Soft Matter

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aFaculty of Physics, Lomonosov Moscow State

2, Moscow, 119991, Russia. E-mail: semisalo

+7 495 939 1847bLappeenranta University of Technology,

FinlandcOptoelectronics Research Centre, Tampere

Tampere, FI- 33101, FinlanddState Scientic Research Institute of Chem

Compounds, Moscow, 105118, Russia

Cite this: DOI: 10.1039/c3sm52523f

Received 14th June 2013Accepted 9th October 2013

DOI: 10.1039/c3sm52523f

www.rsc.org/softmatter

This journal is ª The Royal Society of

Strong magnetodielectric effects in magnetorheologicalelastomers

Anna S. Semisalova,*abc Nikolai S. Perov,a Gennady V. Stepanov,d

Elena Yu. Kramarenkoa and Alexey R. Khokhlova

The effect of a uniform magnetic field on the permittivity of magnetorheological elastomers (MREs) is

studied. MREs were synthesized on the basis of silicone rubber and magnetic fillers of various chemical

nature (Fe, NdFeB and Fe3O4) and particle sizes. The value of permittivity was obtained from the

measurements of the capacity of a plane capacitor with MRE samples. A strong increase of the

permittivity (magnetodielectric effect) was observed when the applied field was perpendicular to

the capacitor plates. The value of the magnetodielectric effect was found to be strongly dependent on

the type of magnetic filler as well as on the size and concentration of magnetic particles within MRE

composites. The highest magnetic response reaching 150% was observed for the MRE based on a

magnetically hard NdFeB filler. A simple model explaining physical reasons for the magnetodielectric

effect in a MRE is proposed. The developed MRE with a strong magnetodielectric effect is very

promising for a wide range of applications, in particular, as magnetic field sensors and actuators.

Introduction

Magnetorheological (MR) materials, consisting of a so mattermedium (uid, elastomer, gel, foam, etc.) lled with magneticparticles, belong to so-called smart or intelligent materials andare of great interest nowadays.1–4 Their properties can be easilyand reversibly tuned by changing the environment, i.e.temperature, electromagnetic elds, stresses, etc.5–8 These arehighly responsive properties that dene practical importance ofMR materials. They are widely used in various elds, fromeveryday life to high technology industry.9–12 Development ofnew smart materials as well as new ways of their effectivecontrol is thus a challenging task.

Recently, special attention has been paid to a quite new classof magnetorheological smart materials, namely, magneto-rheological elastomers (MREs). Based on elastomers lled withmagnetic particles, MREs combine high elasticity of polymernetworks with magnetic response and can be controlled byexternal magnetic elds. During the last few years mainlymechanical and viscoelastic properties of MREs have beenstudied and improved. Developed MREs have demonstrated:

University, GSP-1, Leninskie Gory, 1, bld.

va@magn.ru; Fax: +7 495 939-4787; Tel:

P.O. Box 20, Lappeenranta, FI-53851,

University of Technology, P.O. Box 692,

istry and Technology of Organoelement

Chemistry 2013

- a huge magnetorheological effect. Up to three orders ofmagnitude increase of the elastic modulus as well as the lossmodulus was observed in the magnetic eld of 3 kOe.5,13 Thiseffect has been used in tunable dampers and vibrationabsorbers;14

- an enormous magnetodeformational effect in uniform10,11

as well as in gradient magnetic elds.15 This phenomenonseems to be promising for development of various micro-movements. An electromagnetic valve16 based on this effect hasbeen recently patented;17,18

- a high responsiveness to an alternating magnetic eld atthe frequency of up to 40 Hz can be used for design of variousactuators;19

- a magnetic eld induced plasticity, or memory effect.15,20

All these striking properties are explained to appear due tosome structuring of magnetic llers under the inuence of anexternal magnetic eld.10

One could expect that structuring of metal particles withinMR materials could also cause a change of their electricalproperties. Andrei et al.21 investigated the electrical conduc-tivity of MR suspensions (MRS) in a magnetic eld. Electricconductivity of initially non-conducting MRS, which appearsin the presence of an external magnetic eld, is provided withthe contact resistance between the magnetic dipoles.22,23

The aim of this work was to examine the effect of an externalmagnetic eld on the permittivity of the new MRE.

