Metamagnetism and the fifth-order susceptibility in ${\mathrm{UPt}}_3$

An enhanced susceptibility is a natural consequence of the “heavy fermion” (HF) state, rendering the possibility of measurably large nonlinear susceptibilities. In recent work a universal behavior of the peaks observed in the linear (${\chi }_1$) and the third-order (${\chi }_3$) susceptibility in HF metamagnets has been identified. This universality is well accounted for by a single energy scale model considering on-site correlations only. A prediction of this model is a peak in the fifth-order susceptibility ${\chi }_5$ as well. In measurements on a HF metamagnet, ${\mathrm{UPt}}_3$, reported herein, we find that ${\chi }_5$, rather than attaining a peak, saturates at low temperatures and is positive. The thermodynamic implications of these towards the stability of the metamagnetic HF state are discussed.

Figure 1

Magnetization isotherms of ${\mathrm{UPt}}_3$ with field applied along the $a$ axis. A “normal” paramagnetic response observed at high temperatures with a negative bending gives way to an upward curvature at lower temperatures, signaling the rise of higher-order susceptibilities to positive values prior to the metamagnetic transition itself at 20 T.

Figure 2

Nonlinear part of the magnetic response after subtracting out the linear term. The behavior at high temperatures (lower panels) is almost linear and sloping down, thus implying a negative ${\chi }_3$. Around 14 K ${\chi }_3$ turns positive with a definite indication of a negative ${\chi }_5$. The response at 10 K is largely a straight line, indicating a large positive ${\chi }_3$ and ${\chi }_5$ about to cross over to the positive side. The response at lower temperatures clearly shows both ${\chi }_3$ and ${\chi }_5$ are positive, with the exception of the data at 2 K, which is a perfect parabola, indicating a near zero ${\chi }_3$.

Figure 3

Fifth-order susceptibility ${\chi }_5$ in ${\mathrm{UPt}}_3$ obtained from the quadratic term in fits to the data shown in Fig. 2. The vertical scale is derived from that in Fig. 2. ${\chi }_5$ is negative at high temperatures and increases monotonically as $T\to 0$. The inset shows the calculated ${\chi }_5$ as derived in the single energy scale model.

Figure 4

The quantity on the vertical axis (values derived from vertical scale of Fig. 2) is a measure of the stability of the metamagnetic state. At low temperatures ($\sim$10 K) this quantity assumes a negative value, thus implying that additional terms in the magnetic free energy expansion need to be considered in order to ensure thermodynamic stability. The inset shows the measure of stability [Eq. (8)] as computed from the minimal model. The computed response never crosses zero.