Figure 1

Main figure: Proposed generic phase diagram of a metal near the border of ferromagnetism.[3, 4, 5] As the ferromagnetic transition temperature $T_c$ is suppressed by a control parameter $P$, it changes from second to first order at a tricritical point (TCP). From the line of first-order transitions connecting TCP with the first-order quantum phase transition (QPT), two meta-magnetic “wings” emerge (blue surfaces), corresponding to surfaces in ($T$,$P$,$H$) space at which the magnetization jumps discontinuously [inset (i)]. The line of critical endpoints $T^{*}$ goes to 0 K at the quantum critical endpoint (QCEP). In ultrapure ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, as $T^{*}$ is tuned by the angle of the magnetic field, the QCEP does not appear. Instead, a nematic phase is found, enclosed on the sides by two first-order metamagnetic jumps, and on top by a probable second-order phase boundary [inset (ii)].Reuse & Permissions

Figure 2

Real (a) and imaginary (b) parts of the ac magnetic susceptibility of Sr${}_3$Ru${}_2$O${}_7$ at 0.59 kbar as the in-plane dc field is swept through the MMT. The data are labeled as $\Delta {\chi }^{\prime }$ and $\Delta {\chi }^{″}$, respectively; a slowly varying background has been subtracted. Although we use arbitrary units, the same coil and sample are used in all measurements so relative amplitudes at different pressures can be compared. Three successive peaks are observed in the susceptibility, numbered 1, 2, and 3 in (a). The inset in each panel shows an expanded plot around peak (1), which is the focus of this paper. For peak 1, with decreasing temperature from 1.7 K, $\Delta {\chi }_{\text{max}}^{\prime }$ initially grows, reaches a maximum at $T^{*}=1.55$ K, and then decreases as the temperature is further reduced. (b) The peak in $\Delta {\chi }^{″}$ starts to appear only below $T^{*}=1.55$ K and then increases rapidly in amplitude as the temperature is reduced. No signal in $\Delta {\chi }^{″}$ is observed at the positions of peaks 2 or 3. The small step in $\Delta {\chi }^{″}$ at temperatures above 1.55 K may be the result of changing eddy currents in the sample. (c) Pressure dependence of the critical metamagnetic field $H_c$ at $T^{*}$, as a function of pressure for peaks 1 and 2. For pressures above 13.4 kbar, $H_c$ at $~0.07$ K is used.Reuse & Permissions

Figure 3

Temperature evolution of the ac susceptibility across the MMT for 12.8 kbar (a), 13.4 kbar (b), and 14.2 kbar (c). A secondary maximum to the right of the central peak of $\Delta {\chi }^{\prime }$ is marked by the red arrow. $\Delta {\chi }^{″}$ shows a clear peak below 0.3 K at 12.8 kbar, a much weaker peak below 0.15 K at 13.4 kbar, and no peak down to 0.07 K at 14.2 kbar. At 13.4 kbar, a double-peak feature can be seen in $\Delta {\chi }^{″}$. Note that the scales on both the vertical and horizontal axes are different for the three graphs (a), (b), and (c). (d) Critical metamagnetic field $H_c$ at $T^{*}$ as a function of pressure for peak 1 and of the two secondary maxima in $\Delta {\chi }^{\prime }$ at $T^{*}$. For pressures above 13.4 kbar, $H_c$ at $~$0.07 K is used, as in Fig. 2c.Reuse & Permissions

Figure 4

The phase diagram inferred from susceptibility measurements. The blue and black solid lines are splines of the measured critical endpoints $T^{*}$ (red) and the position of the MMT below $T^{*}$ as a function of temperature and field (black) at each pressure, respectively. (Inset) Projection of the line of critical endpoints in the ($P$,$T$) plane. For pressures larger than 14.2 kbar, 0.07 K is taken as the error bar for the critical temperatures because that was the lowest temperature reached. The quantum critical endpoint is close to 13.6 kbar. The dashed line in the inset is a guide to the eye.Reuse & Permissions

Figure 5

The magnitude of $\Delta {\chi }^{\prime }$ at the MMT field, $\Delta {\chi }_{\text{mmt}}^{\prime }$, as a function of temperature for several pressures, showing the dramatic fall in $\Delta {\chi }_{\text{mmt}}^{\prime }$ as the quantum critical endpoint is approached. (a) Data below $P_c$; note that the data below 13.4 kbar have been offset to avoid overlap. (b) Expanded plot of the higher-pressure data; the datasets for 13.4 kbar show that frequency has little effect on the temperature dependence of $\Delta {\chi }_{\text{mmt}}^{\prime }$. Note that the gain settings for the two datasets at 13.4 kbar are different, so the 83 Hz curve has been rescaled by a multiplicative factor to agree with the 14.1 Hz curve at 0.75 K.Reuse & Permissions

Figure 6

Temperature dependence of the MMT field $H_M$ for each pressure as viewed in the ($H$,$T$) plane, relative to the 70 mK value $H_M^{°}$ at each pressure. (Inset) $H_M$ viewed in the ($P,H,T$) space without offset to show that the curvature of the metamagnetic “wing” is rather small, although on a fine scale, as shown in the main figure, it is clearly visible.Reuse & Permissions