E L E C T R O N I C S T R U C T U R E , M A G N E T I S M A N D D Y N A M I C S

S C I E N T I F I C H I G H L I G H T S

1 0 8 H I G H L I G H T S 2 0 2 2 I

Identifying fractional spin excitations in a 2D cuprate

The 2D antiferromagnetic square-lattice is the scaffold of high Tc superconductivity in cuprates and collective spin excitations are its fingerprint. X-ray scattering measurements reveals that in CaCuO2 the usual magnons can break into pairs of spinons, due to multi-spin exchange interactions.

High-temperature superconducting cuprates share a fundamental building block: CuO2 layers arranged in a square lattice, each site having spin-1/2 and interacting with neighbouring ones through strong antiferromagnetic (AF) couplings. While the magnetic structure is simple, the physics behind it is still not completely understood. In most cases, long-range AF order is stabilised and the elementary excitations are described in terms of bosonic spin waves (or magnons), carrying spin 1. However, different models predict a fragility of this system against large next- nearest neighbour or multi-spin couplings [1]. Even in the absence of geometric frustration, such instabilities can drive quantum phase transitions towards different kinds of quantum spin liquid. The fingerprint of such transitions is the fractionalisation of the usual spin waves into pairs of fermionic excitations (i.e., two-dimensional spinons). Indeed, fractionalisation is characteristic of 1D-spin chain systems but is not incompatible with 2D long-range AF order. Although in cuprates inelastic neutron and X-ray scattering have detected anomalies in the magnetic spectra [2], no definitive evidence of fractionalisation had been found so far, due to the difficulty of distinguishing pairs of spinons from other types of magnetic excitations (e.g., multi-magnons).

Resonant inelastic X-ray scattering (RIXS) was used at beamline ID32 to investigate the magnetic spectrum of the infinite-layer cuprate CaCuO2 (CCO). In this material, the absence of apical oxygens enhances both the nearest- neighbour J and the longer-range super-exchange

interactions with respect to other cuprates [3]. As a result, the multi-spin interaction known as ring exchange Jc is very large too.

The evidence of fractionalisation of magnons can be seen in the Brillouin-zone map of Figure 100a. The sharp spin- wave peak, dispersing across most of the Brillouin zone, breaks into a continuum of high-energy states when approaching the antinodal point X. This continuum shows a broad energy bandwidth, as shown in Figure 100b, and carries the majority of the magnetic spectral weight (Figure 100c).

To unravel its nature, the unique capabilities of the ERIXS spectrometer were employed, including ultrahigh energy resolution (26 meV at the Cu L3 absorption edge) and the soft X-ray polarimeter, which makes it possible to disentangle spin-flip and spin-conserving excitations. Their polarisation dependence reveals a dominant spin-

Fig. 100: a) Momentum- dependence of the magnetic

excitations in CaCuO2, measured along the path

depicted in the inset. b) RIXS spectrum at the X point (1/2,0).

Red curve is the result of a fitting. The light-blue curve

is a Voigt profile representing the magnon, while the deep

blue one fits the putative two- spinon continuum. c) Ratio

between the magnon spectral weight and the total magnetic

spectral weight as a function of momentum along the same

path of panel (a).

Fig. 101: a) Polarisation-resolved spectrum of CCO at the X point. Red is the spin-flip channel, while blue is the spin- conserving one. The green curve is a Voigt curve fitting the

magnon profile. b) Same spectrum on Sr2Cu2OCl2.