The recently discovered multiferroic material CdCr2S4 shows a coexistence of
ferromagnetism and relaxor ferroelectricity together with a colossal
magnetocapacitive effect. The complex dielectric permittivity of this compound
and of the structurally related CdCr2Se4 was studied by means of broadband
dielectric spectroscopy using different electrode materials. The observed
magnetocapacitive coupling at the magnetic transition is driven by enormous
changes of the relaxation dynamics induced by the development of magnetic
order

Fichtl, R.

Hemberger, J.

Loidl, A.

Lunkenheimer, P.

Tsurkan, V.

Weber, S.

English

arXiv

Hemberger, Joachim

Lunkenheimer, Peter

Fichtl, Robert

Tsurkan, Vladimir

Loidl, Alois

OPUS Augsburg

                                            CorrespondiCorrelations anGermany. Tel.:E-mail addre(J. Hemberger).                                                         Multiferroic behavior in CdCr2X4ðX ¼ S; SeÞJ. Hembergera,b,, P. Lunkenheimerb, R. Fichtlb, S. Weberb, V. Tsurkanb,c, A. LoidlbaII. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, D-50937 Köln, GermanybExperimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, D-86135 Augsburg, GermanycInstitute of Applied Physics, Academy of Sciences of Moldova, str. Academiei 5, MD 2028, Chisinau, Republic of Moldova                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ltiferroic materials at least two (in a strict sense)         e order parameters corresponding to different        pic degrees of freedom coexist simultaneously.     scenario can combine, e.g., ferro-orbital order,         ticity, ferromagnetism, or ferroelectricity. Espe-        e coexistence of the latter properties, namely         tricity and ferromagnetism, is rarely found and         s a ‘‘hot’’ topic in recent solid state research [1–3].      sible coupling of both sectors, i.e. the strong         of electric (magnetic) properties under applica-       magnetic (electric) field, which is found in some of       terials, makes them highly attractive not only from      emic point of view, but also for potential         ons in microelectronics. In the present contribu-       eport on magnetization, dielectric polarization, as      broadband dielectric measurements in the multi-ferroic systems CdCr2S4 and CdCr2Se4 and providedetailed information on the dielectric relaxation dynamicsin the paramagnetic and ferromagnetic state. For these                                                              ng author. Experimental Physics V, Center for Electronicd Magnetism, University of Augsburg, D-86135 Augsburg,+49 821 598 3616; fax: +49 821 598 3649.ss: joachim.hemberger@physik.uni-augsburg.deinvestigations special emphasis was put on the influence ofcontacts on the dielectric characterization comparingsputtered gold- and silver-paint electrodes applied onopposite sides of the plate-like single crystalline samples.Dielectric constant and loss were measured over a broadfrequency range ð3Hzono3GHzÞ using frequency–re-sponse analysis and a reflectometric technique [4]. Electricpolarization was detected employing a high-impedanceSawyer–Tower circuit and the magnetization data wererecorded with a commercial SQUID magnetometer(MPMS, QuantumDesign).At room temperature, the recently discovered multi-ferroic CdCr2S4 is a cubic spinel compound [3]. The Cd2þions on the structural A-sites carry neither a magnetic noran orbital degree of freedom. The Cr3þ ions on theoctahedrally surrounded B-sites possess half-filled t2g shellsand thus also are orbitally inactive but due to Hund’scoupling and a quenched orbital moment carry a S ¼ J ¼ 32spin configuration. It shall be noted, that the absence of aJahn–Teller active orbital degree of freedom and the highcrystallographic symmetry allow for a relaxation of thestructure into polar distortions. The spins are coupledferromagnetically and as can be seen in the upper frame ofFig. 