Research article

Received: 10 December 2011 Revised: 28 March 2012 Accepted: 4 April 2012 Published online in Wiley Online Library

(wileyonlinelibrary.com) DOI 10.1002/jrs.4100

Raman scattering studies of spin-waves inhexagonal BaFe12O19

Nguyen Thi Minh Hien,a Kiok Han,a Xiang-Bai Chen,b* Jung Chul Surc

and In-Sang Yanga*

We present the results of polarized Raman spectroscopy of hexagonal BaFe12O19 single crystal. The spectra, recorded from 200to 800 cm–1 and 1100 to 1700 cm–1 in the 20–250K temperature range, are analyzed on the basis of both crystal vibrations andspin-waves. In the low wavenumber range, the Γ-point phonons are observed. In the high wavenumber range, phononmixings are observed; more interestingly, four modes of spin-waves are identified in hexagonal BaFe12O19. Both have notbeen studied previously. Our analyses of the spin-waves provide an optical method for quantitatively estimating the spinexchange interactions in hexagonal BaFe12O19. The four strong exchange integrals are found to have the values of Jce = 1.31meV, Jae = 1.36meV, Jcd = 1.46meV, and Jbd = 1.71meV. Our results also indicate that at ~200 and ~80K, there would beadditional spin-ordering transitions in hexagonal BaFe12O19. Copyright © 2012 John Wiley & Sons, Ltd.

Keywords: hexagonal BaFe12O19; Raman scattering; spin-wave; exchange integral; spin-order transition

* Correspondence to: Xiang-Bai Chen, Department of Nano Science & MechanicalEngineering and Nanotechnology Research Center, Konkuk University, Chungju380-701, Korea. E-mail: xchen@kku.ac.krIn-SangYang, Department of Physics and Division of Nano-Sciences, EwhaWomans University, Seoul 120-750, Korea. E-mail: yang@ewha.ac.kr

a Department of Physics and Division of Nano-Sciences, Ewha Womans University,Seoul 120-750, Korea

b Department of Nano Science & Mechanical Engineering and NanotechnologyResearch Center, Konkuk University, Chungju 380-701, Korea

c Division of Microelectronics and Display Technology, Wonkwang University,Iksan 570-749, Korea

Introduction

Hexagonal barium ferrite, BaFe12O19, has attracted much researchinterest over the past 50 years because of its applications in perma-nent magnets, microwave devices, and recording media.[1–6]

Hexagonal BaFe12O19 has a very complex crystal structure (spacegroup P63/mmc), with 64 ions per unit cell on 11 different symmetrysites.[7] Hexagonal BaFe12O19 also has a highly complex exchange-coupled magnetic structure. Complexity comes from the large num-ber of magnetic ions in the base, the number of crystallographicallydistinct magnetic ion sites, and the result of exchange integralscoupling the ions on various sublattices.[7]

Raman scattering spectroscopy has been widely used to studythe crystal lattice vibrations. Group theory predicts that thereare 42 Raman active Γ-point phonon modes (11A1g + 14E1g + 17E2g) in hexagonal BaFe12O19. The Raman studies of the Γ-pointphonon modes of hexagonal BaFe12O19 have been well investi-gated.[4,8–10] However, in the reported Raman studies of hexago-nal BaFe12O19, only the Γ-point phonon modes in the spectrarange from 150 to 800 cm–1 were reported. In this article, we pres-ent a Raman study of the spin-waves and the mixing of first-orderphonon modes in hexagonal BaFe12O19. Surprisingly, experimen-tal observation of spin-waves in hexagonal BaFe12O19 has notbeen reported, although hexagonal BaFe12O19 has been knownas a permanent magnet for half a century, and the theoreticalcalculation of the spin-wave spectra for hexagonal BaFe12O19 hasbeen reported two decades ago by Marshall and Sokoloff.[7] Fourmodes of spin-waves of hexagonal BaFe12O19 are first observed inthis study, which indicate four strong antiferromagnetic exchangeinteractions. In addition, the analyses of spin-waves provide anoptical method for quantitatively estimating these four spinexchange integrals in hexagonal BaFe12O19.

