Triplons, magnons, and spinons in a single quantum spin system: ${\mathrm{SeCuO}}_3$

Quantum magnets display a wide variety of collective excitations, including spin waves (magnons), coherent singlet-triplet excitations (triplons), and pairs of fractional spins (spinons). These modes differ radically in nature and properties, and in all conventional analyses any given material is interpreted in terms of only one type. We report inelastic neutron scattering measurements on the spin-1/2 antiferromagnet $\mathrm{Se}\mathrm{Cu}{\mathrm{O}}_3$, which demonstrate that this compound exhibits all three primary types of spin excitation. ${\mathrm{Cu}}_1$ sites form strongly bound dimers while ${\mathrm{Cu}}_2$ sites form a network of spin chains, whose weak three-dimensional (3D) coupling induces antiferromagnetic order. We perform quantitative modeling to extract all of the relevant magnetic interactions and show that magnons of the ${\mathrm{Cu}}_2$ system give a lower bound to the spinon continua, while the ${\mathrm{Cu}}_1$ system hosts a band of high-energy triplons at the same time as frustrating the 3D network.

Figure 1

Atomic structure and magnetic interactions of $\mathrm{Se}\mathrm{Cu}{\mathrm{O}}_3$. (a) Schematic representation of the atomic structure showing ${\mathrm{Cu}}_1$ (orange), ${\mathrm{Cu}}_2$ (blue), Se (green), and O (pink) atoms. (b) Projection on the $ac$ and (c) on the $ab$ plane, indicating the magnetic interactions of Table 1. (d) Perspective view highlighting the ${\mathrm{Cu}}_2$ chains and the direct interactions connecting them into coupled, buckled planes. (e) Geometry of the effective interactions mediated between ${\mathrm{Cu}}_2$ atoms by the ${\mathrm{Cu}}_1$ dimer units: ${\mathcal{J}}_{\alpha }$ and ${\mathcal{J}}_{\beta }$ are given in terms of the two different ${\mathrm{Cu}}_1\text{−}{\mathrm{Cu}}_2$ interactions, $J_{12}^{\alpha }$ (green) and $J_{12}^{\beta }$ (purple), and the dimer interaction, $J_D$ (black), by Eq. (2).

Figure 2

Triplon excitation. (a) Intensity, $I\left(\omega \right)$, at $\mathbf{q}=\left(0.530.5\right)$, measured at low (blue) and intermediate (red) temperatures with the difference shown in black. (b) Dispersion, $\omega \left(\mathbf{q}\right)$, of the triplon in two orthogonal $\mathbf{q}$ directions; shading represents the width (FWHM) of the mode at each q point. (c) Integrated intensity, $I\left(\mathbf{q}\right)$, for the same directions. (d)–(f) Thermal evolution at $\mathbf{q}=\left(030\right)$. (d) Lorentzian width, ${\mathrm{\Gamma }}_{\mathcal{L}}$ (red), compared to $k_{\mathrm{B}}T$ (blue). (e) $\omega (\mathbf{q},T)$; shading indicates the instrumental resolution of 1.8(2) meV (red) and the Lorentzian profile (blue). (f) Normalized $I\left(\mathbf{q}\right)$ in red compared with the thermal singlet population (blue).

Figure 3

Magnon peak and scattering continua. $I\left(\omega \right)$ at three different $\mathbf{q}$ points. Measured data (red points) are fitted by a Gaussian peak (blue line) at the lower edge. Green shading indicates a scattering continuum at higher energies.

Figure 4

Magnon and spinon spectra. Colored panels show the scattering intensity, $S(\mathbf{q},\omega )$, for five different $\mathbf{q}$ directions. The black points show the peak centers taken from Fig. 3 and the error bars the extracted width (FWHM) of the Gaussian profiles. The black lines show the two spin-wave branches in the model fit to the lower peak of Fig. 3, one of which (dashed line) has vanishing intensity. The upper panels show the integrated intensities, $I\left(\mathbf{q}\right)$, of the measured spin-wave contribution [$I_{\mathrm{p}}\left(\mathbf{q}\right)$, red points] and the continuum contribution [$I_{\mathrm{c}}\left(\mathbf{q}\right)$, green points], taken respectively from the peak and shaded areas in Fig. 3; the black lines show the spin-wave intensities given by the model parameters. In the panel at right, the intensity is a sum of two modes.