# Low-temperature Magnetic Fluctuations Investigated by 125Te-NMR on the
Uranium-based Superconductor UTe2

Hiroki Fujibayashi1<EMAIL_ADDRESS>Katsuki Kinjo1
Present adress: Institute of Multidisciplinary Research for Advanced
Materials, Tohoku University, Sendai, Miyagi 980-8577, Japan Genki Nakamine1
Shunsaku Kitagawa1 Kenji Ishida1<EMAIL_ADDRESS>
Yo Tokunaga2 Hironori Sakai2 Shinsaku Kambe2 Ai Nakamura3 Yusei Shimizu3
Yoshiya Homma3 Dexin Li3 Fuminori Honda3 and Dai Aoki3,4 1Department of
Physics1Department of Physics Kyoto University Kyoto University Kyoto 606-8502
Kyoto 606-8502 Japan
2Advanced Science Research Center Japan
2Advanced Science Research Center Japan Atomic Energy Agency Japan Atomic
Energy Agency Tokai Tokai Ibaraki 319-1195 Ibaraki 319-1195 Japan
3IMR Japan
3IMR Tohoku University Tohoku University Oarai Oarai Ibaraki 311-1313 Ibaraki
311-1313 Japan
4University Grenoble Japan
4University Grenoble CEA CEA IRIG-PHERIQS IRIG-PHERIQS F-38000 Grenoble
F-38000 Grenoble France France

###### Abstract

To investigate the static and dynamic magnetic properties on the uranium-based
superconductor UTe2, we measured the NMR Knight shift $K$ and the nuclear
spin-lattice relaxation rate $1/T_{1}$ in $H\parallel a$ by 125Te-NMR on a
125Te-enriched single-crystal sample. $1/T_{1}T$ in $H\parallel a$ is much
smaller than $1/T_{1}T$ in $H\parallel b$ and $c$, and magnetic fluctuations
along each axis are derived from the $1/T_{1}T$ measured in $H$ parallel to
all three crystalline axes. The magnetic fluctuations are almost identical at
two Te sites and isotropic at high temperatures, but become anisotropic below
40 K, where heavy-fermion state is formed. The character of magnetic
fluctuations in UTe2 is discussed with the comparison to its static
susceptibility and the results on other U-based superconductors. It is
considered that the magnetic fluctuations probed with the NMR measurements are
determined by the magnetic properties inside the two-leg ladder formed by U
atoms, which are dominated by the $q_{a}$ = 0 ferromagnetic fluctuations.

Superconductivity in UTe2 [Superconducting (SC) transition temperature
$T_{\mathrm{SC}}$ = 1.6 K] was discovered at the end of 2018[1], and was
confirmed by other group immediately[2]. UTe2 has the orthorhombic crystal
structure with the space group $Immm$ (#71, $D^{25}_{2h}$), which belongs to
the symmorphic group [Fig.1(a)][3]. UTe2 is considered to be a spin-triplet
superconductor because its characteristic SC properties, such as extremely
high SC upper critical fields $H_{\rm c2}$[1, 4] and the magnetic-field ($H$)
enhancement of $H_{\rm c2}$[1], are quite similar to those observed in uranium
(U)-based ferromagnetic (FM) superconductors[6] (UGe2 under pressure[7], and
URhGe[8] and UCoGe[9] at ambient pressure), which are spin-triplet
superconductors. However, different from these FM superconductors, UTe2 shows
superconductivity in the paramagnetic state, and does not show any FM ordering
even in the high-pressure region where superconductivity suddenly
disappears[10, 11]. More surprisingly, inelastic neutron scattering (INS)
experiments have revealed the predominance of the incommensurate
antiferromagnetic (AFM) spin fluctuations with the wave-vector $\bm{Q}_{\rm
ic}$ = (0, 0.57, 0) [12, 13]. Since the U atoms in UTe2 form a two-leg ladder
with legs along the $a$ axis and rungs along the $c$ axis [Fig. 1(a)], the AFM
interaction is parallel to the inter two-leg ladder direction along the $b$
axis. Thus, one of the great interests in UTe2 is to understand the magnetic
properties in the normal state, particularly whether FM fluctuations exist or
not inside the two-leg ladder structure above $T_{\rm SC}$, although the INS
measurements could not detect any FM fluctuations[12, 13]. To clarify this
issue, 125Te-NMR measurements for $H\parallel a$ on a single-crystal UTe2 are
crucially important, because the directional magnetic fluctuations can be
known as discussed later.

