Realization of giant magnetoelectricity in helimagnets
Sae Hwan Chun, Yi Sheng Chai, Yoon Seok Oh, Deepshikha Jaiswal-Nagar, So Young Haam, Ingyu Kim, Bumsung Lee, Dong Hak Nam, Kyung-Tae Ko, Jae-Hoon Park, Jae-Ho Chung, Kee Hoon Kim
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J a n Realization of giant magnetoelectricity in helimagnets
Sae Hwan Chun, Yi Sheng Chai, Yoon Seok Oh, Deepshikha Jaiswal-Nagar, So Young Haam, Ingyu Kim, Bumsung Lee, Dong Hak Nam, Kyung-Tae Ko, Jae-Hoon Park, Jae-Ho Chung, and Kee Hoon Kim FPRD, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, South Korea Department of Physics & Division of Advanced Materials Science, POSTECH, Pohang 790-784, South Korea Department of Physics, Korea University, Seoul 136-713, South Korea
We show that low field magnetoelectric (ME) properties of helimagnetsBa . Sr . Zn (Fe − x Al x ) O can be efficiently tailored by Al-substitution level. As x in-creases, the critical magnetic field for switching electric polarization is systematically reduced from ∼ ∼ × ps/m at an optimum x = 0.08. We find that control of nontrivial orbital moment in theoctahedral Fe sites through the Al-substitution is crucial for fine tuning of magnetic anisotropy andobtaining the conspicuously improved ME characteristics. PACS numbers: 75.80.+q, 77.80.Fm, 71.45.Gm, 75.30.Gw
In recent years, extensive researches on multiferroicshave been performed with motivations to understand thenontrivial cross-coupling mechanism between magnetismand ferroelectricity as well as to search for new materialsapplicable in next-generation devices [1–8]. Numerousstudies have focused particularly on the class of so-calledmagnetic ferroelectrics [1–3, 9, 10], in which ferroelec-tricity is induced by magnetic order through either in-verse Dzyaloshinskii-Moriya effects [6–8] or the exchangestriction mechanism [10]. Although dramatic variationof electric polarization P with magnetic field B , often re-alized in the magnetic ferroelectrics [3], might be usefulfor application, the phenomena occur mostly at low tem-peratures [1, 2, 9, 10] and related ME susceptibility is yettoo small [5]. Hence, it is a longstanding challenge in theresearch of multiferroics to improve both the operatingtemperature [11, 12] and the ME sensitivity [13–15].The hexaferrite Ba . Sr . Zn Fe O (BSZFO) withhelical spin order is currently a unique candidate that canshow the B -induced ferroelectricity above room tempera-ture up to ∼
340 K [12]. However, at 300 K, its ferroelec-tric (FE) phase is expected to emerge at B ∼ α ME ≡ µ dPdB at 30 Kshows a maximum value of ∼ × ps/m at B ∼ α ME ∼ - 10 ps/m realized in hetero-geneous films [13] or strain-coupled composites [5, 14].When Zn is replaced by Mg to form a Mg Y-type hex-aferrite, Ba Mg Fe O , the critical magnetic field forinducing P becomes extremely low, ∼
30 mT [15, 16]. Onthe other hand, a maximum operation temperature of theMg Y-type hexaferrite is expected to be lower than 195K. Moreover, a microscopic understanding for the low-ered critical magnetic field remains unclear. Therefore,systematic studies are further required to understand theorigin of the intricate ME effect and improve multiferroicproperties in the hexaferrite system.In this letter, we demonstrate that Al-substituted (c)(b) [100] [010][001] (a) S L S S S L L S S L L tetrahedral siteoctahedral off-centered octahedral x = 0.00 x = 0.08 B = 0 B = 10 mT P = 0 (cid:160) P ≠ 0 B = 0 B = 10 mT k S S L L µ S µ L P = 0 P = 0 k k k Ba Sr Zn (Fe x Al x ) O FIG. 1. (a) Crystal structure of the Zn Y type-hexaferriteBa . Sr . Zn (Fe − x Al x ) O that has alternating stacks ofmagnetic S and L blocks along the c -axis. Schematic illus-tration of rotating magnetic moments in the L ( ~µ L ) and S blocks ( ~µ S ) in the (b) helical ( x = 0.00) and (c) heliconical( x = 0.08) phases under in-plane B = 0 T and 10 mT. ~k isthe spin modulation wave vector parallel to [001]. BSZFO, i.e. Ba . Sr . Zn (Fe − x Al x ) O greatly