Ferromagnetic resonance studies of exchange coupled ultrathin Py/Cr/Py trilayers

Transcription

1 Ferromagnetic resonance studies of exchange coupled ultrathin Py/Cr/Py trilayers R. Topkaya, M. Erkovan, A. Öztürk, O. Öztürk, B. Akta, and M. Özdemir Citation: Journal of Applied Physics 18, 2391 (21) doi: 1.163/ View online: View Table of Contents: Published by the AIP Publishing Articles you may be interested in Ferromagnetic resonance investigation of Py/Cr multilayer system J. Appl. Phys. 11, 2398 (211) 1.163/ Influence of interlayer magnetostatic coupling on the ferromagnetic resonance properties of lithographically patterned ferromagnetic trilayers Appl. Phys. Lett. 92, (28) 1.163/ Ferromagnetic resonance study of the exchange bias field in Ni Fe Fe Mn Ni Fe trilayers J. Appl. Phys. 99, 8C18 (26) 1.163/ Magnetic force microscope study of antiferromagnet ferromagnet exchange coupled films J. Appl. Phys. 91, 6887 (22) 1.163/ Studies of coupled metallic magnetic thin-film trilayers J. Appl. Phys. 84, 958 (1998) 1.163/

2 JOURNAL OF APPLIED PHYSICS 18, Ferromagnetic resonance studies of exchange coupled ultrathin Py/Cr/Py trilayers R. Topkaya, 1,a M. Erkovan, 1 A. Öztürk, 1 O. Öztürk, 1 B. Aktaş, 1 and M. Özdemir 2 1 Department of Physics, Gebze Institute of Technology, P.K. 141, 414 Gebze-Kocaeli, Turkey 2 Department of Physics, Faculty of Science and Letters, Marmara University, Istanbul, Turkey Received 9 December 29 accepted 24 March 21 published online 26 July 21 Magnetic properties of ultrathin Py/Cr/Py trilayers have been investigated as a function of Cr spacer layer thickness by using ferromagnetic resonance FMR and vibrating sample magnetometer VSM techniques. The Cr spacer layer thickness was increased from 4 to 4 Å with 1 Å steps to determine the dependence of interlayer exchange coupling between ferromagnetic layers on the spacer layer thickness. Two strong and well resolved peaks were observed which correspond to a strong acoustic and weak optic modes of magnetization precession in the effective dc field due to the exciting external microwave field as the external dc field orientation comes close to the film normal. The separation of the two modes in the field axis depends on the thickness of Cr spacer layer. An interchange in the relative positions of the acoustic and optic modes has been observed for a particular thickness of Cr spacer layer as well. A computer program for magnetically exchange coupled N magnetic layers was written to simulate the experimental FMR spectra and to obtain the magnetic parameters of ultrathin Py/Cr/Py trilayers. FMR data have been analyzed from every aspect by using this program and interlayer exchange coupling constant was calculated for the prepared structures. It was found that the relative position of the peaks depends on the nature sign of the interlayer exchange coupling between ferromagnetic layers through Cr spacer layer. In Py/Cr/Py trilayers, strength of the interlayer exchange coupling constant oscillates and changes its sign with Cr spacer layer thickness with a period of about 11 Å. 21 American Institute of Physics. doi:1.163/ I. INTRODUCTION Magnetic multilayers consisting of ferromagnetic and nonmagnetic films have attracted considerable attention from researchers since the observation of giant magnetoresistance GMR, Refs. 1 and 2 and tunneling magnetoresistance TMR, Refs. 3 and 4 effects due to their applications in the magnetoelectronics such as data storage, information processing, etc. The GMR effect and spin transfer phenomenon are mainly determined by magnetic, electrical, and geometric properties of superstructured thin films. Interlayer exchange coupling between ferromagnetic layers across nonmagnetic spacer layer was discovered by Grünberg in Fe/Cr/Fe multilayer structures by means of light scattering from spin waves. 5 Parkin showed that interlayer exchange coupling oscillates in NiCo/Ru/NiCo multilayers. 6 Evaluating numerous experiments in Fe/TM/Fe and Co/TM/Co TM: transition metal multilayer structures, 7 9 Parkin concluded that the oscillation is a common property of all transitions metals. 1 Magnetic anisotropy and interlayer exchange coupling parameters play the most important role in GMR effect for sensor applications. The exchange interactions between ferromagnetic layers through a nonmagnetic metallic spacer must be antiferromagnetic in order to have significant GMR effect. Oscillatory interlayer exchange coupling between ferromagnetic layers was explained by Ruderman Kittel Kasuya Yosida interaction which is an indirect a Electronic mail: rtopkaya@gyte.edu.tr. exchange interaction of localized spins in magnetic layers mediated conducting electrons of nonmagnetic spacer. As the need for ultrahigh density data recording is increased, the size of the film used in spintronic applications has to be decreased. 