Figure 1: (Color online) Crystal structure of UTe2 emphasizing the two-leg
ladder structure formed by the U atoms. Two crystallographically inequivalent
Te sites, $4j$ and $4h$, with the point symmetries $mm2$ and $m2m$ are shown
as Te1 and Te2, respectively[3]. (b) Atomic arrangement around each Te site.
$b_{j}$s and $r_{j}$s indicate the transfer-field parameters and the distances
between U and Te site, respectively. Here, $r_{1}=3.0553~{}\AA$,
$r_{2}=3.1817~{}\AA$, $r_{3}=3.1648~{}\AA$, $r_{4}=5.2706~{}\AA$, and
$r_{5}=5.3462~{}\AA$[5].

In the previous measurement[14], we could not observe 125Te-NMR signals in
$\mu_{0}H\sim 2$ T below 20 K for $H\parallel a$ due to the divergence of the
nuclear spin-spin relaxation rate $1/T_{2}$ and the broadening of the
spectrum. To overcome this difficulty, we prepared a 125Te-enriched single
crystal sample with a nearly cubic shape, and successfully observed the 125Te-
NMR signals in low fields parallel to the $a$ axis. We measured the NMR Knight
shift $K$ and nuclear spin-lattice relaxation rate $1/T_{1}$ under magnetic
field in $H\parallel a$ down to 1.5 K. Together with previous NMR results[14],
magnetic fluctuations along each crystalline axis are derived. It was found
that magnetic fluctuations are almost isotropic at high temperatures, and
becomes highly anisotropic below 40 K, as in the case of the static
susceptibility.

Single-crystal UTe2 was grown by the chemical-vapor-transport method with
iodine as the transport agent[1, 2]. Natural U and 99.9% 125Te-enriched metals
were used as starting materials for the present sample. The 125Te (nuclear
spin $I=1/2$, gyromagnetic ratio ${}^{125}\gamma_{n}/2\pi=13.454$ MHz/T)-NMR
measurements were performed on a single crystal of $0.8\times 1.2\times 0.9$
mm3 size. The frequency-sweep NMR spectrum was obtained using the Fourier
transform of a spin-echo signal observed after the spin-echo radio-frequency
pulse sequence with a 5-kHz step in a fixed magnetic field. The magnetic field
was calibrated using 63Cu ($I$ = 3/2, ${}^{63}\gamma/2\pi=11.285$ MHz/T) and
65Cu ($I$ = 3/2, ${}^{65}\gamma/2\pi=12.089$ MHz/T) NMR signals arising from
the NMR coil. We used the split SC magnet, which generates a horizontal field,
and combined it with a single-axis rotator to apply a magnetic field in each
crystalline direction precisely.

Figure 2: (Color online) 125Te-NMR spectrum in $H\parallel a$ shown against
the Knight shift of $K=(f-f_{0})/f_{0}$. The smaller [larger]-$K$ peak is
denoted as a Te(I) [Te(II)] peak. The inset shows the magnetic-field angle
dependence of the Te(I) and Te(II) peaks in the $ab$ plane.

