Antiferromagnetic ordering and critical behavior induced

giant magnetocaloric effect in distorted kagome lattice

Gd3BWO9
Zhuoqun Wang1#, Xueling Cui1#, Tim Treu2, Jiesen Guo1, Xinyang Liu1,3,4,
Marvin Klinger2, Christian Heil2, Nvsen Ma1, Xianlei Sheng1, Zheng Deng3,5,澳
Xingye Lu6, Xiancheng Wang3,5, Wei Li4, 7, Philipp Gegenwart2, Changqing Jin3,5
and Kan Zhao1*

1
School of Physics, Beihang University, Beijing 100191, China

2
Experimentalphysik VI, Center for Electronic Correlations and Magnetism,
University of Augsburg, 86159 Augsburg, Germany.

3
Beijing National Laboratory for Condensed Matter Physics,
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

4
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese
Academy of Sciences, Beijing 100190, China

5
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing
100190, China

6
Center for Advanced Quantum Studies, School of Physics and Astronomy, Beijing
Normal University, Beijing 100875, China

7
Peng Huanwu Collaborative Center for Research and Education, Beihang
University, Beijing 100191, China

# These authors contributed equally to this work

*Corresponding author email: kan_zhao@buaa.edu.cn

Abstract
We synthesize the high-quality Gd3BWO9 single crystal and investigate its low-
temperature magnetic and澳 thermodynamic properties. Below TN = 1.08 K, the
anisotropic behavior of magnetic susceptibilities reveals that the Gd3+ moments exhibit
the dominant antiferromagnetic coupling along the c-axis, while displaying a
ferromagnetic arrangement in kagome plane. With pronounced magnetic frustration, in
adiabatic demagnetization refrigeration experiments starting from initial conditions of
9 T and 2 K, Gd3BWO9 polycrystal reaches a minimum temperature of 0.151 K,
significantly lower than its TN. Due to the high density of Gd3+ ions (S=7/2), the
maximum magnetic entropy change reaches over 50 J kg-1 K-1 under fields up to 7 T in
Gd3BWO9, nearly 1.5 times as large as commercial sub-Kelvin magnetic coolant
Gd3Ga5O12(GGG). The H-T phase diagram of Gd3BWO9 under H//c exhibits field-
induced critical behavior near the phase boundaries. This observation aligns with the
theoretical scenario in which a quantum critical point acts as the endpoint of a line of
classical second-order phase transitions. Such behavior suggests the importance of
further investigations into the divergence of magnetic Grüneisen parameter in the
vicinity of critical field at ultralow temperatures.

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Introduction
Geometrically frustrated magnets are typically characterized by competing interactions
of localized spins that provide a unique platform for exploring exotic quantum magnetic
states. Typical examples are antiferromagnets where transition metal ions or 4f rare-
earth ions form the kagome lattice, giving rise to strong electron correlations, spin-orbit
coupling, and/or magnetic interaction [1-3]. In recent years, various antiferromagnets
based on kagome lattice and its modifications have been extensively studied, including
both insulators and metals, such as the quantum spin liquid candidates ZnCu3(OH)6Cl2
[4], quantum antiferromagnet BaCu3V2O8(OH)2 [5], tripod-kagome-lattice dipolar
magnet Dy3Sb3Zn2O14 [6-7], distorted kagome lattice heavy fermion system CePdAl
[8-11] and kagome spin ice HoAgGe [12-14], and three-dimensional hyperkagome-
lattice quantum spin liquid candidate PbCuTe2O6 [15-16].