It should be noted that a magnetodielectric effect (a changeof permittivity under an applied magnetic eld) is usuallyobserved inmultiferroics24 but it has also been recently found ina number of magnetorheological materials. In particular, a

Soft Matter

Soft Matter Paper

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magnetodielectric effect was reported for magnetic uids basedon iron nanoparticles in elastomer Isopar-M25 and in PDMSferromagnetic gels;26 however, the change of permittivity didnot exceed 15%. Permittivity and magnetodielectric effects inthe ferrouids based on the dielectric liquid were studied in anumber of publications;27–30 the value of permittivity relativechange was found to be about 20% in the mineral-oil-basedferrouids with magnetic magnetite nanoparticles.27 A magne-todielectric effect in Co3O4 nanoparticles within a silica glasshas been recently observed31 to reach only 2% in the magneticeld of 12 kOe.

Here we report for the rst time on a strong magnetodi-electric effect of the developed MRE with up to 150% increase ofthe permittivity in the magnetic eld of 10 kOe. The inuence ofthe chemical nature, size and concentration of the magneticparticles is studied in detail and a mechanism of the magne-todielectric effect is proposed.

ExperimentalMaterials

MRE samples were synthesized on the basis of three magneticllers, namely, Fe, NdFeB and Fe3O4, all commercially avail-able. These materials have different magnetic properties, inparticular, coercivity and saturation magnetization. The Feand Fe3O4 llers are magnetically so, while the NdFeBparticles have a large remanent magnetization. Besides, weused llers with various particle sizes and varied llerconcentrations within the MRE samples. Magnetic propertiesof the MRE llers were measured by the vibrating samplemagnetometer Lake Shore 7407. Scanning electron micros-copy was used to measure the average particle sizes (seeFig. 1). The magnetic and structural characteristics of themagnetic llers are shown in Table 1.

Magnetic particles were modied by triethoxysilane fordehydration and hydrophobisation of their surface to achievebetter compatibility with the polymer.

Fig. 1 SEM image of carbonyl Fe particles. Average particle size – 5 mm.

Soft Matter

Polymer matrices for the MRE were obtained from thesilicone compound SIEL produced by Russian Institute ofChemistry and Technology of Organoelement Compounds. Itconsists of a low-molecular-mass vinyl-containing rubber(component A) and a hydride-containing cross-linking agent(component B):

(A) (CH3)3SiO{[(CH3)2SiO]a � [CH3(H)SiO]b}x � Si(CH3)3

(B) (CH2]CH)3SiO[CH3SiO]y � Si(CH]CH2)3

Polymerization was performed at enhanced temperatures inthe presence of a complex platinum catalyst according to thescheme:

(CH2]CH)3SiO[CH3SiO]y � Si(CH]CH2)3 + Pt-catalyst.

The mechanism of the reaction:

^Si � CH]CH2 + HSi^ � OSiCH2CH2Si^

To prepare MRE samples the polymer and magneticcomponents were mixed together in a roller dispersant, themixture was poured into a mould and polymerized. Micro-waves were applied for a fast heating of the mixture to speedup the polymerization process to prevent particle sedimenta-tion. No external magnetic eld was applied during samplepreparation.

Experimental setup

Our aim was to examine a possible effect of an applied uniformmagnetic eld on the MRE permittivity 3. To obtain the value of3 we measured the capacitance of a plane capacitor containingthe MRE sample as a core material under an applied magneticeld and compared it with the capacitance of an emptycapacitor.

