The magnetization dynamics of Co(5 nm)/Ru/Co(5 nm) trilayers with Ru thicknesses from 0.3–0.6 nm is experimentally and theoretically investigated. The coupling between the Co layers is antiferromagnetic (AFM) and yields a stable AFM domain structure with frozen domain walls. Comparing high-resolution magnetic force microscopy (MFM) and pump-probe measurements, we analyze the behavior of the films for different field-strength regimes. For moderate magnetic fields, pump-probe measurements provide dynamic characterization of the coupled precessional modes in the GHz range. The dynamics at small fields is realized by the pinning of AFM domain walls at inhomogeneities. The MFM images yield a domain-wall width that varies from about 150–60 nm. This behavior is explained in terms of a micromagnetic local-anisotropy model

Chipara, Mircea

Kirby, Roger D.

Li, Zhen

Liou, Sy-Hwang

Michalski, Steven

Skomski, Ralph

English

Scholarworks@UTRGV Univ. of Texas RioGrande Valley

University of Texas Rio Grande Valley ScholarWorks @ UTRGV Physics and Astronomy Faculty Publications and Presentations College of Sciences 2011 Magnetization precession and domainwall structure in cobalt-ruthenium-cobalt trilayers Zhen Li Ralph Skomski Sy-Hwang Liou Steven Michalski Mircea Chipara See next page for additional authors Follow this and additional works at: https://scholarworks.utrgv.edu/pa_fac  Part of the Astrophysics and Astronomy Commons, and the Physics Commons Authors Zhen Li, Ralph Skomski, Sy-Hwang Liou, Steven Michalski, Mircea Chipara, and Roger D. Kirby J. Appl. Phys. 109, 07C113 (2011); https://doi.org/10.1063/1.3540406 109, 07C113© 2011 American Institute of Physics.Magnetization precession and domain-wall structure in cobalt-ruthenium-cobalttrilayersCite as: J. Appl. Phys. 109, 07C113 (2011); https://doi.org/10.1063/1.3540406Submitted: 25 September 2010 . Accepted: 02 November 2010 . Published Online: 28 March 2011Zhen Li, Ralph Skomski, Sy-Hwang Liou, et al.ARTICLES YOU MAY BE INTERESTED INAll-optical measurement of interlayer exchange coupling in Fe/Pt/FePt thin filmsApplied Physics Letters 112, 052401 (2018); https://doi.org/10.1063/1.5004686The design and verification of MuMax3AIP Advances 4, 107133 (2014); https://doi.org/10.1063/1.4899186Conversion of spin current into charge current at room temperature: Inverse spin-Hall effectApplied Physics Letters 88, 182509 (2006); https://doi.org/10.1063/1.2199473Magnetization precession and domain-wall structurein cobalt-ruthenium-cobalt trilayersZhen Li,1,a) Ralph Skomski,1,2 Sy-Hwang Liou,1,2 Steven Michalski,1,2 Mircea Chipara,3and Roger D. Kirby1,21Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588, USA2Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska 68588, USA3Physics and Geology Department, The University of Texas Pan American, Edinburg, Texas 78541, USA(Presented 15 November 2010; received 25 September 2010; accepted 2 November 2010; publishedonline 28 March 2011)The magnetization dynamics of Co(5 nm)/Ru/Co(5 nm) trilayers with Ru thicknesses from 0.3–0.6nm is experimentally and theoretically investigated. The coupling between the Co layers isantiferromagnetic (AFM) and yields a stable AFM domain structure with frozen domain walls.Comparing high-resolution magnetic force microscopy (MFM) and pump-probe measurements, weanalyze the behavior of the films for different field-strength regimes. For moderate magnetic fields,pump-probe measurements provide dynamic characterization of the coupled precessional modes inthe GHz range. The dynamics at small fields is realized by the pinning of AFM domain walls atinhomogeneities. The MFM images yield a domain-wall width that varies from about 150–60 nm.This behavior is explained in terms of a micromagnetic local-anisotropy model.VC 2011 American Institute of Physics. [doi:10.1063/1.3540406]Since the original