Fermi surface studies of the low-temperature structure of sodium

Sodium is the most abundant alkali-metal element and has one of the simplest electronic structures of any metal. At ambient conditions, sodium forms a body-centered-cubic lattice. However, during cooling, it undergoes a partial martensitic phase transition to a complex mixture of rhombohedral polytypes commencing from 36 K. Although the Fermi surface (FS) of bcc sodium has been extensively studied, not much attention has been given to the FS of the martensite structure. Here we report results for the Fermi surface and quantum oscillation (QO) frequencies of several energetically favorable crystal structures of Na at low temperature from first-principles calculations. Interestingly we find that despite drastic differences in the crystal structures of the candidate low-temperature phases of sodium, for all these phases the strongest quantum oscillation peak is centered at 28 kT. Our theoretical results are accompanied by experimental data of QO on a multigrain sodium sample at T = 0.3 K and B-max = 18 T exhibiting a sharp peak at 28 kT, independent of the sample orientation. The persistence of this peak even in the presence of the structural transitions has an implication for using the quantum oscillations of polycrystalline sodium for high magnetic field calibration.