Thermodynamics of the critical fluctuations and nematic phase formation of Sr$_3$Ru$_2$O$_7$

The itinerant metamagnet Sr$_3$Ru$_2$O$_7$ has motivated a wide range of experimental and theoretical work in recent years because of the discovery of an unusual low temperature phase which is forming in the vicinity of a proposed quantum critical point. The transport properties of this phase which exhibit strong electron-nematic-like behaviour [1] have led to a range of theoretical proposals for the underlying physics [2]. A major challenge both experimentally and theoretically is the investigation of the thermodynamic properties of both this unusual phase and the fluctuations associated with the quantum critical point. Here I will report on recent thermodynamic measurements. I will concentrate on new specific heat measurements investigating the nature of the critical fluctuations of the system as well as the low energy excitations of the novel phase. \\[4pt] [1] R.A. Borzi, S.A. Grigera, J. Farrell, R.S. Perry, S. Lister, S.L. Lee, D.A. Tennant, Y. Maeno \& A.P. Mackenzie, Science 315, 214 (2007). \newline [2] For a recent review, see E. Fradkin, S. A. Kivelson, M. J. Lawler, J. P. Eisenstein \& A. P. Mackenzie, Annual Review of Condensed Matter Physics 1, 153 (2010)