Quite recently, the rare-earth-based systems R3BWO9 (R=Pr, Nd, Sm, Gd, Tb, Dy, Ho)
have attracted considerable attention as searching for new kagome antiferromagnets
[17]. These compounds crystallize in a hexagonal coordinated structure with space
group P63 (no. 173), where the R3+ ions are connected by oxygen ions and form a
distorted kagome lattice in the ab-plane [Fig. 1(a)] and stack in an AB-type arrangement
along the c-axis [Fig. 1(b)]. Notably, the interlayer separations between R3+ ions are
slightly smaller than the intralayer distances [Fig. 1(b)], which enhances the three-
dimensional nature of the magnetic interaction in R3BWO9 [17]. The non-Kramers
system Pr3BWO9 has been identified as a frustrated quantum Ising magnet [18-19]. The
Kramer system Nd3BWO9 exhibits short-range correlation below 1 K and enters the
long-range magnetic order state below 0.3 K, accompanied by anisotropic field-induced
metamagnetic quantum criticalities. The rich magnetic behavior of Nd3BWO9 can be
understood through Ising model composed of twisted triangular spin-tubes [20-22]. For
Sm3BWO9, a magnetic phase transition occurs at 0.75 K, and nuclear magnetic
resonance spectra reveal an incommensurate magnetic order [23]. The polycrystalline
studies of Gd3BWO9 demonstrate a giant magnetocaloric effect (MCE) while the
magnetic structure remains unclear [24-25]. Therefore, investigating the anisotropic
properties of Gd3BWO9 single crystals is crucial for understanding the microscopic
mechanism of the MCE.

In this article, based on the magnetic susceptibilities along a-and c-axis, we demonstrate
that the Gd3+ moments are aligned antiferromagnetically along the c-axis and
ferromagnetically in ab-plane below TN = 1.08 K. Below TN, the metamagnetic
transitions of Gd3BWO9 single crystal are identified through magnetization and
thermodynamic measurement under H//c. We continue to construct a phase diagram of
magnetic entropy as a function of temperature and magnetic field along the c-axis,
revealing a giant MCE at low temperature. Our work on Gd3BWO9 single crystal offers
significant insights into its microscopic magnetic structure, magnetic critical behavior,
and the associated giant MCE.
Experiment
The polycrystalline Gd3BWO9 is synthesized using standard solid-state reaction
method by mixing stoichiometric amounts of pre-dried Gd2O3, H3BO3 and WO3. The
powders are ground together and sintered in air at 1200 ℃ for 36 h, with several
intermittent regrindings. High-quality single crystals of Gd3BWO9 were grown via flux
method analogous to Ref. [26].澳 Yellow transparent single crystals with six hexagonal
facets are obtained and have a typical mass ranging from a few milligrams to 100 mg
[inset of Fig. 1(d)]. The X-ray diffraction (XRD) patterns and rocking-curve scans are
collected using a Bruker D8 ADVANCE diffractometer with Cu-Kα radiation (λ =
1.5406 Å) at room temperature. Crystal orientation verification is performed using a
Laue X-ray alignment system (Photonic Science Ltd.). The magnetic susceptibility and
magnetization are measured as a function of the applied field (0 to 7 T) and temperature
(0.4 to 300 K) using a Magnetic Property Measurement System SQUID magnetometer
(MPMS, Quantum Design) equipped with a 3He-refrigerator insert. Specific heat
measurements are performed using a Physical Property Measurement System (PPMS,
Quantum Design) under applied magnetic fields of 3 T and 7 T with a 3He-option, and
in zero field (0 T) with a 3He-4He dilution refrigerator.

For the adiabatic demagnetization refrigeration (ADR) experiment in PPMS, we used

a 4.38 g cylindrical pellet of 15 mm diameter and 4 mm thickness containing equal
weights of Gd3BWO9 and silver powder. The pressed pellet was sintered at 800℃ to
further improve the thermal conductivity. The sample temperature was measured using
a custom-built thermometer based on a commercial ruthenium oxide chip resistor. This
thermometer was calibrated against a known reference thermometer and read out with
a Lake Shore Model 372 AC resistance bridge, equipped with a Model 3726 scanner,
operating at a constant current of 1 nA.