Experiment

The hexagonal BaFe12O19 single crystal was grown in a platinumcrucible using a high-temperature furnace. The primary reagents

J. Raman Spectrosc. (2012)

of BaCO3 and Fe2O3 with the respective mol% according to thecomposition were used for the growth. The blended powderwas filled in a platinum crucible and calcined with the followingsteps: (1) quickly heated from room temperature to 1390 �C withincrease of 200 �C/h, (2) slowly heated to 1420 �C with 5 �C/h, (3)very slowly heated to 1450 �C with 2 �C/h, (4) kept at 1450 �C for1 h, (5) very slowly cooled to 1340 �C with 0.6 �C/h, and (6) quicklycooled to room temperature with 100 �C/h. The obtained crystalwas slowly separated by leaching in hot dilute nitric acid fromthe platinum crucible.

Polarized Raman scattering spectra of the sample were obtainedin a backscattering configuration with a Jobin Yvon T64000 triplespectrometer in the single mode. The proporgation of laser beamis along the c-axis of BaFe12O19 single crystal sample, i.e. the polar-ized Raman experiments were performed under z xxð Þ�z and z yxð Þ�zconfigurations. A 671nm laser was used as the excitation sourcewith a laser power of~ 1mW on the surface of the sample. Thebeam diameter on the sample was ~50mm. The laser beam powerdensity was low enough to avoid laser heating. A long-pass filterwas used so that the spectrum at lower wavenumber below200 cm–1 was blocked. The scattered signal was detected by aliquid-nitrogen-cooled CCD detector. All the spectra have beencalibrated in the wavenumber by using a standard neon source.

Copyright © 2012 John Wiley & Sons, Ltd.

N. T. M. Hien et al.

The sample was mounted in a helium closed cycle cryostat, and thesample temperature was varied from 20 to 250 K.

Results and discussion

Figure 1 shows the polarized Raman spectra of the hexagonalBaFe12O19 single crystal sample in the range of 200–800 cm–1

obtained at 20 K under the z xxð Þ�z and z yxð Þ�z configurations. Ascan be seen in Fig. 1, Raman spectra in the parallel and thecross-polarization show distinctly different characters. The polar-ization dependence of the Raman scattering in the spectra range

Figure 1. Polarized Raman spectra of hexagonal BaFe12O19 single crystalsample in the range of 200–800 cm–1 obtained at 20 K under the z xxð Þ�zand z yxð Þ�z configurations. The black spectrum at bottom is the back-ground (BG) signal.

Table 1. Assignments of observed Raman peaks of hexagonal BaFe12O19

Type of Raman peaks Present work, 20 K wavenumber

Γ-point phonons 321

343

392

422

473

517

536

612

624

692

728

Combination of first-order phonons 1185

1272

1310

1338

1360

1390

1467

1165

Spin-waves 1260

1310

1400

1640

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from 150 to 800 cm–1 has been investigated by Kreisel et al.[4] Inthe z xxð Þ�z configuration, both A1g and E2g phonon modes areallowed, whereas in the z yxð Þ�z configuration, only E2g phononmodes are allowed. The assignment of our observed phononmodes compared with those reported by Kreisel et al. is listedin Table 1. In the table, only the phonons which are clearlyobserved are presented.

The previous Raman studies of hexagonal BaFe12O19 investi-gated only the Γ-point phonon modes in the low wavenumberrange from 150 to 800 cm–1.[4,8–10] In this article, we study thespin-waves and the mixing of first-order phonon modes inhexagonal BaFe12O19 by investigating the Raman spectra in thehigh wavenumber range from 1100 to 1700 cm–1. Figure 2 shows

(cm–1) Ref.[4] 100 K wavenumber (cm–1) Assignments

319 A1g

340 E2g388 E2g422 E2g473 A1g

513 A1g

533 E2g607 E2g620 A1g

688 A1g

722 A1g

2 A1g (624)

A1g (692) + A1g (624)

A1g (728) + E2g (612)

A1g (728) + A1g (624)

2 A1g (692)

A1g (728) + A1g (692)

2 A1g (728)

2 E2g (612)

JceJaeJcdJbd

1200 1300 1400 1500 1600 1700

Z(XX)Z-Z(YX)Z-

1165

1640

14001310

1260

1467139013601338

1310

1272

1185

Ram

an In

ten

sity

Wavenumber/cm-1

Figure 2. Polarized Raman spectra of hexagonal BaFe12O19 single crystalsample in the range of 1100–1700 cm–1 obtained at 20 K under the z xxð Þ�zand z yxð Þ�z configurations.

