Dielectric evidence for possible type-II multiferroicity in α-RuCl3
Dielectric evidence for possible type-II multiferroicity in α-RuCl3
JiaCheng Zheng 1 2
Yi Cui 1
TianRun Li 1
KeJing Ran 0
JinSheng Wen 0 3
WeiQiang Yu 1
0 National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University , Nanjing 210093 , China
1 Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University , Beijing 100872 , China
2 Department of Physics, Beijing Jiaotong University , Beijing 100044 , China
3 Innovative Center for Advanced Microstructures, Nanjing University , Nanjing 210093 , China
•Letter to the Editor• . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . May 2018 Vol. 61 No. 5: 057021 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .https://doi.org/10.1007/s11433-017-9166-1
The Kitaev model in a honeycomb lattice, which has an
exactly solvable spin liquid as the ground state [
attracted a lot of research interests. Recently, Kitaev-type
interactions were discovered in several quasi-2D, honeycomb
lattice compounds, such as A2IrO3 (A=Li, Na) [
]. In these compounds, both the spin-orbit
coupling and electron correlations play an essential role in the
emergent Mott insulator behaviors [
]. Although the
ground states of these compounds are magnetically ordered
] due to non-Kitaev interactions, proximate Kitaev
spin liquid behavior was proposed at high energies [
whereas the low-energy spin fluctuations are strongly
affected by the interplay of non-Kitaev terms [
For α-RuCl3, the Kitaev terms are found to be very strong,
comparing to the non-Kitaev terms including the Heisenberg
exchange couplings and off-diagonal exchange couplings
]. In particular, the magnetic ordering can be easily
suppressed by an external magnetic field, giving rise to a
quantum phase transition at a critical field Hc ≈ 7.6 T
] with field applied in the ab-plane of the lattice, or
much higher fields applied out of the plane [
]. Recently, it
has reported that the magnetic ordering can also be
completely suppressed with a pressure above 1 GPa [
leading to a novel magnetically disordered phase . All
these studies indicate a strong coupling between lattice, spin,
and orbital degrees of freedom.
This paper presents dielectric constant measurements on
αRuCl3 single crystals. An anomalous reduction was found in
the dielectric constant ε when the system enters the magnetic
ordering upon cooling. When the magnetic ordering is
suppressed by the magnetic field, the reduction in ε is absent.
Simultaneously, ε also shows an anomalous reduction when
the system undergoes the structural transition. Our data
reveal a strong coupling among the charge and the magnetism
of the system, and the dielectric constant can be used to
probe the magnetic ordering and the quantum phase
transition of this honeycomb lattice antiferromagnet.
The single crystal was grown by the chemical vapor
transport method [
]. The sample is plate like, with the
crystalline c-axis along the thinnest dimension. The high
quality of sample is demonstrated by the neutron scattering
] and the NMR [
] study on the samples grown by the
same group. For dielectric measurements at the ambient
pressure, a single crystal with a dimension of 18 mm×8 mm
×0.2 mm is chosen.
The dielectric measurements are performed by a
capacitance method. Two copper plates were respectively attached
to the two cleavage surfaces (along the ab-plane) of the
single crystal, and the capacitance between two plates was
measured with an Agilent 4263B LCR meter with an
ex© Science China Press and Springer-Verlag GmbH Germany 2018 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . phys.scichina.com link.springer.com
May (2018) Vol. 61 No. 5. . . . . . . . . . . . . . . . . . . . . . . . . . . 057021-2
citation level of 1.0 V at 100 kHz. The dielectric constant
was then calculated by ε = Cd/S, where C represents the
capacitance measured between two copper plates, d
represents the distance between copper plates, and S represents
the effective surface area of one copper plate. In this paper,
the relative value ε/ε0 are presented for all figures, where ε0 is
the dielectric constant of vacuum. The d and S were
measured at the ambient conditions, whose changes under field
and temperature affect were not considered in the calculation
The dielectric constant was first measured at the ambient
field. In Figure 1, the ac dielectric constant ε along the
crystalline c-axis is shown as a function of temperature from
200 K down to 2 K. Upon cooling, ε decreases
monotonically. By a first derivation of the data, as shown in the
inset of Figure 1, two peaks are shown at temperature about
170 and 7.5 K. The high-temperature peak is consistent with
a structural transition with changing stacking pattern along
the c-axis, as revealed by earlier reports in α-RuCl3 [
When cooled to about 7.5 K, the dε/dT exhibits another peak,
as shown in the inset of Figure 1. Earlier magnetization and
neutron scattering studies have revealed magnetic ordering
of α-RuCl3 crystals, whose transition temperature TN depends
on the stacking pattern along the c-axis [
]. The TN
is about 14 K for the AB stacking and 7.5 K for the ABC
stacking. Our sample is primarily composed of the ABC
]. Therefore, the coincidence of the peak of ε
at 7.5 K is caused by the magnetic transition of the sample
with the ABC stacking. The microscopic origin for this
dielectric anomaly at the magnetic transition suggests a
coupling between magnetic and charge properties, which is
extensively discussed later.