discovery of antiferromagnetic cou-pling in Fe/Cr/Fe layered structures,1 thin films composedof magnetic layers separated by a nonmagnetic spacerhave received considerable attention due to their applica-tions in spin valve devices.2 Compared to the oscillatorybehavior of the interlayer exchange coupling between theferromagnetic (FM) and AFM,3,4 the spin structure anddynamics of the films have attracted much less attention.The dynamics of the trilayers in the GHz range deter-mines the high-speed response and is of fundamental im-portance for the enhancement of the areal density anddata processing speed in magnetic storage devices.5 Themagnetic domain and domain wall configurations of tri-layers with AFM coupling display a number of interestingfeatures.6,7 For example, domain walls in Co/Ru/Co tri-layers with Co layers of equal thickness are frozen, andan applied magnetic field does not change the domain-wall position but leads to a narrowing of the domainwalls.8 Such freezing effects are common in ordinaryantiferromagnets,9 but have not been observed before intrilayers. This paper deals with the ultrathin Co/Ru/Co tri-layers. We previously found that an interlayer Ru thick-ness range of 0.3–0.6 nm results in stable AFM couplingbetween two 5 nm Co layers.8 We use pump-probe tech-niques to analyze the magnetization precession, evaluatethe interlayer exchange coupling with the help of a Lan-dau-Lifshitz-Gilbert (LLG) based model,10 and investigatethe domain-wall narrowing as a function of magnetic field.Co/Ru/Co trilayer thin films were prepared by dc-magnetron sputtering on Si (100) substrates at depositionrates of 0.486 Å/s for Co and 0.276 Å/s for Ru, in a 4 mTorrargon pressure. The base pressure was approximately1 107 Torr. The thicknesses of the top and bottom Colayers were fixed at 5 nm, while the thickness of the Ruinterlayer was varied from 0.3–0.6 nm. The magnetizationprecession measurements were performed using a 150 fem-tosecond laser (50 nJ/pulse, 800 nm) in a pump-probeexperiment with direct optical excitation.11 Room tempera-ture high-resolution MFM imaging in the presence of anin-plane magnetic field was carried out using a DI Dimen-sion 3100 SPM in tapping/lift mode with a lift height of15 nm.In our Co/Ru/Co structures, the ferromagnetic layers arestrongly antiparallel coupled when the Ru interlayer thick-ness is varied from 0.3–0.6 nm. All samples show two typesof coupled modes, classified as acoustic mode (AM) andoptic mode (OM) depending on whether the two film mag-netizations precess in phase or out of phase, respectively.For antiparallel configuration, the two magnetizations pre-cess in opposite directions, and hence their relative phasechanges continuously. Figure 1(a) shows the pump-inducedchanges of Kerr rotation (DKerr) as a function of the delaytime for the 5 nm Co/0.4 nm Ru/5 nm Co sample with vari-ous strengths of applied field at 45 relative to the samplenormal. The clearly visible beats in the precession indicatethe presence of two modes. Figure 1(b) shows the corre-sponding Fourier transformations of Fig. 1(a). The two fre-quency branches start merging with increasing magneticfield until only one broad peak is observed at H¼ 6 kOe.The peaks then separate for larger fields. This behavior isillustrated in Fig. 2 which shows the precessional frequency(solid square) as a function of applied field.To interpret these results, we use a two-layer LLG basedmodel. The energy per unit area of the trilayer system can bewritten as:a)Author to whom correspondence should be addressed. Electronic mail:zhen.li@huskers.unl.edu. Tel.: 402-472-9602. FAX: 402-472-2879.0021-8979/2011/109(7)/07C113/3/$30.00 VC 2011 American Institute of Physics109, 07C113-1JOURNAL OF APPLIED PHYSICS 109, 07C113 (2011)E ¼ t1M*1  H*þ 2pt1M* 21 cos2 h1  t2M*2  H*þ 2pt2M* 22 cos2 h2  JM*1 M*2M1M2: (1)Here, t1;2 is