The size of the capacitor was 3.5 � 13 � 23 mm, and theinner space was fully lled with the MRE material wrapped in apaper sheet to prevent any electrical contact between the metalcapacitor plates and the sample. The capacitor was speciallydesigned to keep the distance, d, between the plates rmly xedduring the measurements to prevent any changes of the MREdimensions in an applied magnetic eld.

The scheme of the experimental setup is depicted inFig. 2. The capacitor (1) was placed between the poles of anelectromagnet (2). Measurements of the capacitance wereperformed with the standard RLC-meter AKTAKOM AM-3016(3). A special holder was used to mount samples in twopositions so that the direction of the magnetic eld lines waseither perpendicular or parallel to the capacitor plates.Capacitance measurements were performed at roomtemperature, and the magnetic eld was varied from zero upto �10 kOe.

The value of the MRE permittivity 3 was obtained from theratio between the capacitance C1 of the capacitor lled with the

This journal is ª The Royal Society of Chemistry 2013

Table 1 Magnetic properties of fillers and MRE sample composition

# Sample Filler Size, mm

Magnetic properties of powder ller

Filler content,mass%

Magnetization,emu/g

Coercivity,Oe

Saturation eld,kOe

1 Fe 2–5 190 � 8 9 � 3 �4 402 563 654 735 806 Fe 5–10 200 � 10 5 � 3 �4 547 678 71.59 7710 Fe3O4 0.5 78 � 10 3 � 2 �6 8011 NdFeB 2 98 � 2 1520 � 30 >10 7512 18 117 � 2 1450 � 30 >10 75

Fig. 2 (a) The scheme of the experimental setup: 1 – a plane capacitor with aMRE sample; 2 – an electromagnet; 3 – an RLC-meter. (b) The sketch of theexperimental setup, showing the orientation of the capacitor.

Fig. 3 Field dependence of effective permittivity 3 for an Fe-based MRE (massconcentration: 73%) at various directions of an external magnetic field. Thearrows point to the sequence of magnetic field changes; black arrow correspondsto the initial magnetization curve.

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MRE and the capacitance C0 of the empty capacitor according tothe following expression

C1 ¼ 330S

d¼ 3C0; (1)

where 30 is the dielectric constant, S is the surface area of thecapacitor plates, and d is the distance between the capacitorplates.

Magnetic eld dependence of the MRE capacitance wasmeasured several times for each sample to examine the repro-ducibility of the results. Before each measurement the sampleswere demagnetized in an alternating magnetic eld withdecreasing amplitude.

Results and discussionFe-based MRE

Magnetic eld dependence of the permittivity 3 for the MREbased on a carbonyl iron powder (sample #4 – size of particlesis 2–5 mm, concentration is 73%) is presented in Fig. 3. Theupper curves (red circles and blue triangles) show the elddependence of 3 obtained for the perpendicular orientation ofthe magnetic eld to the capacitor plates while the lower curve(grey squares) corresponds to the parallel orientation. The 3(H)dependence for both orientations were measured uponincreasing as well as decreasing elds; the arrows indicate theways the magnetic eld was changed.

This journal is ª The Royal Society of Chemistry 2013

One can see that the behaviour of the permittivity ismarkedly different for parallel and perpendicular orienta-tions of the magnetic eld and the capacitor plates. Todistinguish these two cases we denote the correspondingpermittivities as 3k and 3t.

Themost striking phenomenon observed is a giant growth of3t with increasing magnetic eld. In Fig. 3 the change ofpermittivity under an applied magnetic eld (magnetodielectriceffect) reaches 59% in the eld of �10 kOe.

Another feature of 3t(H) behaviour is a well pronouncedhysteresis. The initial magnetization curve of the MRE sampleis shown in Fig. 3 by black squares. When the eld reached 10kOe the demagnetization process started; it is described bythe blue triangles and a blue arrow in Fig. 3. At zero eld,magnetization of the sample in the opposite directionbegan (blue le up arrow) and proceeded up to the eldof �10 kOe. The next demagnetization–magnetization cycle isshown in Fig. 3 by red symbols and arrows. It should be notedthat the dependence 3t(H) is nonlinear and tends to saturatein a high eld.

