Nonlinear Pauli susceptibilities in ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ and universal features of itinerant metamagnetism

We report measurements of the third order, ${\chi }_3$, and fifth order, ${\chi }_5$, susceptibilities in an itinerant oxide metamagnet, ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, 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 $T_i$ is the position in temperature where a peak in the $i\mathrm{th}-\mathrm{order}$ 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 on-site repulsion $U$. The separation of the VHS from the Fermi energy $\mathrm{\Delta }$, sets a single energy scale, which is the primary driver for the observed features of itinerant metamagnetism at low temperatures.

Figure 1

The magnetization isotherms for $B$ perpendicular to the $c$ axis plotted as per Eq. (1) for various temperatures as indicated. Since the slope yields ${\chi }_3$ in such a plot it is immediately seen that ${\chi }_3$ is weakly negative at high temperatures, $T>20$ K, turns positive as $T$ is lowered reaching a maximum around 10 K, and decreasing thereafter. Also noticeable between 3 and 8 K is the positive curvature which implies a nonzero ($+ve$) value for the next higher susceptibility, ${\chi }_5$.

Figure 2

The values of ${\chi }_1,{\chi }_3$, and ${\chi }_5$ obtained from quadratic fits to the lines such as those shown in Fig. 1. Note the distinct peaks in all three of these susceptibilities with each higher-order susceptibility exhibiting a positive peak at temperatures successively lower by approximately a factor of 2.

Figure 3

Shows the calculated susceptibilities ${\chi }_1,{\chi }_3,{\chi }_5$ in the model in arbitrary units. For the results shown the difference between the chemical potential at $T=0$ and the Van Hove singularity $\mathrm{\Delta }/W=({\varepsilon }_{\mathrm{VHS}}-\mu )/W=0.006$, and $U/W=0.16$.

Figure 4

Parts (a) and (b) show the ratio $T_1/T_3$ computed in the model for a range of values $\mathrm{\Delta }$ for specific values of $U$ (left panel) and for a range of values of $U$ for specific values of $\mathrm{\Delta }$ (right panel). Except for very small $\mathrm{\Delta }/W\lesssim 0.01$ and very large $U/W\gtrsim 0.15$ the values of this ratio cluster in the range between 2.4 and 2.0. Part (c) demonstrates that $T_1$ is independent of $U$ but depends only on $\mathrm{\Delta }$. Part (d) shows the ratio ${\chi }_1\left(T_1\right)/{\chi }_1\left(0\right)$ as a function of $U$ for four different values of $\mathrm{\Delta }$ as indicated.

Figure 5

Shows the linear correlation of $T_1$ vs $B_c$ in a wide variety of heavy fermions, oxides, and pnictides.