Result and Discussion

A. Crystal structure

Fig. 1(c) shows the room-temperature powder X-ray diffraction pattern and Rietveld
refinement of Gd3BWO9. The observed profile aligns well with the simulation,
yielding refinement reliability factors Rp=5.12% and Rwp=7.03%. The structural
parameters determined from the Rietveld profile analysis are a = 8.564(1) Å and c =
5.402(1) Å, consistent with previous reports [17,25]. The distances between Gd and Gd
in the kagome plane are 4.212 Å and 4.825 Å [Fig. 1(a)], while those in adjacent
kagome planes are 3.880 Å and 4.311 Å [Fig. 1(b)]. The four comparable distances
highlight the three-dimensional characteristics of the magnetic interaction. The
complete crystal data are provided in the Supplemental Material [27].
澳
Moreover, we have grown large-size single crystals by flux method, with typical
crystals shown in the left inset of Fig. 1(d). The XRD patterns of the bc-plane [Fig. 1(d)]
display dominant (H00) reflections. Rocking curve analysis of the Bragg peak (200)
[right inset of Fig. 1(d)] demonstrates a narrow full-width-at-half-maximum (FWHM)
of 0.11°, indicating high quality of the single crystal. As illustrated in Fig. 1(e-f), the
six-fold symmetry of Laue pattern agrees well with the experimental simulation data,
based on the crystal structure presented in Fig. l(a-b).

B. Magnetic susceptibility and Magnetization

Fig. 2(a) presents the temperature dependence of magnetic susceptibilities χ(T) and
inverse susceptibilities 1/χ(T) for H//a and H//c, measured from 0.4 K to 300 K under
0.05 T. For low-temperature region (4-15 K) in Fig.2(b), the Curie-Weiss temperature
is determined to be -0.6 K for H//a and -0.4 K for H//c, revealing the competition
between predominant antiferromagnetic (AFM) interaction in adjacent layers and
relatively weak intralayer ferromagnetic (FM) interaction within triangular framework
of Gd3BWO9 [inset of Fig. 2(b)]. For high-temperature regime (200-300 K), the
effective moment is calculated to be 7.82 ߤ୆ for both field orientations, close to the
expected value of 7.94 ߤ୆ .

The low-temperature χ(T) [Fig. 2(b)] shows an obvious peak centered at TN = 1.08 K,
signaling long-range AFM ordering. Above TN, isotropic susceptibility behavior
reflects the absent orbital component of Gd3+ moments. Below TN, the χ(T) increases
with the temperature decreasing under H//a, whereas it decreases under H//c. This
anisotropic behavior demonstrates characteristic AFM ordering along the c-axis. As
mentioned above, the nearest interlayer distance between Gd3+ ions significantly
enhances the AFM interaction along the c-axis, serving as the primary reason for
magnetic ground state properties. Our experimental results provide direct evidence
supporting the magnetic structure [inset of Fig. 2(b)] predicted by density functional
theory (DFT) [24].澳Similar phenomena have been observed in Eu2+ containing EuMnBi2
[28]澳 and澳 EuMnSb2 [29]. In EuMnBi2, the Eu moments order ferromagnetically in ab
plane and align along c axis in the sequence of up-up-down-down below TN~22 K,
where the χ(T) parallel to the c-axis steeply decreases while it slightly increases vertical
to the c-axis [28].
澳
Fig. 2(c-d) depicts the isothermal magnetization curves M(H) at various temperatures,
and the magnetic moment澳is derived to be 6.85 μB for H//a and 6.78 μB for H//c at 0.4
K under 7 T, slightly smaller than the theoretical value 7 μB . The M(H) data can be well
fitted to Brillouin function above T = 5 K, which reveals the paramagnetic coupled
nature between Heisenberg-like spins of Gd3+ ions. Below 5 K, the deviation of the
fitted curve at 3 K and 1.8 K indicates the appearance of short-range spin correlations.
To further analyze magnetic property of Gd3BWO9, Fig. 2(e-f) display the field
derivative of magnetization dM/dH curves at 0.4 K. For the dM/dH curve under H//a in
Fig. 2(f), a pronounced peak is observed at 0.58 T, where the magnetization reaches
3.50ߤ୆ , close to 1/2 of the saturated value (‫ܯ‬௦௔ ). Additionally, a shoulder feature is
present at 0.96 T, with the M value of 5.10 ߤ୆ roughly 3/4 ‫ܯ‬௦௔ . In the case of H//c [Fig.
2(e)], a sharp peak appears at 0.40 T, followed by a shoulder at 0.82 T. The respective
M values are 2.17 ߤ୆ and 4.60 ߤ୆ , corresponding to approximately 1/3 and 2/3 of the
saturated value (‫ܯ‬௦௖ ), respectively. It would be valuable to investigate which variations
in magnetic order states are associated with these anomalies in the dM/dH curves.
Remarkably, the magnetization curve of Nd3BWO9 exhibits a 1/3 fractional plateau for
H//c in the AFM order state, where the dM/dH curve approaches zero in the vicinity of
plateau region [20-22].

