Microscopic Theory of the Thermodynamic Properties of Sr_3Ru_2O_7

The thermodynamic properties of the bilayer ruthenate compound Sr_3Ru_2O_7 at very low temperatures are investigated by using a tight-binding model yielding the realistic band structure combined with the on-site interactions treated at the mean-field level. We find that both the total density of states at the Fermi energy and the entropy exhibit a sudden increase near the critical magnetic field for the nematic phase, echoing the experimental findings. A new mechanism to explain the anisotropic transport properties is proposed based on scatterings at the anisotropic domain boundaries. Our results suggest that extra cares are necessary to isolate the contributions due to the quantum criticality from the band structure singularity in Sr_3Ru_2O_7.