We further verify that the above anomaly is always seen in
the magnetic transitions of α-RuCl3, by applying an external
magnetic field. In Figure 2, the dielectric constant is shown
as functions of temperature, with different magnetic fields
applied in the ab-plane of the sample. From 15 K down to
2 K, ε demonstrates an anomalous sharp decrease with
temperature for all fields up to 7.5 T. The onset temperature
for this anomaly, as marked by the black vertical lines,
decreases with field. In fact, earlier NMR and the specific heat
studies have shown that the magnetic ordering diminishes
when the external field exceeds a critical field Hc ≈ 7.6 T
]. For all fields, our onset temperatures for the decreases
of ε coincide with the TN. Therefore, our data confirm that the
sharp drop of ε always accompanies the magnetic transition.
The relation between the dielectric anomaly and the
magnetic order was further investigated by the field
dependence of ε at different temperatures. In Figure 3, the ε values
are shown as functions of fields. At 2 K, a two-stage drop of ε
is seen with a decreasing field. The ε values show a
highfield decrease at about 7.5 T for all temperatures up to 7 K,
which is consistent with the critical field Hc to suppress the
magnetic order, as reported by NMR [
]. With increasing T,
the fields at the drop of ε, as indicated by black lines, are
consistent with the critical field at each temperature again by
earlier reports [
]. A second drop of ε appears at
lower fields, as marked by the pink vertical lines in Figure 3.
This second drop occurs at a nearly constant field at different
The phase diagram of α-RuCl3 determined by our
dielectric data is shown in Figure 4. These data are also
consistent with earlier magnetization measurements [
shown in Figure 4. Therefore, our data clearly demonstrate
that the anomaly in the dielectric constant is caused by the
magnetic ordering in α-RuCl3, and ε can be a simple probe
for magnetic transitions at the ambient condition and
quantum phase transitions under external field. The TN(H) follows
a mean-field function TN ~ (Hc−H)1/2 which supports a second
order phase transition. Therefore, a quantum critical point is
strongly suggested at Hc by our study.
T *(H), defined as the onset temperature, was then plotted
May (2018) Vol. 61 No. 5. . . . . . . . . . . . . . . . . . . . . . . . . . . 057021-3
for a second drop of ε(H) under field at different
temperatures. Since this occurs below TN, this anomaly may be
caused by some inhomogeneity of the system or stacking
faults of the crystal. Local measurements, such as micro
force microscopy (MFM), are requested to understand the
origin of this low temperature anomaly in ε.
In principle, the dielectric constant is affected by the ionic
position, the electronic conductivity, and the dimension of
the sample, all of which change with temperature. To
understand the anomalous behavior of ε close to the magnetic
transition in α-RuCl3, all possible contributions to our ε data
are discussed below.
i) A structural effect. Although a structural transition with
changing stacking pattern along the c-axis has been reported
at about 150 K in α-RuCl3 [
], our ε data only detects a
very small anomaly in dε/dT in this temperature range.
Furthermore, upon cooling, the lattice parameter c should in
principle shrink with a larger extent than a or b for this
quasi2D materials because of a van der Waals coupling along the
]. As a result, an increase of measured
capacitance is expected. However, such a behavior is not seen in
our measured dielectric constant. Therefore, the measured
dielectric constant is not strongly affected by the change of
lattice parameters and the large kinked drop of ε close to the
magnetic transition cannot be attributed to the change of
lattice parameters, especially when the magnetic transition of
α-RuCl3 is a second-order type at zero-pressure, where the
change of the lattice parameters ought to be very small.
ii) Weak electronic conductivity. For α-RuCl3, a Mott gap
is about 1 eV [
], and thermal activated conductivity is
found by the high-pressure transport measurements . In
such cases, the finite conductivity should strongly enhance
the measured ε and lead to a decrease of ε upon cooling for a
gapped system because of reduced thermal activations. This
contribution seems to qualitatively fit in our
high-temperature data: as shown in Figure 1, the measured ε at 180 K is
over 10 times of the vacuum; upon cooling, ε is rapidly
reduced when the temperature is decreased to 50 K.
