Quantum critical point and unusual phase diagram in the itinerant-electron metamagnet UCoAl

We present the temperature–pressure–magnetic-field phase diagram of the itinerant-electron metamagnet UCoAl determined from the ac susceptibility measurement. The quantum critical point (QCP) was found to be located at $2.9\pm 0.2$ GPa ($\equiv P_{\mathrm{QCP}}$) and $130\pm 5$ kOe. In addition to the determination of the phase diagram, we report magnetic and transport properties in the paramagnetic state and around the phase boundary. The critical divergence of the magnetic susceptibility is suppressed toward the QCP. From the longitudinal magnetoresistance and the resistivity under magnetic fields, enhancement of the resistivity is observed in the so-called supercritical region. In the paramagnetic region, the magnetoresistance and temperature dependence of the resistivity exhibit complex behaviors, especially in the vicinity of 1.5 GPa and $P_{\mathrm{QCP}}$.

Figure 1

(a) Temperature variation of the magnetization curves of UCoAl for $H\parallel c$ at 0 GPa. (b) Temperature dependence of the hysteresis width $\mathrm{\Delta }H$, which is defined as the difference between the peak fields of $dM/dH$ in the up and down sweeps indicated in the inset. Negative values of $\mathrm{\Delta }H$ above 10 K are probably due to an inevitable hysteresis of the superconducting magnet in an MPMS.

Figure 2

Real (a) and imaginary (b) parts of the ac susceptibility, ${\chi }^{\prime }$ and ${\chi }^{\prime \prime }$, respectively, as functions of the field for various temperatures at 0 GPa.

Figure 3

Temperature dependence of characteristic parameters at 0 GPa; (a) ${\chi }_{\max }^{\prime }$ and (b) ${\chi }_{\max }^{\prime \prime }$ are defined as the maximum values of ${\chi }^{\prime }\left(H\right)$ and ${\chi }^{\prime \prime }\left(H\right)$ at each temperature. (c) $H_{\mathrm{peak}}$ is the field where ${\chi }^{\prime }\left(H\right)={\chi }_{\max }^{\prime }$. (d) The full width at half maximum (FWHM) of the peak in ${\chi }^{\prime }\left(H\right)$, which reflects the transition width. The broken lines in every graph indicate $T_{\mathrm{cr}}$ and the red star in (c) indicates $H_{\mathrm{cr}}$.

Figure 4

${\chi }_{\max }^{\prime }$ and ${\chi }_{\max }^{\prime \prime }$ as functions of temperature for low pressures (a), (b) and for high pressures (c), (d).

Figure 5

Pressure dependence of characteristic parameters at the CP. (a) Critical temperature $T_{\mathrm{cr}}$. (b) Critical field $H_{\mathrm{cr}}$ and the subpeak field $H_{\mathrm{sub}}$ of ${\chi }^{\prime }\left(H\right)$ at $T_{\mathrm{cr}}$ indicated by closed (red) circles and hollow (blue) triangles. The transition field $H_m$ determined from the magnetostriction and the anomaly field $H^{*}$ in the transverse MR indicated by plus signs and crosses are cited from Ref. [13]. (c) ${\chi }_{\max }^{\prime }$.

Figure 6

$T\text{−}P\text{−}H$ phase diagram of UCoAl determined from the ac susceptibility measurements.

Figure 7

(a) ${\chi }^{\prime }\left(H\right)$ and (b) ${\chi }^{\prime \prime }\left(H\right)$ curves for selected temperatures at 0.57 GPa. (c) Pressure evolution of the ${\chi }^{\prime }\left(H\right)$ curve in the vicinity of $H_{\mathrm{cr}}$ at $T\approx T_{\mathrm{cr}}$.

Figure 8

MR $\rho \left(H\right)$ for various temperatures at (a) 0 GPa and (b) 1.49 GPa. The magnetic field and electrical current are applied along the $c$ axis. Both increase and decrease processes of the field are plotted. The broken curve in (b) is the expected MR, assuming that additional scattering is absent.

Figure 9

MR $\rho \left(H\right)$ for various pressures from 0 to 2.58 GPa. Each curve is plotted at 1.5 K, except for those at 0 GPa (1.3 K) and 2.58 GPa (1.7 K).

Figure 10

Resistivity as a function of (a) $T^{5/3}$ and (b) $T^2$ for various pressures at zero magnetic field.

Figure 11

(a) Resistivity $\rho \left(T\right)$ under various magnetic fields at 1.49 GPa. (b) Magnetic component of the resistivity $\mathrm{\Delta }\rho \equiv \rho \left(H\right)-\rho \left(0\right)$ as a function of temperature. Inset displays the peak positions in $\mathrm{\Delta }\rho \left(T\right)$ (closed circles) and in $\rho \left(H\right)$ (closed triangles). The CP is indicated by the star.

Figure 12

Contour map of the exponent $n$ in the paramagnetic phase. $n$ is derived from a fitting by $\rho \left(T\right)={\rho }_0+A{T}^n$ in the temperature range from 1.5 to 5 K. The plot was constructed by interpolating the results at 0, 0.4, 1.04, 1.49, 1.83, 2.07, 2.42, and 2.58 GPa at magnetic fields from 0 to $H_m$ in $\sim 10$ kOe steps. The hollow circles indicate $H_{\mathrm{cr}}$ and the star denotes the QCP.

Figure 13

MR for different temperatures at 2.58 GPa. The crosses indicate the residual resistivity ${\rho }_0$ estimated from the fitting by $\rho \left(T\right)={\rho }_0+A{T}^n$ in the temperature range from 1.5 to 5 K.