Spin-torque driven ferromagnetic resonance of Co/Ni synthetic layers in spin valves
W. Chen, J-M. L. Beaujour, G. de Loubens, A. D. Kent, J. Z. Sun
aa r X i v : . [ c ond - m a t . m e s - h a ll ] J a n Spin-torque driven ferromagnetic resonanceof Co/Ni synthetic layers in spin valves
W. Chen, J-M. L. Beaujour, G. de Loubens, A. D. Kent
Department of Physics, New York University, New York, NY 10003
J. Z. Sun
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598 (Dated: November 30th, 2007)Spin-torque driven ferromagnetic resonance (ST-FMR) is used to study thin Co/Ni syntheticlayers with perpendicular anisotropy confined in spin-valve based nanojunctions. Field swept ST-FMR measurements were conducted with a magnetic field applied perpendicular to the layer surface.The resonance lines were measured under low amplitude rf excitation, from 1 to 20 GHz. Theseresults are compared with those obtained using conventional rf field driven FMR on extended filmswith the same Co/Ni layer structure. The layers confined in spin valves have a lower resonance field,a narrower resonance linewidth and approximately the same linewidth vs frequency slope, implyingthe same damping parameter. The critical current for magnetic excitations is determined frommeasurements of the resonance linewidth vs dc current and is in accord with the one determinedfrom I-V measurements. Spin-transfer torque has been theoretically predictedand experimentally demonstrated to drive magnetic ex-citations in nanostructured spin valves and magnetic tun-nel junctions [1, 2, 3, 4, 5]. With an rf current, spin trans-fer can be used to study ferromagnetic resonance [6, 7].This technique, known as spin-torque driven ferromag-netic resonance (ST-FMR), enables quantitative studiesof the magnetic properties of thin layers in a spin-transferdevice. Specifically, the layer magnetic anisotropy anddamping can be determined [8], which are important pa-rameters that need to be optimized in spin-torque-basedmemory and rf oscillator applications.Spin-transfer memory devices will likely include mag-netic layers with perpendicular magnetic anisotropy thatcounteracts their shape-induced easy-plane anisotropy.This will allow efficient use of spin current for magneticreversal with a reduced switching threshold [9] and afaster switching process [10]. Recent work by Mangin etal. [11] has demonstrated improvements of spin-torqueefficiency in a spin valve that has perpendicularly mag-netized Co/Ni synthetic layers. For further optimizationof perpendicular anisotropy materials, it is important tohave quantitative measurements of their anisotropy fieldand damping in a nanostructured device, as both of theseparameters directly affect the threshold current for spin-transfer induced switching.In this Letter, we present ST-FMR studies of bilayernanopillars, where the thin (free) layer is composed of aCo/Ni synthetic layer and the thick (fixed) layer is pureCo. The magnetic anisotropy and damping of the Co/Nihave been determined by ST-FMR. We compare theseresults with those obtained from extended films with thesame Co/Ni layer stack measured using traditional rf fielddriven FMR.Pillar junctions with submicron lateral dimensions(Fig. 1(a)) were patterned on a silicon wafer using ananostencil process [12]. Junctions were deposited us-ing metal evaporation with the layer structure k . d V / d I [ O h m ] (d) d V / d I [ O h m ] -15 -10 -5 0 5 10 152468 M a gn e t i c F i e l d [ k O e ] dc Current Bias [mA] (c)(b) Magnetic Field [kG] (a) V H o FIG. 1: (a): Sample layer structure and ST-FMR circuit.(b): Zero current in-plane MR hysteresis loop for a 50 × spin valve junction with t =0.4. (c): dV /dI vs I of thesame junction with a perpendicular magnetic field of 9.5 kOe.(d): Contour plot of dV /dI as a function of both dc currentand perpendicular magnetic field. Data points: critical cur-rents determined from ST-FMR at three different fields andfrequencies (see text). Cr |
