  The discovery of high thermoelectric performance in n-type polycrystalline
Mg3(Sb,Bi)2 based Zintl compounds has ignited intensive research interest.
However, some fundamental questions concerning the anisotropic transport
properties and the origin of intrinsically low thermal conductivity are still
elusive, requiring the investigation of single crystals. In this work,
high-quality p-type Mg3Sb2 and Mg3Bi2 single crystals have been grown by using
a self-flux method. The electrical resistivity \r{ho} of Mg3Bi2 single crystal
displays an anisotropy with \r{ho} in-plane twice larger than out-of-plane. The
low-temperature heat capacity and lattice thermal conductivity of Mg3Sb2 and
Mg3Bi2 single crystals have been investigated by using the Debye-Callaway
model, from which the existence of low-lying vibration mode could be concluded.
Large Gr\"uneisen parameters and strong anharmonicity are found responsible for
the intrinsically low thermal conductivity. Moreover, grain boundary scattering
does not contribute significantly to suppress the lattice thermal conductivity
of polycrystalline Mg3Sb2. Our results provide insights into the intrinsic
transport properties of Mg3X2 and could pave a way to realize enhanced
thermoelectric performance in single-crystalline Mg3X2-based Zintl compounds.