14 Therefore, the accurate magnetic characterization is one of the major issues related to magnetic multilayer structures. So far numerous superlattice structures made of ferromagnetic and nonmagnetic metallic thin layers have been investigated by using different characterization techniques The ferromagnetic resonance FMR was proven to be one of the well established and useful techniques to investigate magnetic materials and to determine magnetic properties, such as magnetic anisotropy, magnetic moment, magnetic damping, etc. In this study, interlayer exchange coupling between ferromagnetic layers separated by nonmagnetic spacer has been studied by the conventional FMR and VSM techniques. Although there are many more useful magnetic multilayer structures for GMR applications, we have chosen Py/Cr/Py trilayers as prototype system in order to show the usefulness of FMR technique for investigating the magnetic properties as a function of nonmagnetic spacer thickness. Since Py is one of the magnetically soft materials with relatively weak magnetic damping, it gives quite well defined FMR signal with narrow resonance line. Thus, relatively sharp peaks for different FMR excitation modes allow us to deduce magnetic parameters by fitting the theoretical values to the experimental data /21/18 2 /2391/9/$3. 18, American Institute of Physics

3 Topkaya et al. J. Appl. Phys. 18, II. SAMPLE PREPARATION Cr 5 Å /Py 3 Å /Cr t /Py 2 Å /Cr 1 Å multilayers were grown onto naturally oxidized p-type single crystal Si 1 substrate by magnetron sputtering where t denotes the thickness of Cr spacer layer and ranges from 4 to 4 Å with 1 Å steps. The substrates were cleaned in ultrasonic bath by using methanol and ethanol consecutively before transferring into the UHV conditions. Then they were annealed up to 6 C for 3 min in UHV to minimize the surface deficiencies. The water-cooled 3 diameter target provides the thickness homogeneity. High purity Permalloy, Ni 8 Fe 2 Py and Cr targets were sputtered by rf 2 Watt and dc 3 W power supplies, respectively. These powers allow the slowest deposition rates with optimum pressure to get an ideal surface morphology. Although the base pressure in the preparation chamber is mbar, the pressure during the sputtering was mbar. The distance between the target and the substrate was 1 mm, allowing 1 Å deposition sensitivity by decreasing deposition rate. A water-cooled Matek TM 35 Quartz Crystal Monitor QCM was used to measure the film deposition rate in situ. At the beginning of film growth, the QCM was calibrated for Py and Cr deposition rates. The calibration of QCM thickness monitor was complemented by monitoring the attenuation of the substrate photoemission signal by XPS from the deposited films. For thickness determination we monitored the Si 2p attenuation as a function of chromium exposure by using XPS signals. Converting this to a Cr thickness, the electron mean free path was calculated by using the TPP formula developed by Tanuma, Powell, and Penn. 35 Since Py has two components, the Veeco Dektak 8 profile-meter was used to calibrate thickness additionally to confirm the results of the photoemission attenuation. The prepared trilayers were covered by a 1 Å Cr cap layer to prevent oxidation of trilayer structures. We have investigated the suitable thickness of magnetic layers to observe measurable exchange coupling between ferromagnetic layers through a metallic Cr spacer. The metallic films have polycrystalline structures. Small samples of mm 2 in lateral size were cut from the deposited films for the FMR measurements. III. EXPERIMENTAL RESULTS The FMR measurements were carried out by using a Bruker EMX model X-band electron spin resonance spectrometer at microwave frequency of 9.5 GHz. The measurements were carried out as a function of the angle of the external dc field with respect to the film normal at room temperature. The sample sketch, relative orientation of the equilibrium magnetization vector M, the applied dc magnetic field vector H, and the experimental coordinate system are shown in Fig. 1 a. The picture of the prepared trilayer structure is shown in Fig. 1 b. The magnetic field component of microwave is always kept perpendicular to the dc field during the sample rotation. The applied microwave field remains always in sample plane for conventional geometry and power is kept small enough to avoid saturation, as well. A x z M H M H 2Å Ni 8 Fe 2 Cr (x) 3Å Ni 8 Fe 2 (a) H M small modulation field of 1 khz was applied in parallel to the dc magnetic field in order to record