the thickness of each Co layer, M*1;2 is themagnetization of each Co layer and h1,2 is the angle of M*1;2with respect to the sample normal. First, the energy is mini-mized to find the equilibrium orientations. The magnetiza-tion of each Co layer was assumed to be uniform andmeasured to be 1225 kA/m. These values were used as inputsin the model. We adjusted interlayer coupling constant J andsolved the LLG equations to obtain frequencies similar tothe experimental frequencies. The solid lines in Fig. 2 arethe simulation curves obtained from this model withJ¼ – 2.1 mJ/m2. The present model provides a good semi-quantitative description of field-dependence precession forour trilayers. Note that the low-frequency branch does notextrapolate to zero frequency at zero field as predicted by thecalculations, and the width of the bump in the low-frequencybranch is greater than predicted. The differences may be dueto structural inhomogeneities. Nevertheless, the value ofJ¼2.1 mJ/m2 here is in reasonable agreement with thevalue of J¼2.6 mJ/m2 found in our previous staticresults, 8 indicating that the dynamic simulation is consistentwith the static simulation. The other three AFM coupledsamples (tRu¼ 0.3, 0.5, and 0.6 nm) show similar behaviorsas the tRu¼ 0.4 nm sample, but with different values of J.The estimated J (J is negative) as a function of the Ruthickness is shown in the inset of Fig. 2. With the increasingthickness of Ru, J monotonically decreases, showing that theinterlayer exchange coupling is getting weaker.Two Co layers are AFM coupled domain by domainwith the top domains antiparallel to the bottom domains,leading to zero net magnetization in the interior of thedomains and so only the domain walls are observed. A highresolution scan of the domain-wall structures was performedin the 5 nm Co/0.4 nm Ru/5 nm Co sample as shown inFig. 3. Although, on average, the contrast becomes weaker,the domain wall profiles do not change much with appliedfield. This frozen effect indicates that the wall position getspinned. As we discussed earlier, structural inhomogeneitiesapparently play a significant role in our ultrathin films. Thepinning at inhomogeneities induces a considerable fluctua-tion of the domain-wall width (dw) as one moves along thewalls, which is clearly observed in Fig. 3(a) at zero field.When the field is increased, the fluctuations become smallerand eventually vanish. Meanwhile, dw shows a monotonicdecrease with an increasing field. Line scans were taken per-pendicular to the length of these regions and averaged alongthe length to improve statistics. A representative one isshown in Figs. 3(g) and 3(h). The box in 3(g) is the regionover which the width was averaged and the length betweenthe two red lines indicating dw is obtained by the trough-to-peak width of line scans in 3(h). Note that the scan profile isasymmetric, probably due to the structural imperfections.Figure 4 shows dw obtained from the MFM line scans asa function of the applied field. We previously predicted8 thatdw 1/H, however, the agreement with the experiments waspoor. We believe that the main reason is that the formerresult was derived by only considering the leading energycontributions, namely the Zeeman energy and the interlayerexchange energy. The exchange energy of the domain wallscales as 1/dw, so that small energy contributions, such asresidual magnetocrystalline anisotropy and magnetostaticdomain-wall interactions, become important for large dw. Asthe anisotropy reflects the density and strength of pinningsites, the fluctuations of dw at small fields should be strongerthan those at large fields, consistent with what we observedFIG. 