im-proves the multiferroic characteristics, resulting in thehighest α ME of single-phase multiferroics near-zero mag-netic field. We find that predominant substitution of Alions into octahedral Fe sites with nontrivial orbital mo-ment is crucial for fine tuning of the magnetic anisotropyand thus for tailoring the ME coupling.Single crystals of Ba . Sr . Zn (Fe − x Al x ) O weregrown from Na O-Fe O flux in air [17]. Crystals werecut into a rectangular form for electric polarization P measurements along the ab -plane while B was appliedalong the direction normal to the P vector in the ab -plane. Before the ME current measurements, each spec-imen was electrically poled in its paraelectric state, for ∆ ε ( B ) / ε ( T ) ( % ) P ( µ C / m ) T = 30 K 0.020.040.06 x = 0.08 (a)(b) Ba Sr Zn (Fe x Al x ) O B c,L B c,L B c,U B //ab 00000.020.040.06 x = 0.08 x
40 6 % B (mT) B (mT) ParaelectricFerroelectricParaelectric x = 0.08 0.04 0.000.010.02050100150200250300 T ( K ) B c,L B c,U (c) FIG. 2. (a) Electric polarization and (b) ∆ ε ( B )/ ε (3 T) ≡ [ ε ( B ) - ε (3 T)]/ ε (3 T) curves for x = 0.02, 0.04, 0.06 and 0.08at T = 30 K. (c) Ferroelectric phase boundaries determinedfrom the ∆ ε -maxima while ramping down B . example, at B = 0 T for x < B = 2.5 T for x> B = 1.2 T). An LCR meter was usedfor dielectric constant ε measurements at 4 MHz. Whiledetermined FE phase boundaries were confirmed to beindependent of frequency from 100 - 10 MHz below 100K, the specific frequency was chosen because the loss wasmore or less minimal ( < ∼ ε ( B ) peaks couldbe clearly identified even up to higher temperatures.BSZFO is one of the Y-type hexaferrites with alternat-ing layers of tetrahedral Fe/Zn and octahedral Fe sites(Fig. 1(a)) [12, 17]. It undergoes a thermal transitionfrom a paramagnetic to a helical spin state at ∼
337 K,in which alternating stacks of magnetic L and S blocksdevelop a proper-screw-type rotation of their magneticmoments ( ~µ L and ~µ S ) along [001]. In each magneticblock, the moment prefers to lie within the ab -planerather strongly so that the moment remains so even un-der an in-plane B = 10 mT (modified helix phase, Fig.1(b))[17]. When B is increased further, BSZFO exhibitsa few successive intermediate phases (I, II, and III) andfinally reaches a collinear ferrimagnetic phase around 2T. Finite P develops only in the intermediate-III phasestabilized around 1 T [12], of which origin remains un-resolved. When a small amount of Al is substituted for Fe inBSZFO, we find remarkable features in curves of P vs.B and ε vs. B (Fig. 2). All the samples yield induced P in finite B -windows between a lower critical field ( B c , L )and an upper critical field ( B c , U ) (Fig. 2(a)). As x in-creases, B c , L is greatly reduced, and thus a finite P isobserved even at B ≦ x = 0.06 and 0.08. Mean-while, the maximum of the electric polarization ( P max )gradually increases with x up to x = 0.08. When x isincreased further, to 0.20, the turn-on behavior of P be-comes broader and P max is substantially reduced (notshown). Figure 2(b) shows the magnetodielectric (MD)effects ∆ ε ( B )/ ε (3 T) ≡ [ ε ( B ) - ε (3 T)]/ ε (3 T) of theselected samples at 30 K. The ∆ ε ( B )/ ε (3 T) curves ex-hibit maxima at positions concomitant with both B c , L and B c , U . Thus, the ∆ ε -maxima can be traced to identifythe FE phase boundaries in a wide temperature-magneticfield window (Fig. 2(c)). As is evident in Fig. 2(c), B c , L systematically decreases from ∼ x = 0.00) to ∼ x = 0.08) at T = 90 K, with a step of B c ∼
100 - 200mT per ∆ x = 0.01, and it becomes lower than 1 mTfor x = 0.08 below 90 K. These results demonstrate thatAl-substitution into BSZFO is one of the most effectiveways to control B c , L , down to 1 mT or even lower.Another conspicuous feature of Al-substituted BSZFOis the realization of giant α ME at extremely low mag-netic fields. Figure 3(a) shows the B -dependent α ME curves at 30 K for different x and the inset summa-rizes their maximum values ( α m ). α m for the undopedsample ( x = 0.00) is about 4.3 × ps/m. As x in-creases, α m increases to 2.0 × ps/m at x = 0.08, 470times larger than at x = 0.00, and then decreases for x> α m could be re-alized because the Al-substitution not only increases P but also induces P in a lower B -region. The present op-timal α m = 2.0 × ps/m is ∼
