Polar phonons in the antiferromagnetic $S=\frac{1}{2}$ spin-chain system ${\mathrm{CuSb}}_2{\mathrm{O}}_6$

Optical properties of an $S=\frac{1}{2}$ antiferromagnetic spin-chain system $\beta -{\mathrm{CuSb}}_2{\mathrm{O}}_6$ are measured in the frequency range 50–10 000 ${\mathrm{cm}}^{\mathrm{-}1}$ at temperatures of 5–300 K for the electric field polarized along the [010] and [001] crystallographic directions. The number of observed polar phonon modes at low temperature is in agreement with the factor-group analysis for the monoclinic form of $\beta -{\mathrm{CuSb}}_2{\mathrm{O}}_6.$ The mode parameters are determined by using the dispersion analysis of the reflectivity spectra at different temperatures. The parameters of several phonon modes show anomalies around 60 K, at the temperature where the one-dimensional magnetic correlations in the copper chains are largest. This may indicate a finite interaction between the phonon and electron subsystems in $\beta -{\mathrm{CuSb}}_2{\mathrm{O}}_6.$ The theoretical group analysis of the possible rutile low-symmetry phases is performed within the framework of Landau’s theory of phase transitions. The trirutile-rutile phase transformation can be uniquely described by an order parameter which transforms according to the two-dimensional irreducible representation ${\Lambda }_4$ with $\mathbf{k}=\frac{1}{3}$ ${\mathbf{b}}_3$ of the Brillouin zone of the proper rutile unit cell only. Optical modes assignment of $\beta -{\mathrm{CuSb}}_2{\mathrm{O}}_6$ performed with use of the aristotype rutile structure allows one to reproduce the tentative picture of the $\alpha -{\mathrm{CuSb}}_2{\mathrm{O}}_6$ phonon dispersion curves.