# Unusual Nonmagnetic Ordered State in CeCoSi Revealed by 59Co-NMR and NQR
Measurements

Masahiro Manago<EMAIL_ADDRESS>Present address: Department of
Physics and Materials Science, Graduate School of Natural Science and
Technology, Shimane University, Matsue, Shimane, Japan.  Hisashi Kotegawa
Hideki Tou  Hisatomo Harima  Department of Physics, Kobe University, Kobe,
Hyogo 657-8501, Japan  Hiroshi Tanida  Liberal Arts and Sciences, Toyama
Prefectural University, Imizu, Toyama 939-0398, Japan

###### Abstract

We performed 59Co nuclear magnetic and quadrupole resonance (NMR and NQR)
measurements under pressure on a single-crystalline CeCoSi, which undergoes an
unresolved phase transition at $T_{0}$. The NQR spectra clearly showed that
the phase transition at $T_{0}$ is nonmagnetic, but any symmetry lowering at
the Co site was not seen irrespective of the feature of second-order phase
transition. By contrast, the NMR spectra were split by the induced magnetic
field perpendicular to the external magnetic field. These results show that
the phase below $T_{0}$ is not a simple paramagnetic state but is most likely
electric multipolar ordered state of Ce $4f$ electrons. The development of the
Kondo effect by applying pressure is thought to be crucial to stabilize this
state and to show novel features beyond commonality of tetragonal Ce-based
systems.

Physical properties of solids are influenced intricately by degrees of freedom
of electrons, that is, charge, spin, and orbital, through their mutual
couplings and many-body interactions of electrons. Phase transition
characterized by an order parameter is one of the demonstrations of their
influence; therefore, it is a fundamental yet profound phenomenon. Rich
interactions in solids induce various types of phase transitions; hence, they
are attractive in condensed matter physics.

Such diversity yields at times a mysterious ordered state. A well-known
example is the “hidden order” state in the $5f$-electron system URu2Si2 Mydosh
and Oppeneer (2011); Mydosh  _et al._ (2020). It is a second-order phase
transition with a symmetry reduction; however, the crystallographic symmetry
of the ordered state is still controversial Okazaki  _et al._ (2011); Tabata
_et al._ (2014); Riggs  _et al._ (2015); Wang  _et al._ (2020). Several
researchers have attempted unmasking the order parameter in URu2Si2 for three
decades because it is just a fundamental question in condensed matter physics;
the mechanism through which degrees of freedom of electrons can affect
physical properties of solids.

The $4f$-electrons system CeCoSi is a potential example exhibiting an
extraordinary order parameter. It crystallizes in the tetragonal $P4/nmm$
($D_{4h}^{7}$, No. 129) space-group symmetry with the CeFeSi-type structure
Bodak  _et al._ (1970). The spacial inversion symmetry is locally absent at
the Ce site, whereas the crystal structure has the global inversion symmetry.
The crystal electric field (CEF) ground state has been reported as the
$\Gamma_{7}$ ($\mp 0.306\ket{\pm 5/2}\pm 0.95\ket{\mp 3/2}$) Kramers doublet,
and the first excited state is separated from it by $\sim 100$ K Nikitin  _et
al._ (2020). It has been established that an antiferromagnetic (AFM)
transition occurs at the Néel temperature $T_{\textrm{N}}=9.4$ K. The
transition is of second-order Chevalier and Matar (2004), and the Ce moments
with sizes of $m_{\textrm{Ce}}\sim 0.37(6)\mu_{\textrm{B}}$ are aligned along
the $[100]$ axis with a $\bm{q}=\bm{0}$ structure, as revealed by a neutron
scattering study Nikitin  _et al._ (2020). Another phase, which is a matter of
interest, has been initially reported to emerge under pressure below $\sim 40$
K at $\sim 1.5$ GPa Lengyel  _et al._ (2013). The first unresolved issue of
this phase is its intrinsic pressure phase diagram. Contrary to some reports
Lengyel  _et al._ (2013); Nikitin  _et al._ (2020), a study on single-
crystalline samples proposed that this “pressure-induced ordered phase”
already exists at ambient pressure below $T_{0}=12$ K Tanida  _et al._ (2019).
The phase below $T_{0}$ at lower pressures seems to continuously connect to
the pressure-induced phase Tanida  _et al._ (2018, 2019). However, the anomaly
at $T_{0}$ at ambient pressure is not sufficiently large to convince a phase
transition. Therefore, microscopic measurements are desired to reveal whether
the phase transition at $T_{0}$ is intrinsic or not at ambient pressure. The
second unresolved issue is the order parameter below $T_{0}$. It seems
different from usual AFM states, as deduced from an enhancement by the
magnetic field Lengyel  _et al._ (2013); Tanida  _et al._ (2019). There have
been various suggestions for the origin of this phase, as follows: the spin-
density-wave order of Co $3d$ electrons, metaorbital transition, and
antiferroquadrupolar (AFQ) ordering Lengyel  _et al._ (2013); Tanida  _et al._
(2018, 2019); however, the order parameter remains unresolved.

