Giant magnetic broadening of ferromagnetic resonance in a GMR Co/Ag/Co/Gd quadlayer
aa r X i v : . [ c ond - m a t . m t r l - s c i ] M a r Giant magnetic broadening of ferromagnetic resonance in a GMR Co/Ag/Co/Gdquadlayer.
S. Demirtas and M. B. Salamon
University of Texas at Dallas
A. R. Koymen
University of Texas at Arlington (Dated: December 14, 2018)Both magnetic-resonance damping and the giant magnetoresistance effect have been predictedto be strongly affected by the local density of states in thin ferromagnetic films. We employ theantiferromagnetic coupling between Co and Gd to provide a spontaneous change from parallel to an-tiparallel alignment of two Co films. A sharp increase in magnetic damping accompanies the changefrom parallel to antiparallel alignment, analogous to resistivity changes in giant magnetoresistance.
The discovery of giant magnetoresistance (GMR) byBaibich et al.[1] has led to important applications in mag-netic recording and data storage. Nonetheless, a fun-damental understanding of the microscopic mechanismremains a subject of continuing research.[2, 3] Earlywork[4, 5] considered spin-dependent scattering to be theprimary mechanism for GMR effects, and indeed suchscattering can considerably enhance them.[6] However,Schep, et al.[7] were the first to demonstrate that sig-nificant GMR (for currents perpendicular to the mag-netic layers (CPP) at least) is possible in a perfect mag-netic superlattice, a consequence of s-d hybridization andresultant differential localization of electronic states be-tweeen parallel (P) and antiparallel (AP) alignment. Thesame quantum-well states strongly modify the effective-ness of scatterers at the interface[3], thereby contributingto GMR for in-plane currents (CIP) as well. The aimof this paper is to provide independent evidence for sub-stantial changes in the local density of states accompa-nying a transition from P to AP alignment. Exploitingthe strong antiferromagnetic coupling between Co andGd, we fabricated a GMR structure that spontaneouslyreverses the relative orientation of two Co layers as thetemperature is reduced. Upon reversal from P to APalignment, the width of the ferromagnetic resonance lineof the free Co layer sharply changes its temperature de-pendence. We interpret these results in the context ofthe so-called torque-correlation model of ferromagneticdamping, [8–10] applicable to Co, in which the linewidthis directly related to the local density of states; by anal-ogy, we term the increased broadening Giant Magneto-Broadening (GMB).We have prepared a trilayer structure of Co/Ag/Cowith an underlying Gd layer; the Ag layer is suffi-ciently thick that there is no exchange coupling of thetwo Co layers. Co and Gd are strongly coupledantiferromagnetically.[11] Above, and somewhat below,the Curie temperature of Gd, the two Co layers are fer-romagnetically aligned in a modest magnetic field. Asthe temperature is reduced, the magnetic moment of Gd
50 100 150 200 250 3000.000000.000020.000040.000060.000080.00010 M agne t i c M o m en t [ e m u ] Temperature [K]H=100 Oe
FIG. 1: Magnetic moment as a function of temperature forthe [Co 40 ˚A/Gd 100 ˚A] bilayer. Minimum corresponds to T comp . increases. Below the compensation temperature T comp ,the Gd moment exceeds that of its adjacent Co layer,causing it to align with the magnetic field, producing APalignment of the two Co layers. In Fig. 1, we show thelow-field magnetization of a Ag(10 nm)/Co(4nm) bilayeron Gd(10 nm). The minimum in net magnetization at T comp = 170 K reflects the point at which the magneti-zation of the underlying Gd and its adjacent Co layer areequal and opposite, oriented perpendicular to the appliedfield. The small paramagnetic moment at T comp resultsfrom the canting of the opposing moments toward theapplied field direction.Multilayer samples were created at room temperatureusing a dc magnetron sputtering system. The base pres-sure of the deposition chamber was 10 − Torr. Ultrahigh purity argon gas was used and the deposition pres-sure was 3 mTorr. An in situ quartz thickness monitor,calibrated by a stylus profilometer, measures the deposi-tion thicknesses. Samples were sputtered from pure Gd,Co and Ag targets on Si (100) substrates. Ag layers 200Angstrom (˚A) thick were used as buffer layers in all sam-ples. The Co(1)/Ag/Co(2)/Gd multilayer was createdwith a 100 ˚A nonmagnetic Ag spacer between the two 4nm-Co layers, thick enough to suppress any long rangeexchange interactions. A 100-˚A Ag cap layer completedthe deposition. The Curie temperature T C of the Gdthin film is 240 K, somewhat below the bulk