1 magnetic order sets in at T c  84K. At the sametime a steep increase of the dielectric constant can beARTICLE IN PRESS50000100301010210110010-1ε''ε'M (emu/mol)0 100 200 300T (K)100 Oe3 Hz53 Hz950 Hz17 kHz95 kHz950 kHz12 MHz83 MHz3 GHzCdCr2S4Fig. 1. Temperature dependence of the low field magnetization (upperframe) and complex dielectric permittivity e (lower frames) of CdCr2S4for various frequencies. The magnetic transition occurs at T  84K and isaccompanied by an increase of the permittivity towards low temperatures.(Note, that the plateau-like low-temperature value of the magnetization isdetermined by the demagnetization factor of the sample in the smallmeasurement field of H ¼ 100 Oe and does not display an intrinsicsaturation.)Fig. 2. Hysteresis loops for the magnetic (MðHÞ, upper frame) anddielectric sector (PðEÞ, lower frame) measured at T ¼ 25K. The magneticdata were mirrored and corrected for demagnetization effects; thepolarization data were measured at n ¼ 1:13Hz.                                             364detected, which for low frequencies reaches relatively highvalues above e0  100 (Fig. 1, middle frame). The details ofthe frequency dependence of the complex permittivity willbe discussed below, but before it shall be pointed out thatthe low-temperature phase of CdCr2S4 exhibits not onlyspontaneous magnetization but in addition the high valuesof e0 can be interpreted as precursor of the onset of remnantdielectric polarization at lower temperatures. Fig. 2 showshysteresis loops taken at T ¼ 25K for both the magnetic aswell as the dielectric sector. MðHÞ shows the characteristicsof a soft ferromagnet reaching nearly the full magneticmoment of 6mB expected for two Cr3þ ions per formulaunit. The small deviations from the full value can beattributed to pronounced magnon features typical for suchsystems. At the same time the PðEÞ curve is quite slim andsmeared out. No real saturation value is reached within theexperimentally accessible electric field range of 400 kV/mand no well-defined coercive electric field strength can beidentified. Such type of hysteresis behavior is typical for so-called relaxor-ferroelectric behavior, where nano-scale ferro-electric clusters determine the polarization response [5].Such type of behavior is also evidenced by the frequencyand temperature dependence of the complex permittivity inCdCr2S4. Fig. 1 shows real and imaginary part of thedielectric constant, e0ðTÞ and e00ðTÞ, for frequencies from3Hz to 3GHz. For T4100K, in e0ðTÞ a peak shifting tolower temperatures and increasing in amplitude withdecreasing frequency shows up. The dashed line indicatesa Curie–Weiss law, / 1=ðT  135KÞ, for the right flank ofthe peaks, which can be taken as an estimate of the staticdielectric constant. The further increase of e0ðTÞ towardshigher temperatures is due to contact and conductivitycontributions as discussed below. Thus, the overallcharacteristics of the relaxational behavior in CdCr2S4resemble that observed in relaxor ferroelectrics [5]. Therethe reduction of e0 below the peak temperature is usuallyascribed to a cooperative freezing-in of ferroelectricclusters on the time scale given by the frequency of theapplied AC electric-field, quite in contrast to canonicalferroelectrics where the frequency dependence of e0ðTÞ isnegligible. Such relaxational features seen in the real partof the permittivity should be accompanied by peaks in theimaginary part. At T4Tc in CdCr2S4, they should appearat the frequency of the point of inflection at the left wing ofthe maxima in e0ðTÞ. However, no such peaks becomeobvious in Fig. 1, which can be ascribed to superimposing              100003001003010-610-910-12σ' (S/cm)ε'M (emu/mol)100 OeCdCr2Se450401501005003 Hz53 Hz950 Hz17 kHz95 kHz950 kHz0 100 200 300T (k)Fig. 3. Temperature dependence of the low field magnetization (upperframe), real part of the dielectric permittivity e0 (middle), and real part ofthe conductivity (lower frame) of CdCr2Se4 for various frequencies. Themagnetic transition occurs at T  125K and is accompanied by anincrease of the permittivity towards low temperatures. (Note, that theplateau-like low-temperature value of the magnetization is determined bythe demagnetization factor of the sample in the small measurement field ofH ¼ 100Oe and does not display an intrinsic saturation.)                                             