12 times larger than α m ∼ × ps/m of Ba Mg Fe O [15], andrecords the highest value among single-phase multifer-roics [18]; for comparison, ∼ ps/m in TbMnO [1]and TbMn O [2] and 4.2 ps/m in Cr O [18] havebeen reported. Ba . Sr . Zn (Fe − x Al x ) O also ex-hibits substantial MD effects at low temperatures. Fig-ure 3(b) shows ∆ ε ( B )/ ε (3 T) curves for x = 0.08 below130 K. The ε , showing a maximum around 0 mT, rapidlydecreases within low B -ranges ( | B | <
50 mT), and B =20 mT is sufficient to induce about 6 % MD effect. Vary-ing x , the MD effects reached as high as 12 % for x =0.00 - 0.03 and 15 % for x = 0.04 - 0.12.The observed ferroelectricity induced at extremely low B is likely associated with a heliconical spin ground state.The emergence of spontaneous magnetization along [001]with the increase of x (Fig. 4(a)) supports the hypothesisthat the Al-substitution progressively stabilizes the lon-gitudinal heliconical state (Fig. 1(c), left) as reported inBa Mg Fe O [15, 16]. The estimated conical orderingtemperature T con is ∼
20 K for x = 0.02, and it increases De ( B ) / e ( T ) ( % ) T (K) x = 0.08 (b) B (mT) B (mT) a M E ( p s / m ) x = 0.00 0.02 Ba Sr Zn (Fe x Al x ) O T = 30 K (a) a m ( x ) x FIG. 3. (a) B -dependence of magnetoelectric susceptibility( α ME ) at T = 30 K. The inset shows the maximum valuesof α ME ( α m ) for each x . (b) Intensity and 3 D-plots of mag-netodielectric effects (∆ ε ( B )/ ε (3 T)) of the x = 0.08 samplebelow 130 K in low B region ( | B | <
50 mT). up to ∼
110 K for x = 0.06 and 0.08. In the phase di-agram of Fig. 2(c), B c , L values for x = 0.06 and 0.08indeed decrease rather abruptly near their T con ∼
110 Kto become less than 10 mT, showing a close link betweenthe heliconical spin state and the extremely low B c , L . Ac-cording to the spin current model [6] that has explainedinduced P in various spiral- or heli-magnets, ~P ∝ ~k × [ ~µ S × ~µ L ]. In the present hexaferrite, ~k is along [001]and thus the model consistently explains why P becomestrivial in the helical or modified helix phases (Fig. 1(b)).Even for the longitudinal conical state (Fig. 1(c), left), P should go to zero as the [ ~µ S × ~µ L ] vector, parallel tothe spin-rotation axis of each cone, is along [001]. Undera small in-plane B , only the spin-rotation axis of the lon-gitudinal conical state is expected to align easily alongthe B -field to form a transverse conical state (Fig. 1(c),right), which then generates a finite P in the ab -plane.Therefore, it is most likely that below T con the spin statechanges from a longitudinal to a transverse conical typeacross B c , L in the x = 0.06 and 0.08 samples.What can be then the spin state of the FE phases inthe low x ( ≤ T con in the high x ( ≥ B c , L is observed? The in-plane magnetization M ab curves (Fig. 4(d)) reveal someclues to this puzzle. According to Ref. [17], the modifiedhelix, intermediate-I, -II, -III and collinear ferrimagneticphases coincide with the first, second and third plateau,the steep ascent, and the last plateau regions, respec-tively. With these criteria, the magnetic phase bound-aries can be roughly estimated from Fig. 4(d); for exam-ple, the x = 0.02 sample exhibits magnetic phase bound-aries similar to BSZFO [12, 17]. However, we noticethat the B -range for the modified helix phase decreasesprogressively as x increases to 0.04. For x = 0.08 (also x = 0.06), the first two plateaus of M ab ( B ) no longer existduring the up-sweep, suggesting that the modified he-lix and intermediate-I phases change into or coexist withthe transverse conical state. These observations suggest (a) M c ( µ B / f . u . ) (b)(c) (d) T ( K ) T (K)0 50 100 1500.00 0.04 0.08 x HeliconicalHelicalParamagnetic T N T con ∆ I ( a r b . un it . ) x = 0.080.060.040.02 x = 0.100.040.08 Photon Energy (eV) M a b ( µ B / f . u . ) Ba Sr Zn (Fe x Al x ) O B (mT) 10001 10 100 x = 0.080.040.02 II III CII III Cmodifiedhelixmodifiedhelix collinear ( C ) III T = 30 K intermediate-II FIG. 4. (a) The c -axis magnetization M c measured at zero B after field cooling at B = 3 T. (b) The magnetic phaseevolution with x , estimated from M c ( T ) and M ab ( T ) curves.