In this Letter, we present the results of 59Co nuclear magnetic and quadrupole
resonance (NMR and NQR) measurements on high-quality single-crystalline CeCoSi
samples to clarify the above-mentioned issues. The combined NMR and NQR
results revealed the intrinsic phase diagram, where the objective phase was
present even at ambient pressure. In the ordered state, there is no clear
indication of symmetry reduction at the Co site under zero field, whereas the
NMR spectra split below $T_{0}$ when the magnetic field tilted from the [100]
axis was applied. This NMR anomaly can be interpreted by the emergence of the
induced magnetic field perpendicular to the external field. Present results
suggest an unusual nonmagnetic ordered state that is most likely an electric
multipole ordered state in CeCoSi.

Plate-shaped single-crystalline CeCoSi samples ($\sim 3\times 4\times 0.5$
mm3) were grown using the Ce/Co eutectic flux method, as described in Ref.
Tanida  _et al._ , 2019. The 59Co ($I=7/2$) NMR and NQR measurements were
performed in the temperature range 1.4–300 K using a standard spin-echo
method. The NMR spectra were obtained under a field of 1 T near the $[100]$
direction, and its angle was deduced from the frequencies of the spectra above
$T_{0}$. The local symmetry of the Co site in the $P4/nmm$ space group is
$\bar{4}m2$ with four-fold improper rotational symmetry. Hydrostatic pressure
was applied up to 2.35 GPa on another sample using a piston-cylinder-type cell
with Daphne 7474 as a pressure-transmitting medium. The pressure was
determined from the superconducting transition temperature of a Pb sample
inside the cell. A LaCoSi sample consisting of single-crystalline pieces was
also measured by NQR at $P=0$ as a reference system.

Figure 1: (Color online) (a–c) Temperature dependence of the 59Co NQR spectra
of CeCoSi at $\nu_{3}\equiv 3\nu_{\textrm{Q}}$ site without a field under a
pressure of (a) 0, (b) 1.09, and (c) 1.52 GPa. The spectra at each temperature
are shifted vertically. (d) Temperature and pressure dependence of
$\nu_{\textrm{Q}}$ of CeCoSi and that of LaCoSi at ambient pressure. The
vertical arrows indicate $T_{0}$ determined by NMR measurements, which
detected it even at ambient pressure. The dashed line for LaCoSi indicates the
conventional temperature dependence of $\nu_{\textrm{Q}}$.

The NQR spectra are sensitive to both the magnetic and electric anomalies and
are suitable for probing the nature of the ordered state. Figures 1(a)–1(c)
show the temperature dependence of the NQR spectra above $T_{\textrm{N}}$ at
the $\nu_{3}\equiv 3\nu_{\textrm{Q}}$ ($\pm 5/2\leftrightarrow\pm 7/2$) site
at 0, 1.09, and 1.52 GPa. The value of the quadrupole frequency
$\nu_{\textrm{Q}}$ was 2.09 MHz at $P=0$ and 20 K. The results on other
pressures are shown in the Supplemental Materials SM . The NQR spectra did not
split nor broaden, although they showed a shift at $T_{0}$. As shown in the
temperature dependence of $\nu_{\textrm{Q}}$ in Fig. 1(d), the kink of
$\nu_{\textrm{Q}}$ is clearer at higher pressures, and it is invisible at
ambient pressure. The kink is not a necessary condition for the phase
transition, and its presence at ambient pressure is proved by NMR measurements
mentioned later. The absence of splitting or broadening NQR spectra
demonstrates that the internal field is absent at the Co sites for
$T_{\textrm{N}}<T<T_{0}$ in the entire pressure range. This clearly excludes
the magnetic ordering of Co $3d$ moments below $T_{0}$. Our results also
indicate that all the Co sites remain equivalent below $T_{0}$ while
maintaining a local tetragonal symmetry, that is, a tetragonal crystal
structure SM . If one considers a possibility of the magnetic ordering of Ce
$4f$ moments, the only explanation for the NQR result is a cancellation of the
internal magnetic field at the Co site, which is surrounded by four Ce ions.
The transition to the underlying AFM state at $T_{\textrm{N}}$ is of second-
order, and this AFM state with $\bm{q}=\bm{0}$ does not break the
translational symmetry of the crystal above $T_{0}$. Then, the intermediate
ordered state in $T_{\textrm{N}}<T<T_{0}$ should maintain the same
translational symmetry, that is, the propagation vector is $\bm{q}=\bm{0}$.
For the $\bm{q}=\bm{0}$ structure, the internal field is canceled only when
the staggered Ce moment is along the $[001]$ axis SM . This possibility is
excluded by the increase of the susceptibility along this axis below $T_{0}$
Tanida  _et al._ (2019). Thus, we concluded that the ordered phase below
$T_{0}$ is nonmagnetic with one tetragonal Co site. The unusual field response
explained later also excludes the possibility of the magnetic state and yet
indicates that this phase is not a simple paramagnetic state.