value.The absorption spectrum as a function of appliedmagnetic field for the Co(1)/Ag/Co(2)/Gd multilayer isshown in Fig. 2 at room temperature. The microwavefrequency is 10 GHz and the applied field is in the planeof the sample. Two Lorentzian derivative fits are alsoshown in Fig. 2 to identify two different resonances. Sep-aration of the adjacent absorption peaks can be made be-cause, as shown previously,[12] a proximate layer of Gdreduces the field for resonance and significantly increasesthe linewidth of Co thin films. This leads to the conclu-sion that the broader reasonance is associated with theCo(2) layer. Fig 3 shows the temperature dependenceof the linewidth associated with Co(1) and Co(2) reso-nances. Above the Curie temperature of Gd ( T C = 240K), both resonance lines broaden slightly with decreasingtemperature. Below T C the Co(2) resonance is no longerseen while the Co(1) resonance first broadens abruptlyand then continues to increase with decreasing tempera-ture to the compensation point, T comp = 170 K. Below T comp , the linewidth increases much more strongly withdecreasing temperature, exceeding the resonant field be-low 100 K.Ferromagnetic resonance is generally treated phe-nomenologically via the Landau-Lifshitz-Gilbert (LLG)equation of motion,[13] d −→ mdt = − γ −→ m × −→ H + α −→ m × d −→ mdt . (1)where −→ m is the reduced magnetization vector, γ, the gy-romagnetic ratio and α, the Gilbert damping parameter.Relaxation in metallic ferromagnet films has convention-ally been attributed to the transfer of angular momen-tum from the precessing magnetization to the spin ofthe conduction electrons via s-d exchange and the subse-quent relaxation of the conduction electron polarizationvia spin-dependent scattering.[14] More recently, atten-tion has been focused on the so-called torque-correlationmodel first introduced by Kambersky.[15] In this pro-cess, the time-dependent magnetization induces charge-currents in the conduction electrons via the spin-orbitinteraction. These, in turn, exert torque on the mag-netization, transferring angular momentum to the latticevia the relaxation of charge currents. The longer the re-laxation time τ of these currents, the greater the torqueand the broader the line. For intraband transitions, A b s o r p t i on I n t en s i t y [ a . u .] Magnetic Field [G]
300 K
FIG. 2: FMR absorption spectra for the [Co 40 ˚A/Ag 100 ˚A/Co 40 ˚A/Gd 100 ˚A] film at room temperature. Linewidthswere found making two Lorentzian fits to the overall absorp-tion spectra
Gilmore, et al.[10] have shown that α ( T ) = γτ ( T )2 µ m X nk | Γ n ( k ) | (cid:18) − ∂f∂ε (cid:19) , (2)where τ is the orbital relaxation time of the conduc-tion electron, Γ n ( k ) is the torque matrix element fromthe spin-orbit interaction, and ( − ∂f /∂ε ) is the negativederivative of the Fermi function. The sum is over bandindices. The interplay between the two mechanisms hasbeen discussed by several authors.[9, 16] By artificiallychanging the Fermi energy in their band calculations,Gilmore et al. demonstrate specfically that the summa-tion in Eq. (2) follows the density of states for Co andother ferromagnetic metals. Note that the linewidth isrelated to the Gilbert parameter by ∆ H = 1 . ωα/γ ,where ω/ π = 10 GHz is the applied microwave fre-quency.As seen in Fig. 3, the Co(1) linewidth gradually in-creases with decreasing temperature from T C to T comp and then increases more rapidly below; this is the GMBeffect. A linewidth that increases with decreasing tem-perature is indicative [9] that the torque-correlation pro-cess dominates over spin damping, evidently becomingeven more dominant below T comp . In the absence oftorque-correlation processes, spin-damping, which varies τ ( T ) − , would require a mechanism that, upon rever-sal of the Co(2) magnetization, increases with decreas-ing temperature at a rate that overcomes the increasein τ ( T ). The band structure of the Co(1) layer, on theother hand, will change dramatically upon the transitionfrom P to AP alignment.[7], thereby changing the den-
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Co(1)Co(2)/GdTcomp Co(1)/Ag/Co(2)/Gd
Co(1) is antiparallel to Co(2)Co(1) is parallel to Co(2) L i ne w i d t h [ O e ] Temperature [K]