Soft Matter

Fig. 4 Fe-concentration dependence of the relative permittivity increase for anFe-based MRE with different sizes of magnetic filler particles.

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In contrast, the value of 3k practically does not change withthe eld; the observed decrease in Fig. 3 is relatively small, andit is within the experimental error and nonhysteretic.

Similar results have been obtained for all Fe-based MREsamples. They are summarized in Fig. 4 where we plot themaximum relative increase of the permittivity 3t as a function ofthe magnetic ller content as well as Fe particle size. For bothmagnetic powder types (smaller and larger particles) the corre-lation between the value of the magnetodielectric effect and themicroparticle concentration is quite similar, namely, thepermittivity change increases approximately linearly withconcentration and reaches 70–80% at the highest Fe llercontent. It should be noted that the absolute value of permittivityat zero eld, 3(H¼0), also slightly depends on the Fe concentrationwithin the MRE; it changes from 2 to 5 with the increase of theller content from 40 to 80 mass% (see Table 2).

The magnetodielectric effect reported here is quite differentfrom the results obtained by Bica et al.32,33 In these papers thechange of capacitance of a plane capacitor lled with a MREunder an applied magnetic eld was observed. Authorsexplained the square-law dependence of capacitance by thechange of linear size of the capacitor, namely, the spacebetween the plates, which are placed on the sides of the MREsample. The MR elastomers elongate along the magnetic elddirection (magnetodeformational effect), causing the control-lable change of distance between the plates of the capacitorand, consequently, the capacitance.

In our case we wanted to prevent any effect of deformationand kept the distance between capacitor plates constant duringthe measurements. Thus, the observed change of the capaci-tance is due to the change of an effective permittivity of theMRE

Table 2 Permittivity and its maximum relative increase in a perpendicularmagnetic field for the MRE samples under study

NdFeB, 2mm

NdFeB, 18mm

Fe, 2–5mm

Fe, 5–10mm Fe3O4

3(H¼0) 9.5 6.4 2–3 2–5 2D3/3(H¼0) 150% 110% 20–80% 50–72% 15%

Soft Matter

in the magnetic eld. It is caused by structural reorganization ofthe magnetic ller within the polymer matrix under the actionof the eld.34 The observed hysteresis can be caused by elasticeffects in the polymer matrix of MRE samples.

Fe3O4-based MRE

The magnetodielectric effect in a Fe3O4-based MRE is shown inFig. 5. The eld dependence of the permittivity is quite similar tothat observed for an Fe-based MRE. In particular, it is eldorientation-dependent. While the value of 3k practically does notchange with the eld (scatter of points is within the experimentalerror), the 3t(H) is a growing nonlinear function with saturationat high magnetic elds. The main difference is the smaller valueof the magnetodielectric effect, namely, the maximal change ofthe permittivity for a Fe3O4-based material does not exceed 12–15% in the magnetic eld of �10 kOe. The smaller magneticresponse could be connected with the difference in electric andmagnetic properties of Fe3O4 and Fe particles. In particular, theconductivity of iron is higher than that of magnetite; besides, theiron particles have larger magnetization leading to their strongerinteractions in the magnetic eld.

NdFeB-based MRE

Themagnetodielectric effect in a NdFeB-based MRE is shown inFig. 6. For these materials we observed the maximum 150%change of permittivity in the magnetic eld of �10 kOe. Qual-itatively, the obtained eld dependence of the permittivity is thesame as that for a MRE based on the other magnetic llersunder study.

