manifestation of magnetic quantum fluctuations in the dielectric properties of a multiferroic

ARTICLE

Received 4 Nov 2013 | Accepted 16 Jun 2014 | Published 29 Jul 2014

Manifestation of magnetic quantum fluctuationsin the dielectric properties of a multiferroicJae Wook Kim1,w, Seunghyun Khim1, Sae Hwan Chun1, Y. Jo2,w, L. Balicas2, H.T. Yi3, S.-W. Cheong3,

N. Harrison4, C.D. Batista5, Jung Hoon Han6 & Kee Hoon Kim1,7

Insulating magnets can display novel signatures of quantum fluctuations as similar to the case

of metallic magnets. However, their weak spin-lattice coupling has made such observations

challenging. Here we find that antiferromagnetic (AF) quantum fluctuations manifest in the

dielectric properties of multiferroic Ba2CoGe2O7, where a ferroelectric polarization develops

concomitant to an AF ordering. Upon application of a magnetic field (H), dielectric constant

shows a characteristic power-law dependence near absolute zero temperature and close to

the critical field Hc¼ 37.1 T due to enhanced AF quantum fluctuations. When H4Hc, the

dielectric constant shows the temperature-dependent anomalies that reflect a crossover from

a field-tuned quantum critical to a gapped spin-polarized state. We uncover theoretically that

a linear relation between AF susceptibility and dielectric constant stems from the generic

magnetoelectric coupling and directly explains the experimental findings, opening a new

pathway for studying quantum criticality in condensed matter.

DOI: 10.1038/ncomms5419

1 CeNSCMR, Department of Physics & Astronomy, Seoul National University, Seoul 151-747, Korea. 2 National High Magnetic Field Laboratory (NHMFL),Florida State University, Tallahassee, Florida 32310, USA. 3 Department of Physics & Astronomy and Rutgers Center for Emergent Materials, RutgersUniversity, Piscataway, New Jersey 08854, USA. 4 NHMFL, Los Alamos National Laboratory (LANL), Los Alamos, New Mexico 87545, USA. 5 TheoreticalDivision, LANL, Los Alamos, New Mexico 87545, USA. 6 Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea. 7 Institute of AppliedPhysics, Seoul National University, Seoul 151-747, Korea. w Present addresses: NHMFL, LANL, Los Alamos, New Mexico 87545, USA. (J.W.K.); Department ofPhysics, Kyungpook National University, Daegu 702-701, Korea. (Y.J.). Correspondence and requests for materials should be addressed to K.H.K. (email:[email protected]).

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Quantum phase transitions (QPT) in correlated electronmaterials have been intensively studied in recent years inan effort to understand quantum critical phenomena and

exotic order realized near a quantum critical point (QCP)1. TheFermi-liquid state of the conduction electrons shows instabilitiesnear a magnetic QCP, often leading to non-Fermi-liquidbehaviour and even exotic superconductivity2,3. In the absenceof conduction electrons, a magnetic QCP has been found in Isingferromagnets by applying a transverse magnetic field4,5 and inspin-dimer compounds that show Bose–Einstein Condensation(BEC)6–8. QPT can also be found in ferroelectric (FE) materialswhere the electric polarization (P) serves as the order parameter.An archetypical case is SrTiO3, in which a huge dielectricconstant (e4104) is observed at low temperatures (T) withoutshowing any long-range order due to quantum fluctuations in thevicinity of a FE QCP9–11. Substituting 16O with 18O as well asapplying external pressure have also been shown to be effectiveways to control the FE transition temperature12,13.

Recently, multiferroic materials have been intensively studieddue to their potential as possible components of multifunctionaldevices14–19. Moreover, efforts to understand the general mecha-nisms of cross-coupling between magnetism and ferroelectricityhave made great progress in the fundamental science ofcompeting magnetic interactions and spin-orbit coupling invarious complex materials20,21. Quantum critical phenomena inthese materials are also of great interest, because one may studythe critical behaviours of coupled ferroic order parameters inthe quantum critical regime possibly due to their rather strongspin-lattice coupling.

