Field Induced Multiple Superconducting Phases in UTe 2along Hard Magnetic Axis H. Sakai1Y. Tokiwa1P. Opletal1M. Kimata2S. Awaji3 T. Sasaki3D. Aoki4S. Kambe1Y. Tokunaga1and Y. Haga1

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Field Induced Multiple Superconducting Phases in UTe2along Hard Magnetic Axis

H. Sakai,1, ∗Y. Tokiwa,1P. Opletal,1M. Kimata,2S. Awaji,3

T. Sasaki,3D. Aoki,4S. Kambe,1Y. Tokunaga,1and Y. Haga1

1Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan

2Institute for Materials Research, Tohoku University, Sendai, Miyagi, 980-8577, Japan

3Institute for Materials Research, Tohoku University, Katahira 2-1-1, Sendai 980-8577, Japan

4Institute for Materials Research, Tohoku University, Oarai, Ibaraki 311-1313, Japan

(Dated: December 21, 2022)

The superconducting (SC) phase diagram in uranium ditelluride is explored under magnetic ﬁelds

(H) along the hard magnetic b-axis using a high-quality single crystal with Tc= 2.1 K. Simultaneous

electrical resistivity and AC magnetic susceptibility measurements discern low- and high-ﬁeld SC

(LFSC and HFSC, respectively) phases with contrasting ﬁeld-angular dependence. Crystal quality

increases the upper critical ﬁeld of the LFSC phase, but the H∗of ∼15 T, at which the HFSC

phase appears, is always the same through the various crystals. A phase boundary signature is also

observed inside the LFSC phase near H∗, indicating an intermediate SC phase characterized by

small ﬂux pinning forces.

Uranium ditelluride (UTe2) has attracted considerable

attention as a strong candidate for spin-triplet and topo-

logical superconductivity. Ran et al. [1] initially reported

unconventional superconductivity of this compound with

a superconducting (SC) transition temperature (Tc) of

1.6 K and vast upper critical ﬁeld (Hc2) that exceeds the

Pauli-limiting ﬁeld. Slight decreases in the nuclear mag-

netic resonance (NMR) shift strongly suggest the spin-

triplet SC pairing under ambient pressure [2–4]. Mean-

while, the discovery of multiple SC phases under pressure

further supports spin-triplet formation with spin-degrees

of freedom [5–8]. The topological aspect of the SC state

is experimentally suggested through scanning tunneling

microscopy [9], polar Kerr eﬀect [10], and London pene-

tration depth [11] measurements.

UTe2crystallizes in a body-centered orthorhombic

structure (Immm) [12, 13]. Magnetic-ﬁeld-reinforced su-

perconductivity, an extraordinary phenomenon in UTe2,

appears when a magnetic ﬁeld (H) is applied along the

crystallographic b-axis, which is perpendicular to the easy

magnetic a-axis, along which uranium 5fspin moments

favor aligning with an Ising character [14–18]. In Hkb,

Tcinitially decreases with increasing H, and then starts

to increase above µ0H∗'15 T, i.e., a characteristic ‘L’-

shape Hc2(T) appears. Superconductivity persists up to

a metamagnetic transition at µ0Hm'34.5 T and sud-

denly disappears above Hm.

Previously, one might assume a uniform SC state was

realized in UTe2below the L-shape Hc2(T) because an

internal transition could not be found. However, two

discernible SC phases in the case of Hkbare reported by

speciﬁc heat measurement using a crystal with Tc= 1.85

K in the case of Hkb[19], which is also detected by AC

magnetic susceptibility (χAC) for a crystal of Tc= 1.85

K [20]. Remarkably, a second-order phase transition is

observed inside the SC state, which separates the low-

and high-ﬁeld SC (LFSC and HFSC, respectively) phases

with µ0H∗'15 T. As a thermodynamic consideration

[21], however, three second-order transition lines cannot

meet at a single point unless another line emerges from

here. These results motivate us to continue the studies

using a higher-quality single crystal.

The SC properties of UTe2clearly depend on the sam-

ple quality. Since impurity eﬀects are completely un-

known in rare spin-triplet SC cases, it is exceptionally

necessary to remove defects as much as possible. Al-

though growth condition optimization using a chemical

vapor transport (CVT) method increased Tcup to 2

K and the residual resistivity ratio (RRR) up to ∼88

[22, 23], CVT crystals still contain a small number of

uranium vacancies within 1% –even in high Tccrystals

[24, 25]. Recently, UTe2crystals higher Tcof 2.1 K and

larger RRRs far over 100 have been grown using the

molten salt ﬂux (MSF) method [26]. Successful detection

of de Haas–van Alphen oscillation signals [27] guarantees

the crystals of high quality with a long mean free path

and lower impurity scatterings. In this letter, we explore

the SC phase diagram of such an ultla-clean UTe2crys-

tal obtained by the MSF growth to search for a missing

phase line inside of the SC state. For this purpose, the

electrical resistivity (ρ) and change of χAC were in situ

measured simultaneously on an identical crystal.

