Observation of magnons by light scattering in epitaxial CoFe/Mn/CoFe trilayersS. Tschopp, G. Robins, R. L. Stamps, R. Sooryakumar, M. E. Filipkowski, C. J. Gutierrez, and G. A. Prinz Citation: Journal of Applied Physics 81, 3785 (1997); doi: 10.1063/1.364769 View online: http://dx.doi.org/10.1063/1.364769 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/81/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetic anisotropy and spin wave relaxation in CoFe/PtMn/CoFe trilayer films J. Appl. Phys. 105, 073910 (2009); 10.1063/1.3093927 Giant magnetoresistance in an epitaxial Ni Mn Sb ∕ Cu ∕ Co Fe multilayer Appl. Phys. Lett. 86, 142503 (2005); 10.1063/1.1897828 Proximity effects at epitaxial Co/FeMn thin film systems (invited) J. Appl. Phys. 93, 6504 (2003); 10.1063/1.1555319 Spin-wave modes and line broadening in strongly coupled epitaxial Fe/Al/Fe and Fe/Si/Fe trilayers observed byBrillouin light scattering J. Appl. Phys. 93, 3427 (2003); 10.1063/1.1554758 Brillouin light scattering investigations of exchange biased (110)-oriented NiFe/FeMn bilayers J. Appl. Phys. 83, 2863 (1998); 10.1063/1.367049

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Observation of magnons by light scattering in epitaxial CoFe/Mn/CoFetrilayers

S. Tschopp, G. Robins, R. L. Stamps, and R. SooryakumarDepartment of Physics, The Ohio State University, Columbus, Ohio 43210

M. E. FilipkowskiDepartment of Physics, University of Arkansas, Fayetteville, Arkansas 72701

C. J. GutierrezDepartment of Physics, Southwest Texas State University, San Marcos, Texas 78666

G. A. PrinzNaval Research Laboratory, Washington, DC 20375

We report on Brillouin scattering measurements on a CoFe/Mn/CoFe trilayer film characterized byunusually large biquadratic coupling. The magnetic field dependence of the exchange coupled in-and out-of-phase magnons as well as their in-plane directional dependence are determined. Thesaturation magnetization of the trilayer was measured independently through superconductingquantum interference device magnetometry. The spin wave data is well represented by ageneralization of the model that takes into account the antiferromagnetic order in the Mn layer.© 1997 American Institute of Physics.@S0021-8979~97!44608-X#

The CoFe/Mn/CoFe trilayer structures are among thefirst systems to exhibit very strong near 90° or biquadraticcoupling between the magnetizationsM1 and M2 of theCoFe layers.1 Using magnetization and magnetic resonancedata Filipkowskiet al. suggested1 that the coupling acrossMn in this system, which reveal very weak 180° or bilinearcoupling, may be described by a higher order biquadraticterm that includes contributions from the internal antiferro-magnetic ordering of the Mn. The precise model of the bi-quadratic coupling was suggested by Slonczewski2 and de-pends on the thickness variations of the Mn spacer. Thisform of the biquadratic coupling is attributed to fluctuationsthat arise from competition between areas of differing inter-layer thickness that deform the quasiantiferromagnetic orderwithin the interlayer to align with the ordered moments at theFeCo interface. Such interlayer coupling is analogous to theM13M2 form of the biquadratic coupling observed inFe/Cr/Fe3,4 but described by the following distinctly differentnontrigonometric functional form:

FC5C1~f12f2!21C2~f12f22p!2, ~1!

whereC1 andC2 are the ferromagnetic and antiferromag-netic coupling constants andFi is the in-plane orientationangle ofM i .

2

In this article, we discuss the results of Brillouin lightscattering from a CoFe/Mn/CoFe structure with strong cou-pling between the magnetic layers. The frequencies of thelong wavelength spin waves yield, in analogy to coupledoscillators, two exchange modes corresponding to acousticand optic magnons with characteristic frequenciesvac andvop. The optic mode~O! in whichM1 andM2 precess 180°out-of-phase is especially interesting since its frequency de-pends on the strength and sign of the bilinear and biquadraticcoupling parameters with~vac2vop! providing a measure ofthe interlayer coupling strength. The magnetic field depen-dence, and hence the effects of tuning the relative orienta-tions betweenM1 andM2, on the magnon frequenciesvac,

vop are readily determined from these measurements. In ad-dition, magnetic anisotropies are also revealed through mea-surements performed along specific crystallographic direc-tions thus providing for a complete description of thecoupling strengths and the anisotropies.