In general, even in multiferroic materials, it is still difficult todirectly observe quantum fluctuations of the antiferromagnetic(AF) order parameter by probing the dielectric properties. This isbecause the dielectric properties are often determined by lowenergy fluctuations near the center of the Brillouin zone (uniformresponse). Moreover, in most multiferroics with magnetically

induced ferroelectricity, frustrated spin interactions are present sothat the magnetic field often induces a first-order transitionbetween different spin structures and related FE phases.Furthermore, due to rather a large exchange interaction amongspins, the magnetic field required to induce such a phasetransition can easily surpass 100 TB10 meV.

Thus far, the search for the non-classical properties inmultiferroic materials is limited to a few cases in metal-organicmaterials22,23. In these systems, magnetic order sets in as anon-collinear arrangement of Cu2þ spins with S¼ 1/2, withsmall exchange energy and low magnetic ordering temperature(TNo2 K). Moreover, they have rather weak magnetodielectriccoupling (De/eo3%) and small electric polarization(Po30 nC m� 2), which makes it challenging to study quantumcritical phenomena through their dielectric properties.

Crystals in the melilite group with magnetic ions (A2BX2O7,A¼Ca, Sr, Ba, B¼Mn, Fe, Co, Cu and X¼ Si, Ge) turn out tohave several features to overcome the above hurdles24–27. Theyexhibit a simple magnetic structure with minimal spin frustrationand a relatively low ordering temperature. In this group, wechoose to study Ba2CoGe2O7 (BCGO), which has the largestelectric polarization (B180 mC m� 2 at 28 T). It is known to forma tetragonal and non-centrosymmetric structure (space groupP421m) with two CoO4 tetrahedra in a unit cell connectedthrough GeO4 tetrahedra in the ab-plane28 (Fig. 1a). Thealternating tilting angle (k) of the CoO4 tetrahedra along thediagonal direction within the ab-plane (Fig. 1a) plays a key role inthe magnetoelectric (ME) coupling between the AF orderparameter and the uniform electric polarization. The Co2þ

spins form simple square lattice layers and are antiferro-magnetically coupled in the ab-plane below 6.7 K. The magneticpropagation vector is Q¼ (1,1,0) and corresponds to the AFlayers that are ferromagnetically ordered along the c-axis28. Thesystem has been known to possess an easy-plane anisotropyas confirmed by magnetic susceptibility (Supplementary Fig. 1),

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30 35 40 45

E ||a

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Figure 1 | Magnetic field-induced phase transition in multiferroic Ba2CoGe2O7. (a) Structure of Ba2CoGe2O7 as perceived from a direction perpendicular

to the ab-plane. Two Co2þ ions sit at the (0,0,0) and (0.5,0.5,0) positions of a unit cell. Co2þ ions are placed inside a oxygen tetrahedra that is tilted

from the [110] direction by angles þ k and�k. (b) Magnetization as a function of the magnetic field along the c-axis. Magnetization saturates

above Hc¼ 37.1 T. Inset shows the canted spin structure at HoHc (top left) and fully saturated spin structure at HZHc (bottom right). (c) Dielectric

constant (e) measured at 1 kHz. (d) Electric polarization (P) along the a-axis as a function of the magnetic field applied along the c-axis. Magnetic

field-sweep rates for e and P measurements are 0.0083 and 0.033 Ts� 1, respectively.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5419

2 NATURE COMMUNICATIONS | 5:4419 | DOI: 10.1038/ncomms5419 | www.nature.com/naturecommunications



inelastic neutron diffraction28, electron spin resonance and farinfrared spectroscopy29. However, recent studies on the latticeand magnetic structure30,31 show that BCGO actually has a lowersymmetry with weak orthorhombic distortion in the plane andresult in magnetic space group Cm0m20.

A change in the FE polarization appears below the AF orderingtemperature (TN¼ 6.7 K, Supplementary Fig. 1)24,26 andoriginates from the p–d hybridization (pdH) mechanism32–34.According to this mechanism, an electric polarization (Pij)develops along the bond direction eij connecting the i-th spin,Si and the j-th ligand in the form

Pij / ðSi � eijÞ2eij ð1Þ

Interestingly, the pdH mechanism does not originate froma frustrated spin structure such as a spiral or a mmkk spinstructure, which spontaneously breaks spatial inversion symmetryupon magnetic ordering14,17,19,35. Instead, P is induced by acombination of spin-orbit interaction and anisotropic hybri-dization between the p- and d-orbitals of oxygen and themagnetic ion. We further note that the ME response of BCGOdescribed above can be explained by following the generalsymmetry arguments without invoking any microscopic model atlow fields36,37.