100 nm Cu |
20 nm Pt |
10 nm Cu | [ t nm Co | t nmNi] × t |
10 nm Cu |
12 nm Co |
200 nm Cu k . We var-ied the Co thickness t from 0.1 to 0.4, tuning the magni-tude of the Co/Ni composite layer’s net anisotropy, whilekeeping the total magnetic moment and thickness of thefree layer constant. For ST-FMR measurements, an rfcurrent generated by a high frequency source is added toa dc current using a bias-T (the dashed-line box in Fig.1(a)). Positive dc currents are defined such that electronsflow from the free layer to the fixed layer.The magnetoresistance (MR) was measured with amagnetic field applied in the film plane using a 4-pointgeometry. A typical MR hysteresis loop of a 50 ×
150 nm junction with t =0.4 is shown in Fig. 1(b). The magne-toresistance MR= ( R AP − R P ) /R P is ≃ ± t , within the range inves-tigated. Here R AP ( R P ) represents the static junctionresistance when the free layer and fixed layer magneti-zations are antiparallel (parallel). Current-voltage mea-surements were conducted with a magnetic field applied nearly perpendicular to the sample surface (The fieldwas applied 2 ◦ from the film normal to produce a smallin-plane field along the easy axis of the junction. Thiswas done to suppress vortex states in the magnetic lay-ers.) Measurements were conducted in a 2-point geome-try where lead resistances are included. Fig. 1(c) shows dV /dI vs I of the same junction in a 9.5 kOe appliedfield. A peak without hysteresis is observed at 9.1 mA,which we interpret as the critical current I c for excitationof the free layer [13]. A contour plot of 2-point dV /dI asthe function of both current and perpendicular magneticfield is shown in Fig. 1(d). The peak in dV /dI is seen asthe bright color at high field and current.At resonance, the rf current and spin valve resistanceoscillate at the same frequency resulting in a dc voltage( V = < I ( t ) R ( t ) > ) [6, 7]. This voltage can be expressedas V = ( R AP − R P ) I rf sin β sin θ . Here β is the an-gle between the free and fixed layers before applying therf current and θ is the precession angle. I rf representsthe rf current amplitude. This is a simplified formulathat assumes small angle precession and a sinusoidal an-gular dependence of junction resistance between paralleland antiparallel states. With a perpendicular magneticfield greater than the free layer’s easy-plane anisotropyfield, the free layer magnetization is normal to the sur-face, while the fixed layer, which has a larger easy-planeanisotropy field, is still mainly magnetized in the filmplane. This non-collinear arrangement of the layer mag-netizations ( β . π/
2) enhances the ST-FMR signal. Tofurther increase the signal (typically in the sub- µ V range)to noise ratio, we modulate the rf current on and off at800 Hz and use a lock-in amplifier to detect the voltageat this frequency.ST-FMR measurements were conducted with the cir-cuit shown in Fig. 1(a). Resonance lines under low am-plitude rf current at zero dc current and different rf fre-quencies f are plotted in Fig. 2(a) versus perpendicularmagnetic field. Different frequencies (3 ∼
20 GHz in 1 GHzsteps) are plotted with each adjacent curve offset by 0.4 µ V. The voltage signals are shown on the left verticalaxis. From the peak height V peak and I rf , we estimatethe precession angle to be ∼ ◦ . We verified that thisset of data was taken in a linear response regime with V peak /I independent of I rf . These data are typical ofall junctions with t =0.4. However, much broader reso-nance peaks and multiple peaks were found on sampleswith t =0.1, 0.2 and 0.3. This is likely associated withthe excitation of higher order spin wave modes, but isnot presently understood. Therefore, data analysis anddiscussion mainly focus on samples with t =0.4.
