Glass-like thermal conductivity in nanostructures of a complex anisotropic crystal

Size effects on vibrational modes in complex crystals remain largely unexplored, despite their importance in a variety of electronic and energy conversion technologies. Enabled by advances in a four-probe thermal transport measurement method, we report the observation of glass-like thermal conductivity in $\sim 20$-nm-thick single crystalline ribbons of higher manganese silicide, a complex, anisotropic crystal with a $\sim 10$-nm-scale lattice constant along the incommensurate $c$ axis. The boundary-scattering effect is strong for many vibrational modes because of a strong anisotropy in their group velocities or diffusive nature, while confinement effects are pronounced for acoustic modes with long wavelengths along the $c$ axis. Furthermore, the transport of the nonpropagating, diffusive modes is suppressed in the nanostructures by the increased incommensurability between the two substructures as a result of the unusual composition of the nanostructure samples. These unique effects point to diverse approaches to suppressing the lattice thermal conductivity in complex materials.

Figure 1

A representative crystal structure and vibrational spectrum of HMS. The Mn atoms (red) form a tetragonal lattice, while the Si atoms (blue) form coupled helices aligned along the $c$ axis to form a homologous series of compounds. The $c$ lattice parameter of the specific ${\mathrm{Mn}}_{11}{\mathrm{Si}}_{19}$ phase shown here, $c_{\mathrm{HMS}}$, is 47.7 Å, while the $a$ lattice parameter, $a_{\mathrm{HMS}}$, is 5.5 Å. The top right inset shows the calculated vibrational spectrum of the ${\mathrm{Mn}}_4{\mathrm{Si}}_7$ phase from Ref. [30].

Figure 2

Electron microscopy images of the nanostructure on the measurement device. (a) Scanning electron microscopy (SEM) images of a suspended measurement device. (b), (c) SEM images of HMS NR1 with false coloring (blue) of the Pd contact pads transferred to the device with the sample. (d) ${85}^{\circ }$ tilted SEM image of NR1. Scale bars are (a) $50\mu \mathrm{m}$, (b) $3\mu \mathrm{m}$, (c) $1\mu \mathrm{m}$, and (d) 500 nm.

Figure 3

Transmission electron microscopy (TEM) analysis of the HMS nanoribbon samples. (a) High resolution TEM (HRTEM) images of NR1. (b) Electron diffraction pattern of NR1 showing the closely spaced satellite peaks associated with the $c$ axis configuration of the Si sublattice. Scale bars are 5 nm in (a) and 2 ${\mathrm{nm}}^{-1}$ in (b).

Figure 4

(a) Measured effective thermal conductivity of NR1 (blue filled circles) and NR2 (orange filled circles). The error bars are dominated by the error in the NR thickness measurement. The maximum thermal conductivity of the HMS core, ${\kappa }_{NR}$, assuming a ${\mathrm{SiO}}_2$ shell thermal conductivity from Ref. [46], is shown as the upper limit to the shaded region. The thermal conductivity of bulk crystalline HMS from Ref. [30] is shown as red and black unfilled circles along the $a$ axis and $c$ axis, respectively. The bulk values along $\theta ={32}^{\circ }$ and ${26}^{\circ }$, which are the transport directions of the two NRs, are shown as the upper and lower limits of the gray shaded region. The thermal conductivity of fused silica glass is shown as the green line for comparison [47]. The solid and dashed blue and orange lines are the calculated Casimir limit and amorphous limit for the two NR samples according to the approaches described in the text. (b) Contributions to the thermal conductivity from phonons (purple) and diffusons (red) for both NR1 (solid lines) and for the bulk crystal (dashed lines). The reduction in the thermal conductivities in the nanostructure samples are shown as the shaded areas between the dashed and solid lines. The experimental thermal conductivity data for NR1 is shown as the shaded blue area. The calculated amorphous limit to the phonon contribution is indicated by the bottom dotted line.