1. (a) Typical pump-probe signals as a function of time for the sample5 nm Co/0.4 nm Ru/5 nm Co with various strengths of applied field at 45 tothe sample normal and (b) the corresponding Fourier transforms.FIG. 2. (Color online) Precessional frequencies as a function of the appliedmagnetic field at 45 for the sample 5 nm Co/0.4 nm Ru/5 nm Co. The solidcurves are the simulation from a LLG based model with J¼2.1 mJ/m2.(Inset) The estimated exchange coupling J obtained from LLG based modelas a function of the interlayer Ru thickness.07C113-2 Li et al. J. Appl. Phys. 109, 07C113 (2011)in Fig. 3. To calculate the effect of the additional terms, weassume a Bloch-type domain-wall fine structure, and thisyields the micromagnetic energy as a function of dw andmagnetization m. The corresponding energy function isE ¼ 2t 4Adwþ lo2MsHmdw þ lom2M2sdwtdw þ 2tþ Kdw : (2)A is the exchange stiffness of Co (about 20 pJ/m). The factorof 4 in the exchange term originates from the exchangeexpression ðr mÞ2and means that m changes from þ1 to1 (or vice versa) over the distance dw. The second term isthe Zeeman energy, the third term is the self interaction ofthe wall, derived from the demagnetizing factor D ¼2t=ðdw þ 2tÞ, shown as an inset in Fig. 4, and the last term isthe magnetic anisotropy. For arbitrary fields, the domain-wallwidth is determined by minimizing Eq. (2) with respect to dw:dw ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4AK þ lo2MsHms: (3)Here, m ¼ loMsHt2 Jj j for small fields and m¼ 1 for large fields.The fitting curve is shown in Fig. 4 as a solid line by usingJ¼2.1 mJ/m2 obtained from the dynamic calculations.Our micromagnetic model quantitatively provides a fairlygood description of the experiments. Note that the value ofK is approximately 3700 J/m3, which is much smaller thanthe value for bulk Co, but this is consistent with observedlow in-plane coercivity.In summary, our dynamic measurements of Co/Ru/Cotrilayers show that the strength of coupling is controlled bythe interlayer thickness. The pump-probe technique yieldstwo precessional frequencies which can be interpreted by aLLG based model. The semiquantitative agreement can beascribed as the effect of structural inhomogeneities. Due tothe pinning at inhomogeneities, MFM images show thefrozen domain walls and a variation of dw. We calculated thefine structure of our films to provide a quantitative simula-tion of dw as a function of field.This work has been supported by NSF-MRSEC (GrantNo. DMR-0820521) and NCMN.1P. Grünberg et al., Phys. Rev. Lett. 57, 2442 (1986).2Z. Zhao et al., Phys. Rev. B 71, 104417 (2005).3S. S. P. Parkin, Phys. Rev. Lett. 67, 3598 (1991).4P. J. H. Bloemen et al., Phys. Rev. B 50, 13505 (1994).5C. H. Back et al., Science 285, 864 (1999).6A. Hubert and R. Schäfer, Magnetic Domains (Springer-Verlag, Berlin 1998).7M. Rührig et al., Phys. Status Solidi A 125, 635 (1991).8Z. Li, R. Skomski et al., J. Appl. Phys. 107, 09D303 (2010).9J. V. Kim and R. L. Stamps, Phys. Rev. B 71, 094405 (2005).10T. L. Gilbert, IEEE Trans. Magn. 40, 3443 (2004).11S. Michalski et al., J. Appl. Phys. 101, 09D115 (2007).FIG. 3. (Color online) High resolution MFM images of the sample 5 nmCo/0.4 nm Ru/5 nm Co at room temperature with in-plane magnetic fields.(a)–(f) correspond to 0, 250, 500, 1000, 1250, 2000 Oe. Each image is2.5 2.5 lm2 in size. (g) Represents the region chosen from (e) with1.25 1.25 lm2 in size and (h) shows the line scans, averaged over theregion enclosed in the box in (g). The y-axis indicates the MFM tipresponse.FIG. 4. (Color online) Domain-wall width as a function of applied magneticfield. Solid squares give the compiled line scan data from Fig. 3. The 15 nmerror bars account for the MFM resolution. The solid line is the model calcu-lation with J ¼ 2.1 mJ/m2. The inset shows the magnetostatic domain-wallinteractions in the trilayer, The energy in the wall is estimated from thedemagnetizing factor D ¼ Rz/(RxþRz) ¼ 2t/(dwþ2t) of a long rod with anellipsoidal cross section.07C113-3 Li et al. J. Appl. Phys. 109, 07C113 (2011)