The temperature dependence of $\nu_{\textrm{Q}}$ usually obeys a conventional
monotonous behavior $\nu_{\textrm{Q}}(T)=\nu_{\textrm{Q}}(0)(1-\alpha
T^{1.5})$ Christiansen  _et al._ (1976) ($\alpha>0$) owing to the lattice
expansion and vibration, as observed in LaCoSi. In contrast, the
$\nu_{\textrm{Q}}(T)$ in CeCoSi deviates from this behavior above $T_{0}$, and
the deviation becomes remarkable as the pressure increases. Such behavior has
been observed in some $4f$-electron systems Shimizu  _et al._ (1987); Kitagawa
_et al._ (2017); Mito  _et al._ (2013); Magishi  _et al._ (2012); Yogi  _et
al._ (2014) and discussed to originate from a CEF splitting, a valence change
of the $4f$ ion, or the Kondo effect. The distinct pressure dependence in
CeCoSi indicates that such multiple effects influence $\nu_{\textrm{Q}}$ at
the Co site through the pressure-enhanced hybridization between the $4f$
electron and conduction electrons.

Figure 2: (Color online) Temperature dependence of 59Co NQR nuclear spin-
lattice relaxation rate $1/T_{1}$ of CeCoSi from the Ce-$4f$ electrons at
$H=0$ under several pressures. The $4f$ part was obtained by subtracting the
$1/T_{1}$ value of LaCoSi. The vertical arrows indicate $T_{0}$ determined by
NMR results. Inset (left panel): $1/T_{1}$ of CeCoSi at ambient pressure
before subtraction as well as that of LaCoSi. The dashed line for LaCoSi shows
the Korringa relation $1/T_{1}\propto T$ in the normal metal.

Figure 2 shows the Ce-$4f$ part of the nuclear spin-lattice relaxation rate
$1/T_{1}$ measured by the NQR at $H=0$. The $1/T_{1}$ has a Co $3d$ component,
and it was subtracted using the result of LaCoSi (see the inset of the left
panel of Fig. 2). The $1/T_{1}$ divided by temperature is shown in
Supplemental Materials SM . The $1/T_{1}$ of LaCoSi shows the weakly-
correlated Pauli paramagnet corresponding to a previous report Welter  _et
al._ (1994). The absence of phase transition in LaCoSi is consistent with the
interpretation that the phase below $T_{0}$ originates from Ce $4f$ electrons.
No divergent behavior was detected near $T_{0}$ in $1/T_{1}$ in CeCoSi,
indicating the absence of the magnetic critical fluctuations. A clear drop was
found at $T_{0}$ only at 2.03 GPa. This may correspond to the gaplike anomaly
in the electric resistivity above $\sim 1.5$ GPa Lengyel  _et al._ (2013) and
suggest the decrease of the density of states. Around $T_{\textrm{N}}$,
$1/T_{1}$ is expected to detect the magnetic fluctuations perpendicular to the
$[001]$ axis SM . $1/T_{1}$ diverged owing to the critical slowing down of the
magnetic fluctuations at ambient pressure (see also Fig. 7 in the Supplemental
Materials SM ). However, the divergence of $1/T_{1}$ is suppressed with
increasing pressure. This is not expected with the magnetic structure of
$\bm{m}\parallel[100]$. Two possibilities are considered to interpret this
result. One is that the magnetic moment is tilted along the [001] axis under
pressure. Another is that the magnetic fluctuation is suppressed as the
ordered state below $T_{0}$ gets stabilized. The $1/T_{1}$ significantly above
$T_{0}$ shows the localized Ce $4f$ electrons ($1/T_{1}=\textrm{const.}$) at
1.52 GPa or below. Meanwhile, $1/T_{1}$ starts to decrease from higher
temperatures than $T_{0}$ at 2.03 and 2.35 GPa. Such an itinerant behavior
owing to coherent Kondo effect in $1/T_{1}$ is also seen in some heavy-fermion
systems including CeCu2Si2 Ishida  _et al._ (1999); Fujiwara  _et al._ (2008).
The $1/T_{1}$ result, combined with the $\nu_{\textrm{Q}}$ behavior, indicate
an enhancement of the Kondo effect by pressure.