For the synthesis of a NdFeB-based MRE we used thepowders with two different average particle sizes, namely, 2 and18 mm (see Table 1). It was found that the particle size inu-ences both the value of the MRE permittivity in the demagne-tized state, 3(H¼0), as well as the value of the magnetodielectriceffect (Table 2). One can see that the smaller particles provide alarger permittivity as well as a higher magnetic response of theMRE. This tendency holds for both NdFeB and Fe-based MREs.We expect smaller particles to have larger mobility within thepolymer matrix facilitating both their agglomeration during the

Fig. 5 Field dependence of effective permittivity 3 for Fe3O4-based MR elasto-mers at various directions of the external magnetic field.

This journal is ª The Royal Society of Chemistry 2013

Fig. 6 Field dependence of the effective permittivity 3 for NdFeB-based MRelastomers at various directions of the external magnetic field.

Fig. 7 Time dependence of permittivity for Fe- and NdFeB-based MREs underthe applied magnetic field. The MRE samples have been demagnetized andplaced under a magnetic field of 3 kOe (at t¼ 0 s) and the value of capacity of theplane capacitor was recorded. The red line represents the exponential decayfitting.

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synthesis and their further displacements from the initialequilibrium positions under the action of the external magneticeld.

The results of the permittivity measurements for differenttypes of the MRE are summarized in Table 2. The largest valueof 3(H¼0) as well as the highest increase of 3t in the eld areobserved for the NdFeB-based MRE. NdFeB is a magneticallyhard material. The particles are highly anisotropic and weexpect that due to a remanent magnetization they interact andbuild some aggregates already during the synthesis of the MRE.

Magnetic particle concentration dependence of the magne-todielectric effect was studied only for iron-lled materials. Asindicated in Table 2 intervals of 3(H¼0) and D3/3(H¼0) values forthe Fe samples are due to variation of the ller concentration.The initial permittivity was found to be an increasing functionof iron concentration for both types of the particle sizes.

Fig. 8 The plane capacitor with a metal parallelepiped particle placed inside andits equivalent scheme of a series of capacitors.

Magnetic viscosity of the MRE

To study the magnetic viscosity of the MRE samples wemeasured time dependence of the permittivity at a newly setvalue of the magnetic eld. The capacitor lled with the MREwas rst placed at zero eld, and then the eld increased up to3 kOe, the orientation of the eld lines was perpendicular to thecapacitor plates. Time dependence was recorded during severalminutes aer the eld stabilized so that the time delay due tothe eld change was excluded.

The relaxation time of the permittivity is found to bedependent on the type and concentration of the magnetic llerwithin the MRE. It is dened by a combination of the visco-elastic properties of the polymer matrix and magnetic proper-ties of the magnetic particles. Typical time dependence of thepermittivity is presented in Fig. 7 for the samples #2 based on2–5 mm Fe particles and #12 based on 18 mm NdFeB particles inthe eld of 3 kOe. One can see that an equilibrium value of 3 ofthe Fe-based MRE is already reached in 30 seconds while thevalue of 3 of the NdFeB-basedMRE still keeps growing even aer5 minutes aer application of the magnetic eld. This differ-ence can be due to a different behaviour of the ller particles inan external magnetic eld. Fe particles are magnetized easily

This journal is ª The Royal Society of Chemistry 2013

and their magnetic moments are turned with the direction ofthe magnetic eld, while the NdFeB particles have highanisotropy and they rotate with their magnetic moments in themagnetic eld. Observed hysteresis in the eld dependence ofthe permittivity as well as the time dependence of MREmagnetic response seems to be caused by non-elastic matrixeffects in particle displacements under the action of the eld.

The observed time relaxation was taken into account duringthe permittivity measurement, i.e. the measured 3 values at eachmagnetic eld were recorded with a time delay needed for thecapacity to reach an equilibrium. This time delay was differentfor different samples depending on the MRE composition.