Magnetization precession and domainwall structure in cobalt-ruthenium-cobalt trilayers

Zhen Li

Ralph Skomski

Sy-Hwang Liou

Steven Michalski

Mircea Chipara

Roger D. Kirby

Crossref

Journal of Applied Physics

Magnetization precession and domain-wall structure in cobalt-ruthenium-cobalt trilayers

University of Texas Rio Grande Valley ScholarWorks @ UTRGV Physics and Astronomy Faculty Publications and Presentations College of Sciences 2011 Magnetization precession and domain-wall structure in cobalt-ruthenium-cobalt trilayers Zhen Li Ralph Skomski Sy-Hwang Liou Steven Michalski Mircea Chipara The University of Texas Rio Grande Valley, mircea.chipara@utrgv.edu See next page for additional authors Follow this and additional works at: https://scholarworks.utrgv.edu/pa_fac Digital Commons Network Logo  Part of the Astrophysics and Astronomy Commons, and the Physics Commons Recommended Citation Li, Zhen, Ralph Skomski, Sy-Hwang Liou, Steven Michalski, Mircea Chipara, and Roger D. Kirby. 2011. “Magnetization Precession and Domain-Wall Structure in Cobalt-Ruthenium-Cobalt Trilayers.” Journal of Applied Physics 109 (7): 07C113. https://doi.org/10.1063/1.3540406. This Article is brought to you for free and open access by the College of Sciences at ScholarWorks @ UTRGV. It has been accepted for inclusion in Physics and Astronomy Faculty Publications and Presentations by an authorized administrator of ScholarWorks @ UTRGV. For more information, please contact justin.white@utrgv.edu, william.flores01@utrgv.edu. Authors Zhen Li, Ralph Skomski, Sy-Hwang Liou, Steven Michalski, Mircea Chipara, and Roger D. Kirby This article is available at ScholarWorks @ UTRGV: https://scholarworks.utrgv.edu/pa_fac/489 J. Appl. Phys. 109, 07C113 (2011); https://doi.org/10.1063/1.3540406 109, 07C113© 2011 American Institute of Physics.Magnetization precession and domain-wall structure in cobalt-ruthenium-cobalttrilayersCite as: J. Appl. Phys. 109, 07C113 (2011); https://doi.org/10.1063/1.3540406Submitted: 25 September 2010 . Accepted: 02 November 2010 . Published Online: 28 March 2011Zhen Li, Ralph Skomski, Sy-Hwang Liou, et al.ARTICLES YOU MAY BE INTERESTED INAll-optical measurement of interlayer exchange coupling in Fe/Pt/FePt thin filmsApplied Physics Letters 112, 052401 (2018); https://doi.org/10.1063/1.5004686The design and verification of MuMax3AIP Advances 4, 107133 (2014); https://doi.org/10.1063/1.4899186Conversion of spin current into charge current at room temperature: Inverse spin-Hall effectApplied Physics Letters 88, 182509 (2006); https://doi.org/10.1063/1.2199473Magnetization precession and domain-wall structurein cobalt-ruthenium-cobalt trilayersZhen Li,1,a) Ralph Skomski,1,2 Sy-Hwang Liou,1,2 Steven Michalski,1,2 Mircea Chipara,3and Roger D. Kirby1,21Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588, USA2Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska 68588, USA3Physics and Geology Department, The University of Texas Pan American, Edinburg, Texas 78541, USA(Presented 15 November 2010; received 25 September 2010; accepted 2 November 2010; publishedonline 28 March 2011)The magnetization dynamics of Co(5 nm)/Ru/Co(5 nm) trilayers with Ru thicknesses from 0.3–0.6nm is experimentally and theoretically investigated. The coupling between the Co layers isantiferromagnetic (AFM) and yields a stable AFM domain structure with frozen domain walls.Comparing high-resolution magnetic force microscopy (MFM) and pump-probe measurements, weanalyze the behavior of the films for different field-strength regimes. For moderate magnetic fields,pump-probe measurements provide dynamic characterization of the coupled precessional modes inthe GHz range. The dynamics at small fields is realized by the pinning of AFM domain walls atinhomogeneities. The MFM images yield a domain-wall width that varies from about 150–60 nm.This behavior is explained in terms of a micromagnetic local-anisotropy model.VC 2011 