Field-induced bound-state condensation and spin-nematic phase in SrCu2(BO3)2 revealed by neutron scattering up to 25.9 T.

In quantum magnetic materials, ordered phases induced by an applied magnetic field can be described as the Bose-Einstein condensation (BEC) of magnon excitations. In the strongly frustrated system SrCu2(BO3)2, no clear magnon BEC could be observed, pointing to an alternative mechanism, but the high fields required to probe this physics have remained a barrier to detailed investigation. Here we exploit the first purpose-built high-field neutron scattering facility to measure the spin excitations of SrCu2(BO3)2 up to 25.9 T and use cylinder matrix-product-states (MPS) calculations to reproduce the experimental spectra with high accuracy. Multiple unconventional features point to a condensation of S = 2 bound states into a spin-nematic phase, including the gradients of the one-magnon branches and the persistence of a one-magnon spin gap. This gap reflects a direct analogy with superconductivity, suggesting that the spin-nematic phase in SrCu2(BO3)2 is best understood as a condensate of bosonic Cooper pairs.

Interlayer electronic hybridization leads to exceptional thickness-dependent vibrational properties in few-layer black phosphorus.

Stacking two-dimensional (2D) materials into multi-layers or heterostructures, known as van der Waals (vdW) epitaxy, is an essential degree of freedom for tuning their properties on demand. Few-layer black phosphorus (FLBP), a material with high potential for nano- and optoelectronics applications, appears to have interlayer couplings much stronger than graphene and other 2D systems. Indeed, these couplings call into question whether the stacking of FLBP can be governed only by vdW interactions, which is of crucial importance for epitaxy and property refinement. Here, we perform a theoretical investigation of the vibrational properties of FLBP, which reflect directly its interlayer coupling, by discussing six Raman-observable phonons, including three optical, one breathing and two shear modes. With increasing sample thickness, we find anomalous redshifts of the frequencies for each optical mode but a blueshift for the armchair shear mode. Our calculations also show splitting of the phonon branches, due to anomalous surface phenomena, and strong phonon-phonon coupling. By computing uniaxial stress effects, inter-atomic force constants and electron densities, we provide a compelling demonstration that these properties are the consequence of strong and highly directional interlayer interactions arising from the electronic hybridization of the lone electron-pairs of FLBP, rather than from vdW interactions. This exceptional interlayer coupling mechanism controls the stacking stability of BP layers and thus opens a new avenue beyond vdW epitaxy for understanding the design of 2D heterostructures.