Here we present experimental and theoretical study of thefield-induced QPT in BCGO, around which the signatures of AFquantum fluctuations are reflected in its dielectric constant due tostrong ME coupling. Our analysis based on a Ginzburg–Landau(GL) free energy shows that the dielectric constant of BCGO andthe universality class of mean-field type emerges due to increasedeffective dimension at the putative QCP, being consistent withexperimental results.

ResultsMagnetic field-dependence of magnetization. A QPT from AFto paramagnetic (PM) is realized in this system at high magneticfields. In BCGO, spins are confined in the ab-plane with a simpleAF configuration28. Sublattice magnetization (L) also lies in theab-plane with weak ferromagnetic moment perpendicular to L atzero field. When H is applied along the c-axis, spins graduallyrotate towards the c-axis and L decreases simultaneously. Finally,above Hc, all the magnetic moments become nearly parallel to thec-axis. This scenario is supported by the magnetization curvesM(H) measured for H8c-axis and is shown in Fig. 1b. At 0.5 K, Mincreases monotonically up to a saturation value of B3.1 mB perf.u. above Hc¼ 37.1 T, which is consistent with full saturation ofthe S¼ 3/2 spins. However, the signatures of the AF–PM phasetransition are not so apparent in the M(H) curves because theorder parameter is staggered, and M(H) is the response to auniform field38.

Magnetic phase transition observed by FE properties. Counter-intuitively, the magnetic phase transition is clearly observed in theFE properties of BCGO due to a combination of two properties:(1) a strong ME coupling and the staggered tilting (k) angle of theCoO4 tetrahedra that allows coupling between the uniformpolarization and (2) the staggered moment (order parameter).Figure 1c shows the e(H) curves measured along the a-axis whenH is applied along the c-axis. The AF transition is marked by theonset of a peak in e (ref. 24). Upon cooling, the peak shifts tohigher magnetic fields and eventually gets very close to Hc at0.57 K. The peak intensity increases concomitantly showing alarge magnetodielectric effect of De/e(0 T)B66 % at 3 K with adecrease upon further cooling. The field-induced shift of the AFtransition is also reflected in the P(H) curves measured in thesame configuration (Fig. 1d). P increases linearly in H at low

fields (o15 T)24, reaches a maximum, and then decreases rapidlyto reach a constant negative value above Hc. The field value atwhich P decreases rapidly shifts to higher magnetic fields up to Hc

upon cooling thus indicating the suppression of the magneticallyinduced polarization.

The magnetic field-dependence of P can be explained by thepdH mechanism. By calculating equation (1) explicitly for eachinequivalent Co2þ spin, the a-axis polarization has contributionsfrom two Co2þ sites26.

Pa ¼ Pa1þPa2

/ sin2y1sinðf1� 2kÞþ sin2y2sinðf2þ 2kÞ; ð2Þ

where yi, fi are the spherical coordinates of the correspondingspins. Under a magnetic field applied along the c-axis, only theout-of-plane spin component (cosyi pMc�M) contributes to theelectric polarization. Therefore, equation (2) can be rewritten

as Pa / Mffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�ðM=MsÞ2

q/ ML. This expression predicts P¼ 0

when M is fully saturated to become MS, that is, L is suppressed tozero.

However, P shows a finite negative value at H4Hc inexperiments (Fig. 1d). In addition, we found that the P(H) datashown in Fig. 1d could not be reversed by a negative polingprocedure. To account for such negative P contribution, a slighttilting of magnetic field (o4� away from the c-axis), which canpractically exist in high field experiments, should be considered.In such a situation, a small in-plane magnetization coming from asmall in-plane field (o2.6 T) is likely to exist even above Hc.Given that BCGO belongs to a non-centrosymmetric space groupthat allows piezoelectric coupling, the in-plane magnetization cannaturally generate an additional in-plane P through themagnetostriction. Moreover, due to the pdH mechanism, thesmall tilting of magnetic field away from the c-axis can alsoinduce additional P component perpendicular to the in-planemagnetization direction as demonstrated by Murakawa et al.26 ina low field study. It can be simply shown that the additional in-plane P contribution from either the magnetostriction effect orthe pdH mechanism should be roughly proportional to M2.Therefore, by adding the additional P term that is proportional to�M2 to Equation (2), we can quantitatively explain the full P(H)curve in our experiments (see Supplementary Fig. 2 andSupplementary Note 1 for details).

