Collective excitations in the metallic triangular antiferromagnet $\mathrm{Pd}\mathrm{Cr}{\mathrm{O}}_2$

We report a combined Raman-scattering and electron spin resonance (ESR) study of the metallic triangular compound $\mathrm{Pd}\mathrm{Cr}{\mathrm{O}}_2$ along with lattice dynamic calculations. Our Raman data reveal (i) an exponential increase of the 706 cm${}^{-1}$ $A_g$ mode involving the out-of-plane motions of the oxygen atoms and (ii) electronic Raman scatterings whose scattering rate is strongly suppressed as the temperature approaches $T_N=37.5$ K. The temperature dependence of the ESR linewidth is described by a critical broadening $\Delta H_{pp}\left(T\right)\propto {(T-T_N)}^{-p}$ with the exponent $p=0.63\pm 0.05$. These are interpreted in terms of coherence of interplane hoppings along the $c$ axis and a reconstruction of electronic bands on approaching $T_N$. Our results suggest a significant role of an interference between metallic and magnetic layers in explaining collective excitations in $\mathrm{Pd}\mathrm{Cr}{\mathrm{O}}_2$.

Figure 1

Representative Raman spectrum at $T=5$ K in ($xx$) and ($xy$) polarization. The strong peak at 710 cm${}^{-1}$ is assigned to the $A_{1g}$ mode and the weak peak at 556 cm${}^{-1}$ to the $E_g$ mode according to the lattice dynamical calculations; see the text for details. Inset: Zoom of the 710 cm${}^{-1}$ $A_{1g}$ mode in ($xx$) polarization as a function of temperature.

Figure 2

Schematic representation of calculated eigenvectors of the 550 cm${}^{-1}$ $E_g$ and the 706 cm${}^{-1}$ $A_{1g}$ symmetry mode at room temperature. The amplitude of the vibrations is represented by the arrow length. Green balls stand for Pd ions, red balls for O ions, and blue balls for Cr ions, respectively.

Figure 3

(a) Temperature dependence of the frequency of the 706 cm${}^{-1}$ mode. The solid line is a fit to Eq. (1). (b) Temperature dependence of the full width at half maximum. The solid line is a fit to Eq. (2). (c) Temperature dependence of the normalized intensity. The inset plots the normalized intensity on a semilogarithmic scale.

Figure 4

Bose-corrected Raman spectra Im $\chi \left(\omega \right)$ at $T=5$, 100, and 240 K. The Raman responses are vertically shifted for clarity. The solid lines are fits to Eq. (3). The inset plots the scattering rate ${\Gamma }_e\left(T\right)$ as a function of temperature.

Figure 5

(a) Derivative of the ESR absorption spectra of the PdCrO${}_2$ crystal measured at $\nu =240$ GHz for the $H\perp ab$ plane as a function of temperature. The spectra are vertically shifted for clarity. The asterisk denotes an impurity signal. Representative fits of the amplitude of the ESR signal to Lorentzian profiles at (b) $T=220$ K and (c) $T=70$ K are shown together with their phase.

Figure 6

Upper panel: Temperature dependence of the ESR linewidth $\Delta H_{pp}\left(T\right)$. The dashed line is a fit to a power law. Lower panel: Temperature dependence of the resonance field $H_{\mathrm{res}}\left(T\right)$. The dashed line is a guide to the eye.