Below 50 K, however, ε levels off with a large value,
which suggests that an additional contribution, other than
conductive electrons, is effective.
iii) Magnetoelectric coupling. This is in analogy to the
type-II multiferroics, whose ferroelectricity is driven by
magnetic ordering just below the magnetic ordering
]. However, in such cases, spiral magnetism or
other types of non-collinear magnetic structures are
requested to produce the charge polarization [
]. For α-RuCl3,
a collinear zigzag magnetic ordering is established in each
], which is different from most type-II
multiferroics. However, this study shows a dramatic drop of the
dielectric constant just at the magnetic transition, analogous
to other type-II multiferroics. Hence, α-RuCl3 is also a likely
type-II multiferroics with magnetic driven charge
polarization. Indeed, the drop of the ε below TN in α-RuCl3 suggests
an antiferroelectric phase rather than a ferroelectric type, as
seen in Cu3Bi(SeO3)2O2Cl .
Recently, an anisotropic magnetodielectric measurement
has also been reported in α-RuCl3 [
]. By contrast, their
drop of ε is consistent with the AB stacking with a higher TN
(~14 K). Our crystals are confirmed to be of ABC stacking
from previous studies and therefore the same TN (~7.5 K) by
different probes drawing a direct coupling between
magnetism and dielectric properties.
In addition, the interlay coupling of α-RuCl3 is a Van der
Waals type [
], which in principle is too weak to account for
such a strong magnetodielectric coupling. Aoyama et al. [
proposed that the antiferroelectricity in α-RuCl3 originates
from the in-plane zigzag magnetic ordering. The competition
between the broken inversion symmetry among the
neighboring zigzag magnetic chains and the remaining inversion
symmetry, causes an anti-parallel ionic displacement among
the neighboring Ru3+ sites along each zigzag chain. As a
result, the local polarizations of the nearest-neighbor Ru3+
May (2018) Vol. 61 No. 5. . . . . . . . . . . . . . . . . . . . . . . . . . . 057021-4
In summary, we have resolved a sudden change of the
dielectric constant in α-RuCl3 at the magnetic ordering
temperature and below a critical magnetic field which
suppresses the magnetic ordering. This change is not seen at
high fields, when the magnetic transition is absent. Our data
also suggests a second-order quantum phase transition.
Although an exact understanding for this novel observation
requests further studies, this work suggests that α-RuCl3 is a
possible type-II antiferroelectric material and reveals
dielectric measurement as an alternative probe for magnetic
phase transition in α-RuCl3.
This work was supported by the Ministry of Science and Technology of
China (Grant No. 2016YFA0300504), the National Natural Science
Foundation of China (Grant No. 11374364), and the Fundamental Research
Funds for the Central Universities and the Research Funds of Renmin
University of China (Grant No. 14XNLF08).
2. . . . . . . . . . . . . . . . . . . . J. C. Zheng , et al. Sci. China-Phys. Mech . Astron.
3. . . . . . . . . . . . . . . . . . . . J. C. Zheng , et al. Sci. China-Phys. Mech . Astron.
1 A. Kitaev , Ann. Phys. 321 , 2 ( 2006 ).
2 G. Jackeli , and G. Khaliullin, Phys. Rev. Lett . 102 , 017205 ( 2009 ), arXiv: 0809 . 4658
3 J. Chaloupka , G. Jackeli, and G. Khaliullin, Phys. Rev. Lett . 105 , 027204 ( 2010 ), arXiv: 1004 . 2964
4 Y. Singh , S. Manni , J. Reuther , T. Berlijn , R. Thomale , W. Ku , S. Trebst , and P. Gegenwart , Phys. Rev. Lett . 108 , 127203 ( 2012 ), arXiv: 1106 . 0429
5 H. Gretarsson , J. P. Clancy , X. Liu , J. P. Hill , E. Bozin, Y. Singh , S. Manni , P. Gegenwart , J. Kim , A. H. Said , D. Casa , T. Gog , M. H. Upton , H. S. Kim , J. Yu , V. M. Katukuri , L. Hozoi , J. van den Brink, and Y. J. Kim , Phys. Rev. Lett . 110 , 076402 ( 2013 ), arXiv: 1209 . 5424
6 H. S. Chun , J. W. Kim , J. Kim , H. Zheng , C. C. Stoumpos , C. D. Malliakas , J. F. Mitchell , K. Mehlawat , Y. Singh , Y. Choi , T. Gog , A. Al-Zein , M. M. Sala , M. Krisch , J. Chaloupka , G. Jackeli, G. Khaliullin, and B. J. Kim , Nat. Phys . 11 , 462 ( 2015 ).
