SciPost Phys. Proc. 11, 012 (2023)

High field magnetism of the triangular lattice
antiferromagnet CsFeCl3 under high pressure
Katsuki Nihongi1 , Takanori Kida1 , Yasuo Narumi1 , Nobuyuki Kurita2 ,Hidekazu Tanaka2 , Yoshiya Uwatoko3 , Koichi Kindo3 and Masayuki Hagiwara1⋆
1 Center for Advanced High Magnetic Field Science (AHMF), Graduate School of Science,
Osaka University, Toyonaka, Osaka 560-0043, Japan
2 Department of Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan
3 The Institute for Solid State Physics, The University of Tokyo,
Kashiwa, Chiba 277-8581, Japan⋆ hagiwara@ahmf.sci.osaka-u.ac.jp
International Conference on Strongly Correlated Electron Systems(SCES 2022)
Amsterdam, 24-29 July 2022
doi:10.21468/SciPostPhysProc.11

Abstract
Magnetization measurements of the triangular lattice antiferromagnet CsFeCl3 at 1.4 K
for H ∥ c were performed in pulsed high magnetic fields of up to 51 T under high pressures of up to 0.80 GPa. At ambient pressure, the magnetization below Hc1 = 4 T issmall, and then it changes steeply between Hc1 and Hc2 = 12 T, followed by a gradualincrease in magnetization up to Hm = 33 T where a two-step metamagnetic transition
occurs. With increasing pressure, the Hc1 and Hm shifted to the low-field side, while the
Hc2 shifted to the opposite side. The change in Hm may depend on the difference in the
single-ion anisotropies on pressure in the lowest J = 1 and the excited J = 2 states.
Copyright K. Nihongi et al.
This work is licensed under the Creative Commons
Attribution 4.0 International License.
Published by the SciPost Foundation.

1

Received 22-07-2022
Accepted 25-04-2023
Check forupdatesPublished 05-06-2023
doi:10.21468/SciPostPhysProc.11.012

Introduction

Gapped spin systems with a singlet ground state are attractive quantum spin systems, because the gap is suppressed by the applied magnetic field, pressure, or chemical doping, causing a quantum phase transition (QPT). In the vicinity of the quantum critical point (QCP)
where the QPT occurs at zero temperature, some exotic phenomena are expected to be observed by the effect of quantum fluctuations.
CsFeCl3 is one of the hexagonal ABX3 -type families that possesses the magnetic frustrationin the triangular-lattice antiferromagnetic plane and belongs to a space group P63 /mmc [1].
Figure 1(a) shows the crystal structure of CsFeCl3 . Magnetic Fe2+ ions, which are surrounded

012.1

SciPost Phys. Proc. 11, 012 (2023)

(a)

(b) 5

5

Eg

D
L=2
S=2

J=3
(7)

Fe2+
J0

J1
z

5

T 2g

J=2
(5)

Cubic
Cs

c

2l
J =1

+

Cl-

a

J =0
De z2
J 2 = ±1De2Dez

J 2 = ±2z

(3)

D

Spin-orbit
coupling Trigonalb

J 1 = ±1z
J 1= 0Figure 1: (a) Crystal structure of CsFeCl3 . Magnetic Fe2+ ions are surrounded octahedrally by six Cl− ions. FeCl6 octahedra form the chain along the c axis by sharing
Cl-triangular faces. The exchange interactions between Fe2+ ions are denoted by the
intra-chain ferromagnetic constant J0 and the inter-chain antiferromagnetic constantJ1 . (b) Expected energy scheme of Fe2+ ion in CsFeCl3 .
octahedrally by six Cl− ions, form a chain structure with ferromagnetic (FM) exchange interactions (J0 ) along the c axis (chain direction) and a triangular lattice with antiferromagnetic(AFM) exchange interactions (J1 ) in the a b plane [2]. The energy scheme of Fe2+ ion in
CsFeCl3 is depicted in Fig. 1(b). The 5 T2g lowest state in a cubic crystalline field splits into
three states owing to spin-orbit coupling. The energy gap between the lowest J = 1 state
and the next excited J = 2 state is 2λ(≈ 200 cm−1 ) where λ is the spin-orbit coupling constant of Fe2+ ion. The J = 1 state consists of a singlet ground state and doublet excited statewith a spin gap (∆s ) owing to easy-plane single-ion anisotropy. Considering only the energy
scheme of the J = 1 state, the magnetic interaction terms of Fe2+ ions (fictitious spin S = 1) in
CsFeCl3 in magnetic fields applied along the z axis (c direction) are described by the following
Hamiltonian [3]