Model

To describe the observed effect of a magnetic eld on 3 let usconsider how the capacitance of the system “plane capacitor +MRE” is determined. In the absence of any external magneticeld the MRE sample represents a dielectric medium withhomogeneously distributedmetal particles. In the simplest caseits capacitance can be estimated as the capacitance of acapacitor with a parallelepipedmetal particle placed between itsplates as shown in Fig. 8. The dimensions of this metal paral-lelepiped are dened by the total volume concentration cvol ofthe magnetic ller within the MRE, if cvol ¼ h3 then

x ¼ ha, y ¼ hb, z ¼ hc. (2)

The effective capacity of the capacitor a � b � c with themetal particle x � y � z (x, y, z < a) shown in Fig. 8 can be easily

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calculated; it is determined as a capacitance of parallelconnection of capacitors with different areas of plates anddistance between the plates:

C1 ¼ 303ðbc� yzÞ

a; C2 ¼ 303

yz

a� x: (3)

Thus, the nal capacitance reads:

Cfinal ¼ 303abcþ xyz� bcx

aða� xÞ : (4)

The value of Cnal depends on the size x of the metal paral-lelepiped particle.

This simple consideration shows that the capacity of a planecapacitor partly lled with a conducting material depends notonly on the volume fraction of the metal part but also on itsspatial distribution.

When a uniformmagnetic eld is applied to a piece of aMREthe magnetic moments of the ller particles tend to orient withthe magnetic eld lines, and the particles try to organizethemselves into chains parallel to the magnetic eld.34 In thecourse of this structuring, the particle density in the direction ofthe eld increases while that in the perpendicular directiondecreases. Thus, coming back to the representation of Fig. 8, wecan say that the particle structuring does not change the volumeof the equivalent metal parallelepiped v ¼ xyz, instead itchanges the size of the parallelepiped, in particular, the size x,thus, changing the capacitance according to eqn (4).

Let us assume that the magnetic eld is directed perpen-dicular to the plane of the capacitor. In this case the size x0 ofthe equivalent metal parallelepiped becomes larger and thesizes y0 and z0 become smaller in comparison with those for thehomogeneous distribution of particles without the magneticeld (x, y, z). Let x0 ¼ bx, b > 1. As a result, the capacity of thecapacitor increases.

The dependence of the magnetodielectric effect (D) on thevalue of b calculated according to the proposed model for theMRE samples with various volume concentrations cvol ofthe magnetic particles is shown in Fig. 9. One can see that at thesame values of b the higher the ller concentration is the largeris the value of D. It should be noted that in reality, the value ofb itself should depend on the type and concentration of the

Fig. 9 Calculated values of magnetodielectric effects for different volumeconcentrations of particles cvol.

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magnetic ller. In the case of a magnetic eld applied parallel tothe capacitor plane y0 ¼ yb, x 0 ¼ yb�1/2 and the sign of the effectis opposite (Fig. 9).

The proposed model and the performed calculations shouldbe considered only as a qualitative explanation of the experi-mental results and a demonstration of some physical reasons ofthe magnetodielectric effect observed in this work. To describethe experimental results in detail a more rigorous analysis isnecessary taking into account the shape of the magnetic parti-cles, their interaction with the elastic matrix, magnetic eld andbetween each other as well as the magnetization processes.

It should be noted that a long-chain model of the magne-todielectric effect developed by Xu Pei-Ying et al.35 has beenapplied by Kopcansky and coworkers to describe the effectobserved in magnetite-based ferrouids.27,28 This model seemsto work well for ferrouids with small concentrations ofmagnetic particles, so that distances between the magneticparticles are much higher than the particles' size and theirinteractions can be described in terms of point-like dipoles. Inour case the magnetic ller concentration within elastomers isclose to percolation and the model of point-like dipoles cannotbe applied. Nowadays there are no adequate phenomenologicalapproaches describing interacting dipoles at small distances.The proposed model is presented only as a reasonable way todescribe qualitatively our results and to illustrate the role ofparticle reorganisation under the action of a magnetic eld.

