Phonon anomalies and magnetic excitations in ${\mathrm{BaFe}}_2{\mathrm{Se}}_2\mathrm{O}$

We report a temperature- and magnetic-field-dependent Raman-scattering study of the spin-ladder compound ${\mathrm{BaFe}}_2{\mathrm{Se}}_2\mathrm{O}$. Temperature evolution of the $B_{1g}$ mode self-energies revealed anomalous behavior at about 100 and 240 K with strong temperature-dependent Fano asymmetry. Furthermore, the $A_g$ modes integrated intensity exhibits an additional change in tendency at about 50 K. All the observed anomalies can be traced back to spin-phonon interaction contributions as well as multiple magnetic phase transitions present in ${\mathrm{BaFe}}_2{\mathrm{Se}}_2\mathrm{O}$ also detected in the Raman continuum induced by the spin fluctuations. Moreover, the absence of magnetic-field dependence of the magnetic mode observed at $436{\mathrm{cm}}^{-1}$ and the small linewidth and high intensity are different from the magnetic modes at about $650{\mathrm{cm}}^{-1}$. This suggests a two-magnon continuum and a two-magnon bound state resonance for this mode.

Figure 1

Identification and temperature dependence of phonon modes in ${\mathrm{BaFe}}_2{\mathrm{Se}}_2\mathrm{O}$. No change of crystal structure fingerprint was observed in the phonon spectra down to 10 K.

Figure 2

Anomalies of $B_{1g}$ modes induced by spin-lattice coupling. (a) Temperature dependence of Raman spectra for the $c\left(ab\right)\overline{c}$ polarization configuration, in which only the $B_{1g}$ modes can be observed. The solid black line is a fit to a Fano line shape. Temperature dependence of the (b) frequency shift, (c) linewidth, and (d) Fano asymmetry parameters $|1/q|$ of $B_{1g}^1$ (left axis, black) and $B_{1g}^2$ (right axis, red) modes. The solid lines in (b) represent a fit to Eq. (1) and the dotted line in (c) represents the behavior expected from anharmonicity.

Figure 3

(a) Integrated intensity of the $A_g^1, A_g^2$, and $A_g^3$ symmetry modes as a function of temperature. (b) Temperature evolution of Raman susceptibility data for ${\mathrm{BaFe}}_2{\mathrm{Se}}_2\mathrm{O}$ obtained in parallel scattering configuration. The pronounced Raman continuum evolution is observable only in parallel [i.e., $\left(aa\right)$ or $\left(bb\right)]$ and absent in cross polarization configurations [i.e., $\left(ab\right)$ or $\left(ba\right)]$ (not shown). (c) Temperature dependence of dynamical susceptibility ${\chi }^{\mathrm{dynamic}}\left(T\right)$ obtained from the Raman data.

Figure 4

Identification of magnetic excitations in ${\mathrm{BaFe}}_2{\mathrm{Se}}_2\mathrm{O}$. (a) Field-dependent Raman spectra, measured at 10 K with 532-nm laser line (solid lines). The spectrum (dotted line) collected at 0 T with a 633-nm laser are also shown for comparison. Inset: Schematic spin excitation spectrum of ${\mathrm{BaFe}}_2{\mathrm{Se}}_2\mathrm{O}$. The green dashed line represents a possible two-magnon bound state. Field dependence of the (b) energy and (c) intensity of the $M0$ mode. Inset of (b): Schematic representation of the periodic magnetic structure in the $\left(ab\right)$ plane. $J$ represents Fe-O-Fe antiferromagnetic (AFM) exchange interaction along the rungs; $J^{\prime }$ is the interladder Fe-Se-Fe AFM exchange interaction. $J^{\prime \prime }$ is the ferromagnetic Fe-Se-Fe exchange interaction along the ladder legs and can be neglected.

Figure 5

Anharmonic (solid line) and spin-phonon (dashed line) contribution to the temperature dependence of the energy of (a) $B_{1g}^1$ and (b) $B_{1g}^2$ phonon modes obtained by fitting Eq. (1) to the experimental data.

Figure 6

Temperature-dependent spectra of the $M0, M{1}^{\prime }$, and $M{1}^{\prime \prime }$ modes at 0 and 9 T.