C. Specific heat, Magnetic entropy and澳Magnetocaloric effect澔

To study thermodynamic properties of Gd3BWO9, the specific heat澳 Cp(T)
measurements are performed down to 0.05 K in zero field, and 0.39 K in applied fields
of 3 T and 7 T, as depicted in Fig. 3(a). The zero-field specific heat data displays a λ-
shaped anomaly at TN, consistent with the magnetic result above. The peak shape in
Cp(T) changes to a Schottky-type anomaly in an applied field of 3 T and 7 T.

Below TN, the specific heat mainly comes from the magnetic contribution. As shown in
inset of Fig. 3(a), the zero-field Cmag (T) from 0.05 K to 0.2 K is fitted to a power law
expression: Cmag (T)̱T γ , yieldingγ = 2.39(3) , lower than the value of 3 typically
observed in conventional gapless antiferromagnets [30]. In the triangular
antiferromagnet KBaGd(BO3)2, the power law relationship with澳 an exponent γ=2ǤͲ
reflects the two-dimensional (2D) magnetic interaction intrinsic to the system [31-33].
In the pyrochlore Heisenberg antiferromagnet Gd2Sn2O7, specific heat and inelastic
neutron scattering (INS) measurements reveal the presence of magnon excitations with
a gap ~ 1.5 K [34-36]. According to INS, the spin-spin correlations begin to develop
around 20 K, and eventually form a gapped long-range ordered ‘Palmer Chalker’ state
below TC = 1 K. Below 0.3 K, the Cmag(T) drops exponentially, and its value drops to
0.02 J mol-1
Gd K
-1
near 0.1 K [35]. In contrast, the Cmag(T) of Gd3BWO9 displays a
value around 0.2 J mol-1
Gd K
-1
at 0.1 K, an order of magnitude larger than that of
Gd2Sn2O7. Furthermore, the Cmag (T)/T approaches a constant value of 4.3 J mol-1 K-
2
below 0.07 K [Fig. 3(b)], indicating the unconventional gapless low-energy
excitations in Gd3BWO9.

The lattice contribution arising from thermal vibration dominates the high temperature
region. As shown in Fig. S1, an analysis is performed by fitting the zero-field specific
heat data using a polynomial expression Cph =β1 T3 +β2 T5 +β3 T7 +…… [24], between
20 K and 50 K. The magnetic specific heat is obtained by subtracting the lattice
contributions Cmag =Cp -Cph . As temperature decreases, the zero-field Cmag(T)/T curve
of Gd3BWO9 begins to increase below 5 K and reaches its maximum value at TN [Fig.
3(b)].澳The magnetic entropy Smag(T) is obtained by integrating Cmag(T)/T data [Fig. 3(b)],
and the value of Smag(T) is澳slightly larger than 3Rln8 at 20 K in zero field [Fig. 3(c)].

To estimate the minimum temperature in ADR, the adiabatic demagnetization process

is roughly depicted by arrows in Fig. 3(c) [31-32]. The Smag(T) is reduced by 44.02 J
mol-1 K-1 when applying a field of μ0H = 7 T from an initial temperature T0 = 2 K
(isothermal). Driving the field back to 0 T adiabatically is supposed to cool the material
to 0.21 K. When initiating from T0 = 5 K under 7 T, the material could cool down to澳
0.60 K with the Smag(T) reduction of 37.33 J mol-1 K-1. Similarly, the commercial
magnetic coolant Gd3Ga5O12 (GGG) achieves a minimum temperature of 0.32 K with
an initial condition of T0 = 2 K and μ0H = 6 T [33,37], and another spin chain containing
antiferromagnet NaGdP2O7 achieves a minimum temperature of 0.22 K with T0 = 2 K
and μ0H = 5 T [38].