(c) X-ray absorption intensity for several x at the Fe L , -edge after subtraction of the intensity of x = 0.00 (∆ I =-[ I ( ω , x )- I ( ω , x = 0.00)]). The data for x ≥ M ab ( B ) curves at T = 30 K.The dashed lines represent the phase boundaries estimatedfor the down-sweep following the criteria in Ref. [17]. Theblack triangles represent B c , L for x = 0.02 and 0.04. that the in-plane magnetic anisotropy decreases with in-creasing x , allowing the nontrivial moment along [001] todevelop at smaller B . Meanwhile, the location of B c , L for the x = 0.02 and 0.04 (black triangles) is not any-more coincident with the intermediate-III phase bound-ary but is well inside the intermediate-II or modified helixphases. Therefore, it is likely that the low x -samples alsoform a kind of transverse conical spin state across their B c , L , which can coexist with the helical phases, and gen-erate nontrivial ab -components of [ ~µ S × ~µ L ] and thus P . A previous study of Ba . Sr . Zn Fe O supportsthis possibility through neutron scattering and mag-netic torque measurements [19]; near the intermediate-IIIphase boundary, a cone of easy magnetization, compati-ble with the transverse conical state in Fig. 1(c), developsand coexists with a basal plane of easy magnetization,compatible with the helical phases in Fig. 1(b).To understand the role of Al-substitution microscopi-cally, we have performed Fe L , -edge X-ray absorptionspectroscopy. The spectra taken for each x were sub-tracted from that of x = 0.00 to plot the difference spec-tra as shown in Fig. 4(c). The systematic increase in theintensity of the difference spectra near the octahedral Fe L , -edge supports that Al replaces the octahedral Fe-sites in proportion to x . Furthermore, comparative neu-tron diffraction studies for x = 0.00 and 0.06 produced agood refinement for x = 0.06 when the fraction of Al ionsat the octahedral (tetrahedral) sites are 0.9920 (0.0080),directly supporting that Al ions mostly replaces the oc-tahedral Fe sites for x = 0.06. These results support thatAl ions in Ba . Sr . Zn (Fe − x Al x ) O highly prefer tooccupy the octahedral Fe sites.Moreover, magnetic circular dichroism measurementsat the Fe L , -edge in the undoped sample revealed a con-siderable orbital magnetic moment of 0.30 ± µ B /f.u.along the ab -plane [20]. Note that ionic Fe has a half-filled d configuration and its total angular momentum L = 0. Thus the orbital moment is expected to vanish.If the Fe ion, however, is not at the center of an octa-hedron, i.e., off-centered, then the hybridization with O2 p becomes anisotropic and contributes a non-vanishingorbital moment, as observed in GaFeO [21]. Accord-ing to our structural refinements as well as those in Ref.[17], the Fe ions in the green octahedra (Fig. 1(a)) areindeed off-centered, being shifted along the c -axis, whichresults in the nontrivial orbital moment and the easy spinaxis in the ab -plane. Based on the octahedral site prefer-ence of the Al ions, it is likely that the main role of theAl-substitution is to reduce the magnetic anisotropy en-ergy, through either dilution of the off-centered Fe sitesor reduction of their off-centering deformation. Indeed,subsequent measurements for a x = 0.08 sample showeddecrease of the in-plane orbital magnetic moment by ∼