7 J. G. Rau , E. K. H. Lee , and H. Y. Kee , Annu. Rev. Condens. Matter Phys. 7 , 195 ( 2016 ), arXiv: 1507 . 06323
8 I. Pollini , Phys. Rev. B 53 , 12769 ( 1996 ).
9 K. W. Plumb , J. P. Clancy , L. J. Sandilands , V. V. Shankar , Y. F. Hu , K. S. Burch , H. Y. Kee , and Y. J. Kim , Phys. Rev. B 90 , 041112 ( 2014 ), arXiv: 1403 . 0883
10 H. S. Kim , V. Vijay Shankar , A. Catuneanu , and H. Y. Kee , Phys. Rev. B 91 , 241110 ( 2015 ), arXiv: 1411 . 6623
11 L. J. Sandilands , Y. Tian , K. W. Plumb , Y. J. Kim , and K. S. Burch , Phys. Rev. Lett . 114 , 147201 ( 2015 ), arXiv: 1504 . 05202
12 Y. Kubota , H. Tanaka , T. Ono , Y. Narumi , and K. Kindo , Phys. Rev. B 91 , 094422 ( 2015 ), arXiv: 1503 . 03591
13 L. J. Sandilands , Y. Tian , A. A. Reijnders , H. S. Kim , K. W. Plumb , Y. J. Kim , H. Y. Kee , and K. S. Burch , Phys. Rev. B 93 , 075144 ( 2016 ), arXiv: 1503 . 07593
14 A. Koitzsch , C. Habenicht , E. Müller, M. Knupfer , B. Büchner , H. C. Kandpal , J. van den Brink, D. Nowak , A. Isaeva , and T. Doert , Phys. Rev. Lett . 117 , 126403 ( 2016 ), arXiv: 1603 . 05507
15 K. Ran , J. Wang , W. Wang , Z. Y. Dong , X. Ren , S. Bao , S. Li , Z. Ma , Y. Gan , Y. Zhang , J. T. Park, G. Deng, S. Danilkin , S. L. Yu , J. X. Li , and J. Wen , Phys. Rev. Lett . 118 , 107203 ( 2017 ), arXiv: 1702 . 04920
16 B. J. Kim , H. Ohsumi , T. Komesu , S. Sakai , T. Morita , H. Takagi , and T. Arima , Science 323 , 1329 ( 2009 ).
17 K. Foyevtsova , H. O. Jeschke , I. I. Mazin , D. I. Khomskii , and R. Valentí , Phys. Rev. B 88 , 035107 ( 2013 ), arXiv: 1303 . 2105
18 T. Birol , and K. Haule , Phys. Rev. Lett . 114 , 096403 ( 2015 ), arXiv: 1408 . 4852
19 J. Chaloupka , and G. Khaliullin, Phys. Rev. B 94 , 064435 ( 2016 ), arXiv: 1607 . 05676
20 J. M. Fletcher , W. E. Gardner , B. F. Greenfield , M. J. Holdoway , and M. H. Rand , J. Chem. Soc. A 0 , 653 ( 1968 ).
21 F. Ye , S. Chi , H. Cao , B. C. Chakoumakos , J. A. Fernandez-Baca , R. Custelcean , T. F. Qi , O. B. Korneta , and G. Cao, Phys. Rev. B 85 , 180403 ( 2012 ), arXiv: 1202 . 3995
22 S. K. Choi , R. Coldea , A. N. Kolmogorov , T. Lancaster , I. I. Mazin , S. J. Blundell , P. G. Radaelli , Y. Singh , P. Gegenwart , K. R. Choi , S. W. Cheong , P. J. Baker , C. Stock , and J. Taylor , Phys. Rev. Lett . 108 , 127204 ( 2012 ), arXiv: 1202 . 1268
23 J. A. Sears , M. Songvilay , K. W. Plumb , J. P. Clancy , Y. Qiu , Y. Zhao , D. Parshall , and Y. J. Kim , Phys. Rev. B 91 , 144420 ( 2015 ), arXiv: 1411 . 4610
24 R. D. Johnson , S. C. Williams , A. A. Haghighirad , J. Singleton , V. Zapf , P. Manuel , I. I. Mazin , Y. Li , H. O. Jeschke , R. Valentí , and R. Coldea , Phys. Rev. B 92 , 235119 ( 2015 ), arXiv: 1509 . 02670
25 H. B. Cao , A. Banerjee , J. Q. Yan , C. A. Bridges , M. D. Lumsden , D. G. Mandrus , D. A. Tennant , B. C. Chakoumakos , and S. E. Nagler , Phys. Rev. B 93 , 134423 ( 2016 ), arXiv: 1602 . 08112
26 M. Majumder , M. Schmidt , H. Rosner , A. A. Tsirlin , H. Yasuoka , and M. Baenitz , Phys. Rev. B 91 , 180401 (R) ( 2015 ), arXiv: 1411 . 6515
27 J. Zheng , K. Ran , T. Li , J. Wang , P. Wang , B. Liu , Z. X. Liu , B. Normand , J. Wen , and W. Yu , Phys. Rev. Lett . 119 , 227208 ( 2017 ).
