Magnons in tetragonal CuO

We investigate by resonant inelastic x-ray scattering the magnetic excitations in thin films of tetragonal CuO. We identify a spin wave excitation, dispersing on two cupratelike antiferromagnetic sublattices. Its energy at the boundary of the Brillouin zone (220 meV), is significantly lower than typical values $(E\sim 300$ meV) found in two-dimensional cuprates. A spin wave expansion starting from an extended Hubbard model suggests two possible scenarios for this energy lowering.

Figure 1

Corner-sharing ${\mathrm{CuO}}_2$ (a) and edge-sharing CuO (b) layers. Red and blue contours indicate Cu $d_{x^2-y^2}$ and O $p_x/p_y$ orbitals, respectively. The CuO layer is seen as the superposition of two corner-sharing sublattices (I) and (II). The effective hopping terms are indicated by arrows. Additionally, we mark the effective exchange terms of the $J_1\text{−}{J}_2$ model.

Figure 2

(a) The structure of a CuO layer, with Cu (O) ions indicated in red (blue). The red square is the unit cell. The (blue dashed) black square is the (magnetic) unit cell of one sublattice. The corresponding Brillouin zones are shown in (b). (c) RIXS spectrum taken at the $A$ point, on the magnetic BZ boundary. The inset shows the Cu $L_{2,3}$ x-ray absorption spectrum. (d), (e) Cu $L_3$ RIXS spectra measured along the $\mathrm{\Gamma }X$ (d) and $\mathrm{\Gamma }{X}^{\prime }$ (e) high-symmetry directions. The light polarization and momentum ranges are shown by yellow arrows in (a) and by thick black lines in (b), respectively.

Figure 3

(a) Second derivative map extracted from the data of Fig. 2. Data for SCOC [7] are shown as red circles. The lines are $t\text{−}{t}^{\prime }\text{−}{t}^{\prime \prime }\text{−}U$-Hubbard model fits to the data: (red) SCOC, (black) SCOC + $t_d=100$ meV, (orange) parameter set (i), (blue) parameter set (ii), and (purple) parameter set (iii) of Table 1. The average of the two possible columnar orderings is plotted. (b) Band dispersion corresponding to parameter set (ii) (blue) and (iii) (purple). Solid (dashed) lines refer to the branch along the AFM (FM) direction. (c)–(e) Magnetic structures: independent sublattice model (c); columnar ordering with FM direction along (1,1) (d) and $(-1$,1) (e).

Figure 4

Effective exchange interaction terms of the first five nearest neighbors, calculated for SCOC (red), and with parameter sets (i) (orange) and (ii) (blue) of Table 1, respectively. Dark blue corresponds to the AFM direction, and light blue to the FM direction. Inset: Definition of the effective exchange interaction terms on the T-CuO lattice (red: copper; blue: oxygen). Primed (unprimed) numbers correspond to the AFM (FM) direction of the columnar phase.