We continue to directly test the refrigeration performance of Gd3BWO9 polycrystal

using the modified ADR cooling setup reported in Ref. [32,38-39]. Starting from an
initial condition 2 K and 9 T, the sample temperature instantaneously decreases as soon
as the field begins to decrease. Upon ramping the field down to zero at a sweep rate of
5 mT/s, a local minimum Tmin2 = 0.156 K is achieved at μ0H = 0.90 T, and another
minimum Tmin1 = 0.151 K is achieved at μ0H = 0.22 T in Run 1 [Fig. 3(d)], consistent
with the estimated value 0.21 K under 2 K and 7 T condition. We will discuss the
temperature minimum and phase boundary later. The temperature starts to increase
from T0 = 0.164 K as magnetic field drops to zero [inset of Fig. 3(d)]. As depicted in
Fig.3(e), the warm-up time from T0 up to 0.48 K exceeded 24 hours in Run 1, indicating
exceptional holding time.

To calculate the specific heat of Gd3BWO9 sample from ADR, we conduct a second run
with a resistance heater on the pellet. As shown in Fig. 3(e), there seems a slope change
in the warming curve around TN = 1.08 K, due to the AFM ordering of Gd3BWO9. As
the external resistive heat input was accurately measured and found to be nearly
constant as Qሶ =1.4 μW, much larger than the natural heat leakage into the system,
which is below 100 nW, the slope of the warming curve is closely associated with the
sample’s heat capacity. According to Qሶ =CADR Tሶ , CADR obtained in Run 2 is good
agreement with the ‘directly’ measured heat capacity [Fig. 3(f)].
In order to gain deeper insights into the MCE of Gd3BWO9, the magnetic entropy
change -ΔSmag is calculated based on the M(H) curves in Fig. S2, through Maxwell’s
H ∂M
thermodynamic relation -ΔSmag = - ‫׬‬0 ( ∂T )P,H dH [24]. For each curve, we have used
two sets of M(H) data at temperatures ǦΔ and T+ΔT . Through
μM/μT ≈ΔM/ΔT = [M (T+ΔT, H)-M (T-ΔT, H)]/2ΔT [Fig. 4(a-b)], the field
dependence of the entropy -ΔSmag (H) could be obtained by integrating ΔM/ΔT over
the field range [38,40]. For instance, the -ΔSmag (H) of 0.7 K is calculated from the M(H)
of 0.4 K and 1 K.

The field variation of -ΔSmag is shown in Fig. 4(c) for H//a and Fig. 4(d) for H//c,
respectively.澳 The contour plots of -ΔSmag for H//c [Fig. 4(e)] are similar to the
polycrystalline data [24-25]. According to the澳 -ΔSmag for H//c, the temperature
dependence of -ΔSmag is depicted under different fields in Fig. 4(f), and the -ΔSmag(T)
derived from Cmag(T, H) data closely matches the -ΔSmag(T) curves calculated from M(H,
T) data. Given the high spin state and high density of Gd3+ ions, the theoretically
calculated -ΔSmag reaches 51.87 J mol-1 K-1 (63.99 J kg-1 K-1) for Gd3BWO9, and the
volumetric entropy density reaches 483 mJ K-1 cm-3, surpassing most Gd-oxide magnets,
including GGG (363 mJ K-1 cm-3), GdPO4 (401 mJ K-1 cm-3), and KBaGd(BO3)2 (192
mJ K-1 cm-3), while remaining comparable to Gd9.33[SiO4]6O2 (509 mJ K-1 cm-3) [41].澳
During our experiment, the -ΔSmag achieves the maximum value 43.32 J mol-1 K-1
(53.45 J kg-1 K-1) and 42.82 J mol-1 K-1 (52.83 J kg-1 K-1) at 2.1 K under field up to 7 T
along a and c axes, accounting for 83.5% and 82.6% of the theoretical value,
respectively. These values exceed the maximum value of GGG (38.4 J kg-1 K-1) at澳2 K
under a 7 T field [42-43]. The large volumetric entropy density, magnetic entropy
change, and low temperature in ADR suggest that Gd3BWO9 holds significant potential
for refrigeration applications.澳

