Magnetic excitations and phonons in the spin-chain compound $\mathrm{Na}{\mathrm{Cu}}_2{\mathrm{O}}_2$

We report an inelastic light scattering study of single-crystalline $\mathrm{Na}{\mathrm{Cu}}_2{\mathrm{O}}_2$, a spin-chain compound known to exhibit a phase with helical magnetic order at low temperatures. Phonon excitations were studied as a function of temperature and light polarization, and the phonon frequencies are compared to the results of ab initio lattice dynamical calculations, which are also reported here. The good agreement between the observed and calculated modes allows an assignment of the phonon eigenvectors. Two distinct high-energy two-magnon features as well as a sharp low-energy one-magnon peak were also observed. These features are discussed in terms of the magnon modes expected in a helically ordered state. At high temperatures, the spectral features attributable to magnetic excitations are replaced by a broad, quasielastic mode due to overdamped spin excitations.

Figure 1

(Color online) Pictorial representation of the lattice structure of $\mathrm{Na}{\mathrm{Cu}}_2{\mathrm{O}}_2$. The red balls stand for the oxygen ions, the blue ones for sodium, the yellow ones for the ${\mathrm{Cu}}^{+2}$, and the orange ones for the ${\mathrm{Cu}}^{+1}$.

Figure 2

(Color online) Polarization dependence of Raman spectra at 5 and $295\mathrm{K}$ in $bb$-, $ba$-, and $aa$-polarizations, respectively. The downward vertical arrows indicate magnetic excitations while the upward one denotes a Fano-shaped dip corresponding to the phonon at $502{\mathrm{cm}}^{-1}$.

Figure 3

(Color online) Calculated normal frequencies and eigenvectors of the $A_g$-symmetry modes. The relative amplitude of the vibrations (arrow length) is correct within each mode. For the sake of clarity a multiplication factor has been applied to some modes. The red balls stand for the oxygen ions, the blue ones for sodium, the yellow ones for the ${\mathrm{Cu}}^{+2}$, and the orange ones for the ${\mathrm{Cu}}^{+1}$. The color scheme is identical to that of Fig. 1.

Figure 4

(Color online) Calculated normal frequencies and eigenvectors of the $B_{1g}$-symmetry modes. The relative amplitude of the vibrations (arrow length) is correct within each mode. For the sake of clarity a multiplication factor has been applied to some modes.

Figure 5

(Color online) (Left panel) Temperature dependence of the peak frequencies of selected phonons. (Right panel) Phonon linewidths as a function of temperature.

Figure 6

(Color online) Temperature dependence of magnetic Raman spectra in $ba$-polarization at 5, 20, 40, 60, and $80\mathrm{K}$ (from upper to lower curve).

Figure 7

(Color online) (a) Low-frequency magnetic Raman spectra in $ba$-polarization as a function of temperature. (b) and (c) Temperature dependence of the peak position and integrated intensity on a reduced temperature scale, respectively.

Figure 8

(Color online) Raman spectra in $bb$-polarization as a function of temperature; 290, 150, 80, 50, and $5\mathrm{K}$ from upper to lower curve.

Figure 9

(Color online) Result of a fit of the quasielastic response to a Lorentzian profile at $295\mathrm{K}$. Inset: Temperature dependence of the integrated scattering intensity of this profile.