American Institute of Physics. [doi:10.1063/1.3540406]Since the original discovery of antiferromagnetic cou-pling in Fe/Cr/Fe layered structures,1 thin films composedof magnetic layers separated by a nonmagnetic spacerhave received considerable attention due to their applica-tions in spin valve devices.2 Compared to the oscillatorybehavior of the interlayer exchange coupling between theferromagnetic (FM) and AFM,3,4 the spin structure anddynamics of the films have attracted much less attention.The dynamics of the trilayers in the GHz range deter-mines the high-speed response and is of fundamental im-portance for the enhancement of the areal density anddata processing speed in magnetic storage devices.5 Themagnetic domain and domain wall configurations of tri-layers with AFM coupling display a number of interestingfeatures.6,7 For example, domain walls in Co/Ru/Co tri-layers with Co layers of equal thickness are frozen, andan applied magnetic field does not change the domain-wall position but leads to a narrowing of the domainwalls.8 Such freezing effects are common in ordinaryantiferromagnets,9 but have not been observed before intrilayers. This paper deals with the ultrathin Co/Ru/Co tri-layers. We previously found that an interlayer Ru thick-ness range of 0.3–0.6 nm results in stable AFM couplingbetween two 5 nm Co layers.8 We use pump-probe tech-niques to analyze the magnetization precession, evaluatethe interlayer exchange coupling with the help of a Lan-dau-Lifshitz-Gilbert (LLG) based model,10 and investigatethe domain-wall narrowing as a function of magnetic field.Co/Ru/Co trilayer thin films were prepared by dc-magnetron sputtering on Si (100) substrates at depositionrates of 0.486 Å/s for Co and 0.276 Å/s for Ru, in a 4 mTorrargon pressure. The base pressure was approximately1 107 Torr. The thicknesses of the top and bottom Colayers were fixed at 5 nm, while the thickness of the Ruinterlayer was varied from 0.3–0.6 nm. The magnetizationprecession measurements were performed using a 150 fem-tosecond laser (50 nJ/pulse, 800 nm) in a pump-probeexperiment with direct optical excitation.11 Room tempera-ture high-resolution MFM imaging in the presence of anin-plane magnetic field was carried out using a DI Dimen-sion 3100 SPM in tapping/lift mode with a lift height of15 nm.In our Co/Ru/Co structures, the ferromagnetic layers arestrongly antiparallel coupled when the Ru interlayer thick-ness is varied from 0.3–0.6 nm. All samples show two typesof coupled modes, classified as acoustic mode (AM) andoptic mode (OM) depending on whether the two film mag-netizations precess in phase or out of phase, respectively.For antiparallel configuration, the two magnetizations pre-cess in opposite directions, and hence their relative phasechanges continuously. Figure 1(a) shows the pump-inducedchanges of Kerr rotation (DKerr) as a function of the delaytime for the 5 nm Co/0.4 nm Ru/5 nm Co sample with vari-ous strengths of applied field at 45 relative to the samplenormal. The clearly visible beats in the precession indicatethe presence of two modes. Figure 1(b) shows the corre-sponding Fourier transformations of Fig. 1(a). The two fre-quency branches start merging with increasing magneticfield until only one broad peak is observed at H¼ 6 kOe.The peaks then separate for larger fields. This behavior isillustrated in Fig. 2 which shows the precessional frequency(solid square) as a function of applied field.To interpret these results, we use a two-layer LLG basedmodel. The energy per unit area of the trilayer system can bewritten as:a)Author to whom correspondence should be addressed. Electronic mail:zhen.li@huskers.unl.edu. Tel.: 402-472-9602. FAX: 402-472-2879.0021-8979/2011/109(7)/07C113/3/$30.00 VC 2011 American Institute of Physics109, 07C113-1JOURNAL OF APPLIED PHYSICS 109, 07C113 (2011)E ¼ t1M*1  H*þ 2pt1M* 21 cos2 h1  t2M*2  H*þ 2pt2M* 22 cos2 h2  JM*1 M*2M1M2: (1)Here, t1;2 is the thickness of each