D. Phase diagram and Magnetic critical behavior under H//c

More interestingly, at T = 0.7 K< TN, the value of -ΔSmag is negative when the magnetic
field is less than 1 T for H//c, while it is always positive for H//a [Fig. 4(c-d)]. This
anisotropic response can be attributed to the dominant AFM coupling along the c-axis
between Gd3+ ions. The emergence of two anomalies in the dM/dH curve under μ0H =
0.40 T and 0.82 T at T = 0.4 K may be associated with critical behavior in
thermodynamic properties. Below, we map the phase diagram for H//c with more
detailed magnetic and thermodynamic data.

As shown in Fig. 5(a), the low temperature χ(T) curves of Gd3BWO9 are measured
under several small fields along c-axis, whose peak shifts to lower temperature as field
increases. In addition, we conducted the M(H) measurements with more data points
below 3 T at 0.4 K, 0.6 K, 0.8 K, 1.0 K and 1.2 K, respectively [Fig. S3] [27].
Correspondingly, the Fig. 5(c-d) and Fig. S4 show low field variation of ΔSmag curves
at various temperatures, calculated based on the M(H) curves in Fig. S3 [27]. Since
∆Smag ሺHሻ=Smag ሺHሻ-Smag (0 T) , the Smag(H) curve at a constant temperature can be
obtained through vertically shifting the ΔSmag(H) curve by the zero-field entropy value,
as shown in Fig.5(b). It is worth noting that a shoulder around μ0Hc1 = 0.42 T and a
peak at μ0Hc2 = 0.84 T are observed for the Smag(H) curve at 0.5 K, which gradually
evolve into one single peak as temperature increases. Taken the features mentioned
above, Fig. 5(e) displays an H-T phase diagram of Gd3BWO9 under H//c, with the color
coding representing Smag(H, T) in Fig. 5(b).

The isothermal field scans on Cmag (H) are measured under H//c at 0.9 K and 0.4 K,
respectively. As shown in the top panel of Fig. 5(c-d), a peak is identified on Cmag (H)
curve at μ0H = 0.5 T at 0.9 K, while upon cooling to 0.4 K, a shoulder is observed
around μ0H = 0.85 T in addition to the peak at μ0H = 0.55T. The magnetic Grüneisen
1 dT 1 dS 1 dSmag
parameter is calculated through Гmag ≡ T ( dμ H )S = െ μ ≈െμ , which the
0 0 C dH 0 Cmag dH

non-magnetic specific heat is much smaller than the magnetic component below TN.
∂ ∂M
Combined with Maxwell’s thermodynamic relation( ∂H )P, ൌ ( ∂T )P,H , the Гmag (H)
curves are shown in Fig. 5(c-d).

At 0.9 K, the sign of Гmag (H) curve changes from negative to positive at μ0Hc = 0.5 T,
indicating a local maximum in entropy Smag(H) at this field, as well as a respective
minimum in the adiabatic temperature trace T(H)S, arising at the phase boundary. At T
= 0.4 K, there is a local maximum in Гmag (H)curve at μ0Hc1 = 0.42 T, with its value
approaching zero. As the magnetic field increases beyond μ0Hc2 = 0.85 T, the Гmag (H)
curve changes its sign from negative to positive, reaching to a constant value up to 1.5
T. The lower critical field μ0Hc1 = 0.42 T may indicate a metamagnetic transition within
the AFM regime, and the system subsequently reaches a fully polarized state above
upper critical field μ0Hc2 = 0.85 T. This behavior is similar to that in Nd3BWO9, which
a proximate quantum bicritical point (BCP) is observed along the c-axis. In the
magnetocaloric effect results of Nd3BWO9, a temperature diplike feature appears near
the critical fields BBCP ‫ ׽‬0.61 T, where magnetic entropy change ΔSmag(H) accumulates
its maximum value [21].

