Ultralow Thermal Conductivity in Nanoporous Crystalline Fe₃O₄

While there is no known fundamental lower limit to the thermal conductivity of a material, the lowest thermal conductivities are typically found in amorphous and strongly disordered materials, not highly crystalline materials. Here, we demonstrate a surprising nanostructuring route to ultralow thermal conductivity in a large-unit-cell oxide crystal (Fe3O4) containing close-packed nanoscale pores. The electrical conductivity of this material reduces by a factor of 5 relative to dense Fe3O4, independent of pore size. In contrast, thermal conductivity has a strong dependence on pore size with a factor of 40 of suppression relative to dense Fe3O4 for 40 nm pores vs a factor of 5 for 500 nm pores. The matrix thermal conductivity of Fe3O4 containing 40 nm pores falls below the predicted minimum thermal conductivity by a factor of 3. We attribute this to strong acoustic phonon scattering and intrinsically limited contributions to thermal conductivity from optical phonons with small dispersion.