Common acoustic phonon lifetimes in inorganic and hybrid lead halide perovskites

The acoustic phonons in the organic-inorganic lead halide perovskites have been reported to have anomalously short lifetimes over a large part of the Brillouin zone. The resulting shortened mean free paths of the phonons have been implicated as the origin of the low thermal conductivity. We apply neutron spectroscopy to show that the same acoustic phonon energy linewidth broadening (corresponding to shortened lifetimes) occurs in the fully inorganic ${\mathrm{CsPbBr}}_3$ by comparing the results on the organic-inorganic ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbCl}}_3$. We investigate the critical dynamics near the three zone boundaries of the cubic $Pm\overline{3}m$ Brillouin zone of ${\mathrm{CsPbBr}}_3$ and find energy and momentum broadened dynamics at momentum points where the Cs-site ($A$-site) motions contribute to the cross section. Neutron diffraction is used to confirm that both the Cs and Br sites have unusually large thermal displacements with an anisotropy that mirrors the low temperature structural distortions. The presence of an organic molecule is not necessary to disrupt the low-energy acoustic phonons at momentum transfers located away from the zone center in the lead halide perovskites and such damping may be driven by the large displacements or possibly disorder on the $A$ site.

Figure 1

(a) Crystallographic structure of ${\mathrm{CsPbBr}}_3$ in the cubic phase. The Pb site is represented by the gray sphere, the Br ions are in light brown, and the Cs ions are in blue. The figure on the top shows the high symmetry points in the first Brillouin zone of a primitive cubic lattice. $X$, $M$, and $R$ represent $\mathbf{Q}=(\frac{1}{2},0,0),(\frac{1}{2},\frac{1}{2},0)$, and $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$, respectively. (b) Temperature dependence of the superlattice intensities at the three zone boundaries $X$ (2,$\frac{1}{2}$,0), $M$ ($\frac{3}{2},\frac{1}{2}$,0) and $R$ ($\frac{1}{2},\frac{1}{2},\frac{3}{2}$). The colored dashed lines indicate the two transition temperatures.

Figure 2

(a) Constant-Q cuts through the acoustic phonon ${\mathrm{TA}}_1$ for several Q positions from the (2 0 0) Bragg peak towards the $X$ point. (b) Dispersion curves associated to the ${\mathrm{TA}}_1$ mode towards the $X$ point. The data is compared to the organic-inorganic compound ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbCl}}_3$ in its cubic phase (gray circles, from Ref. [1]). The blue and gray dashed lines are a fit to a sine function performed near the $q\to 0$ limit. (c) Q dependence of the ${\mathrm{TA}}_1$ phonon linewidths extracted from the constant-Q cuts as described in the text and compared to the phonon linewidth for ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbCl}}_3$ (gray diamonds, from Ref. [1]). The gray dashed areas represent the instrumental resolution of SPINS ($q<0.22$) and IN22 ($q>0.22$).

Figure 3

(a) Constant-Q cuts through the acoustic phonon ${\mathrm{TA}}_2$ for several Q positions from the (2 2 0) Bragg peak towards the $M$ point. (b) Dispersion curves associated with the ${\mathrm{TA}}_2$ mode towards the $M$ point. The data is compared to the organic-inorganic compound ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbCl}}_3$ in its cubic phase (gray triangles, from Ref. [1]). The blue and gray dashed lines are a fit to a sine function performed near the $q\to 0$ limit. (c) Q dependence of the ${\mathrm{TA}}_2$ phonon linewidths extracted from the constant-Q cuts as described in the text and compared to the phonon linewidth for ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbCl}}_3$ (gray squares, from Ref. [1]). The blue and gray dashed lines are a guide to the eye. The gray dashed area represents the instrumental resolution of IN22.

Figure 4

(a) Powder neutron diffraction data performed on BT1 ($\lambda =2.079\AA$) at $T=365$ K. The red dots and black line represent the measured and calculated intensities, respectively. The blue tick marks indicate the calculated reflections and the blue line represents the difference between measured and calculated intensities. (b) Thermal parameters for the three spatial components associated with the ${\mathrm{Br}}_1$, ${\mathrm{Br}}_2$, and Cs sites, respectively, as a function of temperature. The colored areas and dashed lines indicate the tetragonal and orthorhombic transitions.

Figure 5

(a),(b) Thermal displacements of Cs ions (blue ellipsoids) and $\mathrm{Pb}{\mathrm{Br}}_6$ octahedra tiltings (right panels) in the tetragonal and orthorhombic phases, respectively. The arrows indicate atomic displacements and octahedral rotations.

Figure 6

(a) Constant-Q cuts through the ${\mathrm{TA}}_1$ mode at the $M$ point ($\frac{3}{2},\frac{1}{2}$,0) measured on IN22 at 300 K and 420 K. (b) Constant-Q cuts through the ${\mathrm{TA}}_1$ mode at the $R$ point ($\frac{1}{2},\frac{1}{2},\frac{3}{2}$) measured on SPINS at 300 K and 420 K.

Figure 7

(a) Constant-Q cuts through the ${\mathrm{TA}}_1$ mode at the $X$ point measured on IN22 at 300 K (orthorhombic phase) and 420 K (cubic phase). (b) Temperature dependence of the energy position (black circles) and the energy linewidth (white circles) of the ${\mathrm{TA}}_1$ phonon at the $X$ (2,$\frac{1}{2}$,0) zone boundary. The vertical dashed line indicates the orthorhombic transition.

Figure 8

(a) Energy scans measured on SPINS at the $R$ point ($\frac{1}{2},\frac{1}{2},\frac{3}{2}$) in the cubic and orthorhombic phases. The black dashed line indicates the instrumental energy resolution, extracted from the incoherent signal of vanadium. (b) Elastic scans measured on SPINS at the $R$ point ($\frac{1}{2},\frac{1}{2},\frac{3}{2}$) at several temperatures. The black dashed line shows the Bragg instrumental resolution in momentum. (c) Temperature dependence of the energy linewidth extracted from the quasi-elastic scans at the $R$ point. (d) Temperature dependence of the spatial correlation (inverse of the momentum linewidth) extracted from the elastic scans at the $R$ point. The vertical dashed line indicates the temperature transition to the orthorhombic phase.

Figure 9

(a),(b) Energy scans measured on SPINS and IN22 at the $X$ and $M$ points, respectively, in the cubic and orthorhombic phase.