365contributions from charge carrier transport. As the di-electric loss and the real part of the conductivity are linkedvia the relation e00 / s0=n, the staggered behavior of thedielectric loss curves can be attributed to the presence ofconductivity contributions.The most remarkable feature in Fig. 1 is the strongincrease of e0ðTÞ below the ferromagnetic transitiontemperature T c ¼ 84K, indicating the close coupling ofmagnetic and dielectric properties. It can be explainedassuming that the frozen-in dynamics of the dielectricrelaxor entities are melting due to the onset of magnetizationand become fast again, which restores a large contributionin the dielectric response [6]. At the same time the dielectricloss is increasing below T c. As mentioned before, this in partmay be influenced by changes in the conductivity. Magne-toresistive effects have been reported for CdCr2S4 andCdCr2Se4 in the literature [7].For CdCr2Se4, the magnetic transition is shifted tohigher temperatures. The magnetic order sets in at Tc 125K as monitored in the upper frame of Fig. 3. At thistemperature an increase of e0ðTÞ towards lower tempera-tures is detected, too. Thus, similar to CdCr2S4 [3], theclosely related CdCr2Se4 also exhibits a strong magneto-dielectric coupling. The typical relaxor peaks in the realpart of the permittivity at T4T c are shifted to highertemperatures and only can be detected for the lowestfrequencies within the examined temperature regime below300K. The superimposed influence of conductivity ishigher in CdCr2Se4 compared to CdCr2S4. For this in thelowest frame of Fig. 3, s0 is plotted. For low frequencies thedata fall onto one curve reflecting the DC value ofconductivity. The higher-frequency curves successivelybranch off from this curve pointing to additional relaxa-tional and/or AC conductivity contributions.It has to be mentioned that even though the observedeffects are stable against the exchange of the chalcogen ion,the occurrence of the observed dielectric features dependssensitively on the stoichiometry. Annealing of the samples,both, in vacuum or sulfur/selen atmosphere, leads to asuppression of the frequency depend relaxor peaks in e0ðTÞabove Tc and no remanent electric polarization can befound at low temperatures. Also, these features so far couldnot be detected in polycrystalline samples.Also, one should consider the possibility that theobserved relaxation features are not a bulk property, butof the so-called Maxwell–Wagner type [8], i.e. caused bypolarization effects at or close to the surface of the samples.A prominent example for Maxwell–Wagner relaxations arethe so-called ‘‘colossal dielectric constant’’ materials [9]. Inmost (if not all) of these materials, relaxational behaviorwith very high (typically 103–105), non-intrinsic dielectricconstants arise from the formation of depletion layers atthe interface between sample and metallic contacts. Thehigh capacitance of these insulating layers at the samplesurface can lead to apparently high dielectric constants andrelaxational behavior. Thus in the present case, we variedthe electrode materials, to check for such a scenario. Fig. 4shows measurements of e0ðTÞ for contacts made fromsilver-paint or sputtered gold. For high temperaturessignificant differences between both measurements can bedetected. However, the relaxation features are still presentat the same temperatures and for temperatures below thedata match each other. This clearly points towards adominance of intrinsic effects.Concerning the microscopic origin of the polar momentsin CdCr2S4 and CdCr2Se4 it can be assumed that theferroelectric distortions result from an off-center positionof the Cr3þ-ions which generates a locally polar butmacroscopically isotropic cluster