20 GHz (b) V l o ck - i n [ (cid:80) V ] Magnetic Field [kOe](a) F r e qu e n cy [ G H z ] L i n e w i d t h [ k O e ] Frequency [GHz]
FIG. 2: (a): Lock-in voltage signal as a function of appliedperpendicular magnetic field at different rf frequencies from3 up to 20 GHz in 1 GHz steps. N : H res of a 50 ×
150 nm , t =0.4 Co/Ni synthetic free layer in a spin valve; black dashedline: corresponding linear fit; gray dashed line: a linear fitof H res vs f of an extended film with the same Co/Ni layerstack. (b): ∆ H vs f for the spin valve junction ( N ) and theextended film ( (cid:4) ), together with their corresponding linearfits. We also measured resonance lines on an extended filmwith the same Co/Ni synthetic layer stack sandwichedbetween 10 nm Cu on each side. These measurementswere conducted with a traditional rf field driven FMRusing a flip-chip method [14]. Broader resonance peakswere not found in extended films with t =0.1, 0.2, and0.3.The resonance field H res of the Co/Ni element in thespin valve increases linearly with f above 4 GHz, asshown in Fig. 2(a) ( N symbols). At lower frequencies,the free layer magnetization tilts into the plane, lead-ing to a lower resonance field. A linear fit of H res vs f of the extended film is also plotted with a gray dashedline (to the right of the N symbols) in Fig. 2(a). Alinear relationship between f and H res in extended mag-netic films is expected when the magnetization is normalto the film surface hµ B f = g ( H res − πM eff ) [15]. Here g is the Land´e g factor and the easy-plane anisotropyis 4 πM eff = 4 πM s − H P , where M s and H P repre-sent the saturation magnetization and the perpendicularanisotropy field. A linear fit of each data set (dashed linesin Fig. 2(a)) gives g =2.17 and 4 πM eff = 2 .
58 kOe forthe extended film, and a slightly larger slope (2.28) anda smaller field-axis intercept (1.92 kOe) for the Co/Nielement confined in the spin valve. This consistency be-tween data sets confirms that the main peak of the ST-FMR signal is associated with the Co/Ni synthetic freelayer rather than the other magnetic layers. The differ-ences are associated with the static dipolar fields fromother magnetic layers and finite size effects on the spinwave modes, which is discussed in detail in a forthcoming (b)
Magnetic Field [kG] V l o ck - i n [ (cid:80) V ] -4 mA6 mA (a) Current Bias [mA] (cid:39) H [ k O e ] FIG. 3: (a): ST-FMR signal as a function of applied field atdifferent dc currents. The rf frequency was set at 18 GHz,and the rf amplitudes were 595, 595, 470, 470, 315 and 315 µ A respectively for each dc current from -4 to 6 mA in 2 mAsteps. Each adjacent curve is offset by 0 . µ V. Solid linesare Lorentzian fits of each data set. (b): ∆ H (full width athalf maximum) vs dc current. publication [16].Here we focus on the resonance linewidth ∆ H . ∆ H vs f at zero dc bias is plotted in Fig. 2(b). ∆ H of boththe Co/Ni layer in spin valve ( N ) and the same-stackextended film ( (cid:4) ) increases linearly with f . Linear fitsare shown as solid lines in Fig. 2(b), and give an interceptand slope: ∆ H = ∆ H + 2 αhgµ B f (1)where h is the Planck Constant and µ B is the Bohr Mag-neton. The first term ∆ H describes the inhomogeneousbroadening, and the second term is related to the damp-ing α [17]. ∆ H vs f of the spin valve and that of the ex-tended film have a similar slope, implying a similar damp-ing parameter ( α =0.036 ± ± H =24 ± ±
30 Oe.When a dc current bias is applied to a spin-value, thereis an additional spin transfer torque that modifies thefree layer’s effective damping, α eff = α (1 − II c ), where I is the dc current. Thus α eff decreases with increasingpositive current up to a critical current I c , that definesthe threshold for magnetic excitation of the free layer.The critical current in the Slonczewski model [1] is givenby I c = e ~ P αM s V cos β ( H − πM eff ), where P is the spin po- larization factor and V is the volume of the magnetic el-ement. So with a dc bias, ∆ H -∆ H = αhfgµ B (1 − II c ), andtherefore at fixed frequency ∆ H -∆ H depends linearlyon current and goes to zero at the critical current. Weplot resonance lines of the spin valve with f = 18 GHzat different dc currents from -4 to 6 mA in 2 mA steps inFig. 