SrCu 2 (BO 3 ) 2 is the archetypal quantum magnet with a gapped dimer-singlet ground state and triplon excitations. It serves as an excellent realization of the Shastry-Sutherland model, up to small anisotropies arising from Dzyaloshinskii-Moriya interactions. Here we demonstrate that these anisotropies, in fact, give rise to topological character in the triplon band structure. The triplons form a new kind of Dirac cone with three bands touching at a single point, a spin-1 generalization of graphene. An applied magnetic field opens band gaps resulting in topological bands with Chern numbers ±2. SrCu 2 (BO 3 ) 2 thus provides a magnetic analogue of the integer quantum Hall effect and supports topologically protected edge modes. At a threshold value of the magnetic field set by the Dzyaloshinskii-Moriya interactions, the three triplon bands touch once again in a spin-1 Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.

A promising route to tailoring the electronic properties of quantum materials and devices rests on the idea of orbital engineering in multilayered oxide heterostructures. Here we show that the interplay of interlayer charge imbalance and ligand distortions provides a knob for tuning the sequence of electronic levels even in intrinsically stacked oxides. We resolve in this regard the d-level structure of layered Sr2IrO4 by electron spin resonance. While canonical ligand-field theory predicts g||-factors less than 2 for positive tetragonal distortions as present in Sr2IrO4, the experiment indicates g|| is greater than 2. This implies that the iridium d levels are inverted with respect to their normal ordering. State-of-the-art electronic-structure calculations confirm the level switching in Sr2IrO4, whereas we find them in Ba2IrO4 to be instead normally ordered. Given the nonpolar character of the metal-oxygen layers, our findings highlight the tetravalent transition-metal 214 oxides as ideal platforms to explore d-orbital reconstruction in the context of oxide electronics.

We studied spin excitations of the non-centrosymmetric Ba2CoGe2O7 in high magnetic fields up to 33 T. In the electron spin resonance and far infrared absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two-sublattice antiferromagnet. We show that a multi-boson spin-wave theory describes these unconventional modes, including spin-stretching modes, characterized by oscillating magnetic dipole and quadrupole moment. The lack of the inversion symmetry allows each mode to become electric dipole active. We expect that the spin-stretching modes can be generally observed in inelastic neutron scattering and light absorption experiments in a broad class of ordered S > 1/2 spin systems with strong single-ion anisotropy and/or non-centrosymmetric lattice structure. Magnons are collective spin excitations in crystals with long-range magnetic order, often investigated by electromagnetic absorption and neutron scattering experiments. Both classical and quantum spin-wave theory of S = 1/2 systems predict one magnon branch in the spin-excitation spectrum for each spin in the magnetic unit cell [1]. This rule about the number of magnon branches is generally accepted and experimentally verified for S > 1/2 spin systems as long as the conventional spin-wave theory applies, requiring that the lengths (i.e., the absolute values of the expectation values) of the spins are preserved in the excited states and only their orientations change relative to the ground-state configuration [2]. However, the picture of one magnon mode per spin in the magnetic unit cell needed to be surpassed in several f -electron compounds with complicated quadrupolar ordering, such as CeB 6 [3] and UO 2 [4].Recently, additional spin-wave modes have been observed by far infrared (FIR) spectroscopy [5] and inelastic neutron scattering (INS) [6] in Ba 2 CoGe 2 O 7 , a simple two-sublattice easy-plane antiferromagnet (AF) with S = 3/2 spins [7, 8]. This material has attracted much interest owing to its multiferroic ground state where delicate magnetic control of the ferroelectric polarization [8, 9] and chirality [10] were realized. Moreover, spin waves in Ba 2 CoGe 2 O 7 exhibits giant directional dichroism and natural optical activity at THz frequencies due to the large ac magnetoelectric effect [5, 10]. A recent numerical diagonalization study on finite spin clusters found, besides the two conventional AF modes, additional spin resonances with peculiar optical properties [10, 11]. Nevertheless, the understanding of the unconventional magnon modes and the coupled dynamics of spins and electronic polarization on a fundamental level remained an open issue.In this Letter, we investigate the spin-wave excitations in Ba 2 CoGe 2 O 7 over a broad photon energy range combining electron spin resonance (ESR) and high-resolution FIR spectroscopy. The largest magnetic field, 33 T, applied in this study drastically changes the antiferromagnetic spin configuration for any field direction, in contrast to former e...