Figure 2 shows the 125Te-NMR spectra for $H\parallel a$, which are shown
against the NMR shift $K=(f-f_{0})/f_{0}$. Here, $f$ is the NMR frequency, and
$f_{0}$ is the reference frequency determined as
$f_{0}=(^{125}\gamma_{n}/2\pi)\mu_{0}H$. There are two crystallographically
inequivalent Te sites, $4j$ and $4h$, with the point symmetries $mm2$ and
$m2m$ in UTe2, and these are denoted as Te1 and Te2 sites [Fig. 1(a)],
respectively. Correspondingly, we observed two 125Te-NMR peaks as reported in
the previous paper[15, 16, 17]. An NMR peak with the smaller [larger] $K$ in
$H\parallel b$ is assigned as Te(I) [Te(II)] by following the previous
paper[14]. The inset of Fig. 2 shows the $H$ angular dependence of the NMR
Knight shift at both the Te(I) and Te(II) peaks measured in the $ab$ plane at
4.2 K. These angle dependence are well fitted by the theoretical curves of
$K(\theta)=K_{a}\sin^{2}\theta+K_{b}\cos^{2}\theta$, where $K_{a}$ ($K_{b}$)
is the Knight shift in $H\parallel a$ ($b$). The $a$-axis aligned NMR spectra
of the Te(I) and Te(II) peaks were detected by following the angle dependence
in the $ab$ plane from the observed $b$-axis NMR spectra[14, 15, 16, 17].
$K_{a}$ of the Te(I) and Te(II) peaks at 4.2 K is 27.9% and 35.2%,
respectively. In the present measurement, the smaller magnetic field of
$\mu_{0}H$ = 1.35 T than in the previous study[14] makes the NMR peak sharper.

From the present measurement, it turned out that the previous NMR-peak
assignment in $H\parallel a$ should be reinterpreted. Although the Te(I) and
Te(II) peaks were overlapped in $H\parallel c$ in the previous study[14],
there are found to be no crossing nor overlapping in the angle dependence of
the two peaks in the present study. The present peak assignment results in
nearly isotropic values of the hyperfine coupling constants at the two Te
sites, as shown in Table I. Note that the peak assignment presented here
[Te(I) and Te(II)] does not correspond to the crystallographical site (Te1 and
Te2).

Table 1: Hyperfine coupling constants $A_{\rm hf}^{\alpha}$ evaluated from the linear relation between Knight shift and bulk susceptibility along $\alpha=a,b$ and $c$. This corresponds to the diagonal term in the hyperfine tensor.  | $H\parallel a$ | $H\parallel b$ | $H\parallel c$
---|---|---|---
|  $A_{\rm hf}^{a}$ (T / $\mu_{\rm B}$) |  $A_{\rm hf}^{b}$ (T / $\mu_{\rm B}$) |  $A_{\rm hf}^{c}$ (T / $\mu_{\rm B}$)
Te(I) | 3.8 | 3.4 | 3.9
Te(II) | 4.7 | 5.2 | 3.9
Figure 3: (Color online) Temperature dependence of the Knight shift determined
from the Te(I) and Te(II) peaks. The $K_{a}$ above 30 K[14] and $\chi_{a}$
above 5 K[18] are quoted from the references.

Figure 3 shows the temperature ($T$) dependence of $K_{a}$ measured in 0.69
and 0.99 T below 100 K. In the figure, the $K_{a}$ data measured in 3.26 T
above 30 K[14] and the $\chi_{a}$ measured in 1 T are also shown[18]. As
reported in the paper[19], the $K_{a}$ is proportional to $\chi_{a}$ above 10
K, but is nearly saturated and remains almost constant at low temperatures.
This is in contrast to the continuous increase in $\chi_{a}$ below 10 K, which
would be ascribed to the extrinsic effect induced by the U-atom
deficiency[20].

Figure 4: (Color online) Temperature dependence of $1/T_{1}T$ at Te(I) and
Te(II) in (a) $H\parallel a$, (b) $H\parallel b$ and (c) $H\parallel c$. The
data of $1/T_{1}T$ in $H\parallel b$ and $H\parallel c$ above 4.2 K are quoted
from the reference[14]. $1/T_{1}T$ in $H\parallel c$ below 4.2 K was measured
at the broad NMR peak arising from the Te(I) and Te(II) signals.