More evidence for a phase transition at high magnetic fields isprovided by T-dependent measurements under constantH. Figure 2a shows the T-dependence of e under differentmagnetic fields below Hc. A small peak appears at TN for lowfields and grows while shifting to lower temperatures forincreasing values of H. The peak saturates above 34 T, which isquantitatively consistent with the isothermal magnetic field-sweep measurements. Additional evidence for a thermodynamicphase transition is provided by the T-dependence of the magnetictorque (t/H, Fig. 2b). The minima in t/H denote values of TN thatcoincide with the peak positions of e and further prove that e isdirectly related to the AF order. The absence of hysteresis in theH- and T-dependence of e suggests that the phase transition iscontinuous (see Supplementary Fig. 3 and Supplementary Note 2for details).

Gapped spin-polarized state above. Remarkably, another energyscale is found through e measurements when magnetic field isfurther increased above Hc. Figure 3a shows e(T) curves at aconstant magnetic field for H4Hc. At 39 T, e increases mono-tonically on cooling because it is very close to the T¼ 0 criticalfield Hc. Notice that the e(T) curves show the changes in slope atlow temperatures at fields of 40 and 41 T. Strikingly, this feature

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5419 ARTICLE




becomes a shoulder at 42 T and B5.2 K and evolves to a broadmaximum when the magnetic field is further increased. Thesefeatures, denoted as T* (indicated by filled triangles in Fig. 3a, seeSupplementary Fig. 4 and Supplementary Note 3 for details),indicate the emergence of an energy scale that characterizes thegapped spin-polarized state. At 45 T, T* is found at B7 K ande(T) data can be fitted with an energy gap as e ¼ A

T2 � e�D=T þ e0(inset in Fig. 3a). We note that this fit is not applicable to e(T)data at lower magnetic fields, possibly due to a higher orderbackground.

In the absence of spin anisotropy, the induced magnon gapfrom Zeeman energy can be calculated as D¼ gmB(H�Hc)DS.Using the g-factor value (gzz¼ 2.1) reported in a far infraredspectroscopy work29, we obtain D¼ 11.2 K, which is smaller thanthe fitted value D¼ 14.7±1.1 K from the e data at 45 T. Thisdiscrepancy seems to decrease once the effect of spin anisotropy istaken into account (see Supplementary Fig. 5 and SupplementaryNote 4 for details).

Non-classical behaviour in dielectric constant in a broad fieldand temperature window. For a classical FE or AF system, oneexpects a Curie-law behaviour, that is, linear dependence ofinverse susceptibility on T. However, we find that the inversedielectric constant follows a quadratic dependence on tempera-ture in a broad field and temperature window. Figure 3b shows(e� e0)� 1 as a function of (T�TN)2, demonstrating the quad-ratic dependence that can be observed as high as 12 K above TN

around Hc (also see Supplementary Fig. 6 and SupplementaryNote 5 for details). The quadratic dependence is also robust in awide range of fields, that is, between 9 and 38 T, showing that the

non-classical behaviour manifests itself in a wide region of theH–T phase diagram due to quantum fluctuations.

Phase diagram alluding the magnetic QPT. All T- andH-dependent experiments are summarized in the H–T phasediagram (Fig. 4). The resultant phase boundaries resemblearchetypal phase boundaries for a continuous QPT, namely,the V-shaped quantum critical region between two differentphases1–3,7,39. The AF order appears below TN¼ 6.7 K at H¼ 0and is continuously suppressed to T¼ 0 by the c-axis magneticfield at Hc¼ 37.1 T. M saturates above Hc and a gapped spin-polarized state develops with a characteristic energy scale that isobserved by the dielectric constant measurement.

DiscussionTo understand the link between FE and AF in BCGO, weconstruct a phenomenological GL free energy based on the pdHmodel. Based on the analyses of the GL model, we found that the

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Figure 2 | Suppression of magnetic long-range order by magnetic field.

(a) Dielectric constant and (b) magnetic torque normalized by the

magnetic field (t/H) as a function of temperature at HoHc. For the torque

measurements, the magnetic field was slightly canted away from

the c-axis (B1�). t/H versus T curves are shifted for clarity. Minimum

points (indicated by black triangles) in t/H denote TN. Typical temperature

sweep rate is 0.0167 K s� 1.