Conclusions

In conclusion, we present the rst experimental resultsdemonstrating a huge magnetic eld dependence of dielectricpermittivity in magnetorheological elastomers. The effects of amagnetic eld on 3 were found to be up to 150% and 80% inMREs based on NdFeB and Fe powders, respectively, and, thus,can be considered as strongmagnetodielectric effects (as well asstrong magnetopermittivity or magnetocapacitance).

Investigation of the MRE lled with various types ofmagnetic materials (Fe, NdFeB, Fe3O4) has revealed that satu-ration magnetization and coercivity are the most importantfactors affecting the eld dependence of permittivity. In addi-tion, the size and concentration of themagnetic particles as wellas conductivity of magnetic materials have a signicant inu-ence on the magnetodielectric effect.

The highest magnetic response was found in a highly coer-cive NdFeB-based MRE, while the smallest one was observed forthe magnetite-based MRE. Magnetite has the lowest magneti-zation determining the strength of magnetic microparticleinteractions in an external magnetic eld. Besides, the electricconductivity of magnetite is several orders of magnitude smallerthan that of metal Fe and NdFeB particles, inuencing thecharacter of the eld effect on the MRE capacitance.

A model revealing the main mechanism of the magnetodi-electric effect in elastomers is proposed. It is based on theassumption of structuring of the magnetic ller under theapplied magnetic eld and explains the observed effect ofthe magnetic ller properties on the permittivity of the MRE.

This journal is ª The Royal Society of Chemistry 2013

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Equilibrium arrangement of the magnetic particles isdened by the balance between the magnetic and elasticinteractions thus depending not only on the ller magnetic andstructural properties but also on polymer elasticity. The inu-ence of the polymer matrix elasticity will be studied in furtherpublications, as well as the inuence of external stresses.

Our nding of a strong magnetodielectric effect in a MRE issignicant for design of magnetic eld sensors and variousactuators.

Acknowledgements

Financial support of the Russian Foundation for Basic Research(grants no. 13-03-00914, 11-02-00906, 13-02-90491, 13-02-12443)is gratefully acknowledged.

References

1 B. J. Park, F. F. Fang and H. J. Choi, SoMatter, 2010, 6, 5246.2 J. de Vicente, D. J. Klingenberg and R. Hidalgo-Alvarez, SoMatter, 2011, 7, 3701.

3 M. T. Lopez-Lopez, G. Vertelov, G. Bossis, P. Kuzhir andJ. D. G. Duran, J. Mater. Chem., 2007, 17, 3839.

4 A. Gomez-Ramirez, M. T. Lopez-Lopez, J. D. G. Duran andF. Gonzalez-Caballero, So Matter, 2009, 5, 3888.

5 G. V. Stepanov, S. S. Abramchuk, D. A. Grishin, L. V. Nikitin,E. Yu. Kramarenko and A. R. Khokhlov, Polymer, 2007, 48, 488.

6 X. Gong, Y. Fan, S. Xuan, Y. Xu and C. Peng, Ind. Eng. Chem.Res., 2012, 51, 6395.

7 S. Xuan, Y. Zhang, Y. Zhou, W. Jiang and X. Gong, J. Mater.Chem., 2012, 22, 13395.

8 G. V. Stepanov, A. V. Chertovich and E. Yu. Kramarenko,J. Magn. Magn. Mater., 2012, 324, 3448.

9 C. A. Grimes, S. C. Roy, S. Rani and Q. Cai, Sensors, 2011, 11,2809.

10 S. Abramchuk, E. Kramarenko, G. Stepanov, L. V. Nikitin,G. Filipcsei, A. R. Khokhlov and M. Zrinyi, Polym. Adv.Technol., 2007, 18, 883.

11 S. Abramchuk, E. Kramarenko, D. Grishin, G. Stepanov,L. V. Nikitin, G. Filipcsei, A. R. Khokhlov and M. Zrinyi,Polym. Adv. Technol., 2007, 18, 513.