Figure 3: (Color online) (a) 59Co NMR spectra of CeCoSi at ambient pressure at
10 and 20 K with the field $\mu_{0}H=1.011$ T and angles $\theta=87.8$° and
90°. The blue solid and dashed lines indicate the simulated peak frequencies
at $T=10$ K assuming the staggered field of $\sim\pm 15$ mT along the $[001]$
axis. The vertical arrow indicates the central ($1/2\leftrightarrow-1/2$)
line, whereas the vertical black dashed line indicates the frequency of $K=0$
of the central line. (b–d) Temperature dependence of the spectra under
pressures of (b) 0, (c) 1.09, and (d) 1.52 GPa with $\mu_{0}H=1.0$ T slightly
titled from the $[100]$ axis. The spectra are shifted vertically with an
offset proportional to the temperatures. The horizontal arrows indicate
$T_{0}$. (e) Schematic of the induced field $\bm{H}_{\textrm{ind}}$ under the
external field $\bm{H}_{\textrm{ext}}$ at the Co sites below $T_{0}$. Only the
$[001]$ components of $\bm{H}_{\textrm{ind}}$ are drawn for simplicity.

Further information on the ordered state is provided by the spectra measured
under a magnetic field. Figure 3(a) shows the full set of the NMR lines at
ambient pressure at 10 K below $T_{0}=12$ K with a field strength of
$\mu_{0}H=1.0$ T in addition to the results of 20 K. Here, $\theta=87.8$° and
90° are the field angles from the $[001]$ to $[100]$ axes. At 20 K, seven NMR
lines were observed owing to the nuclear quadrupole interaction of $I=7/2$
59Co nucleus. Meanwhile, at 10 K, the third satellite at the lowest frequency
split when the field was tilted from the $[100]$ axis, clearly indicating the
symmetry reduction below $T_{0}$. The two-split peaks merged just when
$H\parallel[100]$, which was consistent with the NQR data and suggesting that
the crystallographic Co site remains one site below $T_{0}$. Similar split and
merging of the spectra were observed when the magnetic field is around $[001]$
axis (not shown).

Figures 3(b)–3(d) show the temperature dependence of the NMR third satellite
line with the field of $\mu_{0}H=1.0$ T slightly tilted from the $[100]$ axis
under pressures of 0, 1.09, and 1.52 GPa. The results under other pressures
are shown in Supplemental Materials SM . The spectra started to split at
$T_{0}$ at all pressures, and the value of $T_{0}$ corresponds with the
previous reports Tanida  _et al._ (2018, 2019). This is the first microscopic
evidence for the phase transition at $T_{0}$ at ambient pressure. Careful
measurements just below $T_{0}$, especially at ambient pressure, indicate that
the transition is of second-order SM . Three peaks were observed at
intermediate temperatures at 1.52 GPa and other pressures SM , although it is
unclear whether this is intrinsic or not. Here we assume the two-peak
structure to be intrinsic because it is also observed at ambient pressure,
where the stress or inhomogeneity owing to pressure is free.

The NMR line split is remarkable at the low-frequency third satellite line and
disappears for $H\parallel[100]$. This situation is reproduced only when the
induced magnetic field $\bm{H}_{\textrm{ind}}$ is perpendicular to the
external field, as shown in Fig. 3(e). The blue solid and dashed lines in Fig.
3(a) indicate the simulated NMR frequencies, where
$\mu_{0}H_{\textrm{ind},c}\sim\pm 15$ mT along the $[001]$ axis are adopted.
When the external field $\bm{H}_{\textrm{ext}}$ is tilted from $[100]$ to the
$[001]$ axis, the total field at two Co sites,
$\bm{H}_{\textrm{ext}}+\bm{H}_{\textrm{ind}}$, differs from each other,
leading to the splitting of the NMR frequency. The field
$\mu_{0}H_{\textrm{ind},z}\sim\pm 15$ mT is absent in the NQR spectra, and
thus, this is induced by the external field. Such an induced field cannot be
explained by a simple paramagnetic response of Ce $4f$ magnetic moment SM .
Notably, this excludes the possibility that the internal field at the Co site
is canceled out in the AFM alignment of the Ce moments because tilting of the
AFM moments under an external field yields a similar response to the
paramagnetic response without splitting of the NMR line.