2 John Wiley & Sons, Ltd. J. Raman Spectrosc. (2012)

Raman spectroscopy of hexagonal BaFe12O19

the polarized Raman spectra of the hexagonal BaFe12O19 singlecrystal sample in the range of 1100–1700 cm–1 obtained at 20 Kunder the z xxð Þ�z and z yxð Þ�z configurations. The Raman spectrain the high wavenumber range also show distinctly differentcharacters between the parallel and cross-polarizations, whichcan be attributed to the differences of their phonon and magnonorigins, respectively.

In the parallel polarization, seven Raman peaks can be identi-fied, i.e. at ~1185, 1272, 1310, 1338, 1360, 1390, and 1467 cm–1.Considering all the possible combinations of the first-orderphonon modes, we have assigned the origins of these sevenphononic Raman peaks, the results of which are presented inTable 1 (high wavenumber optical phonons have relatively flatdispersion curves; thus, the wavenumber of second-orderphonons can be simply estimated by adding the wavenumberof Γ-point phonons). Figure 1 shows that the A1g at 692 cm–1

has the strongest intensity and that the A1g at 624 and 728 cm–

1 has weaker and similar intensity. These three phonons havesimilar linewidth. Figure 2 shows that the second order(1467 cm–1) of A1g (728 cm

–1) has a strong intensity and a narrowlinewidth, whereas the second order (1185 cm–1) of A1g (624 cm

–

1) has very weak intensity and broad linewidth. Therefore, our as-signment indicates that the high wavenumber A1g phonon at728 cm–1 would have flatter phonon dispersion curve than lowwavenumber A1g phonons. The phonon dispersion curves of hex-agonal BaFe12O19 were calculated on the basis of the rigid-ionmodel by Marshall and Sokoloff.[11] Their calculation predictedthat for the phonon spectrum with k directed along the c-axisof the crystal, the high wavenumber phonon dispersion curveis flatter than the low energy wavenumber phonon, consistentwith our results.

In the cross-polarization of Fig. 2, five Raman peaks can beidentified, i.e. at ~1165, 1260, 1310, 1400, and 1640 cm–1. How-ever, when considering all the possible combinations involvingthe first-order E2g phonon modes, only the peak at 1165 cm–1

could be related with the second order of E2g at 612 cm–1. Asshown in Fig. 2, the second-order peak at 1165 cm–1 has veryweak intensity and relatively broad linewidth, similar features

300 450 600 750

Ram

an In

ten

sity

Wavenum

Figure 3. Temperature-dependent (20–250 K) Raman spectra of hexagonal Bfive representative spectra are shown.

J. Raman Spectrosc. (2012) Copyright © 2012 John Wiley

as the second-order peak at 1185 cm–1 in the parallel configu-ration. This is consistent with the dispersion curve calculationsthat their first-order phonon modes do not have flat dispersioncurves. Therefore, the second-order phonons would not belocated at exactly twice the wavenumbers of the first-orderphonons, and their intensity would be weak, and the linewidthwould be broad.

To understand the origins of the other four peaks, the tem-perature-dependent Raman scattering in the crossed configura-tion was investigated; the results are presented in Fig. 3. For aclear observation on the temperature dependence of thesepeaks, the temperature dependence of integrated intensitywas plotted, as shown in Fig. 4. The integrated intensity wasobtained by first normalizing all the spectra using the intensityof the phonon peak at 536 cm–1 as the reference and thentaking the integrated intensity in the range of 1200–1500and 1580–1680 cm–1 for the z yxð Þ�z configurations. To clearlyidentify the different characters between the parallel andcross-configuration Raman peaks, the temperature dependenceof Raman spectra in the parallel configuration was also investi-gated. The temperature dependence of the integrated intensityin the range of 1150–1530 cm–1 of the z yxð Þ�z configurations isplotted in Fig. 4.