3(a). ∆ H vs dc current bias is shown in Fig. 3(b).The intercept of ∆ H vs I is 7.8 mA. Inclusion of ∆ H decreases the intercept by no more than 0.2 mA, because∆ H is small compared to the linewidth at the dc cur-rents studied. Critical currents determined for f =10, 14and 18 GHz are plotted in Fig. 1(d), and agree well withthose obtained from the I-V measurements. Further, I c is quantitatively consistent with the Slonczewski modeltaking a spin polarization factor P ∼ H originates fromfilm inhomogeneities: roughness, polycrystalline struc-ture, as well as defects. The scale of the inhomogeneitiesis likely the film grain size, 5 ∼
10 nm. In a simple model,fluctuations in H res from grain to grain result in an in-homogeneously broadened resonance line [18]. However,it is likely that the exchange coupling between grains isimportant to a detailed understanding of the linewidth[19].The free layer in the nanostructured device containsat most a few hundred grains, therefore one expects lessinhomogeneity than that in extended film. More im-portantly, the lateral magnetic confinement results instrongly varying internal field in the plane of the nanos-tructure that lifts the degeneracy between different spinwave modes. Numerical and analytical calculations ofnormal modes in the Co/Ni rectangular element are pre-sented and compared with our ST-FMR data in Ref. [16].The separation between them is more than the inhomo-geneous broadening ∆ H in the extended film, thereforewe expect that the linewidth measured on an individ-ual mode is close to its intrinsic value (the term propor-tional to f in Eq. 1) [20]. The remaining inhomogeneousbroadening in the nanostructure may be attributed to thequasi-degeneracy subsisting between some very closelyspaced modes resulting from film inhomogeneities.In summary, ST-FMR has been used to study the mag-netic properties of Co/Ni synthetic layers with perpendic-ular anisotropy in spin valves. The ST-FMR resonancelines were compared with those of traditional FMR onsame-stack extended film. The damping of the ST-devicefree layer is essentially the same as that of an unpat-terned film and the critical currents determined from theST-FMR homogeneous linewidth are in agreement withthose of quasistatic I-V measurements.This research is supported by NSF-DMR-0706322 andan NYU-Research Challenge Fund award. [1] J. C. Slonczewski, J. Magn. Magn. Mater. , L1(1996). [2] L. Berger, Phys. Rev. B , 9353 (1996). [3] J. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers,and D. C. Ralph, Phys. Rev. Lett. , 3149 (2000).[4] J. Z. Sun, J. Magn. Magn. Mater. , 157 (1999).[5] Y. Huai, F. Albert, P. Nguyen, M. Pakala, and T. Valet,Appl. Phys. Lett. , 3118 (2004).[6] A. A. Tulapurkar, Y. Suzuki, A. Fukushima, H. Kub-ota, H. Maehara, K. Tsunekawa, D. D. Djayaprawira,N. Watanabe, and S. Yuasa, Nature , 339 (2005).[7] J. C. Sankey, P. M. Braganca, A. G. F. Garcia, I. N.Krivorotov, R. A. Buhrman, and D. C. Ralph, Phys. Rev.Lett. , 227601 (2006).[8] G. D. Fuchs, J. C. Sankey, V. S. Pribiag, L. Qian,P. M. Braganca, A. G. F. Garcia, E. M. Ryan, Z.-P. Li,O. Ozatay, D. C. Ralph, and R. A. Buhrman, Appl. Phys.Lett. , 062507 (2007).[9] J. Z. Sun, Phys. Rev. B , 570 (2000).[10] A. D. Kent, B. ¨Ozyilmaz, and E. del Barco, Appl. Phys.Lett. , 3897 (2004).[11] S. Mangin, D. Ravelosona, J. A. Katine, M. J. Carey,B. D. Terris, and E. E. Fullerton, Nature Materials ,210 (2006).[12] J. Z. Sun, Appl. Phys. Lett. , 2202 (2002). [13] B. ¨Ozyilmaz, A. D. Kent, D. Monsma, J. Z. Sun, M. J.Rooks, and R. H. Koch, Phys. Rev. Lett. , 067203(2003).[14] J.-M. Beaujour, W. Chen, K. Krycka, C.-C. Kao, J. Z.Sun, and A. D. Kent, Eur. Phys. J. B , 475 (2007).[15] C. Kittel, Introduction to Solid State Physics (John Wi-ley & Sons, Inc., New York, 1996).[16] W. Chen, G. de Loubens, J.-M. L. Beaujour, A. D.Kent, and J. Z. Sun, to be published in J. Appl.Phys. as MMM’07 Conference Proceeding, preprinted atarXiv:0712.0404 (2007).[17] D. L. Mills and S. M. Rezende,
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