20% [20]. As a consequence, the magnetic moment can tiltaway from the ab -plane more easily with Al-substitution,resulting in reduced B c , L at low x , and the heliconicalspin state seems to emerge for x = 0.06 - 0.08 with re-duced in-plane anisotropy. Therefore, decrease of the in-plane orbital moment with the Al-substitution seems tobe an essential process for lowering magnetic anisotropyand thus improving the low field ME response [22].The mechanism uncovered here is also applicable toBa Mg Fe O [15, 16], in which Mg ions occupyboth tetrahedral and octahedral Fe sites in an arbi-trary fraction. Here, the partial occupation of Mg inthe octahedral Fe-sites seems to also reduce the mag-netic anisotropy [23], via the decrease of the orbital mo-ment. In comparison, Al-substitution in BSZFO seemsto be more effective for systematic control of magneticanisotropy and B c , L as it can directly control the orbitalmoment in the system.Finally, it is noteworthy that the helical spin order-ing temperatures of Al-substituted BSZFO remain rela-tively high (Fig. 4(b)); for instance, T N = 337 K at x = 0.00 and 263 K at x = 0.08. Although the FE phaseboundaries could not be determined above 220 K dueto electrical leakage, we expect that the low B -inducedFE switching will be observable up to T N upon furtheroptimization of the resistivity. In our recent work on aheat-treated BSZFO sample, B c , L could be determinedup to T N = 315 K due to dramatic increase of resis-tivity [24]. Therefore, there is high hope that the Al- substituted BSZFO also exhibits low B -induced ferro-electricity even near room temperature.In summary, we have shown that Al-substitution intohexaferrites provides an unprecedented opportunity todecrease effectively the critical magnetic field for inducingferroelectricity as well as to obtain gigantic low field mag-netoelectricity through the control of orbital moment.Upon optimization of spin ordering temperature and elec-trical resistivity, the helimagnetic insulators may providea pathway to the realization of novel magnetoelectric de-vices at room temperature under low magnetic fields.This work is supported by NRL (M10600000238),GPP (K20702020014-07E0200-01410), and Basic Sci-ence Research (2009-0083512) programs. JHP is sup-ported by National Creative Initiative Center and WCUprogram (R31-2008-000-10059-0) and JHC by KOSEF(20090059529) and BAERI programs. SHC is supportedby Seoul R&BD (10543) and Seoul Science Fellowship. [1] T. Kimura et al. , Nature (London) , 55 (2003).[2] N. Hur et al. , Nature (London) , 392 (2004).[3] S.-W. Cheong and M. Mostovoy, Nature Mater. , 13(2007).[4] R. Ramesh and N. A. Spaldin, Nature Mater. , 21(2007).[5] C.-W. Nan et al. , J. Appl. Phys. , 031101 (2008).[6] H. Katsura, N. Nagaosa, and A. V. Balatsky, Phys. Rev.Lett. , 057205 (2005).[7] M. Mostovoy, Phys. Rev. Lett. , 067601 (2006).[8] I. A. Sergienko and E. Dagotto, Phys. Rev. B , 094434(2006).[9] M. Kenzelmann et al. , Phys. Rev. Lett. , 087206(2005).[10] L. C. Chapon et al. , Phys. Rev. Lett. , 177402 (2004).[11] T. Kimura et al. , Nature Mater. , 291 (2008).[12] T. Kimura, G. Lawes, and A. P. Ramirez, Phys. Rev.Lett. , 137201 (2005).[13] W. Eerensiein et al. , Nature Mater. , 348 (2007).[14] S. Dong, J. Zhai, J. Li, and D. Viehland, Appl. Phys.Lett. , 252904 (2006).[15] S. Ishiwata et al. , Science , 1643 (2008).[16] K. Taniguchi et al. , Appl. Phys. Express , 031301(2008).[17] N. Momozawa and Y. Yamaguchi, J. Phys. Soc. Jpn. ,1292 (1993).[18] H. Schmid, in Introduction to Complex Mediums for Op-tic and Electromagnetics , ed. by W. S. Weiglhofer and A.Lakhtakia, (SPIE Press, Bellingham, 2003), pp.167.[19] T. M. Perekalina et al. , Sov. Phys. JETP , 266 (1967).[20] W.-S. Noh et al. , to be published.[21] J.-Y. Kim, T. Y. Koo, and J.-H. Park, Phys. Rev. Lett. , 047205 (2006).[22] For x > P already exists even at zero B , resultingin less change of P with B , and P max decreases system-atically, both of which can explain the decrease of MEsuceptibility.[23] S. Ishiwata et al. , Phys. Rev. B , 180408(R) (2009).[24] Y. S. Chai et al. , New. J. Phys.11