Phonon and magnon Raman scattering in CuB${}_2$O${}_4$

The Brillouin-zone-center phonons and two-magnon excitations in CuB${}_2$O${}_4$ are studied experimentally by polarized Raman spectroscopy. Most of the expected modes are clearly pronounced and their symmetry unambiguously identified from the polarization selection rules. The experimentally observed transverse optical phonon frequencies are in good agreement with those obtained by means of density functional theory. The two-magnon scattering band is centered at 82 cm${}^{-1}$ and is clearly identified at temperatures below the Néel temperature $T_{\text{N}}$. The spectral shape of the two-magnon band confirms the existing theoretical models of magnon dispersion in the commensurate phase of CuB${}_2$O${}_4$ and suggests an exchange integral of $J=33$ cm${}^{-1}$ (48 K) between the nearest-neighbor Cu(A) ions. The quantitative line-shape analysis of the two-magnon band evidences for additional magnon self-energy contributions below the temperature $T^{*}$ of the commensurate-to-incommensurate phase transition.

Figure 1

Polarized room-temperature Raman spectra of CuB${}_2$O${}_4$ for 458-nm excitation. Frequencies are shown only for those lines, which are allowed in a given scattering configuration. Raman lines of equivalent symmetries are labeled with one and the same color. The unlabeled lines correspond to polarization leakage from other scattering configurations.

Figure 2

Raman spectra of CuB${}_2$O${}_4$ obtained in $y\left(zz\right)\overline{y}$ scattering configuration at 300 K with four different laser lines. Only $A_1$ lines are allowed in this configuration.

Figure 3

Evolution of the Raman spectra of CuB${}_2$O${}_4$ in $y\left(xx\right)\overline{y}$ scattering configuration and 488-nm excitation upon decreasing the temperature from 180 to 4 K.

Figure 4

Raman spectra of CuB${}_2$O${}_4$ at 6 K in $z\left(xx\right)\overline{z}$, $z\left(x^{\prime }{x}^{\prime }\right)\overline{z}$, $z\left(x^{\prime }{y}^{\prime }\right)\overline{z}$, $z\left(xy\right)\overline{z}$, $y\left(xx\right)\overline{y}$, $y\left(xz\right)\overline{y}$, and $y\left(zz\right)\overline{y}$ scattering configurations.

Figure 5

The sublattice of the Cu(A) ($4b$) positions. Indicated are the strong ($J_1$) and the weak ($J_2$) exchange interactions.

Figure 6

Comparison between the experimental line shape of the two-magnon band at 4 K (dots) and the model of interacting magnons (10) (solid line).

Figure 7

Temperature dependence of the renormalization coefficient $r$ in the vicinity of IC-C phase transition. The solid line is a guide for the eye.