28 I. A. Leahy , C. A. Pocs , P. E. Siegfried , D. Graf , S. H. Do , K. Y. Choi , B. Normand , and M. Lee , Phys. Rev. Lett . 118 , 187203 ( 2017 ), arXiv: 1612 . 03881
29 A. Banerjee , C. A. Bridges , J. Q. Yan , A. A. Aczel , L. Li , M. B. Stone , G. E. Granroth , M. D. Lumsden , Y. Yiu , J. Knolle , S. Bhattacharjee , D. L. Kovrizhin , R. Moessner , D. A. Tennant , D. G. Mandrus , and S. E. Nagler , Nat. Mater . 15 , 733 ( 2016 ), arXiv: 1504 . 08037
30 A. Banerjee , J. Yan , J. Knolle , C. A. Bridges , M. B. Stone , M. D. Lumsden , D. G. Mandrus , D. A. Tennant , R. Moessner , and S. E. Nagler , Science 356 , 1055 ( 2017 ).
31 R. Hentrich , A. U. B. Wolter , X. Zotos , W. Brenig , D. Nowak , A. Isaeva , T. Doert , A. Banerjee , P. Lampen-Kelley , D. G. Mandrus , S. E. Nagler , J. Sears , Y.-J. Kim , B. Büchner , and C. Hess ,. arXiv: 1703 . 08623
32 S. H. Baek , S. H. Do , K. Y. Choi , Y. S. Kwon , A. U. B. Wolter , S. Nishimoto , J. van den Brink, and B. Büchner , Phys. Rev. Lett . 119 , 037201 ( 2017 ), arXiv: 1702 . 01671
33 Z. Wang , J. Guo , F. F. Tafti , A. Hegg , S. Sen , V. A. Sidorov , L. Wang , S. Cai , W. Yi , Y. Zhou , H. Wang , S. Zhang , K. Yang , A. Li , X. Li , Y. Li , J. Liu , Y. Shi , W. Ku , Q. Wu , R. J. Cava , and L. Sun,. arXiv: 1705 . 06139
34 Y. Cui , J. Zheng , K. Ran , J. Wen , Z. X. Liu , B. Liu , W. Guo , and W. Yu , Phys. Rev. B 96 , 205147 ( 2017 ).
35 M. Ziatdinov , A. Banerjee , A. Maksov , T. Berlijn , W. Zhou , H. B. Cao , J. Q. Yan , C. A. Bridges , D. G. Mandrus , S. E. Nagler , A. P. Baddorf , and S. V. Kalinin , Nat. Commun . 7 , 13774 ( 2016 ).
36 J. A. Sears , Y. Zhao , Z. Xu , J. W. Lynn , and Y. J. Kim , Phys. Rev. B 95 , 180411 ( 2017 ), arXiv: 1703 . 08431
37 H. S. Kim , and H. Y. Kee , Phys. Rev. B 93 , 155143 ( 2016 ), arXiv: 1509 . 04723
38 X. Zhou , H. Li , J. A. Waugh , S. Parham , H. S. Kim , J. A. Sears , A. Gomes , H. Y. Kee , Y. J. Kim , and D. S. Dessau , Phys. Rev. B 94 , 161106 ( 2016 ).
39 S. W. Cheong , and M. Mostovoy , Nat. Mater . 6 , 13 ( 2007 ).
40 H. C. Wu , K. D. Chandrasekhar , J. K. Yuan , J. R. Huang , J. Y. Lin , H. Berger , and H. D. Yang , Phys. Rev. B 95 , 125121 ( 2017 ).
41 T. Aoyama , Y. Hasegawa , S. Kimura , T. Kimura , and K. Ohgushi , Phys. Rev. B 95 , 245104 ( 2017 ).