the field derivative of absorption power. The magnetization measurements were performed by using VSM Quantum Design PPMS 9T at room temperature for both in plane geometry IPG field parallel to the sample plane and out of plane geometry OPG field perpendicular to the sample plane. FMR spectra are very sensitive to the relative orientation of the external dc field. The spectra also strongly depend on both ferromagnetic and nonmagnetic Cr spacer layer thickness. After a few quick trials it has been seen that the thicknesses and/or magnetic anisotropies of two ferromagnetic layers should be different from each other to observe the influence of exchange interactions on FMR spectra. Therefore, the thicknesses of bottom and upper Py layers were chosen as 2 Å and 3 Å, respectively. The samples were labeled as Sx, where x is the Cr spacer thickness in angstrom. Figure 2 shows two representative FMR spectra solid circle for the external field applied parallel and/or perpendicular to the Py 3 Å /Cr 7 Å /Py 2 Å trilayer. This figure also shows simulated spectra continuous lines obtained us- y 1Å Cr 2Å Ni 8Fe 2 Cr (x) 3Å Ni 8 Fe 2 5Å Cr Si (b) FIG. 1. a Relative orientations of the external dc magnetic field and magnetization vectors with respect to the sample plane, b A representative picture for Py 2 Å /Cr x /Py 3 Å trilayer films. Amplitude (arb. units) parallel geometry A 12 =.65 erg/cm 2 Experiment Simulation perpendicular geometry Magnetic Field (koe) FIG. 2. Experimental and simulated FMR spectra of Py 2 Å /Cr 7 Å / Py 3 Å trilayer film for the external field parallel and perpendicular to the sample plane.

4 Topkaya et al. J. Appl. Phys. 18, real(m )x1-8 real(m )x (a1) (a2) 3Å Py 2Å Py 3Å Py 2Å Py M 1 (b1) (b2) 3Å Py 2Å Py 3Å Py 2Å Py h H M 2 Acoustic Mode h H M 1 M2 Optic Mode H R (koe) H R (koe) Angle ( H ) Angle( H ) Acoustic mode of t Cr =1Å Optic mode of t Cr =1Å Acoustic mode of t Cr =4Å Optic mode of t Cr =4Å Simulation Amplitude (arb. units) 3Å Py/4Å Cr /2Å Py Experiment Simulation (a3) A 12 =.11 erg/cm Magnetic Field (koe) 3Å Py/1Å Cr /2Å Py Experiment Simulation (b3) A 12 =.85 erg/cm Magnetic Field (koe) FIG. 3. FMR curves for ferromagnetically on the left and antiferromagnetically on the right exchange coupled two samples. The real values of azimuth a1 and b1 and polar a2 and b2 components of ac magnetizations for each layer are given as a function of the external dc magnetic field to show relative phase of the dynamic components of the magnetization for the acoustical and the optical modes. The field-derivative FMR absorption curves for S4 and S1 are given in a3 and b3, respectively. ing the theoretical model described below. There are two excited FMR modes for OPG case. However when the field is applied parallel to the sample plane IPG, a single FMR mode takes place. The FMR spectra in Fig. 3 are two selected examples to show the effect of spacer thickness. The two well-resolved FMR modes were observed for both samples S4 and S1 at OPG case. As can be seen in the Fig. 3 a3, b3, the relative intensities of the two modes optic and acoustic modes are different from each other. The weaker mode named as optic mode appeared at lower field side of the strong mode main or acoustic mode for sample S4 shifts to higher field side for the sample S1. The angular variations of resonance fields for two different samples are given in Fig. 4. Theoretical resonance field values have been obtained by using the theoretical model described below. The resonance field values for both samples are almost same for a broad range of angle. However there are noticeable differences where the field is applied very close to the film normal, that is, the resonance field values for S4 is higher compared to that for S1 at OPG case. This means that the thicker spacer weakens the magnetic coupling between the ferromagnetic layers to allow more freedom for them to act as independent ultrathin magnetic layers. However, when the spacer becomes thinner, both layers are more strongly coupled and act almost as a single thicker layer. Since the uniaxial perpendicular anisotropy for thinner film is generally higher compared to that for thicker layer the resonance for OPG case is expected to occur at higher field for S4. The strong angular dependence is due to mainly shape anisotropy demagnetizing field. FIG. 4. Dependence of the experimental and simulated resonance field values as a function of H for the samples S4 and S1. The inset shows a small region of the curves for the field oriented very close to the film normal. Two strong and well resolved peaks were observed for the two main modes of FMR excitation as the field orientation comes close to the film normal for most of the