H=

X
i

D(Siz )2 + J0

chain
X

S i · S j + J1

<i, j>

plane
X
<i,k>

S i · S k − gµB H

X

Siz ,

(1)

i

where D (>0) is the single-ion anisotropy constant, J0 and J1 are the ferromagnetic (along
the chain) and antiferromagnetic (in the a b plane) exchange constants, respectively. g andµB in the forth term are the g factor for the z axis and the Bohr magneton, respectively. The
coupling constants determined from the energy-dispersion relations in the inelastic neutron
scattering (INS) experiments [4] are D = 2.18 meV, J0 = -0.454 meV, and J1 = 0.024 meV.
As aforementioned, CsFeCl3 possesses a singlet ground state with a spin gap to the excited
doublet state owing to this positive D.
With increasing applied pressure at zero field, ∆s was reported to diminish and then vanish
above Pc = 0.90 GPa to exhibit a magnetically ordered state with a 120◦ spin structure in thea b plane at low temperatures [5, 6]. In the INS experiments of this compound under highpressure, the excitation modes, in which the longitudinal and transverse fluctuations of spinsare hybridized, were observed at 1.4 GPa [7].
As for the magnetic-field experiments, the magnetization curve at 1.3 K for H || c increases
gradually up to Hc1 = 4 T, and then increases rapidly between Hc1 and Hc2 = 12 T [8]. Neutron
scattering experiments in magnetic fields revealed that the ground-state spin configuration isa 120◦ spin structure in the triangular-lattice plane between Hc1 and Hc2 [9]. Above Hc2 ,012.2

SciPost Phys. Proc. 11, 012 (2023)

the magnetization, increases slightly with magnetic field, which is attributed to the Van Vleckparamagnetism, and then exhibits a metamagnetic transition around Hm = 33 T [8]. This
metamagnetic transition was suggested to be caused by an unconventional level crossing between the J1z = −1 and J2z = −2 states in magnetic fields as indicated in Fig. 1 (b). In thisstudy, we performed high-field magnetization measurements of CsFeCl3 at 1.4 K for H ∥ cunder pressures of up to 0.80 GPa and constructed the magnetic-field (H) versus pressure (P)phase diagram to discuss the pressure dependence of Hc1 , Hc2 and Hm .

2

ExperimentSingle crystals of CsFeCl3 were grown by the vertical Bridgman method described inRef. [5]. The sample was a cylindrical single crystal with 4 mm in length along the c axis
and 1.6 mm in diameter in the a b plane. Pulsed high magnetic fields of up to 51 T with theduration of 35 ms were generated with a non-destructive pulsed magnet at AHMF in Osaka
University. High-field magnetization measurements were performed with an induction method
using a pick-up coil at the temperature of 1.4 K under high pressures of up to 0.80 GPa. In
this study, we used a NiCrAl piston-cylinder-type pressure cell (PCC) with inner and outer diameters of 2.0 mm and 6.0 mm, respectively, and a mixture of Fluorinert FC70:FC77 = 1:1 as
the pressure medium. The applied pressure in the sample space was calibrated by the pressure dependence of the superconducting transition temperature of Sn [10]. When putting thesample into the PCC, the sample could be adjusted by hand to apply the magnetic field tothe c axis of the sample within ∼ 4◦ . The magnetization measurement of CsFeCl3 at ambientpressure was performed without the NiCrAl PCC. Pulsed magnetic field induced eddy current
in metallic parts of the NiCrAl PCC, resulting in the Joule heating. When the NiCrAl PCC isplaced in liquid 4 He cryostat at 1.4 K, the temperature at the sample position does not changemuch (less than 0.1 K) until 6.5 ms (approximately 40 T at this moment in the field ascending
process when the maximum field was 51 T) from the start of magnetic-field generation [11],thus allowing high-field measurements up to ∼40 T at 1.4 K in the ascending process. It should
be noted that the temperature of the pressure cell rises immediately, but the time delay of theheat flow via the pressure medium from the cell to the sample position occurs.

3

Results and Discussion

The magnetization (M ) curves normalized by the M at Hc2 and d M /d H of CsFeCl3 at 1.4 K
for H || c under various pressures are shown in Figs. 2 (a) and (b), respectively. M /MHc2 andd M /d H at ambient pressure are in good agreement with those in a previous paper [8]. The
M /MHc2 around 33 T exhibits a metamagnetic transition with two steps at Hm1 = 32.2 T
and Hm2 = 32.9 T, which corresponds to two peaks in d M /d H. With increasing pressure,the transitions fields Hc1 , Hm1 and Hm2 shift to the low-field side, while the Hc2 shifts to thehigh-field side. The change in M (∆M ) or the slope between Hc2 and the magnetic field
just below Hm1 was close to each other independent of pressure. Therefore, the Van Vleckparamagnetism is almost independent of pressure, suggesting weak pressure dependence ofthe spin-orbit coupling constant λ.
Figure 3 shows the magnetic field versus pressure phase diagram of CsFeCl3 at 1.4 K for
H || c. The calculated formula for Hc1 within the mean-field theory [12] is given by,
Hc1 = ∆s /gµB =Æ

D2 − 2D(2J0 + 3J1 )/gµB .