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Figure 3 | Gapped spin-polarized state above the critical field and T2

power-law behaviour in the dielectric constant. (a) Dielectric constant as

a function of temperature above the saturation magnetic field. Black

triangles point to anomalies in e that appear above 40 T. Inset shows the

expanded e(T) curve at 45 T, which show a sudden drop of e below B6.5 K.

Dotted line is the fit to the equation with a spin gap with 14.7±1.1 K

explained in text. (b) Inverse of e� e0 as a function of (T� TN)2 at HrHc.

at constant magnetic fields (triangles, inverses triangles, and diamonds

indicate magnetic field below, at, and above the Hc). The linear behaviour in

(e� e0)� 1 supports that the T2 behaviour is robust within a wide magnetic

field range up to 12 K above TN. Solid lines are guides for the eyes. Inset

shows the same plot at H4Hc. The T2 behaviour is satisfied when the

magnetic field is close to Hc, but deviates quickly as an anomaly in e is

observable at higher magnetic fields.





alternating distortion of CoO4 tetrahedra along the [110]direction (Fig. 1a) plays a key role in realizing the linear couplingterm that is proportional to lsin2k � PyLxM in the free energy(x- and y-directions refers to the [110] and [110] directions in thetetragonal setting, respectively). Ultimately, through thiscoupling, we find a linear relation between the magneticcontribution to the dielectric constant and the AF susceptibilitywL (Supplementary Note 4):

e� e0 ¼ wLe20ðlsin2kÞ2M2

S ; ð3Þwhere MS is the saturation value of the magnetization, e0 is thelattice contribution to the dielectric constant (e-e0 for T44TN),and l is the ME coupling coefficient. The proportionality betweene� e0 and wL qualitatively explains the occurrence of a peak ine(T) at the AF phase transition and the increase ofe on cooling due to enhanced fluctuations of L near T¼ 0(Supplementary Note 4). This relation is especially useful forstudying the AF susceptibility when L is almost suppressed to 0(that is, when M is nearly saturated by the applied magnetic field).We note that fluctuations of the AF order parameter usually donot affect the dielectric constant and can only be measured withtools that can detect excitations on the zone boundary, such asneutron scattering.

It is then worth discussing the implications of the dielectricproperties, for example, characteristic power law, in relation tothe AF QCP. Earlier studies of BCGO suggested a tetragonalcrystal symmetry, and thus the fourfold or U(1) symmetry fordescribing the in-plane magnetization26,28. However, recentdetailed investigations indeed revealed the presence of thetwofold magnetization in the plane and an orthorhombicCm0m20 magnetic space group30,31. The twofold symmetry islikely to be reinforced by the small but unavoidable in-planemagnetic field component, coming from the tilting of themagnetic field from the c-axis. Therefore, the proper effectivetheory close to the QCP should become the Ising model, whichpredicts an effective dimension D¼ dþ z¼ 4, where d is thespatial dimension of the system (d¼ 3) and z¼ 1 the dynamicalexponent. On the other hand, a U(1) symmetric model wouldlead to a QCP that belongs to the BEC universality class, of whichdynamic exponent is z¼ 2. It is noted that at least threeexperimental observations are supportive of the scenario of a

dynamical exponent z¼ 1. The first observation is the measuredfield dependence of TN near the QCP: TNp|H�Hc|1/2 (Fig. 4and Supplementary Fig. 5a). This should be contrasted with theTNp|H�Hc|2/3 dependence that would be obtained for a BEC-QCP in d¼ 3. The second observation is that a linearextrapolation of the measured spin gap at high fields crossesthe T¼ 0 line at a magnetic field value, which is significantlylower than Hc (Supplementary Fig. 5b). Because Dp|H�Hc|zn

and n¼ 1/2, this observation is again consistent with z¼ 1 andnot with z¼ 2. Finally, according to equation (3),(e� e0)pwLpT� (2� Z)/z¼T� 2 for d¼ 3 and z¼ 1 (up tologarithmic corrections), in agreement with our observations (seeFig. 3b). In contrast, e� e0pwLp1/T3/2 for a d¼ 3 BEC-QCP.Thus, D¼ dþ z¼ 4 is equal to the upper critical dimension,justifying the mean-field GL description that we used to deriveequation (3).