FIG. 3: FMR linewidth as a function of temperature for par-allel and antiparallel alignment of Co layers in [Co 40 ˚A/Ag100 ˚A /Co 40 ˚A/Gd 100 ˚A] film. sity of states in the Co(1) layer. Further, Binder et al.[3]showed that impurities located within a Co layer in GMRstructures exhibit dramatically larger relaxation rates inAP vs P alignment, again reflecting an increase in the lo-cal density of states. Impurities located at the interfacebetween Co and Cu, in their calculation, are seven timesmore effective as scatterers in the AP configuration; theeffect is even larger for impurities in the center of the Colayer. Similarly, the torque matrix element Γ n ( k ), whichtracks with the density of states, [10] should reflect thesame increase in local density of states in the AP configu-ration. We attribute the seven-fold increase in the slopeof ∆ H ( T ) shown in Fig. 3, therefore, to an increase inthe summation in Eq.(2) and consequently, to a strongerdependence on τ ( T ). Further, Steiauf and F¨ahnle[17]have shown, in the context of the torque-correlation ap-proach, that band-structure effects in lower-dimensionalstructures dramatically increase the Gilbert parameterof Co relative to the bulk metal. We suggest that, inthe single layer considered by Steiauf and F¨ahnle, bothspin sub-bands are localized, much as in the case of APalignment, while only one sub-band is localized in the Pconfiguration. We conclude that the large enchancementof the temperature dependence of the linewidth in ourGMR structure–the GMB effect–confirms both the dom-inance of the torque-correlation process in spin dampingand the importance of electron localization in the GMReffect.There have been, of course, many studies of magneticrelaxation in thin metallic films and multilayers. For ex-ample, an experiment by Urban, et al.[18] found thatthe relaxation rate for a thin Fe layer was larger when a second Fe layer, separated by an Au spacer, was added.Because the increase depends on the thickness d of theresonating layer, they ascribed it to torques that occurat single ferromagnetic-normal metal interfaces, with norole proposed for the thicker Fe layer beyond acting as asink for spin currents. We suggest that localization effectsmay play a role, even though the conduction electrons inFe are less polarized than in Co. A very similar exper-iment [19] showed that when the resonance of the twolayers in an Fe/Au/Fe are made to coincide by judiciouschoice of in-plane field angle, the linewidths are equaland narrowest. This was interpreted in terms of spinpumping between the two layers. In that picture, theoff-resonance ferromagnetic layer acts as a perfect spinsink, except when the two layers have a common reso-nant field. Then spin currents generated in each layercompensate the spin-sink effect of the other.However, theresonances coincide when the effective field is the samein each layer, which may also maximize ferromagneticalignment and minimize localization. As seen in Fig. 2in the present experiment, the Co(2) and Co(1) reso-nances overlap at room temperature, and therefore eachmay be narrowed by spin pumping. Below T c , however,the Co(2) resonance is no longer detected, with the anti-ferromagnetic coupling to the ferromagnetic moment ofGd shifting the resonance out of the observed field range.As a consequence, we expect dynamical coupling due tospin-pumping to disappear below the Gd transition, giv-ing rise to the observed jump in the linewidth of the Co(1)resonance.To summarize, we argue that the change in the tem-perature dependence of the ferromagnetic linewidth thatoccurs at the transition between P and AP alignment,provides independent confirmation of the role of quan-tum confinement in GMR structures. At the same time,it provides further evidence that the torque-correlationmodel plays a substantial role in spin relaxation in metal-lic ferromagnets, especially in Co, which is nearly a half-metal. Clearly, similar experiments using Fe and permal-loy, where the torque-correlation model may be less dom-inant, are clearly in order.One of us (ARK) wishes to acknowlege the support ofthe Welch Foundation through Grant No. Y-1215. [1] M. N. Baibich, J. M. Broto, A. Fert, Nguyen Van Dau,F. Petroff, P. Etienne, G. Creuzet, A. Friederich and J.Chazelas, Phys. Rev. Lett. , 2472 (1988).[2] P. Zahn, J. Binder, I. Mertig, R. Zeller and P.H. Ded-erichs, Phys. Rev. Lett. , 4309 (1998).[3] J. Binder, P. Zahn, and I. Mertig, J. Appl. Phys. ,7107 (2001).[4] R. E. Camley and J. Barna´s, Phys. Rev. Lett. , 664(1989).[5] P. Levy, S. Zhang, and A. Fert, Phys. Rev. Lett. , 1643 (1990).[6] P. Zahn, I. Mertig, M. Richter and H. Eschrig, Phys. Rev.Lett. , 2996 (1995).[7] Kees M. Schep, Paul J. Kelly and Gerrit E. W. Bauer,Phys. Rev. Lett. , 586 (1995).[8] J. Kune˘s and V. Kambersk´y, Phys. Rev. B65 , 212411(2002).[9] K. Gilmore, Y. U. Idzerda and M. D. Stiles, Phys. Rev.Lett. , 07D303 (2008).[11] S. 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