Magnetic Raman scattering is typically much more sensitiveto temperature effect than is vibrational scattering. Thetemperature dependent results show that in comparison withthe phononic peaks in the parallel configuration, the integratedintensities in the cross-configuration show a significantly fasterintensity change – an abrupt increase as the temperature islowered below ~200 K. This anomalous behavior of theintegrated intensity in the range of 1200–1500 and 1580–1680 cm–1 suggests that the four peaks at 1260, 1310, 1400,and 1640 cm–1 in the cross-configuration have the same originand are originated from magnetic ordering of hexagonalBaFe12O19.

Hexagonal BaFe12O19 has a highly complex magnetic structure.The hexagonal unit cell of BaFe12O19 contains two formula units.Only the Fe3+ has a magnetic moment, each with spin 5/2. These

1200 1350 1500 1650

ber/cm-1

aFe12O19 single crystal sample obtained in the z yxð Þ�z configurations. Only

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0 50 100 150 200 250 0 50 100 150 200 250

Inte

gra

ted

Inte

nsi

ty

Temperature/K

Figure 4. Temperature dependence of the integrated intensities of the magnon peaks (the ranges of 1200–1500 and 1580–1680 cm–1) in the z yxð Þ�zconfigurations (square shape) and the phonon peaks (the range of 1150–1530 cm–1) in the z xxð Þ�z configurations (triangle shape).

N. T. M. Hien et al.

24 ions are differentiated by five magnetically nonequivalentsites, which mean there are five magnetic sublattices (Table 1of Ref.[7] for the magnetic ion locations in a unit cell ofBaFe12O19). The 24 magnetic ions would have a possibility of 15exchange integrals. This number is reduced to seven by consider-ing only the nearest neighbor interactions. These seven nearest-neighbor integrals are Jbd, Jec, Jcd, Jcb, Jae, Jcc, and Jdd.

[7] Thereare two factors which weaken the superexchange interaction:distance between the magnetic ions and the angle formed bythe ions and the intervening oxygen (maximum value at 180�

and minimum for 90�).[12] Using these criteria to isolate thedominant exchange integrals, the seven integrals would reduceto just four: Jbd, Jec, Jcd, and Jae.

[7] All these four integrals are an-tiparallel exchange interactions. By applying the Weiss molecularfield (WMF) model including single-ion anisotropy to fit thesublattice magnetizations, Marshall and Sokoloff calculated thatJae = Jce = 14.6 K (1.26meV), Jcd = 15.5 K (1.34meV), and Jbd = 21.9K (1.89meV) or proportionalities of 1 : 1 : 1.06 : 1.5.[7]

The wavenumber ratios of the four peaks at 1260, 1310, 1400,and 1640 cm–1 are 1.00 : 1.03 : 1.11 : 1.30, which is close to theproportionalities of the four exchange integrals Jae, Jce, Jcd, andJbd; further supporting that these four peaks would have mag-netic origins. For attiferromagnetic spin ordering, two-magnonRaman scattering is typically much stronger than one-magnonscattering.[13] Thus, these four peaks at 1260, 1310, 1400, and1640 cm–1 can be assigned to the two-magnon scatteringscorrelated with the exchange integrals of Jce, Jae, Jcd, and Jbd,respectively (the distance between A–E Fe ions is slightly smallerthan that between C–E Fe ions; thus, we assign 1260 cm–1 to Jceand 1310 cm–1 to Jae, although the Jce and Jae values calculatedin Ref.[7] are the same).The spin-wave spectra can be estimated from the ion anisot-

ropy Hamiltonian model. For a system of interacting magneticmoments that includes exchange and single-ion anisotropy, theHamiltonian is[7]

