Anomalous electromagnetic response in the spin-triplet superconductor ${\mathrm{UTe}}_2$

The recently discovered heavy-fermion superconductor ${\mathrm{UTe}}_2$, as a promising candidate for an odd-parity superconductivity, exhibits anomalous magnetic-field reinforced superconductivity with a huge upper critical field of 35 T. However, the thermodynamic properties of this unconventional superconductivity still remain unclear. Herein we present the results of dc magnetization and heat capacity measurements in ${\mathrm{UTe}}_2$ to probe the magnetic response at low temperatures. The obtained isothermal magnetization in the superconducting state of ${\mathrm{UTe}}_2$ clearly demonstrates the anomalous magnetic flux pinning effect, which is most likely related to the peculiar electromagnetic response of the spin-triplet pairing state in the hard-magnetization axis (orthorhombic $b$ axis). The ac susceptibility measurements support the anomalous vortex states in ${\mathrm{UTe}}_2$. We also found evidence for the Lifshitz transition just above $H_{\mathrm{c}2}$ and the anomalous flux pinning anomalies for the easy-magnetization axis ($a$ axis).

Figure 1

Temperature dependence of heat capacity in the single-crystalline ${\mathrm{UTe}}_2$ (No. 1), measured at zero and magnetic fields up to 13 T applied along the orthorhombic $b$ axis. Here, $C_{\mathrm{ele}}/T$ denotes the electronic contribution: $C_{\mathrm{ele}}/T\equiv [C\left(T\right)-C_{\mathrm{nuc}}\left(T\right)]/T$.

Figure 2

(a) Magnetization curves $M\left(H\right)$ of ${\mathrm{UTe}}_2$ (No. 2) in fields along $H\parallel a$ at 0.26 K. (b) The $M\left(H\right)$ curves of ${\mathrm{UTe}}_2$, at 0.28 and 0.80 K in fields up to 8.5 T (No. 1) applied along $H\parallel b$, where the data for 0.80 K are shifted vertically for clarity. The shifted values are shown with the data. The differential of magnetization curves, i.e., $dM\left(H\right)/dH$, are plotted for increasing and decreasing processes for (c) $H\parallel a$ (0.28, 0.64, and 0.80 K) and (d) $H\parallel b$ (0.28 and 0.80 K). The dashed arrows indicate the increasing and decreasing processes.

Figure 3

Magnetization curves $M\left(H\right)$ of ${\mathrm{UTe}}_2$ (No. 1) in fields along $H\parallel b$ at 0.11 K. The dashed arrows indicate the field sweep direction.

Figure 4

Temperature dependence of magnetization $M\left(T\right)$ of single-crystalline ${\mathrm{UTe}}_2$, measured at constant fields for No. 1 (${\mu }_{0}H=5$, 6, 9, 10, 11, 12, 14 T) and No. 2 (${\mu }_{0}H=2$, 3, 7, 8, 10, 11 T), applied along the orthorhombic $b$ axis. The solid and the open symbols show the data obtained in the warming up process after zero-field cooling and that obtained in subsequent cooling process, respectively (dashed arrows).

Figure 5

Magnetic field dependences of ac susceptibility in ${\mathrm{UTe}}_2$ for (a) $H\parallel a$ ($T=0.04$, 0.2, 0.4, 0.8, 1, 1.2, 1.39, and 1.59 K) and (b) $H\parallel b$ ($T=0.03$, 0.4, 0.6, 0.8, 1, 1.2, 1.29, 1.39, and 1.59 K). The solid and dashed arrows indicate the anomalies inside the SC state and the upper critical field, respectively.

Figure 6

$H\text{−}T$ SC phase diagram of ${\mathrm{UTe}}_2$ in magnetic fields applied along (a) the easy-magnetization axis $H\parallel a$ and (b) the hard-magnetization axis $H\parallel b$, obtained from the present dc magnetization, ac susceptibility, and heat capacity measurements. The previously published data taken from Refs. [37, 44] are also plotted for comparison.