Figure S2(a) schematically illustrates the experimen-

tal setup of this study. A crystal was selected with

a size of 0.73 ×0.75 ×4.6 mm3and RRR=180. The

crystal was mounted on a two-axis goniostage, and the

probe was inserted into a 3He cryostat. ρ(T, H) was

measured using the AC four-probe method with a cur-

rent of 0.3 mA. The resonance frequency of the LC cir-

cuit is νTune = (2π√LC)−1, where Land Care the

inductance and capacitance, respectively. If χAC is re-

duced due to SC diamagnetism, L=L0(1 + χAC) de-

creases, where is a ﬁlling factor of the sample to the

coil. Consequently, the onset Tcwas detected as a kink

in ∆νTune = (νTune −ν0)/ν0∝1/√∆χAC. Here, we set

ν0'3.7 MHz by tuning the variable capacitors shown

arXiv:2210.05909v2 [cond-mat.supr-con] 20 Dec 2022

in Fig. S2(a), which were ﬁxed during measurements.

External ﬁelds were applied using a 25 T cryogen-free

SC magnet (25T-CSM) in the High Field Laboratory

for Superconducting Materials (HFLSM), IMR, Tohoku

University. We could precisely adjust the Horientation

along the crystal b-axis by monitoring ρand the quality

factor (Q) of the RF circuit by rotating the goniostage, as

shown in Fig. S2(b), where Qis proportional to pL/C.

In this study, the distinction between the LFSC and

HFSC phases was observed based on their Horientation

dependence, which is summarized as a three-dimensional

phase diagram in Fig. S2(c). To determine Tcof each

phase, the kink of ∆νTune(φ) is tracked by rotating the

ﬁeld angle φfrom the band adirections (See the Sup-

plementary Material (SM)[28].) As also shown in this

ﬁgure, the HFSC phase is rapidly suppressed when H

is turned away from the bdirection, whereas the LFSC

phase is much more robust to the φ. The strong φde-

pendence of the HFSC state is consistent with that of a

previous study on CVT-grown crystals [15]. The narrow

ﬁeld-angle HFSC phase is also observed in ferromagnetic

(FM) superconductors UCoGe and URhGe when the ﬁeld

is rotated around the magnetically hard axis [29, 30]. For

these FM superconductors, the behavior is considered

FIG. 1. (a) Schematic illustration of the simultaneous mea-

surement of ρand ∆χAC. The RF circuit comprises a solenoid

coil ﬁlled with the sample and two variable capacitors placed

at room temperature. The deﬁnitions of angles θand φwith

the external ﬁeld (H) are also presented here. (b) φ-rotation

dependence of ρand Qof the RF circuit with a ﬁxed angle

of θ= 90˚(H⊥c). (c) Three-dimensional schematic plot on

the angular dependence of the LFSC and HFSC phases from

the b-axis to the a-axis for UTe2.

a consequence of H-induced suppression of Ising-type,

longitudinal FM spin ﬂuctuations, as detected by NMR

[31, 32]. However, this longitudinal mode of ﬂuctuations

in the high Hhas not been conﬁrmed yet in UTe2.

Hereafter, we focus on the experiments of applying H

along the b-axis. Figure 2(a) shows the Tdependence

of ρ(T) at various Halong the b-axis (also see the SM

[28]). The change of AC magnetic susceptibility is deﬁned

as ∆χAC ≡(∆νTune)−2. The results of simultaneous

∆χAC(T) measurements are presented in the SM [28]. At

zero ﬁeld, as shown in Figs. 2(a) and 2(b), ρ(T) drops at

Tρ-onset = 2.1 K and becomes zero below Tρ-kink = 2.02

K. ∆χAC also exhibits a kink at the same temperature

(denoted as Tχ-kink). Similarly, we can recognize related

anomalies that correspond to Tρ-onset,Tρ-kink, and Tχ-kink

for the data in µ0H0= 8.18 T.

As for the data in µ0H= 17.01 T, we can still recog-

FIG. 2. (a) ρvs Tplots for various Happlied along the b-axis.

Temperature dependence of ρand ∆χAC for (b) zero ﬁeld

and µ0H= 8.18 T, (c) µ0H= 17.01 T, and µ0H= 24.93 T

applied along the b-axis. Here, ∆χAC is deﬁned as (∆νTune )−2

with ∆νTune ≡ {νTune −ν0}/ν0. The resonant frequency ν0

was set to 3.7 MHz, and the matching for the RF circuit

was adjusted at T= 4.2 K. (e) ρvs Tplots measured with

several AC currents of IAC = 0.3, 0.47, 0.65, and 1 mA for

µ0H= 19.87 T.

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FieldInducedMultipleSuperconductingPhasesinUTe2alongHardMagneticAxisH.Sakai,1,Y.Tokiwa,1P.Opletal,1M.Kimata,2S.Awaji,3T.Sasaki,3D.Aoki,4S.Kambe,1Y.Tokunaga,1andY.Haga11AdvancedScienceResearchCenter,JapanAtomicEnergyAgency,Tokai,Ibaraki319-1195,Japan2InstituteforMaterialsResearch,TohokuUniversity,Se...

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Field Induced Multiple Superconducting Phases in UTe 2along Hard Magnetic Axis H. Sakai1Y. Tokiwa1P. Opletal1M. Kimata2S. Awaji3 T. Sasaki3D. Aoki4S. Kambe1Y. Tokunaga1and Y. Haga1

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