Anomalous anisotropy of the lower critical field and Meissner effect in ${\mathrm{UTe}}_2$

We report on low-temperature susceptibility and magnetization measurements made on single crystals of the recently discovered heavy-fermion superconductor ${\mathrm{UTe}}_2$ and compare the results with the two ambient pressure ferromagnetic superconductors URhGe and UCoGe. Hysteresis curves in the superconducting phase show a familiar diamond shape superimposed on a large paramagnetic background. The Meissner state was measured by zero-field cooling in small fields of a few Oe as well as ac susceptibility measurements in small fields and resulted in 100% shielding, with a sharp transition. However, the field-cooling Meissner-Ochsenfeld effect (expulsion of flux) was negligible in fields greater than just a few Oe, but becomes nearly 30% of the perfect diamagnetic signal when the field was reduced to 0.01 Oe. The critical current due to flux pinning was studied by ac susceptibility techniques. Over the range in fields and temperature of this study, no signature of a ferromagnetic transition could be discerned. The lower critical field $H_{\mathrm{c}1}$ has been measured along the three crystallographic axes, and surprisingly, the anisotropy of $H_{\mathrm{c}1}$ contradicts that of the upper critical field. We discuss this discrepancy and show that it may provide additional support for a magnetic field-dependent pairing mediated by ferromagnetic fluctuations in ${\mathrm{UTe}}_2$.

Figure 1

Magnetization vs field for ${\mathrm{UTe}}_2$ (sample 1) at 100 mK and 1 K below $T_{\mathrm{c}}$, and at 1.5 K just above $T_{\mathrm{c}}$ in the normal state with the field along the $a$ axis (easy axis). The inset shows the magnetization of ${\mathrm{UTe}}_2$ (blue) at 1.5 K, URhGe (red) at 500 mK, and UCoGe (black) at 600 mK, i.e., just above their respective $T_{\mathrm{c}}$ in the normal state, with the field along the easy axis.

Figure 2

(a) $M/H$ vs $T$ of ${\mathrm{UTe}}_2$ (sample 1) for various applied fields ranging from 0.01 to 200 Oe from zero-field-cooled (ZFC) and field-cooled (FC) measurements. (b) The percent Meissner-Ochsenfeld effect (expulsion of flux) plotted against the applied field for ${\mathrm{UTe}}_2$ (red points) and for UCoGe (blue points). Note that the field range in UCoGe cannot extend below 100 mT as the sample needs to be monodomain. Over the comparable field range, the expulsion of flux is much greater in UCoGe.

Figure 3

Current density $J_{\mathrm{c}}$ derived from the critical state model vs temperature for ${\mathrm{UTe}}_2$ (sample 2) measured along the $a$ and $b$ axes, and for UCoGe along the $c$ axis. The solid round points are data derived from the imaginary part of ac susceptibility, and the open square points are data derived from the remanent magnetization (discussed in the Supplemental Material [21]).

Figure 4

(a) Initial magnetization $M$ vs $H$ taken a various constant temperatures for ${\mathrm{UTe}}_2$ (sample 1) with the field along the $a$ axis. The dashed line is a linear fit to the 100 mK data at low fields, and represents 100% shielding. (b) Series of minor hysteresis loops for sample 1 at 1.1 K where the magnitude of the field was systematically increased in steps of 1 Oe, and then returned to zero to measure the point at which a remanent magnetization begins to appear in the sample (the remanent magnetization has been multiplied by 10). (c) The remanent magnetization is plotted as $\sqrt{M_{\mathrm{r}}}$ vs $H_{\mathrm{before}}$ for the $a$ axis for sample 1. The solid lines are linear fits to the data above the cutoff line. (d) $H_{\mathrm{c}1}\left(T\right)$ for ${\mathrm{UTe}}_2$ along the $a$ axis for sample 1 (red) and for sample 2 along the $a$ (black), $b$ (blue), and $c$ (green) axis after correcting for demagnetization effects. The lines are guides to the eye.