Nonlinear Pauli Susceptibilities in Sr$_3$Ru$_2$O$_7$ and Universal Features of Itinerant Metamagnetism

We report, for the first time, measurements of the third order, $\chi_3$ and fifth order, $\chi_5$, susceptibilities in an itinerant oxide metamagnet, Sr$_3$Ru$_2$O$_7$ for magnetic fields both parallel and perpendicular to the c-axis. These susceptibilities exhibit maxima in their temperature dependence such that $T_1 \approx 2T_3 \approx 4T_5$ where the $T_i$ are the position in temperature where a peak in the $i$-th order susceptibility occurs. These features taken together with the scaling of the critical field with the temperature $T_1$ observed in a diverse variety of itinerant metamagnets find a natural explanation in a single band model with one Van Hove singularity (VHS) and onsite repulsion $U$. The separation of the VHS from the Fermi energy $\Delta$, sets a single energy scale, which is the primary driver for the observed features of itinerant metamagnetism at low temperatures.