Figures 4(a)-(c) show the $T$ dependence of $1/T_{1}T$ of Te(I) and Te(II)
measured in $H$ parallel to each crystalline axis, respectively. $1/T_{1}T$ in
all directions of Te(I) and Te(II) roughly follows the Curie-Weiss behavior
with different Curie terms above 45 K, which is consistent with the
resistivity behavior, suggestive of the localized $5f$ state. With decreasing
$T$, all $1/T_{1}T$s deviate from the Curie-Weiss behavior and almost saturate
below 15 K in $H\parallel b$ and $c$. This temperature might be related to a
broad Schottky-like anomaly observed at $\sim 12$ K with the various
thermodynamic, transport probes[21] and the nuclear spin-spin relaxation rate
$1/T_{2}$[19]. In contrast, $1/T_{1}T$ in $H\parallel a$ shows a broad maximum
at around 20 K for Te(I) and 30 K for Te(II), respectively. The magnitude of
$1/T_{1}T$ at low $T$ is different between Te(I) and Te(II) in $H\parallel a$
and $b$, but the difference is small in $H\parallel c$. Below 4 K, 1/$T_{1}T$
increases again. This increase is stronger at Te(II), and would be relevant to
the low-$T$ increase reported in the relaxation rate in the $\mu$SR[22] and
$1/T_{2}$[19].

Following the previous procedure[14], we derived the directional dynamic
susceptibility components $R_{i,\alpha}$ for Te($i$) along each orthorhombic
crystal axis $\alpha$ with using the relation of
$(1/T_{1}T)_{i,\gamma}=R_{i,\alpha}+R_{i,\beta}$. Here, $i$ = I and II,
$\alpha,\beta,\gamma=\\{a,b,c\\}$, and $(1/T_{1}T)_{i,\gamma}$ is the
$1/T_{1}T$ of Te($i$) measured in $H\parallel\gamma$. In general,
$R_{i,\alpha}$ is expressed as

$R_{i,\alpha}=\sum_{\mbox{\boldmath$q$},\xi}A_{i}^{\alpha\xi}(\mbox{\boldmath$q$})^{2}\frac{\chi_{\xi}^{{}^{\prime\prime}}(\mbox{\boldmath$q$},\omega_{\rm
N})}{\omega_{\rm N}}.$ (1)

with the $\omega_{\rm N}$ and
$\chi_{\xi}^{{}^{\prime\prime}}(\mbox{\boldmath$q$},\omega_{\rm N})$ are the
NMR frequency and the imaginary part of the dynamic susceptibility along
$\xi=\\{a,b,c\\}$, respectively. $A_{i}^{\alpha\xi}(\mbox{\boldmath$q$})$ is a
$q$-dependent hyperfine coupling tensor at Te($i$), which is assumed to be
expressed as
$A_{i}^{\alpha\xi}(\mbox{\boldmath$q$})^{2}\sim\left|A_{i}^{\alpha\xi}(0)F_{i}(\mbox{\boldmath$q$})\right|^{2}$
with
$F_{i}(\mbox{\boldmath$q$})=\sum_{j}b_{j}e^{i\mbox{\boldmath$q$}\cdot\mbox{\boldmath$r$}_{j}}$
for simplicity. Here, $F_{i}(\mbox{\boldmath$q$})$ is the site-dependent form
factor, which consists of the transfer-field parameters $b_{j}$ from the
$j$th-U atoms surrounding the Te($i$) as shown in Fig. 1 (b), and this acts as
the filter of spin fluctuations.