Cr thickness except 11, 22, and 33 Å. However, these two modes come closer and overlap giving rise to a single peak as the field orients close to film plane. The relative position and separation of the two modes in the field axis depend on the thickness of the Cr spacer. An interchange in the relative positions of the strong and the weak modes for a particular thickness of Cr has been observed for OPG case. Figure 5 shows magnetic hysteresis curves of the samples S4 and S1 for both IPG and OPG cases. For OPG, the magnetization of the sample S1 saturates at about 7 koe that corresponds to the effective uniaxial anisotropy containing demagnetizing field and induced perpendicular axial anisotropy field. The sudden jump in the field range of 1 Oe for OPG case can be attributed to a small misorientation of the external field, since the projection of the field onto the sample plane can saturates magnetization. Thus, detection coils can detect a significant dc signal due to M saturated in M/M s 1-1 M/M s 1 t Cr =4Å easy axis (a) Magnetic Field (Oe) M/M s Magnetic Field (Oe) t Cr =1Å easy axis Magnetic Field (koe) t Cr =1Å hard axis FIG. 5. Hysteresis curve recorded at room temperature of sample S1 for the external magnetic field applied along the hard magnetization axis perpendicular to the film plane. The hysteresis curves for the easy directions in the film plane of the magnetizations for S4 and S1 are given in the insets a and b, respectively. (b)

5 Topkaya et al. J. Appl. Phys. 18, sample plane. For IPG case, the hysteresis curves have been given as insets in Fig. 5 for both samples S4 and S1. As seen in these insets, the magnetization saturates at very low field even below 1 Oe for the two samples. The hysteresis for sample S4 is wide, square-like at IPG case and its remanence is very close to saturation value. However for sample S1, the remanence value at IPG case is almost one fifth of saturation magnetization value and the magnetization gradually goes to saturation compared to that for S4. Similar behavior has been reported in the literature for Py/Cr/Py multilayers. 33 This could be considered as a sign for antiferromagnetic interactions between the ferromagnetic layers through the nonmagnetic spacer for the sample S1. IV. THEORETICAL MODEL The experimental data were analyzed for a system consisting of N magnetic layers with saturation magnetization M s and layer thickness t i by using magnetic energy density N t i M i,s H cos H cos i + sin H sin i cos H i i=1 N i + t i K eff cos i=1 E = 2 i N1 2. A i,i+1 cos i+1 cos i + sin i+1 sin i cos i i+1 i=1 N1 B i,i+1 cos i+1 cos i + sin i+1 sin i cos i i+1 i=1 1 Here i, H, i+1 and i, H, i+1 are, respectively, the polar and azimuth angles for magnetization vector M and external dc field vector H with respect to the film normal. The first term the first line is the usual Zeeman energy of the structure in the external dc field. The second term represents the magnetostatic energy due to demagnetizing field and any induced perpendicular anisotropy energy. Both of these energies qualitatively have the same angular dependence with respect to the film normal. That is why we used the same parameter, namely, K eff to describe these anisotropy energies. The last two terms come from indirect exchange interactions of ferromagnetic layers through nonmagnetic spacer via conduction electrons. The interlayer exchange coupling energy densities between nearest layers are determined by bilinear A i,i+1 and biquadratic B i,i+1 coupling constants. A i,i+1 can be either positive or negative depending on ferromagnetic or antiferromagnetic interactions, respectively. The parallel and antiparallel perpendicular alignments of magnetizations of neighboring layers are energetically favorable for a positive negative value of B i,i+1. The biquadratic term is smaller compared to the bilinear term therefore, it can be neglected for most of the ferromagnetic systems. Usually direct exchange interaction energy between neighboring spins is much larger compared the other terms. On the other hand, indirect exchange energy depends on spacer thickness and even shows oscillatory behavior with spacer thickness This term for the thinnest spacer can be comparable or even larger to the Zeeman and magnetocrystalline energy. This interlayer exchange term becomes smaller and smaller as the nonmagnetic spacer thickness increases. In our case this term is smaller compared to the other energy terms. When the magnetization vectors of neighboring layers start to deviate from each other, the system gains energy and this energy manifests itself in FMR spectra as will be explained later. As well known the microwave power absorption FMR curve as a