As detailed in Fig. 4 of Ref. [44], when the quantum critical point (QCP) serves as the
endpoint of a line of classical second order transitions, the isentropes (dS=0), i.e. the
contour lines in Smag(H, T) would exhibit minima values close to the phase boundary.
Intriguingly, the contour lines in Smag(H, T) in Fig. 5(e) explicitly illustrate the evolution
of temperature during an adiabatic sweep of the field along c axis at T > 0.4 K. This
observation aligns precisely with the light blue contour line depicted in Fig. 5(e). It also
includes the adiabatic temperature traces of field sweep T(H)S of Gd3BWO9 polycrystal.
These sweeps were measured by ramping the magnetic field from 9 T to 1.5 T, as in the
ADR runs. Subsequently, the field was swept repeatedly at a substantially reduced rate
of 1.5 mT/s from 1.5 T to 0 T and back to 1.5 T. Though the critical field might be
slightly different from the polycrystal compared with single crystal under H//c axis, the
temperature traces T(H)S fit quite nicely into the phase diagram based on Smag(H, T).
By drawing boundary lines through local minima of the temperature traces, the phase
boundaries could be extended to lower temperatures.

For a quantum-critical point (QCP), there shall be the sign change at the critical field
Bc and also a divergence Гmag ~|B-Bc|-1 at very low temperature. Thus, the quantum
critical phenomena in Gd3BWO9 at T < 0.1 K, including the enhanced MCE
approaching the putative QCPs warrant further investigation in the future [40, 44-47].

Summary
In summary, we have performed magnetic and thermodynamic characterization of
distorted kagome lattice Gd3BWO9 single crystal. Below TN = 1.08 K, the Gd3+
moments exhibit AFM alignment between layers and FM alignment within layers,
resulting in alternating AFM-FM stripes along the c-axis, as confirmed by magnetic
susceptibility measurements. Compared to the GGG case, the maximum -ΔSmag of
Gd3BWO9 shows larger values of 53.45 J kg-1 K-1 for H//a and 52.83 J kg-1 K-1 for H//c
under 7 T, presenting the giant MCE related to its AFM order. Given the long-range
order at TN = 1.08 K, the strong magnetic frustration of Gd3BWO9 suppresses the release
of magnetic entropy down to low temperature, resulting in a Tmin = 0.151 K far below
TN in the ADR measurement. Furthermore, the constructed H-T phase diagram of
Gd3BWO9 under H//c reveals evidence of magnetic critical behavior, as indicated by
the sign change of Гmag (H) near the metamagnetic transitions.

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Acknowledgements

The authors would like to thank Peijie Sun, Zhaoming Tian, Junsen Xiang, Huifen Ren
and Shaokui Su for helpful discussions and experimental support. The work was
supported by the National Key R&D Program of China (Grant No. 2023YFA1406003),
National Natural Science Foundation of China (Grants No. 12274015), the Beijing
Natural Science Foundation (Grant No. JQ24012), and the Fundamental Research
Funds for the Central Universities. The work in Augsburg was supported by the
Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Grants No.
514162746 (GE 1640/11-1) and No. TRR 360-492547816. The authors acknowledge
the facilities, and the scientific and technical assistance of the Analysis & Testing
Center, Beihang University. A portion of this work was carried out at the Synergetic
Extreme Condition User Facility (SECUF).

Data Availability

The data that supports the findings of this article are available upon reasonable request
from the authors.
Figures and Captions

(a) (c) (e)

a/[110]

a*/[-110]

(b) (d) (f)

c/[001]
c
4.311Å

a b 3.880Å
a/[110]

Fig. 1: Crystal structure of Gd3BWO9. (a)The schematic structure of Gd3BWO9 reflecting the
distorted kagome lattice in the crystallographic ab plane. (b)The well-separated distorted kagome
planes are stacked along the c axis of Gd3BWO9. (c) The experimental XRD patterns of Gd3BWO9
powder. (d) X-ray diffraction pattern of Gd3BWO9 single crystal. Left inset: An optical image of
typical single crystal. Right inset: the rocking curve (black line) of the (200) Bragg peak, together
with the Gaussian fitting (red line) of Gd3BWO9. (e) and (f) The experimental and simulated Laue
diffraction patterns of the bc and ac plane of Gd3BWO9, respectively.
(a) (c) (e)

