Microscopic Theory of the Thermodynamic Properties of Sr$_3$Ru$_2$O$_7$

TL;DR

This paper develops a microscopic theoretical model to understand the thermodynamic behavior of Sr$_3$Ru$_2$O$_7$ at low temperatures, emphasizing the impact of spin-orbit coupling and magnetic field on its electronic structure and phase transitions.

Contribution

It introduces a realistic tight-binding model incorporating spin-orbit coupling and orbital effects to explain the thermodynamic anomalies near the nematic phase transition.

Findings

Fermi surface topology changes significantly with magnetic field.

Density of states and entropy sharply increase near the critical field.

Band structure effects are crucial for interpreting quantum criticality.

Abstract

The thermodynamic properties of the bilayer Sr$_3$Ru$_2$O$_7$ at very low temperatures are investigated by a realistic tight-binding model with the on-site interactions treated at the mean-field level. Due to the strong spin-orbit coupling, the band structure undergoes a significant change in Fermi surface topology as the external magnetic field is applied, invalidating the rigid band picture in which the Zeeman energy only causes chemical potential shifts. In addition, since Sr$_3$Ru$_2$O$_7$ is a $t_{2g}$ active system with unquenched orbital moments, the orbital Zeeman energy is not negligible and plays an important role in the phase diagram on the magnetic field orientation. 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. Our results suggest that extra cares are necessary to isolate the contributions due to the quantum criticality from the band structure singularity in this particular material. The effects of quantum critical fluctuations are briefly discussed.