function of external dc field by the sample is proportional to ac magnetic susceptibility. Therefore, one has to derive suitable theoretical expression in order to deduce magnetic parameter for ac susceptibility. A brief description for the derivation of ac susceptibility is as follows: the equation of precessional motion for magnetization of the i th layer in an external field applied in general direction with respect to the film plane can be written as: 1 dm i dt = 1 t i M i M i,s Mi E 1 t i M i h rf + M i,s M i dm i dt m i T 2 ê i m i T 2 ê i. Here, the effective field in the first term on the right-hand side is obtained from the gradient of total magnetic energy density with respect to magnetization vector. The second term on the right-hand side represents the microwave excitation torque. The third and fourth terms on the right-hand side represent the Landau Lifshitz Gilbert and Bloch type damping of dynamic transverse components magnetization, respectively. One or both type of the damping terms can be necessary to explain experimental data depending on film nature. Since the effective static field is much stronger com- 2

6 Topkaya et al. J. Appl. Phys. 18, pared to the microwave field components, the magnetization saturates along the effective dc field, H, and magnetization vector is expected to precess around the effective dc field vector due to the perpendicular transverse magnetic field components of applied microwave. Thus ac microwave and magnetization vector components in polar coordinate system as shown in Fig. 1 can be, respectively, written as h x rf = h x o e j t, M i = M i,s ê r + m i ê i + m i ê i. Due to this microwave excitation field, time-dependence of transverse components of the magnetization can be assumed as m i = m i e j t, m i = m i e j t. Since the magnetization vector is parallel to the effective field, the static torque becomes zero in static equilibrium case magnetization component parallel to static effective field is constant. When microwave field is applied, the magnetization deviates from static equilibrium direction due to microwave excitation torque given by the second term on the right-hand side of Eq. 2. Thus the first term on the righthand side of Eq. 2 can also contribute to dynamic torque as explained below. For small deviations in each layer magnetization from equilibrium orientation, the differential of Eq. 2 can be written as 1 i d dt M i = M i M i,s 1 t i Mi,s E. Here contribution from the second and the third terms on the right-hand side of Eq. 2 are neglected. Thus the right-hand side of Eq. 6 can be expanded as M i M i,s 1 t i Mi,s E = 1 M i 1 Mi,s E + M i M i,s t i 1 t i Mi,s E. M i,s The first term on the right-hand side is zero for saturated static magnetization. Expending the differential in the second term in polar coordinates and summing over whole layers one can get following expression N1,j+1 = i=2,j=i1 M i M i,s 1 t i Mj,s E N1,j+1 1 i=2,j=i1 cosec i E j t i M i m j j N1,j cosec j E j i m j ê i + E j i=2,j=i1 M j,s t i m j i + cosec j E i j m j ê i Here, E j i, E j i, and E j i represent second order partial derivations of energy density with respect to the polar angles of the magnetization for each layer. The radial components of magnetization in polar coordinates are time independent. Thus the first term on the right-hand side of Eq. 2 makes following contribution to time dependence of transverse components of magnetization as i+1 1 d i dt m i = 1 1 t i sin i i+1 1 d i dt m i = 1 t i j=i1 j=i1 E j i M j m j + E j i M j,s m j + 1 E i j M j sin j m j E j i M j,s sin j m j Putting the right-hand side of these expressions for the first term on the right-hand side of Eq. 2 that include also damping torque, one can get following coupled equations for amplitudes of time varying components of each layer magnetization, M i as: j i m i = m i1 t i M i1,s sin i E i1 i m i1 t i M i1,s sin i sin i1 E i1 i m i+1 m i+1 E i+1 t i M i+1,s sin i E i i t i M i+1,s sin i sin i+1, i+1 m i t i M i,s sin i E i i m i t i M i,s sin 2 i E i i j i m i = m i1 t i M i1,s E i1 i + m i1 t i M i1,s sin i1 E i i1 + m i t i M i,s E i i + m i t i M i,s sin i E i i + m i+1 t i M i+1,s E i i+1 + m i+1 t i M i+1 sin i+1 E i i+1. 1

