High-energy continuum of magnetic excitations in the two-dimensional quantum antiferromagnet ${\mathrm{Sr}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$

We have measured the magnetic excitation spectrum of the model square-lattice spin-1/2 antiferromagnet ${\text{Sr}}_2{\text{CuO}}_2{\text{Cl}}_2$  over a broad range of energies and momenta using high-resolution inelastic neutron scattering (INS). The magnon dispersion along the zone boundary was accurately measured to be a 43 meV between $(1/2,0)$ and $(3/4,1/4)$ indicating the importance of coupling beyond nearest neighbors in the spin Hamiltonian. We observe a strong momentum dependent damping of the zone-boundary magnons at $(1/2,0)$ revealing a high-energy continuum of magnetic excitations. A direct comparison between our INS measurements and resonant inelastic x-ray scattering (RIXS) measurements shows that the RIXS spectrum contains significant contributions from higher energy excitations not previously considered. Our observations demonstrate that this high-energy continuum of magnetic fluctuations is an ubiquitous feature of insulating monolayer cuprates, apparent in both inelastic neutron and light scattering measurements.

Figure 1

Representative constant energy transfer slices displaying the raw INS intensity at$T=5$ K, the corresponding momentum transfer along (0,0,$\ell$) is labeled in each panel. Data in panel (a) were collected with and incident energy of $E_i=150$ meV and a total proton charge of 47.5 C. Data in panels (b)–(e) were taken with$E_i=450$ meV and a proton charge of 186 C. All data were scaled to absolute units by normalizing with incoherent elastic scattering from the sample.

Figure 2

(a), (b) Constant energy cuts near the antiferromagnetic zone center for an incident neutron energy of 150 meV, integrated over $h\pm$0.1 r.l.u. (c), (d) Constant momentum transfer cuts through the zone boundaries integrated over $h,k\pm$0.1 r.l.u. for an incident neutron energy of 450 meV. An energy dependent background, measured near Q = (1,0), has been subtracted from the constant momentum transfer cuts. Horizontal black solid lines in (c) and (d) indicate the time-of-flight spectrometer resolution FWHM at the zone boundaries. Red lines are fits to the resolution convolved model cross section, including the anisotropic form factor for ${\text{Cu}}^{2+}{d}_{x^2-y^2}$ orbitals [15]. Triangles in (c) and (d) are the corresponding RIXS data from Ref. [10].

Figure 3

(a) Magnon dispersion along high symmetry directions measured by INS in ${\text{Sr}}_2{\text{CuO}}_2{\text{Cl}}_2$  at $T=5$ K. Each point was extracted by fitting to individual constant momentum or energy transfer cuts. Square points were obtained from the $E_i=150$ meV data, and the circles from the $E_i=450$ meV data. The solid black line is the best fit to the spin-wave dispersion relation, and the red filled area is the difference between the RIXS results of [10] and the INS measurement. (b) Wave-vector dependence of the integrated spin-wave intensity. The black solid line is the prediction of linear spin-wave theory including an intensity renormalization factor $Z_d=0.48\left(5\right)$ [17].