(b) (d) (f)

Fig. 2: Magnetic properties of Gd3BWO9 under H//a and H//c. (a) The susceptibility χ(T) and
the inverse magnetic susceptibility [1/χ(T)] of Gd3BWO9 for H//a and H//c under 500 Oe. (b)The
low-temperature part of (a). The insert of (b): A schematic of the magnetic structure in Gd3BWO9,
the green and purple lines constitute triangles connecting Gd ions in adjacent kagome plane (3.880
Å) and within kagome plane (4.825 Å). (c)-(d) Isothermal magnetization M(H) and the derivative
[dM(H)/dH] curves for selected temperatures of 1, 1.8, 3, 5, and 10 K along c and a-axis. The solid
red lines show the Brillouin function fits. (e)-(f) M(H) and dM(H)/dH curves along c and a-axis at
0.4 K. The dotted lines represent the features.
(a) (b) (c)

(d) (e) (f)

Fig. 3: Specific heat result of Gd3BWO9 along H//c and ADR of Gd3BWO9 polycrystal. (a) Total
specific heat Cp(T) measured down to 0.05 K in zero field, and 0.39 K in applied fields 3 T and 7 T
along H//c. The inset shows a power law fit from 0.05 to 0.2 K in zero field. (b) Magnetic specific
heat as Cmag(T)/T in a logarithmic presentation at 0, 3, and 7 T. The inset shows a photo of the
sample on the platform of the specific-heat puck. (c) Temperature variation of the magnetic entropy
Smag computed from the heat capacity data of Gd3BWO9 for H//c. The arrows designate the adiabatic
demagnetization process starting from initial temperatures of 2 K and 5 K under 7 T. (d) The cooling
curve of Gd3BWO9 polycrystal in the ADR process starting from 9 T and 2 K (slightly shifted due
to the neglect of the magnetoresistance of the thermometer). The inset shows the process around
Tmin. (e) The temperature evolution was measured over a period exceeding 30 hours, with Run 1
conducted in the absence of a resistance heater. (f) The heat capacity calculated from the warming
curve of the ADR experiment and directly measured in the PPMS.
(a) (c) (e)

(b) (d) (f)

Fig. 4: Magnetic entropy and Magnetocaloric effect analysis of Gd3BWO9. (a)-(b) Derivative of
the magnetization with respect to temperature as a function of the applied magnetic field for H//a
and H//c. (c)-(d) Field variation of the magnetic entropy change -ΔSmag calculated from isothermal
magnetization curves for different temperature of Gd3BWO9 for H//a and H//c, respectively. (e)
Contour plots for -ΔSmag as a variation of applied field and temperature. (f) Temperature variation
of -ΔSmag obtained from isothermal magnetization curves and heat capacity data, with vertical axes
representing units in volumetric J mol-1 K-1 (left) and J kg-1 K-1 (right).
(a) (c) (d)

(b)

(e)

Fig. 5: The phase diagram of Gd3BWO9 single crystal under H//c. (a) The low-temperature
susceptibility χ(T) curves under 0.05, 0.2, and 0.4 T for H//c, the purple stars indicate the positions
of peaks. (b) The low field variation of magnetic entropy Smag(H) for H//c at 0.5, 0.7, 0.9, and 1.1
K, respectively; the green rhombuses denote the positions of local peaks. The magnetic specific heat
Cmag, the derivative of magnetization with respect to temperature dM/dT, magnetic entropy change
ΔSmag, magnetic Grüneisen parameter Гmag at 0.4 K (the Cmag and Гmag of 0.4 K would be
similar with that of 0.5 K) (c) and 0.9 K (d) under H//c. (e) The H–T phase diagram of Gd3BWO9
as derived from χ(T) (purple stars), dM/dH (blue triangles), Smag(H) (green rhombuses), and T(H)S
(blue lines), with the dashed lines guiding the eyes and the color coding representing Smag(H).