12 Y. Shiao and Q.-A. Nguyen, Smart Mater. Struct., 2013, 22,065008.

13 A. V. Chertovich, G. V. Stepanov, E. Yu. Kramarenko andA. R. Khokhlov, Macromol. Mater. Eng., 2010, 295, 336.

This journal is ª The Royal Society of Chemistry 2013

14 G. J. Liao, X.-L. Gong, S. H. Xuan, C. J. Kang and L. H. Zong,J. Intell. Mater. Syst. Struct., 2011, 23, 25.

15 L. V. Nikitin, G. V. Stepanov, L. S. Mironova and A. I. Gorbunov,J. Magn. Magn. Mater., 2004, 272–276, 2072.

16 G. V. Stepanov, E. Yu. Kramarenko and D. A. Semerenko,J. Phys.: Conf. Ser., 2013, 412, 012031.

17 G. V. Stepanov and D. A. Semerenko, Patent RU 2320912 C2,2008.

18 T. Heier and C. Schuber, Patent WO 2010054775 A1, 2009.19 O. V. Stolbov, Yu. L. Raikher, G. V. Stepanov, A. V. Chertovich,

E. Yu. Kramarenko and A. R. Khokhlov, Polym. Sci., Ser. A,2010, 52, 1344.

20 S. S. Abramchuk, D. A. Grishin, E. Yu. Kramarenko,G. V. Stepanov and A. R. Khokhlov, Polym. Sci., Ser. A,2006, 48, 138.

21 O.-E. Andrei and I. Bica, J. Ind. Eng. Chem., 2009, 15, 573.22 I. Bica, J. Magn. Magn. Mater., 2004, 283, 335.23 I. Bica, Smart Mater. Struct., 2006, 15, N147.24 A. V. Pavlenko, A. V. Turik, L. A. Rezhnichenko, L. A. Shilkina

and G. M. Konstantinov, Tech. Phys. Lett., 2013, 39, 78.25 P. C. Fannin, B. K. Scaife and S. W. Charles, J. Magn. Magn.

Mater., 1993, 122, 168.26 L. Kubisz, A. Skumiel, E. Pankowski and D. Hojan-Jezierska,

J. Non-Cryst. Solids, 2011, 357, 767.27 P. Kopcansky, J. Cernak, P. Macko, D. Spisak and K. Marton,

J. Phys. D: Appl. Phys., 1989, 22, 1410.28 P. Kopcansky, P. Macko, M. Koneracka and V. Zavisova, J.

Magn. Magn. Mater., 1996, 157/158, 587.29 M. Timko, K. Marton, L. Tomco, J. Kiraly, M. Molcan,

M. Rajnak, P. Kopcansky, R. Cimbala, F. Stoian, S. Holotescuand A. Taculescu, Magnetohydrodynamics, 2012, 48, 427.

30 M. Rajnak, J. Kurimsky, B. Dolnik, K. Marton, L. Tomco,A. Taculescu, L. Vekas, J. Kovac, I. Vavra, J. Tothova,P. Kopcansky and M. Timko, J. Appl. Phys., 2013, 114,034313.

31 P. Haira, S. Dutta, P. Brahma and D. Chakravorty, J. Magn.Magn. Mater., 2011, 323, 864.

32 I. Bica, J. Ind. Eng. Chem., 2012, 18, 1666.33 I. Bica, Y. D. Liu and H. J. Choi, Colloid Polym. Sci., 2012, 290,

1115.34 G. V. Stepanov, D. Yu. Borin, Yu. L. Raikher,

P. V. Melenev and N. S. Perov, J. Phys.: Condens. Matter,2008, 20, 204121.

35 X. Pei-Ying, S. Dong-Ning and L. Huai-Xian, Acta Phys. Sin.,1988, 37, 1192.

Soft Matter