Phonon spectrum of ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ and ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ as evidence of coupling of the lattice with electronic and magnetic degrees of freedom

Magnetic materials with pyrochlore crystal structure form exotic magnetic states due to the high lattice frustration. In this work we follow the effects of coupling of the lattice and electronic and magnetic degrees of freedom in two praseodymium-based pyrochlores ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ and ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. In either of these materials, the presence of magnetic interactions does not lead to magnetically ordered low temperature states; however, their electronic properties are different. A comparison of Raman phonon spectra of ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ and ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ allows us to identify magnetoelastic coupling in ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ that elucidates its magnetic properties at intermediate temperatures and allows us to characterize phonon-electron scattering in the semimetallic ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. We also show that the effects of random disorder on the Raman phonon spectra is small.

Figure 1

Raman scattering spectra of (a) ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ and (b) ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ at 14 K in parallel polarization configuration. Solid black curve shows the experimental data after a linear background subtraction. Dashed gray line shows the overall fitting.

Figure 2

Temperature dependence of the Raman scattering spectra of ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ in (a) $(x,x)$ channel and (b) $(x,y)$ channel.

Figure 3

Temperature dependence of the Raman scattering spectra of ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ in $(x,x)$ channel.

Figure 4

(a) Temperature dependence of Raman scattering spectra of ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ in the region of $A_{1g}\to E_g$ crystal electric field transitions in $(x,y)$ channel. (b) Temperature dependence of spectral weight $I\left(T\right)={\int }_{430{\mathrm{cm}}^{-1}}^{330{\mathrm{cm}}^{-1}}{\chi }^{″}\left(\omega \right)d\omega$. (c) Atomic displacement of $T_{2g}^{\left(2\right)}$ phonon mode. (d) Raman spectra of ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ (upper panel) and ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ (lower panel) at 14 K in $(x,x)$ and $(x,y)$ channel on a log scale. Crystal field excitations are marked in different colors. Note the double feature of the excitation at about $450{\mathrm{cm}}^{-1}$ for both materials. (e) Crystal field scheme of ${\mathrm{Pr}}^{3+}$ ions in $D_{3d}$ crystal environment. Energy values are provided for ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$.

Figure 5

Temperature dependence of (a) linewidths and (b) positions for ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ (blue) and ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ (red). Black lines are fits of linewidth of ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ phonons with extended Klemens model. Dashed lines show the same temperature dependence with ${\mathrm{\Gamma }}_0$ increased for ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. Green lines are the fits of linewidth of ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ phonons by the phonon-electron scattering model. Note that the temperature dependence for ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ phonons is best fit by phonon-electron scattering.