory for systems with very different band filling and FS topologies.An important case of distinct FS topology was first established in alkali-metal intercalated Fe selenides [12], which have no hole pocket at the Γ point as a result of heavy electron doping [13][14][15]. Later it became clear that the electron doping can be achieved with various methods, including intercalation into bulk FeSe [16][17][18][19][20][21], epitaxial growth of a single atomic layer of FeSe on a charge-transferring SrTiO 3 substrate (FeSe/STO) [22][23][24], and surface dosing of FeSe with potassium [25][26][27], all of which end up with similar electronic structures. It is intriguing that the absence of hole pockets at the Γ point is empirically linked to the much higher values of T c than in bulk FeSe [28]. The associated pairing symmetry is considered to be of great theoretical importance but has remained unsettled [11,[29][30][31][32][33][34][35], in part because of seemingly contradictory results fro...

Cuprate superconductors have the highest critical temperatures (Tc) at ambient pressure, yet a consensus on the superconducting mechanism remains to be established. Finding an empirical parameter that limits the highest reachable Tc can provide crucial insight into this outstanding problem. Here, in the first two Ruddlesden-Popper members of the model Hg-family of cuprates, which are chemically nearly identical and have the highest Tc among all cuprate families, we use inelastic photon scattering to reveal that the energy of magnetic fluctuations may play such a role. In particular, we observe the single-paramagnon spectra to be nearly identical between the two compounds, apart from an energy scale difference of ~30% which matches their difference in Tc. The empirical correlation between paramagnon energy and maximal Tc is further found to extend to other cuprate families with relatively high Tc’s, hinting at a fundamental connection between them.