state [10]. Geometricalfrustration within the at room temperature highly sym-metric cubic lattice drives the observed relaxor-like freezing[11]. On the other hand, the origin of the strong coupling ofmagnetization and dielectric permittivity in this compoundis so far unknown. As pointed out the relaxation dynamicsof the polar moments are accelerated below Tc [6], but itARTICLE IN PRESS100500ε'0 100 200 300T (K)3 Hz53 Hz950 HzCdCr2S4Fig. 4. Temperature dependence of the real part of the dielectricpermittivity e0 of CdCr2S4 measured for various frequencies. The symbolsrepresent measurements employing sputtered gold electrodes; the linesdenote the results obtained with electrodes of silver paint.                                             366remains to be clarified what is the microscopic origin of thedetected relaxation dynamics and why this dynamicscouples so strongly to the magnetic order parameter. Acoupling via exchangestriction, i.e. volume changes arisingfrom the magnetic exchange energy [12] seems possible.The onset of spin order leads to a softening of the latticethereby reducing the energy barriers against dipolarreorientation and thus enhancing the mean relaxation rate.As an alternative explanation one could consider amagnetic-field-induced variation of charge-carrier mobilityor density. As mentioned before, a sizable DC magnetor-esistive effect is well known for CdCr2S4 [7], but it cannotbe responsible for the observed anomalies of e0 as the DCresistivity only contributes to e00. In contrast, hopping-typecharge transport is known to give rise to frequency-dependent AC conductivity, which via the Kramers–Kro-nig relation would lead to a contribution to the dielectricconstant [13].In conclusion, our results clearly reveal that in CdCr2S4and CdCr2Se4 canonical ferromagnetism coexists at sizableordering temperatures with a relaxor-ferroelectric state,characterized by a significant relaxational behavior. Bothorder parameters are strongly coupled. There is a radicalchange of the dielectric relaxational dynamics driven by theonset of magnetization that leads to the observed strongincrease of the dielectric permittivity in these compounds.The present dielectric experiments cannot provide finalevidence on the microscopic origin of this puzzlingbehavior. While contact effects could be ruled out andthe influence of charge transport seems unlikely, a scenarioin which the relaxation mechanism interacts with magneticorder via exchangestriction can be considered the mostplausible.This work was partly supported by the DeutscheForschungsgemeinschaft via the Sonderforschungsbereich484 and partly by the BMBF via VDI/EKM, FKZ13N6917.References[1] T. Kimura, et al., Nature 426 (2003) 55;N. Hur, et al., Phys. Rev. Lett. 429 (2004) 392;Th. Lottermoser, et al., Nature 430 (2004) 541.[2] T. Goto, et al., Phys. Rev. Lett. 92 (2004) 257201;N. Hur, et al., Phys. Rev. Lett. 93 (2004) 107207.[3] J. Hemberger, P. Lunkenheimer, R. Fichtl, H.-A.K. von Nidda,V. Tsurkan, A. Loidl, Nature 434 (2005) 364.[4] P. Lunkenheimer, et al., Contemp. Phys. 41 (2000) 15;U. Schneider, et al., Ferroelectrics 249 (2001) 89.[5] G.A. Samara, J. Phys.: Condens. Matter 15 (2003) R367;L.E. Cross, Ferroelectrics 76 (1987) 241.[6] P. Lunkenheimer, R. Fichtl, J. Hemberger, V. Tsurkan, A. Loidl,cond-mat/0505629.[7] H.W. Lehmann, M. Robbins, J. Appl. Phys. 37 (1966) 1389.[8] J.C. Maxwell, Treatise on Electricity and Magnetism, third ed.,Dover, New York, 1991;R.J. Wagner, Ann. Phys. (Leipzig) 40 (1913) 817.[9] P. Lunkenheimer, et al., Phys. Rev. B 66 (2002) 052105;P. Lunkenheimer, et al., Phys. Rev. B 70 (2004) 172102.[10] N.W. Grimes, Philos. Mag. 26 (1972) 1217.[11] A.P. Ramirez, Nature 421 (2003) 483;D. Cao, et al., Phys. Rev. Lett. 89 (2002) 215902.[12] G.W. Martin, et al., J. Appl. Phys. 40 (1969) 1015.[13] A.K. Jonscher, Dielectric Relaxations in Solids, Chelsea DielectricsPress, London, 1983.

Multiferroic behavior in CdCr2X4 (X = S, Se)

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