7 Topkaya et al. J. Appl. Phys. 18, Similar equations without damping torque were given in literature 18 2 to get dispersion relations. But, in order to obtain full FMR absorption curves we have included damping torque in dynamic equation of motion for magnetization. The coupled equations Eq. 1 can be put in a more compact matrix form in dimensions of 2N 2N. C. Z = Y, 11 Here C isa2n 2N dimensional matrix whose nonzero matrix elements are: C m,m = j l E l l t l M l,s sin l 1 l T 2 C m,m+1 = j E l l l t l M l,s sin 2 l Y T = m s1 h 1,m s1 h 1,m s2 h 2,m s2 h 2,..., m si h i,m si h i,...,m sn h N,m sn h N, 13 where: h l = h o x sin l, h l = h o x cos l. cos l. 14 Thus one can obtain components of ac magnetization vector of each layer from elements of following matrix, Z, as Z = C 1 Y. 15 Since the microwave power absorption is proportional to average magnetization of layer one must project each m i onto h x o and divide the resultant values by magnetic field amplitude h x o of external microwave field. In another word, each layer contributes to the magnetic susceptibility. That is, the average magnetic susceptibility is obtained as = m x /h x o, 16 C m,m+2 = C m,m+3 = E l+1 l t l M l+1,s sin l E l l+1 t l M l+1,s sin l sin l+1 where N l l m x = t l m cos l. cos l m sin l. l=1 17 C m+1,m = E l l t l M l,s j l C m+1,m+1 = j l + E l l t l M l,s sin l + 1 l T 2 C m+1,m+2 = E l l+1 E l C m+1,m+3 = l+1 t l M l+1,s t l M l+1,s sin l+1 C m+2,m = C m+2,m+1 = E l l+1 t l+1 M l,s sin l+1 E l l+1 t l+1 M l,s sin l sin l+1 C m+3,m = E l l+1 E l+1 C m+3,m+1 = l, t l+1 M l,s t l+1 M l,s sin l where l runs from 1 to N while m runs from 1 to 2N1. Here E j i, E j i, and E j i must be calculated for equilibrium orientations corresponding to total energy minima of each layer magnetizations. In Eq. 11 the Z represents a column matrix whose elements are made from transfer components of all magnetic layers. Transpose of Z is a row matrix as, Z T = m 1,m 1,m 2,m 2,...,m i,m i,...,m N,m N, 12 On the other hand Y is a column matrix whose elements obtained from the multiplication of saturation value of each layer magnetization, M i,s by the projection of external microwave field on polar unit vectors of each magnetic layer as follows: V. SIMULATIONS OF THE FMR SPECTRA We have developed a general computer program for the structure consisting of magnetically exchange coupled N layers to fit theoretical FMR spectra to the experimental FMR spectra by using the theoretical model given above. The damping parameter has very minor effects on the resonance field value, but it basically determines the resonance line shape. Although the model and computer program are suitable for both the Gilbert and Bloch type dampings, we have used only the Gilbert type damping to get satisfactory fit between the experimental and the simulated line shape of field derivative FMR spectra for general directions of external dc field. For magnetically homogeneous films one can successfully fit the data by using only the Gilbert type damping term. However if there is a magnetic inhomogeneity, the Bloch type damping term can be included as well. The experimental FMR spectra could be fitted using the Zeeman, the demagnetizing and the uniaxial anisotropy energies the uniaxial axis is along the film normal. The induced uniaxial energy strictly depends on the magnetic layer thickness. Especially for ultrathin films this term sometimes can become comparable to the demagnetizing energy. As the magnetic layer becomes thinner than 5 Å, the magnetization does not saturate easily, and this is why we used thicker magnetic layers in order to saturate magnetization to a constant value that we assumed in the development of the theory. Since the angular dependencies of perpendicular anisotropy and the demagnetizing energy are determined by the saturation magnetization, it is very difficult to extract induced perpendicular anisotropy by using FMR data only. Actually the FMR intensity is linearly proportional to the saturation magnetization. Thus one can use reference sample to calibrate the spectrometer signal for exact magnetization

8 Topkaya et al. J. Appl. Phys. 18, measurements. But it seems to be more convenient to have magnetization values obtained by using dc magnetization measurement techniques. As can be seen in Figs. 2 4 there is a good agreement between the experimental and the calculated FMR spectra. A careful analysis shows that the position of the resonance peaks are determined by the saturation magnetization M s, the effective anisotropy and the exchange coupling of the magnetic layers. In fact, in the case of magnetically equivalent layers, the ferromagnetic exchange interaction has no effect on the resonance field, that is, a single resonance peak is observed due to simultaneous excitations of precession of magnetization in all layers. However when magnetic properties of individual magnetic layers slightly differ from each other, then, the exchange coupling between successive ferromagnetic layers starts to play an important role on the FMR curve. Thus, as the external dc field is scanned in a constant microwave frequency, the magnetization vector in one of the layers comes close to resonance