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

We present the measurements of the third order, $\chi_3$ and fifth order, $\chi_5$, susceptibilities (for magnetic fields both parallel and perpendicular to the c-axis) in an itinerant oxide metamagnet, Sr$_3$Ru$_2$O$_7$. 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. Similar relations between these maximum temperatures are also observed in several other metamagnetic materials. Here we show that these relations are a universal feature of electron systems whose Fermi level is proximate to a van Hove singularity (vHS).
Our results also shed light on the linear correlation between the critical field and the temperature $T_1$ that is observed in a diverse variety of itinerant metamagnets.