Figure 4: (Color online) Temperature–pressure phase diagram of CeCoSi
determined by the NMR and NQR results. The solid lines are guides to the eye.
The transitions are of second-order across $T_{0}$ and $T_{\textrm{N}}$. The
disappearing pressures of two phases are from Ref. Lengyel  _et al._ , 2013.

Figure 4 shows the temperature–pressure phase diagram of CeCoSi determined by
our NMR and NQR results. The phase transition at $T_{0}$ at ambient pressure
was unambiguously confirmed to be intrinsic from the microscopic point of
view. Our results clearly demonstrate that second-order transitions occur
successively across $T_{0}$ and $T_{\textrm{N}}$. The pressure dependence of
$T_{0}$ is reminiscent of the Doniach-type phase diagram, implying that the
$c$–$f$ hybridization assists the stabilization of the ordered state at lower
pressures. Two ordered phases are suppressed with increasing pressure,
accompanied by the development of the Kondo effect, and the nonmagnetic ground
state is realized in the pressure range of 1.4–2.15 GPa.

Our NMR and NQR results limit possible order parameters in CeCoSi as follows:
in $T_{\textrm{N}}<T<T_{0}$, they exclude magnetically ordered states arising
from Ce-$4f$ and Co-$3d$ electrons. Nonmagnetic ordered states arising from
Co-$3d$ electrons, such as a charge density wave (CDW) or orbital ordering are
also unlikely. If the CDW transition occurs, the spectra will be split into
several sites corresponding to the superlattice formation. Similarly, if the
phase transition lifts the Co-$3d$ orbital degeneracy protected by local
tetragonal symmetry, orthorhombic transition is essential similar to an
electronic nematic state in Fe pnictide systemsKasahara  _et al._ (2012). The
on-site NMR and NQR results did not show the corresponding symmetry reduction.
As an ordered state of nonmagnetic Ce origin, the “metaorbital” transition
Hattori (2010), across which the occupancy of the Ce-$4f$ electrons changes
steeply, is proposed Lengyel  _et al._ (2013); however, it does not correspond
with the second-order transition with a symmetry reduction. The remaining
possibility that should be considered is the contribution of electric degrees
of freedom of Ce $4f$ electrons; that is, an electric multipole ordering. The
CEF ground state of tetragonal CeCoSi is a Kramers doublet, but the AFQ
ordering is possible if the state including the first-excited level possesses
a large interlevel interaction Yatsushiro and Hayami (2020a), which is most
likely enhanced by the Kondo effect. Quadrupolar degrees of freedom involving
CEF excited states are also known in PrOs4Sb12 Kohgi  _et al._ (2003); Goto
_et al._ (2004) and CeTe Kawarasaki  _et al._ (2011).

Before deepening this discussion, we provide a general symmetry consideration,
as discussed for the hidden-order state in URu2Si2 Harima  _et al._ (2010);
Kambe  _et al._ (2018). Because the transition to the nonmagnetic state across
$T_{0}$ in CeCoSi is second-order, the space group below $T_{0}$ must be one
of the subgroups of the room-temperature phase of No. 129 ($P4/nmm$).
Moreover, the underlying AFM state orders to $\bm{q}=\bm{0}$ structure,
preserving the translational symmetry Nikitin  _et al._ (2020) while excluding
the possibility of superlattice formation above $T_{\textrm{N}}$. Thus, the
possible maximal subgroups are as follows: No. 59 ($Pmmn$), 85 ($P4/n$), 90
($P42_{1}2$), 99 ($P4mm$), 113 ($P\bar{4}2_{1}m$), and 115 ($P\bar{4}m2$) Hahn
(2005); SM . Because the Co site remains one site below $T_{0}$, the space
group with two Co sites, namely, No. 115, is unlikely. The breaking of the
four-fold symmetry was not detected at the Co site, which contradicts No. 59,
90, and 99 with two-fold symmetry at the Co site. Therefore, the space group
No. 85 or No. 113 is preferable for the state below $T_{0}$ in CeCoSi. An
interesting feature is that the symmetry reduction to No. 85 or No. 113 does
not require the shift of the atomic positions SM ; Hahn (2005), that is, it
can be satisfied by symmetrical change of electronic configurations of the Ce
ions. If that is the case, the lattice distortion is triggered by the weak
coupling to the electrons, and the detection of the symmetry change may not be
straightforward in X-ray measurements. This would happen in URu2Si2 Harima
_et al._ (2010); Kambe  _et al._ (2018). Moreover, the No. 113 lacks global
inversion symmetry; therefore, experimental methods that can observe the
splitting of bands will be effective to confirm this.