The @001# oriented trilayer was grown by molecularbeam epitaxy~MBE! methods as described elsewhere.1,5 TheFe0.25Co0.75 alloy layers had atotal thickness of 168 Å whilethe Mn spacer thickness was 7.6 Å. The low field supercon-ducting quantum interference device~SQUID! magnetizationdata shows apparent easy^100& and hard̂ 110& behavior forthe trilayer and yield a value of 1.53103 emu/cc for thesaturation magnetization. We note, as discussed in Ref. 1,that these apparent axes of the trilayer differ from the easyand hard axes of the individual CoFe films. The Brillouinmeasurements were performed at room temperature utilizingup to 100 mW ofp-polarizedl5514.5 nm laser light at 45°angle of incidence.6 Thes-polarized back-scattered light wasanalyzed with a six-pass tandem Fabry–Perot interferometer.The external magnetic field~H0! was applied in the filmplane and oriented such that the plane of incidence was al-ways normal to the direction ofH0.

The measured spin wave spectra as a function of mag-netic field with in plane wavevectorq along the@110# and@001# directions are shown in Figs. 1 and 2. The strongestfeature~A! is the acoustic magnon whereM1 andM2 precessin phase and display a characteristic strong Brillouin inten-sity. With increasingH0, vac increases steadily. The weakerpeak labeled O is the corresponding out-of-phase mode and,due to canceling contributions to the scattered intensity fromeach layer, is much weaker. With increasing applied field,the two modes approach and cross each other around 8.5kOe. Reflecting the magnetic anisotropies in the film,vacandvop each differ in frequency along the@110# and@001# direc-tions. The corresponding spin wave frequencies are plottedas a function ofH0 in Fig. 3. The solid lines are a fit to thefield dependent data based on the analysis discussed below.

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Spin wave frequencies were calculated in a long wave-length limit suitable for comparison to Brillouin light scat-tering data. The wavelength of the scattered light is on theorder of 1025 cm which means that contributions from dipo-lar fields are significant for the lowest frequency observedmodes. The magnetic film thicknesses are thin enough sothat the exchange modes are shifted well above the surfacemode frequency. Since the acoustic and optic spin waves areformed by surface spin waves on the individual films andtherefore primarily magnetostatic in character, to good ap-proximation the contribution from intralayer exchange canbe neglected in calculating the acoustic and optic mode fre-quencies.

A theory for the acoustic and optic modes in the pres-ence of bilinear interfilm exchange coupling is given in Ref.7. Our calculations are based on this formalism except thatwe used an interfilm energy related to Eq.~1! in place of thebilinear exchange term. In the present formulation, the cal-culation consists of solving the equations of motion for themagnetization given by

dM1 /dt5gM13H1

~2!dM2 /dt5gM23H2 .

In Eq. ~2!, g is the gyromagnetic ratio andM1~2!~x,t! is theinstantaneous magnetization for film 1~2!. The effectivefields are described byH1~2!. The effective fields contain thestatic applied fieldH0, fourfold anisotropyK1, an in-planeanisotropyKu , an out-of-plane anisotropyK and the inter-film exchange coupling terms. They also include inter- and

FIG. 1. Brillouin spectra from CoFe/Mn/CoFe@001# oriented trilayer. Thethickness of the Mn spacer and alloy layer are, respectively, 7.6 and 84 Å.Peaks A and O are the acoustic and optic exchange modes. The magnonwavevectorq lies parallel to the film surface along@110# and was normal toan external applied in-plane fieldH0.

FIG. 2. Brillouin spectra from CoFe/Mn/CoFe@001# oriented trilayer. Thethickness of the Mn spacer and alloy layer are, respectively, 7.6 and 84 Å.Peaks A and O are the acoustic and optic exchange modes. The magnonwavevectorq lies parallel to the film surface along@010# and was normal toan external applied in-plane fieldH0.

FIG. 3. Summary of the field dependence of the acoustic and optic magnonfrequencies. The triangles~circles! correspond to the data associated withthe magnon wavevectorq parallel to @010# ~@110#!. Note the different be-havior of the optic~high frequency! and acoustic~low frequency! modeswith increasing applied field. The solid lines are fits based on the calcula-tion.

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intrafilm demagnetizing fields that depend on wavevector,CoFe film thickness, and the Mn film thickness. Except foran average effective biquadratic coupling, roughness at theinterface is assumed to have a negligible effect on the fre-quencies and the time dependent magnetization is expandedin terms of plane waves traveling parallel to the interfacewith a time dependence given by exp~2ivt!.