Co layer, M*1;2 is themagnetization of each Co layer and h1,2 is the angle of M*1;2with respect to the sample normal. First, the energy is mini-mized to find the equilibrium orientations. The magnetiza-tion of each Co layer was assumed to be uniform andmeasured to be 1225 kA/m. These values were used as inputsin the model. We adjusted interlayer coupling constant J andsolved the LLG equations to obtain frequencies similar tothe experimental frequencies. The solid lines in Fig. 2 arethe simulation curves obtained from this model withJ¼ – 2.1 mJ/m2. The present model provides a good semi-quantitative description of field-dependence precession forour trilayers. Note that the low-frequency branch does notextrapolate to zero frequency at zero field as predicted by thecalculations, and the width of the bump in the low-frequencybranch is greater than predicted. The differences may be dueto structural inhomogeneities. Nevertheless, the value ofJ¼2.1 mJ/m2 here is in reasonable agreement with thevalue of J¼2.6 mJ/m2 found in our previous staticresults, 8 indicating that the dynamic simulation is consistentwith the static simulation. The other three AFM coupledsamples (tRu¼ 0.3, 0.5, and 0.6 nm) show similar behaviorsas the tRu¼ 0.4 nm sample, but with different values of J.The estimated J (J is negative) as a function of the Ruthickness is shown in the inset of Fig. 2. With the increasingthickness of Ru, J monotonically decreases, showing that theinterlayer exchange coupling is getting weaker.Two Co layers are AFM coupled domain by domainwith the top domains antiparallel to the bottom domains,leading to zero net magnetization in the interior of thedomains and so only the domain walls are observed. A highresolution scan of the domain-wall structures was performedin the 5 nm Co/0.4 nm Ru/5 nm Co sample as shown inFig. 3. Although, on average, the contrast becomes weaker,the domain wall profiles do not change much with appliedfield. This frozen effect indicates that the wall position getspinned. As we discussed earlier, structural inhomogeneitiesapparently play a significant role in our ultrathin films. Thepinning at inhomogeneities induces a considerable fluctua-tion of the domain-wall width (dw) as one moves along thewalls, which is clearly observed in Fig. 3(a) at zero field.When the field is increased, the fluctuations become smallerand eventually vanish. Meanwhile, dw shows a monotonicdecrease with an increasing field. Line scans were taken per-pendicular to the length of these regions and averaged alongthe length to improve statistics. A representative one isshown in Figs. 3(g) and 3(h). The box in 3(g) is the regionover which the width was averaged and the length betweenthe two red lines indicating dw is obtained by the trough-to-peak width of line scans in 3(h). Note that the scan profile isasymmetric, probably due to the structural imperfections.Figure 4 shows dw obtained from the MFM line scans asa function of the applied field. We previously predicted8 thatdw 1/H, however, the agreement with the experiments waspoor. We believe that the main reason is that the formerresult was derived by only considering the leading energycontributions, namely the Zeeman energy and the interlayerexchange energy. The exchange energy of the domain wallscales as 1/dw, so that small energy contributions, such asresidual magnetocrystalline anisotropy and magnetostaticdomain-wall interactions, become important for large dw. Asthe anisotropy reflects the density and strength of pinningsites, the fluctuations of dw at small fields should be strongerthan those at large fields, consistent with what we observedFIG. 1. (a) Typical pump-probe signals as a function of time for the sample5 nm Co/0.4 nm Ru/5 nm Co with various strengths of applied field at 45 tothe sample normal and (b) the corresponding Fourier transforms.FIG. 2. (Color online) Precessional frequencies as a function of the appliedmagnetic field at 45 for the sample 5 nm Co/0.4 nm Ru/5 nm Co. The solidcurves are the simulation from a LLG based model with J¼2.1 mJ/m2.