Identifying fractional spin excitations in a 2D cuprate

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., 2-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 had 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” J_c is very large too.

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Fig. 1: 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).

The evidence of fractionalisation of magnons can be seen in the Brillouin-zone map of Figure 1a. 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. Such continuum shows a broad energy bandwidth, as shown in Figure 1b, and carries the majority of the magnetic spectral weight (Figure 1c).

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Fig. 2: 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.

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 allows to disentangle spin-flip and spin-conserving excitations. Their polarisation dependence reveals a dominant spin-flip character (Figure 2a), which, together with their incident-energy behaviour, rules out a more trivial multi-magnon origin. As a comparison, Figure 2b shows the corresponding spectrum in Sr₂CuO₂Cl₂ (SCOC), which has a much smaller ring exchange J_c than CaCuO₂. In SCOC, the magnon peak is the dominant excitation even at the X point. Therefore, sound evidence links such anomaly in CCO to a two-spinon continuum, and correlates its presence with an exceptionally high J_c∼J.

This work confirms that in the CuO₂ planes of cuprates, long-range antiferromagnetism can coexist with spin-glass phenomena and paves the way for future RIXS studies on quantum magnetism.

Principal publication and authors
Fractional Spin Excitations in the Infinite-Layer Cuprate CaCuO₂, L. Martinelli (a), D. Betto (b), K. Kummer (b), R. Arpaia (c), L. Braicovich (a,b), D. Di Castro (d,e), N.B. Brookes (b), M. Moretti Sala (a), G. Ghiringhelli (a,f), Phys. Rev. X 12, 021041 (2022); https://doi.org/10.1103/PhysRevX.12.021041
(a) Politecnico di Milano (Italy)
(b) ESRF (France)
(c) Chalmers University of Technology (Sweden)
(d) Università di Roma Tor Vergata (Italy)
(e) CNR-SPIN, Roma (Italy)
(f) CNR-SPIN, Milano (Italy)

References
[1] H. Shao et al., Phys. Rev. X 7, 041072 (2017).
[2] N.S. Headings et al., Phys. Rev. Lett. 105, 247001 (2010).
[3] Y.Y. Peng et al., Nat. Phys. 13, 1201-1206 (2017).