A clue to understand the origin of this phase is the unusual field response,
i.e., the induced field perpendicular to the external field. Such a behavior
is reminiscent of an AFQ state Shiina  _et al._ (1997); Sakai  _et al._
(1997), as observed in ferro- or antiferroquadrupolar systems CeB6 Takigawa
_et al._ (1983), PrFe4P12 Ishida  _et al._ (2005); Kikuchi  _et al._ (2007),
PrTi2Al20 Taniguchi  _et al._ (2016), and NpO2 Tokunaga  _et al._ (2005).
Therefore, it is reasonable to consider the ordered state in CeCoSi as an AFQ
state. Along this line of thought, a crucial point is consistency between the
experiment and theoretical suggestion Yatsushiro and Hayami (2020a). In the
case of multipolar states, the space groups No. 85 and 113, suggested by the
NQR result, correspond to the hexadecapolar and $O_{xy}$-type AFQ states,
respectively. The symmetry of the Ce site reduces to four-fold symmetry
without mirror operations ($4..$) in the No. 85 and two-fold symmetry ($2.mm$)
in the No. 113 space group SM . Meanwhile, identification of the AFQ order
parameter is possible in principle from the NMR-line splitting by a
theoretical workYatsushiro and Hayami (2020b). For example, the NMR line can
split in the $O_{zx}$-type AFQ state when $H\perp[010]$, except for
$H\parallel[100]$ and $H\parallel[001]$. Therefore, the induced field detected
by our NMR suggests the $O_{zx}$-type AFQ state. In the case of $O_{xy}$ type,
which is proposed by the zero-field result, the line splitting does not occur
by the component along [001] of the field. Thus, we need to resolve this
discrepancy between zero- and finite-field results to settle the origin of the
ordered state. A point to be considered is the switching of the order
parameter under field, as in some quadrupole systems such as CeB6 Nakamura
_et al._ (1995) and PrTi2Al20 Taniguchi  _et al._ (2019). Such a signature has
not been observed thus far in CeCoSi, but investigations for the field-induced
switching may unravel this issue. Another point is the lack of local inversion
symmetry at the Ce site. In this case, odd-parity multipoles, such as electric
octapole, are active in principle through the antisymmetric spin-orbit
interaction at the Ce site, but the mechanism through which this effect
influences the field response is unknown. In any case, our results capturing a
peculiarity of the ordered state in CeCoSi will offer theoretical and further
experimental challenges for the complete elucidation of the order parameter.

In conclusion, we have performed single-crystalline NMR and NQR measurements
to investigate the unresolved ordered state in CeCoSi. The absence of any
signature of symmetry reduction in the 59Co-NQR spectra indicates that the
ordered phase below $T_{0}$ is nonmagnetic and originates from Ce $4f$
electrons. An unusual field response, proved by the NMR-line splitting,
characterizes the extraordinary ordered state, indicating that it is most
likely the electric multipole state. Our results show that CeCoSi undergoes
two types of second-order phase transitions with different symmetry lowerings,
and the nonmagnetic phase can be the ground state above $\sim 1.4$ GPa. It is
interesting to consider why CeCoSi differs from other non-cubic systems. As an
idea, we expect that parity mixing by absence of the local inversion symmetry
at the Ce site may be a key factor to induce this peculiar behavior in CeCoSi.
In any case, CeCoSi is a novel example offering profound physics originating
from the $4f^{1}$ state.

###### Acknowledgements.

The authors thank M. Yatsushiro, S. Hayami, H. Hidaka, Y. Tokunaga, K. Ishida,
and Y. Kuramoto for their insightful discussions. This work was supported by a
Grant-in-Aid for Scientific Research on Innovative Areas “J-Physics” (Grants
No. 15H05882, No. 15H05885, No. JP18H04320, and No. JP18H04321), and a Grant-
in-Aid for JSPS Research Fellow (Grant No. JP19J00336) from JSPS.

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