Figure 5: (Color online) Temperature dependence of (a) $R_{i,a}$, (b)
$R_{i,b}$, and (c) $R_{i,c}$ ($i$ = I and II) evaluated from the data shown in
Fig. 4. Temperature dependence of $K_{\alpha}$ ($\alpha$ = $a$, $b$, and $c$)
at Te(I) is also shown by the solid curves[14]

Figures 5(a)-(c) show the $T$ dependence of $R_{i,\alpha}$ derived from
$1/T_{1}T$ of Te(I) and Te(II) signals with the above relations. The magnitude
and temperature dependence of $R_{i,\alpha}$ are almost the same between two
signals, although the magnitude of $R_{c}$ at low temperatures is different.
In addition, it was found that the anisotropy of $R_{i,\alpha}$ becomes
remarkable below 40 K where the $\chi$ along the $b$ axis shows a maximum.
This temperature is called $T_{\chi_{\rm max}}$ and is regarded as the
formation of the heavy-fermion state. $1/T_{1}T$ results also show that the
anisotropic heavy-fermion state is formed, consistent with the Knight-shift
results.

Here, we consider the effect of AFM fluctuations along the $b$ axis detected
by the INS measurements with $\mbox{\boldmath$Q$}=(0,q_{b},0)$[12, 13]. As
seen in Fig. 1(b), the Te1 site is located at the center of the above two U
atoms along the $b$ axis and the bottom two U atoms along the $a$ axis. The
Te2 sites are at the nonsymmetric position in the unit cell, and thus,
$1/T_{1}T$ at the Te2 site can also probe the AFM fluctuations. The form
factor at the Te$x$ ($x$ = 1 and 2) site against $q_{b}$ along (0, $q_{b}$, 0)
$F_{x}(q_{b})$ is calculated in the presence of the three-dimensional coupling
as[23],

$\displaystyle\left|F_{1}(q_{b})\right|^{2}=$ $\displaystyle
4b_{1}^{2}+4b_{2}^{2}\cos^{2}{\left(q_{b}/2\right)}+8b_{1}b_{2}\cos{\left(q_{b}/2\right)}$
$\displaystyle\left|F_{2}(q_{b})\right|^{2}=$ $\displaystyle
16\left[|b_{3}-b_{5}|^{2}+4b_{3}b_{5}\cos^{2}{\left(q_{b}/2\right)}\right]$
$\displaystyle+4b_{4}^{2}+16(b_{3}b_{4}+b_{4}b_{5})\cos{\left(q_{b}/2\right)}.$

As for the form factor of the Te2 site, the second and third nearest neighbor
U sites are taken into account. As the distances between the Te1 site and the
surrounding four U atoms ($r_{1}$ and $r_{2}$) are almost the same, we assumed
that the $b_{1}$ and $b_{2}$ are the same ($b_{1}=b_{2}$). At the Te2 site, as
$r_{4}\sim r_{5}$, we assumed $b_{4}=b_{5}$. $b_{3}/b_{4(5)}$ is the ratio of
the hyperfine coupling constants for the nearest and second (third) nearest-
neighbor sites at the Te2 site, and are estimated as
$\sim(r_{4(5)}/r_{3})^{3}\sim 4.7$ by assuming the Ruderman-Kittel-Kasuya-
Yosida type interaction[23].

Figure 6: (Color online) $q_{b}$ dependence of the hyperfine form factor
$|F_{x}(q_{b})|^{2}$ at the Te1 and Te2 sites. The dotted curves (Te1’ and
Te2’) are the $q_{b}$ dependence of $|F_{x}(q_{b})|^{2}$, which are the Te1
and Te2 form factor without the $c$-axis interladder coupling. Each form
factor is normalized to be $\sum_{q_{b}}|F_{x}(q_{b})|^{2}=1$.