The observation of AF quantum fluctuations by means ofintrinsic ME coupling in BCGO opens a new pathway to studycoupled orders in condensed matter physics. Enhancement of e atthe magnetic field-induced phase transition close to T¼ 0, and itsnon-classical power-law behaviour in an insulating magnetpresent an interesting counterpart to the non-Fermi-liquidbehaviour found near a magnetic QCP in metallic systems2,3.It should be noted that this phenomena can be observed in othermultiferroics with a similar structural staggering feature for therelevant magnetic ions. Therefore, the discovery provided hereprompts further investigations to search for this novel possibilityin other systems and reflects the extreme versatility of themultiferroic phenomena, even at the quantum mechanical level.

MethodsSample synthesis. Single crystalline samples were grown using the floating zonemethod. The feed rods for the floating zone method were prepared by a solid-statereaction method in air.

Measurement of FE properties. For dielectric constant and electric polarizationmeasurements, electrical contacts were made by using silver epoxy on both sides ofrectangular thin platelet samples. Dielectric constants were measured using capa-citance bridges (GR1615A, General Radio and AH2700A, Andeen–Hagerling).e(H) curve at different frequencies (0.2, 2 and 2 kHz) was measured usingAH2700A. Electric polarization was obtained by integrating the pyro- and mag-neto-electric currents using an electrometer (KE617, Keithley). P(T) or P(H) curveswere obtained after poling samples from B30 K down to the measuring tem-perature in a static poling electric field of 300 kV m� 1. To obtain accurate T valuesfor the polarization and dielectric constant measurements in high magnetic fields,we pre-calibrated a capacitance sensor (Lakeshore) at zero field between 0.5 and30 K prior to the measurement and used it in a finite magnetic field. We main-tained the temperature below 30 K until the experiment was completed to avoidthermal hysteresis in the capacitance sensor.

Measurement of magnetic properties. Torque signals were measured using acapacitive cantilever made of BeCu foil. For torque measurements, a Cernox sensor(Lakeshore), without magnetic field correction, was used. Magnetization curveswere measured using a pickup-coil/extraction magnetometer in a short pulsemagnet at NHMFL-LANL, Los Alamos. These data were calibrated against theabsolute value found using a vibrating sample magnetometer (PPMS-9, QuantumDesign). All direct current high magnetic field measurements were performedusing either a resistive magnet (r35 T) or a hybrid magnet (11 TrHr45 T) atNHMFL, Tallahassee.

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8

7

6

5

4

3

2

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M / H–T

P–H� / H–T

�–H�–T

1

00 5 10 15 20 25 30 35 40

SPAF

PM

45 50

Magnetic field (T)

Tem

pera

ture

(K

)

Figure 4 | H�T phase diagram of Ba2CoGe2O7. AF to PM phase boundary

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AcknowledgementsThis work is supported by the CRI (2010-0018300), BSR (2009-0083512) programs, andthe Fundamental R&D program for the Core Technology of Materials. Work at NHMFLPulsed Field Facility at LANL and NHMFL DC Field facility was supported by the NSFgrant DMR-0654118, the State of Florida, and the US DOE-BES project ‘Science at 100tesla’ BES FWP LANLF100. L.B. is supported by DOE-BES through Grant No. DE-SC0002613. The work at Rutgers was supported by the DOE:DE-FG02-07ER46382.J.H.H. is supported by NRF Grants No. 2013R1A2A1A01006430.

Author contributionsS.-W.C. and K.H.K. initiated the project. J.W.K., S.K., S.H.C., Y.J., L.B., H.T.Y., S.-W.C.and N.H. performed the experiments. C.D.B. and J.H.H. conceived the theoretical model.J.W.K. and K.H.K. analyzed the data. J.W.K. C.D.B., J.H.H. and K.H.K. wrote themanuscript with input from all other authors.

Additional informationSupplementary Information accompanies this paper at http://www.nature.com/naturecommunications

Competing financial interests: The authors declare no competing financial interests.

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How to cite this article: Kim, J. W. et al. Manifestation of magnetic quantumfluctuations in the dielectric properties. Nat. Commun. 5:4419 doi: 10.1038/ncomms5419(2014).






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manifestation of magnetic quantum fluctuations in the dielectric properties of a multiferroic

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