(Inset) The estimated exchange coupling J obtained from LLG based modelas a function of the interlayer Ru thickness.07C113-2 Li et al. J. Appl. Phys. 109, 07C113 (2011)in Fig. 3. To calculate the effect of the additional terms, weassume a Bloch-type domain-wall fine structure, and thisyields the micromagnetic energy as a function of dw andmagnetization m. The corresponding energy function isE ¼ 2t 4Adwþ lo2MsHmdw þ lom2M2sdwtdw þ 2tþ Kdw : (2)A is the exchange stiffness of Co (about 20 pJ/m). The factorof 4 in the exchange term originates from the exchangeexpression ðr mÞ2and means that m changes from þ1 to1 (or vice versa) over the distance dw. The second term isthe Zeeman energy, the third term is the self interaction ofthe wall, derived from the demagnetizing factor D ¼2t=ðdw þ 2tÞ, shown as an inset in Fig. 4, and the last term isthe magnetic anisotropy. For arbitrary fields, the domain-wallwidth is determined by minimizing Eq. (2) with respect to dw:dw ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4AK þ lo2MsHms: (3)Here, m ¼ loMsHt2 Jj j for small fields and m¼ 1 for large fields.The fitting curve is shown in Fig. 4 as a solid line by usingJ¼2.1 mJ/m2 obtained from the dynamic calculations.Our micromagnetic model quantitatively provides a fairlygood description of the experiments. Note that the value ofK is approximately 3700 J/m3, which is much smaller thanthe value for bulk Co, but this is consistent with observedlow in-plane coercivity.In summary, our dynamic measurements of Co/Ru/Cotrilayers show that the strength of coupling is controlled bythe interlayer thickness. The pump-probe technique yieldstwo precessional frequencies which can be interpreted by aLLG based model. The semiquantitative agreement can beascribed as the effect of structural inhomogeneities. Due tothe pinning at inhomogeneities, MFM images show thefrozen domain walls and a variation of dw. We calculated thefine structure of our films to provide a quantitative simula-tion of dw as a function of field.This work has been supported by NSF-MRSEC (GrantNo. DMR-0820521) and NCMN.1P. Grünberg et al., Phys. Rev. Lett. 57, 2442 (1986).2Z. Zhao et al., Phys. Rev. B 71, 104417 (2005).3S. S. P. Parkin, Phys. Rev. Lett. 67, 3598 (1991).4P. J. H. Bloemen et al., Phys. Rev. B 50, 13505 (1994).5C. H. Back et al., Science 285, 864 (1999).6A. Hubert and R. Schäfer, Magnetic Domains (Springer-Verlag, Berlin 1998).7M. Rührig et al., Phys. Status Solidi A 125, 635 (1991).8Z. Li, R. Skomski et al., J. Appl. Phys. 107, 09D303 (2010).9J. V. Kim and R. L. Stamps, Phys. Rev. B 71, 094405 (2005).10T. L. Gilbert, IEEE Trans. Magn. 40, 3443 (2004).11S. Michalski et al., J. Appl. Phys. 101, 09D115 (2007).FIG. 3. (Color online) High resolution MFM images of the sample 5 nmCo/0.4 nm Ru/5 nm Co at room temperature with in-plane magnetic fields.(a)–(f) correspond to 0, 250, 500, 1000, 1250, 2000 Oe. Each image is2.5 2.5 lm2 in size. (g) Represents the region chosen from (e) with1.25 1.25 lm2 in size and (h) shows the line scans, averaged over theregion enclosed in the box in (g). The y-axis indicates the MFM tipresponse.FIG. 4. (Color online) Domain-wall width as a function of applied magneticfield. Solid squares give the compiled line scan data from Fig. 3. The 15 nmerror bars account for the MFM resolution. The solid line is the model calcu-lation with J ¼ 2.1 mJ/m2. The inset shows the magnetostatic domain-wallinteractions in the trilayer, The energy in the wall is estimated from thedemagnetizing factor D ¼ Rz/(RxþRz) ¼ 2t/(dwþ2t) of a long rod with anellipsoidal cross section.07C113-3 Li et al. J. Appl. Phys. 109, 07C113 (2011)

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Magnetization precession and domainwall structure in cobalt-ruthenium-cobalt trilayers

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