Figure 6 shows the $q_{b}$-dependent form factor $|F_{x}(q_{b})|^{2}$, where
each $\sum_{q_{b}}|F_{x}(q_{b})|^{2}$ is normalized to the unit. It is noted
that the $q_{b}$ dependence of $|F_{x}(q_{b})|^{2}$ is different between two
sites, and thus, $T$ dependence of $1/T_{1}T$ should be different between two
Te sites in general, as the site difference of $|F_{x}(q_{b})|^{2}$ yields the
difference of
$\sum_{q_{b}}|F_{x}(q_{b})|^{2}\chi^{{}^{\prime\prime}}(\mbox{\boldmath$q$},\omega_{\rm
N})$. The difference is mainly due to the presence of the third term in
$|F_{1}(q_{b})|^{2}$, which arises from the $c$-axis interladder coupling.
However, the INS measurements revealed that the interladder magnetic coupling
along the $c$ axis is negligibly weak, and the AFM coupling along the $b$ axis
would induce the frustration in the magnetic coupling along the $c$ axis.
Thus, it is reasonable to neglect the interladder magnetic coupling along the
$c$ axis. In this case, the terms related to the $c$-axis interladder
correlation ($8b_{1}b_{2}\cos{\left(q_{b}/2\right)}$ and
$16(b_{3}b_{4}+b_{4}b_{5})\cos{\left(q_{b}/2\right)}$) become zero. Thus, the
form factor at Te1 and Te2 sites are expressed as,

$\displaystyle\left|F_{1^{\prime}}(q_{b})\right|^{2}=$ $\displaystyle
4b_{1}^{2}+4b_{2}^{2}\cos^{2}{\left(q_{b}/2\right)}$
$\displaystyle\left|F_{2^{\prime}}(q_{b})\right|^{2}=$ $\displaystyle
16\left[|b_{3}-b_{5}|^{2}+4b_{3}b_{5}\cos^{2}{\left(q_{b}/2\right)}\right]+4b_{4}^{2}.$

The $q_{b}$-dependence of the above form factors at the Te1 and Te2 sites is
shown by the dotted curves (Te1’ and Te2’) in Fig. 6, which are quite similar
to each other. Therefore, the AFM fluctuations with $q_{b}\sim$ 0.57 observed
with the INS measurements[12, 13] are detectable in the same manner with
$1/T_{1}T$ at both the sites. The similar $1/T_{1}T$ behavior at Te(I) and
Te(II) are interpreted with the absence of the interladder magnetic coupling
along the $c$ axis.

To investigate the properties of the magnetic fluctuations, $R_{i,\alpha}$ is
compared with $K_{\alpha}$ at Te(I), as shown in Figs. 5(a)-(c). Almost linear
relations between $R_{i,a}$ and $K_{a}$ are observed. This indicates that the
diagonal component in the hyperfine coupling tensor is dominant in the $a$
axis. It is noted that $K_{a}$ and $R_{a}$ continue to increase even below
$T_{\chi_{\bf max}}$, where U-5$f$ electron is in the itinerant regime. This
implies that the most dominant contributions in
$\chi_{a}^{{}^{\prime\prime}}(\mbox{\boldmath$q$},\omega)$ is $\chi_{a}(0,0)$,
indicative of the dominance of the $q_{a}$ = 0 fluctuations. This seems
consistent with the INS result that the nearest U atoms have in-phase
correlations[13]. It is suggested that the fluctuations detected with the NMR
measurement would be confined in the low-energy regions ($\sim 10^{-4}$ meV),
since the appreciable FM fluctuations are not detected with the INS
measurements above 0.7 meV[12]. We also point out that the $T$ dependence of
the incommensurate AFM fluctuations is almost the same as that of
$\chi(0)$[13]. This implies that the magnetic fluctuations might be $q$
independent at the low-energy region. This indicates that the local-moment
character might remain even below $T_{\chi_{\rm max}}$. It is important to
investigate the energy dependence of the magnetic fluctuations to make clear
the relation between NMR and INS results.