condition in a particular field value while the other layer is still far from resonance for nonexchange coupled case that is, the directions of dynamic magnetizations of neighboring layers become different from each other. Now when exchange coupling is switched on, it tries to make magnetization vector in nonresonating layer parallel to that of resonating layer. Thus, additional inertia torque due to the magnetic field produced by the other layer arises and this torque has to be balanced by changing the resonance field. Similarly as the field scan is continued beyond the first resonance value, then, it reaches to the value that would correspond to resonance value for noncoupled second layer. Again due to exchange coupling with the first layer, the resonance field differs from that of noncoupled layer. For ferromagnetic antiferromagnetic coupling the optical mode occurs at lower higher field side of the main acoustic mode. The separation between the optic mode and acoustic mode in the field axis is determined by orientation of the external field, the saturation magnetization, the anisotropy field, and the exchange coupling parameter. In fact, the separation between the modes generally increases with absolute value of exchange parameter. That is, if interlayer exchange coupling strength increases, the optic mode moves away the acoustic mode, and the relative intensities, and the separation between the modes increase. On the other hand, if interlayer exchange coupling strength decreases, the optic mode comes close to the acoustic mode, and the relative intensities, and the separation between the modes decrease. As a result of exchange coupling of magnetically nonequivalent neighboring layers, two resonance modes are observed in FMR curves for OPG case. Figure 3 also shows the calculated real values of azimuthal a1 and b1 and polar a2 and b2 components transverse components of ac magnetizations for each layer of the samples S4 and S1 which are given as a function of the external dc magnetic field. These components also allow us to get the relative phase of the dynamic components of ac magnetization as a function of the external dc field. As can be seen in the Fig. 3 a1 and a2 and b1 and b2, the real values of azimuthal and polar components of ac magnetizations for the two samples are different from each other. This means that the magnetization vector makes an elliptical rather than circular precession about the dc magnetization and the effective dc field component. The magnetization of each layer contributes to the resonance absorption for each FMR mode. Since the excitation amplitude and the phase of precession of dc magnetizations of neighboring layers continuously changes with the dc field, the phase difference becomes either zero or at the exact resonance field values of the two modes. The mode for the first case in phase is called as acoustic mode while the other is called as optical mode to make analogy with phonon spectra. While the relative contributions from the different modes continuously change evolve with the external dc magnetic field, one of the layers makes dominant contribution to the FMR signal amplitude ac susceptibility for each mode about the resonance field. Since the average magnetic susceptibility is proportional to the vector sum of transfer components of ac magnetization, the intensity of the acoustical mode is always higher than that of optical mode at exact resonance fields. The relative positions of the modes depend on the sign of exchange coupling parameters A 12 and B 12 as well. As mentioned before, these parameters represent the exchange field on a magnetic layer due to the neighboring layer. This field depends on the relative orientation of the magnetization. For independent determination of these parameters one needs to control the relative orientations of M 1 and M 2. Unfortunately, since the demagnetizing energies of neighboring layers are close to each other, and the Zeeman energy is too large compared to the exchange energy, the magnetization vectors of neighboring layers remain almost always parallel to each others at the resonance field. So, the effective exchange field on one of the magnetic layer due to the other magnetic layer does not depend on the external field direction. Therefore, it is not practical to get additional information for different angles to deduce both exchange coupling terms independently. If we had been able to rotate the magnetization of individual magnetic layers with respect to each other, then, we would have determined both parameters independently. But we do not have possibility to fix the magnetization of the one layer and sweep the external field gradually to rotate the