(2)

The pressure dependences of the exchange interaction and the single-ion anisotropy deter012.3

SciPost Phys. Proc. 11, 012 (2023)

3.5 CsFeCl
3

H || c, T = 1.4 K
0.80 GPa

H || c, T = 1.4 K(b)

3.0 (a)0.64 GPadM /dH (a.u.)

M/MHc2

2.5
2.0
Hm2

1.5

Hm1

0.42GPa

Hc2

0.06 GPa

1.00.80 GPa0.64 GPa0.42 GPa
0.06 GPa
Ambient (no PCC)

0.5
Hc1

0
0

10

20

30

40

m0H (T)Hm1 Hm2

Ambient (no PCC)
Hc2
Hc1

0

10

20

m0H (T)

30

40

Figure 2: (a) Magnetization (M ) curves of CsFeCl3 at 1.4 K for H || c normalized
by the M at Hc2 under various pressures. The curves are shifted up by 0.5 from theambient-pressure curve with increasing pressure for clarity. (b) The field derivativesof the magnetization (d M /d H) curves in (a). The d M /d H curves in (b) are shifted
arbitrarily along the vertical direction for clarity.
mined from the INS study [7] were described as follows; J0 (meV) = -0.5 -0.14P,
J1 (meV) = 0.0312 -0.0015P, and D (meV) = 2.345 +0.365P, where the P (GPa) is the value ofpressure. The dashed line in Fig. 3 expresses the pressure dependence of Hc1 given by Eq. (2),in which the pressure-dependent exchange constants and the single ion anisotropy constantgiven above are substituted. The comparison of the experimental data to the calculated one
is made and these are closely placed to each other. The Hc1 from our magnetization measurement, however, is slightly higher than that obtained from the INS experiment at high pressures.
This might be attributed to the quantum fluctuation enhanced near the QCP (Pc =0.9 GPa), because Eq. (2) is derived under the mean field. The spin states of Fe2+ ion with the fictitious
spin S = 1 in CsFeCl3 are composed of a singlet-ground state (S z = 0) and the doublet-excitedstate (S z = ±1) separated by a single-ion anisotropy D as shown in Fig. 1(b). However, theexcited state has a finite energy band that becomes broad with increasing pressure. Between
Hc1 and Hc2 , the lower doublet state with a finite bandwidth comes down to cross the singlet
ground state. Therefore, the Hc1 goes down and the Hc2 goes up with increasing pressure,indicating the increases in the single-ion anisotropy and the bandwidth of the energy dispersion curve, the former of which is consistent with the pressure dependence of the single-ion
anisotropy as mentioned above.
The transition fields Hm1 and Hm2 decrease almost linearly with increasing pressure asshown in Fig. 3. These extremely low transition fields could not be explained by the levelcrossing of J = 1 and J = 2 states in a conventional energy scheme of Fe2+ ion in Fig. 1(b),and its origin is unknown yet. The pressure dependence of the metamagnetic transition field
may be explained by the pressure effect on the single-ion anisotropy D and the single-ion
anisotropy De in the excited J = 2 quintet states as shown in Fig. 1(b). These D and De
values may change largely by δ/λ where δ is the parameter that describes the splitting of theorbital triplet state dε by the tetragonal crystalline field as discussed for FeCl2 ·2H2 O in Fig. 2of Ref. [3]. To clarify this interpretation, the pressure dependence of the energy difference
between J1z = ± 1 in J = 1 state and J2z = ± 2 in J = 2 needs to be investigated by INS and
ESR measurements.
012.4

SciPost Phys. Proc. 11, 012 (2023)

40

Hm2

m0H (T)

30

Hm1
20
Hc2
10

Hc1
0
0

0.2

0.4

0.6

0.8

P (GPa)Figure 3: Magnetic field (µ0 H) vs pressure (P) phase diagram of CsFeCl3 at 1.4 K for
H || c constructed from the high-field magnetization measurements. A dashed line is
the pressure dependence of Hc1 provided in a previous study [5].

4Summary

We performed magnetization measurements of CsFeCl3 at 1.4 K in pulsed high magnetic
fields under high pressures. The pressure dependence of Hc1 is explained fairly by the formulaEq. 2 using the pressure-dependent values of the exchange constants and single-ion anisotropy
constant obtained from the INS experiment under pressures. The metamagnetic transition fieldaround 33 T decreases linearly with pressure, which may be explained by the change in the
single-ion anisotropy D in the J = 1 state and the single-ion anisotropy De in the excited J = 2
state under pressure.

Acknowledgements
This study was supported by the Sasakawa Scientific Research Grant from The Japan Science Society, JST, the establishment of university fellowships towards the creation of science
technology innovation, Grant Number JPMJFS2125 and the Motizuki Fund of Yukawa Memorial Foundation, and also supported by JSPS KAKENHI (Grant Nos JP17H06137, JP17K18758,
19K03711, JP21H01035, JP19H00648).

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