In contrast, $R_{b}$ is smaller than $K_{b}$ and almost zero below 10 K at
Te(I) and Te(II). This indicates that the magnetic fluctuations are absent
along the $b$ direction at low $T$, although the static spin component is
finite in the whole $T$ range. Furthermore, the $R_{c}$ at Te(I) is
significantly larger than $K_{c}$, although $R_{c}$ at Te(II) is almost the
same as $K_{c}$ at Te(II). This suggests the presence of the additional
$R_{c}$, which is related to the off-diagonal component in the hyperfine
coupling tensor at Te(I). Since the Te2 site is located at the symmetric
position with respect to the two-leg-ladder chain, in which the U atoms have
the in-phase correlations[13], it is considered that the Te2 site does not
have off-diagonal components in the hyperfine coupling tensor. One possibility
is that the average effective field along the $c$ axis can arise, when the U
electronic spins near the Te1 site are aligned to the $a$ or $b$ axis with the
incommensurate AFM coupling along the $b$ axis, and that the fluctuations of
the $c$-axis effective field can induce the additional $R_{c}$. The difference
of $R_{c}$ values of the Te(I) and Te(II) peaks might give useful information
about the NMR-signal assignment arising from the two Te sites. Recently, it
was reported that low-$T$ $1/T_{1}T$ in $H\parallel b$ for the two Te sites
becomes different by applying pressure ($P$), and that $1/T_{1}T$ of Te(I) is
more enhanced than $1/T_{1}T$ of Te(II), which is clearly recognized near
critical pressure[24]. Since the low-$T$ magnetic susceptibility along the $b$
axis ($\chi_{b}$) increases with $P$[18], the enhancement of $1/T_{1}T$ in
$H\parallel b$ of Te(I) might be understood by the increase of $R_{c}$ with
the above scenario.

Finally, we compare the present results to those observed in other U-based
compounds. In the U-based heavy-fermion superconductors such as URu2Si2[25],
UPt3[26], and UPd2Al3[27], U-5$f$ electrons show the crossover from high-$T$
localized to the low-$T$ heavy-fermion states, as observed in UTe2. In these
compounds, AFM fluctuations appear to be responsible for the crossover process
and dominate the low-frequency magnetic properties. The presence of the AFM
fluctuations is recognized from the comparison of the $T$ dependence between
$R_{\alpha}$ and $K_{\alpha}$, and the development of $R_{\alpha}$ is much
larger than that of $K_{\alpha}$ with decreasing $T$. On the other hand, as
discussed above, $R_{a}$ is well scaled to $K_{a}$ even below $T_{\chi_{\rm
max}}$ down to the lowest $T$ in UTe2. This is quite in contrast with the
behavior observed in these compounds, and reminiscences the FM SC UCoGe[28,
29] and nearly FM UCoAl[30]. Our NMR results in UTe2 would be dominated by the
magnetic properties inside the two-leg ladder formed by the U atoms, since the
two Te sites are located in the vicinity of the ladder.

In summary, we observed the $a$-axis NMR signals down to 1.5 K, and found that
there are no crossing nor overlapping of the Te(I) and Te(II) peaks in the
angle dependence in the $ab$ plane. This makes the previous peak assignment
revised: the hyperfine-coupling constants at two Te-NMR peaks are nearly
isotropic. From the results of $H\parallel a$, the magnetic fluctuations along
each axis $R_{\alpha}$ were derived. We found the predominance of the FM
fluctuations along the $a$ axis, which would be the properties inside the two-
leg ladder along the $a$ axis.

###### Acknowledgements.

The authors would like to thank Y. Yanase, S. Fujimoto, W. Knafo, K. Kaneko,
G. Knebel, J.-P. Brison, S. Raymond, and J. Flouquet for their valuable
discussions. This work was supported by the Kyoto University LTM Center,
Grants-in-Aid for Scientific Research (Grant Nos. JP15H05745, JP17K14339,
JP19K03726, JP16KK0106, JP19K14657, JP19H04696, JP20H00130, JP20KK0061,
JP22H01168 and JP22H04933) from JSPS.

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