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We report the magnetoresistance under pressure in the novel spin-triplet superconductor UTe2 close to the critical pressure Pc, where the superconducting phase terminates, for field along the three a, b, and c-axes in the orthorhombic structure. The superconducting phase for

The recent discovery of superconductivity in the heavy fermion paramagnet UTe2 has attracted a lot of attention.1,2) Although UTe2 at ambient pressure does not show a long-range magnetic order down to low temperatures, many similarities to ferromagnetic superconductivity are pointed out. The microscopic coexistence of ferromagnetism and superconductivity is established in uranium compounds, namely UGe2, URhGe, and UCoGe,3–5) where the
On the other hand, UTe2 with the body-centered orthorhombic structure (space group: #71,
The most remarkable feature of UTe2 is the huge
Another important point in UTe2 is the emergence of multiple superconducting phases under pressure (P) clarified by AC calorimetry measurements.23) As shown in Fig. 1(a),
Figure 1. (Color online) (a) T–P phase diagram at zero field in UTe2. SC1, SC2, and SC3 denote the multiple superconducting phases. PM, MO, and WMO denote paramagnetism and magnetic ordered phase and weakly magnetic order, respectively. Here we define
AC calorimetry measurements under pressure with the magnetic field applied along the a-axis confirmed the occurrence of multiple superconducting phases in UTe2 and that the sudden increase of
The remarkable evolution of
Here, we present magnetoresistance measurements under pressure, focusing on the results near
High quality single crystals of UTe2 were grown using the chemical vapor transport method. The off-stoichiometric amounts of starting materials with the atomic ratio
The magnetoresistance was measured by the four-probe AC or DC method in a piston cylinder cell at pressure up to 1.6 GPa with Daphne 7373 as pressure transmitting medium. Three samples for
Figure 1(a) shows the T–P phase diagram at zero field. The data points are plotted from the present results as well as previous results by resistivity and AC calorimetry measurements.23,24) Similar phase diagrams are reported in Refs. 25 and 26. As we already mentioned, multiple superconducting phases appear under pressure, and superconductivity collapses at
In resistivity measurements, a drastic increase of residual resistivity,
Next we focus on the results for
Figure 2. (Color online) (a) Temperature dependence of the magnetoresistance at different fields for
In the field scan, the field-reinforced superconductivity is more significant. As shown in Fig. 2(b), superconductivity appears from 0 to 7 T at 0.04 K, but at higher temperature, 1.05 K, superconductivity is observed at finite field range from 2 to 5.8 T. At 2 and 2.5 K, superconductivity is no more visible, but a magnetic anomaly is detected. It should be noted that the magnetoresistance at high temperature, 5 K, decreases significantly with field. This is also shown in the field dependence of the residual resistivity,
Figure 2(c) shows the H–T phase diagram for
Figure 3(a) shows the field dependence of the magnetoresistance for
Figure 3. (Color online) (a) Field dependence of the magnetoresistance at different temperatures for
Next we show in Fig. 4 the temperature and field dependence of magnetoresistance for
Figure 4. (Color online) (a) Temperature dependence of the magnetoresistance for
The H–T phase diagrams for
Figure 5. (Color online) H–T phase diagrams for
The evolution of H–T phase diagrams in Fig. 5 indicates that the emergence of magnetism suppresses superconductivity, which survives for
Initially it has been proposed that superconductivity in UTe2 occurs at the border of a ferromagnetic state and that the concomitant ferromagnetic fluctuations are responsible for the spin-triplet superconductivity.35,36) Contrarily, the recent high pressure studies raise questions about the pure ferromagnetic state under pressure, and there are strong evidences for antiferromagnetic order rather than ferromagnetic order above
The competition between ferromagnetism, antiferromagnetism and sharp crossover between weakly and strongly polarized state is well illustrated in the case of CeRu2Ge241) and CeRu2Si2 under pressure or doping.42,43) Similar interplays may occur here in UTe2. However, it must be stressed that the novelty in U heavy fermion materials is that “hidden” valence fluctuations may exist between U3+ and U4+ configurations which can both lead to long-range magnetic order. In addition, it is not easy to distinguish the two configurations because the effective moments expected for U3+ (
Let us compare the present results with the case for ferromagnetic superconductivity. In UCoGe and URhGe, the field-reentrant or field-reinforced superconductivity is observed when the field is applied along the hard-magnetization axis (b-axis). The enhancement of ferromagnetic fluctuations are induced by the suppression of
In UTe2, the occurrence of superconductivity in a spin-polarized state appears quite different. One novelty is the mark of antiferromagnetic order (MO) coupled with the strong correlations (WMO). Our observation points out that pressure and magnetic field lead to drastic changes of the superconducting boundaries. A next important step will be to determine the nature of the MO and WMO phases, the link between the MO,
The magnetoresistance measurements along the three main a, b, and c-axes in UTe2 give a rather complex response to the competition of superconductivity and magnetic order near
Acknowledgements
We thank K. Miyake, A. Miyake, H. Harima, K. Machida, Y. Yanase, V. Mineev, S. Fujimoto, K. Ishida, Y. Tokunaga, and F. Hardy for fruitful discussion. This work was supported by ERC starting grant (NewHeavyFermion), ANR (FRESCO) and KAKENHI (JP19H00646, JP20K20889, JP20H00130, JP20KK0061), GIMRT (20H0406), and ICC-IMR.
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