H ¼ �X

i;j;a;b

Jja;ib!Sja�

!Sib �

X

i;a

Dia Szia� �2

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Indices i, j label the unit cells, and a, b label the magnetic ions inthe cell. Jja,ib are the exchange integrals, and Dia are the single-ionanisotropy constants. Unlike WMF approximation, which neededthe number of nearest neighbors of a magnetic ion only, theabove model also takes into account the relative positions ofthe ions. The calculated spin-wave spectra for hexagonalBaFe12O19 were shown in Fig. 3 of Ref.[7] Our experimental resultsshow that the magnon peaks have relatively high energy andnarrow linewidth. Thus, these magnon peaks would be correlatedwith optical magnon branches with flat spin-wave dispersioncurves. Figure 3 of Ref.[7] showed that the flat dispersion curvehigh-energy one-magnon scattering would have energy of~60 J. Thus, the two-magnon peaks at 1260, 1310, 1400, and1640 cm–1 would have energy of ~120 Jce, ~120 Jae, ~120 Jcd,and ~120Jbd, respectively. Therefore, the Raman measurementsindicate that Jce = 1.31meV, Jae = 1.36meV, Jcd = 1.46meV, andJbd = 1.71meV, which are consistent with the theoretical valuescalculated by Marshall and Sokoloff.[7]

Figure 4 indicates that the magnon scattering intensityenhances rapidly below ~200 K, whereas above this temperature,the magnon scattering intensity is weakly affected by the tem-perature and the linewidth gets significantly broader. In addition,at ~80 K, the magnon scattering has a rapid intensity increase.For the magnetic ordering of ferrites, there are several possibili-ties,[14] Gorter[15] predicted a ferrimagnetic ordering picture forhexagonal BaFe12O19.

[16,17] It had been reported that hexagonalBaFe12O19 has a high Curie temperature (Néel temperature)above ~700 K.[7,18,19] Our spin-waves study indicates that therewould be additional spin-ordering transitions at ~200 and ~80 Kin BaFe12O19. Above 200 K, the three two-magnon peaks at1260, 1310, and 1400 cm–1 merge into a very broad peak, and thisbroad peak persists at temperatures above 200 K (Fig. 3); below80 K, all the two-magnon peaks have rapid intensity increases.Therefore, above 200 K, there would be strong spin fluctuation,and below 80 K, the spins would become highly ordered inhexagonal BaFe12O19.

In a Mössbauer study of hexagonal BaFe12O19,[20] it was

shown that the quadrupole splitting of the subspectrum

2 John Wiley & Sons, Ltd. J. Raman Spectrosc. (2012)

Raman spectroscopy of hexagonal BaFe12O19

corresponding to the bipyramidal lattice site started to increasebelow ~200 K, and below ~80 K, the splitting became moresignificant. It was also reported that the anisotropy constantof hexagonal BaFe12O19 has a different temperature behaviorbelow ~200 K.[18] In addition, the analyses of spin-phonon cou-pling in hexagonal BaFe12O19 show that the phonon modeshave significantly softening below ~80 K; this study will bepresented elsewhere. Furthermore, in multiferroic BiFeO3, whichhas a Néel temperature of ~643 K, previous Raman studiessuggested that at ~200 and ~140 K, there would be additionalspin reorientation transitions.[21,22] These results are in goodagreement with our Raman study that there would be addi-tional spin-ordering transitions at ~200 and ~80 K inhexagonal BaFe12O19. We suggest that for Fe-ion spin-orderingnetwork, it would be strongly affected by the temperature effect.Below Curie temperature (Néel temperature), there could beadditional spin-ordering transitions. Raman scattering spectroscopywould offer a unique opportunity as a sensitive probe for the spindynamics and studying the effect of magnetic ordering.

Conclusion

In conclusion, the temperature-dependent polarized Ramanscattering of hexagonal BaFe12O19 single crystal was studied.Four modes of spin-waves of hexagonal BaFe12O19 were firstobserved, which are correlated with the exchange integrals ofJce, Jae, Jcd, and Jbd. An optical method for quantitatively estimat-ing these exchange integrals was presented, and Jce = 1.31meV,Jae = 1.36meV, Jcd = 1.46meV, and Jbd = 1.71meV were obtainedby this method. The Raman results also suggest that there isa magnetic transition at ~200 K, above which strong spin fluc-tuations persist; and below 80 K, the spins would becomehighly ordered in hexagonal BaFe12O19.

J. Raman Spectrosc. (2012) Copyright © 2012 John Wiley

Acknowledgements

X. B. Chen acknowledges the National Research Foundation ofKorea Grant No. 2010-0022857. I. S. Yang acknowledges thefinancial support by the Ministry of Education, Science andTechnology of Korea (2011-0028736).

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