While setting up the equations, the equilibrium configu-ration is first found by minimizing the corresponding totalstatic energy. The equilibrium directions for the magnetiza-tions are found by minimizing the corresponding total staticenergy. The equilibrium directions for the magnetization arethen used to write equations of motion from Eqs.~2! and~3!.The resulting equations of motion are linearized, written asfour coupled equations, and solved for the frequencyv. Fi-nally, we note that the problem is most easily solved inspherical coordinates.

In order to calculate the spin wave frequencies, Eq.~1!must be generalized by introducing the instantaneous anglea. Herea is the instantaneous angle between the magnetiza-tions of the two films given by arc cos~M1•M2/uM1uuM2u!.This form reduces to Eq.~1! in the limit of in-plane orienta-tion of the magnetization@a→~f12f2!#.

The use of the instantaneous anglea rather than~f12f2! is very important. This angle is distributed acrossthe antiferromagnetic layers and thereby involves the ex-change energy of the antiferromagnet in the effective cou-pling between the two ferromagnetic films. Whilea mea-sures the actual angular deviation of the two time dependentmagnetizations, the difference~f12f2! measures only theprojection of this difference in the plane of the film. This isappropriate for finding the static configuration but is clearlyinadequate to describe the dynamic behavior.

The main effect of making this change to~f12f2! in Eq.~1! is to introduce a field dependence in the exchange split-ting between the acoustic and optic modes. We see this inFig. 3 where the data is fit using parametersC1 and C2

equal to 0.95 and 1.07 erg/cm2 values that were deducedfrom magnetization data in Ref. 1. The nearly equal valuesof C1 andC2 in this model imply the existence of equalnumber of parallel and antiparallel coupling regions. Thevalue ofM51.53103 emu/cm3 as derived from magnetiza-tion measurements andK15223105 erg/cm3 as determined

from bulk FeCo films8 were utilized.Ku was taken to be zerosince there was no evidence for uniaxial contributions to theanisotropy and thusKu/M is negligible. Results are shownfor the field aligned in the hard and easy directions. The solidlines in Fig. 3 are from the calculation, and they agree rea-sonably well with the data.

We note that the spin wave theory described above as-sumes uniformly magnetized thin ferromagnetic films andonly bulk anisotropies. The discrepancies between the theoryand data may be due to anisotropies introduced by the inter-face or exchange coupling to the Mn. Another cause may bea twist in the magnetization of the FeCo layers as the outer-most spins try to align with the magnetic field.

In summary, we have measured the field and directionaldependence of the spin waves in an exchange coupled CoFe/Mn/CoFe trilayer through Brillouin light scattering methods.The results were described within a framework that considersthe competition due to interlayer thickness fluctuations thatdeforms the quasiantiferromagnetic order within the Mnlayer. The different rates at which the acoustic and opticmodes increase with field illustrates the importance of re-placing ~f12f2! with a in Eq. ~1!. The anglea involvesexchange coupling to the antiferromagnet for out-of-planefluctuations whereas Eq.~1! describes only contributions viain-plane contributions.

Acknowledgments:Work at Ohio State University wassupported by the National Science Foundation, while that atthe Naval Research Laboratory by the Office of Naval Re-search.

1M. E. Filipkowski, J. J. Krebs, G. A. Prinz, and C. J. Gutierrez, Phys. Rev.Lett. 75, 1847~1995!.

2J. C. Slonczewski, J. Magn. Magn. Mater.150, 13 ~1995!.3M. Ruhrig, R. Schafer, A. Hubert, R. Mosler, J. A. Wolf, S. Demokritov,and P. Grunberg, Phys. Status Solidi A125, 635 ~1991!.

4U. Kobler, K. Wagner, R. Wiechers, A. Fuss, and W. Zinn, J. Magn.Magn. Mater.102, 236 ~1992!.

5J. J. Krebs, G. A. Prinz, M. E. Filipkowski, and C. J. Gutierrez, J. Appl.Phys.79, 4525~1996!.

6S. Subramanian, X. Liu, R. Stamps, R. Sooryakumar, and G. A. Prinz,Phys. Rev. B52, 10 194~1995!.

7R. Stamps, Phys. Rev. B49, 339 ~1994!.8C. J. Gutierrez, J. J. Krebs, and G. A. Prinz, Appl. Phys. Lett.61, 2476~1992!. Note that theK1 values listed need to be multiplied by a factor of105.

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