magnetization of second layer in order to determine A 12 and B 12 independently. Therefore we have used only the bilinear term, that is, A 12 in the simulations. Maybe in the future, we can achieve this with different multilayer structures. The deduced interlayer exchange coupling parameter, A 12 is plotted in Fig. 6 as a function of nonmagnetic spacer Cr thickness. It should be remembered that both the bilinear and the biquadratic exchange energies are represented by a deduced effective parameter, A 12. As can be seen from this figure, the exchange parameter qualitatively exhibits oscillatory behavior. The absolute value decreases with increasing spacer thickness. However interlayer exchange coupling constant changes its sign and oscillates with a period of about 11 Å. This result is consistent with the theory given by Fert et al. 36 The deduced value of exchange parameter for Py 2 Å /Cr 1 Å /Py 3 Å trilayer film is nearly half of the values given for Py/Cr 12 Å 4 multilayer system prepared by electron beam deposition system. 33 However, the

9 Topkaya et al. J. Appl. Phys. 18, A 12 (1-3 erg / cm 2 ) deduced value in our case is still almost 2 times less than that found for Fe/Cr superlattice in the literature. 34 The period of the oscillation of the interlayer exchange coupling is very close to that for Py/Cr 12 Å 4 but is significantly smaller than that given for Fe/Cr multilayers. 7 The smaller oscillation period was attributed to interface roughness or interdiffusion between the two interfaces of the trilayer. 33 VI. CONCLUSIONS t Cr (Å) FIG. 6. Effective interlayer exchange coupling parameter, A 12, obtained from the fitting as a function of nonmagnetic spacer Cr thickness. The sign of exchange parameter changes with the spacer thickness and causes parallel or antiparallel alignment of the magnetization of neighboring layers as shown by arrows for some spacer thicknesses. Ultrathin Py/Cr/Py trilayer films grown on Si 1 substrate by magnetron sputtering technique under UHV conditions have been studied by VSM and FMR techniques. In the present study we have investigated the dependence of the interlayer exchange coupling on Cr spacer layer thickness in interval from 4 to 4 Å. The computer program was written to deduce the interlayer exchange parameter for magnetically exchange coupled magnetic multilayers and it was applied to the Py/Cr/Py trilayers. The deduced magnetic parameters strictly depend on the layer thicknesses as well. Actual line shapes, resonance positions, the relative intensities of the different FMR modes, and angular dependence of these modes are successfully simulated by using only single set of parameters like M s, K p, A 12, and with the written program. Particular parameters have dominant effect on some particular aspects of the FMR spectra. For instance, the angular dependence of the resonance field is mainly determined by M s and the perpendicular anisotropy. But relative position and especially relative mode intensities are well accounted for the interlayer exchange coupling. The damping parameter determines the line shapes. The angular dependence allows us to get more accurate parameters and sufficiently good fitting by using as many data as we need since we have freedom to do experiment for any direction of external static magnetic field. It was understood that the FMR is a very sensitive and powerful technique to study magnetic properties of single and/or layered ferromagnetic thin even at nanometer range films separated by a very thin nonmagnetic spacer layer. As a result of fitting the theoretical values to the experimental data, it has been seen that the interlayer exchange coupling constant has qualitatively oscillatory behavior with respect to the nonmagnetic spacer thickness. The oscillation period was found to be about 11 Å for Py/Cr/Py trilayers. The value of this parameter reduces with increase in Cr thickness and it becomes undetermined beyond 3 Å. If magnetic properties of different layers are very close to each other, two modes comes close to each other and additionally if damping parameter is relatively larger broad peaks, then, these two peaks overlap and give a distorted single line. In this case, accuracy of exchange parameter decreases. ACKNOWLEDGMENTS This work was partly supported by the Ministry of Industry and Trade of TURKEY Project No. 185.STZ.27-2, State Planning Organization of Turkey DPT-Project No. 29K1273, and Marmara University DPT Project No. 23K1281. We gratefully acknowledge that all samples used in this study grown at Nanotechnology Center of Gebze Institute of Technology. 1 M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, G. 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