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IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 10, OCTOBER 2006
Magnetization Relaxation in Sputtered Thin Fe Films: An FMR Study Bijoy K. Kuanr1 , Alka V. Kuanr3 , R. E. Camley2 , and Z. Celinski2 Physics Department, University of Colorado, Colorado Springs, CO 80903 USA and Zakir Husain College, Jawahar Lal Nehru Marg, Delhi University, Delhi, India Physics Department, University of Colorado, Colorado Springs, CO 80903 USA Shaheed Rajguru College of Applied Science for Women, Jhilmil Colony, Delhi University, Delhi, India Recently, various groups have proposed competing relaxation mechanisms on the magnetization damping in thin magnetic films. We used the ferromagnetic resonance (FMR) technique to understand this behavior from FMR linewidths of sputtered thin Fe films sandCu, Al, Ti, and Ta) of 30 on each side. We made samples of Fe(d)/GaAs(100), Al/Fe(d)/Al/GaAs(100), wiched by normal metals ( 20 to 300 . H scales with 2 in bare Fe/GaAs Cu/Fe(d)/Cu/GaAs(100), Ti/Fe(d)/Ti/GaAs(100), and Ta/Fe(d)/Ta/GaAs(100), with and Al/Fe(d)/Al series of samples following the well-known two-magnon mechanism. The sandwich Fe series with Cu, Ti, and Ta follow 1 behavior attributed to recently proposed spin pumping process. After analyzing the data, we conclude Ti/Ta as good spin sink materials, with a mixing conductance twice/thrice larger than Cu. We termed Cu as poor spin sink material in the sandwich Fe structures. Our analysis shows that FMR linewidth data is a powerful tool to investigate interfacial transport properties of magnetic sandwich structures.
=
A
=
A 1
Index Terms—Damping, magnetic films, microwave measurements, thin films.
I. INTRODUCTION
T
HE renewed interest in studying the ferromagnetic resonance (FMR) linewidth [1]–[4] to understand the relaxation mechanism of thin magnetic films is due to their technological relevance for magnetic recording. Modern disk drives can read and write a binary bit in every 2 ns. This time scale is similar to the magnetic damping time of a ferromagnetic thin film used in the head. The local magnetization dynamics in a ferromagnetic thin film can be described by the Landau–Lifshitz–Gilbert (LLG) equation, involving a Gilbert damping constant . In thin nanostructured samples, the magnetization dynamics is no longer a highly coherent process because interface and surface roughness are relatively more important. Many–magnon processes [5] can acquire a sizeable spectral and are observable as an increased line width of the FMR. Another source of FMR broadening is nonlocal, depending on the interfaces into which the ferromagnet is embedded. In this situation, a time-dependent ferromagnetic order parameter pumps spin currents, carrying angular momentum and energy, into adjacent conducting materials. This angular-momentum loss, in turn, is equivalent to an additional damping torque on the magnetization. The spin-pumping concept of Tserkovnyak et al. [6] for the magnetization dynamics of nanostructures has far-reaching consequences. It gives rise to an enhanced Gilbert damping of magnetic films in contact with conducting ˇ media. Simánek et al. [7] pointed out that time-dependent linear-response theory could be used to calculate the spin flows generated by a ferromagnet with a time-varying magnetization in contact with a nonmagnetic conductor. Therefore, the analysis of experimental FMR results probes the magnetization dynamics [8] in magnetic system.
Digital Object Identifier 10.1109/TMAG.2006.878408
The present investigation deals with the study of FMR linewidth of thin polycrystalline Fe films on GaAs(100) substrates in NM/Fe/NM structures (NM [30 ] of Al, Cu, Ti, and Ta). It aims to clarify the effect of two-magnon mechanism and spin transport phenomenon on different NM/Fe(d)/NM system. II. EXPERIEMNT Polycrystalline Fe films, with thickness (d) of 20 to 300 in steps of 20 were grown by magnetron sputtering on GaAs(100) substrates with a background pressure 10 torr. After cleaning the GaAs substrate in an ultrasonic bath, we annealed it to 300 C inside the vacuum chamber. All the depositions were done at room temperature. We grew five series of Fe films: 1) Fe directly on GaAs substrate dusted with a very at the top to prevent oxidation, 2) Fe thin layer of Cu 5 film sandwiched by 30 Al on GaAs(100), 3) Fe sandwiched by 30 Cu on GaAs(100), 4) Fe film sandwiched by 30 Ti on GaAs(100), and 5) Fe sandwiched by 30 Ta on GaAs(100). We have used 10-GHz FMR systems to study the and linewidth as a function of in-plane FMR field was measured field angle. The peak-to-peak linewidth from the differential FMR signal and the reported value is an average over the angular variation. From the in-plane angular we calculated uniaxial anisotropy 10– Oe variation of for all the samples irrespective of different buffer and capping layers. Further, microstructure characterization was made by X-ray diffraction (XRD) to determine the porosity and the grain size of the samples. From the full width of the half maximum of the XRD peak, the average grain size ( ) of the sample – . The grain size of the sample was found [9] to be is important to determine the exact theory applicable to the model calculation for the relaxation processes. The uniaxial anisotropy of the Fe film measured from Magneto Optic Kerr Effect (MOKE) hysteresis loop measurements are 12– Oe.
0018-9464/$20.00 © 2006 IEEE
KUANR et al.: MAGNETIZATION RELAXATION IN SPUTTERED THIN Fe FILMS; A FMR STUDY
Fig. 1. FMR linewidth as a function of Fe layer thickness in the series of bare Fe(d) film, Al/Fe(d)/Al, Cu/Fe(d)/Cu, Ti/Fe(d)/Ti, and Ta/Fe(d)/Ta on GaAs(100) substrates. The solid and the dashed lines are fits to d and d functions, respectively, as described in the text. The insets give the fitting parameters.
III. RESULTS and DISCUSSION Fig. 1 shows the average FMR linewidth as a function of Fe thickness ( ) for: part “A” Fe(d)/GaAs(100), part “B” Al/Fe/Al/GaAs, part “C” Cu/Fe/Cu/GaAs, part “D” Ti/Fe/Ti/GaAs, and part “E” Ta/Fe/Ta/GaAs films, respectively. The NM thickness was kept as 30 , keeping in mind that at this limit the absorption of spin-current [6] pumped from a ferromagnet is maximum. In all the five cases, decreases with the increase of Fe thickness. However, the rate of decrease is different from case to case. is very large for 20 and 40 samples in all the five cases as surface-to-volume ratio is significantly large for this ultrathin limit. saturates with increasing Fe film thickness above 150 in all cases. The solid line and the dotted lines to the experimental results were obtained from and fits plus a constant term. These two fits were arrived by considering different mechanisms in the investigation of magnetization relaxation of ferromagnetic thin films. According to two-magnon theory proposed by Arias and Mills [5], the uniform precession mode can scatter off the defects and imperfections on the surfaces/interfaces into degenerate volume modes. This process becomes prominent in ultrathin films, since the dominant energy contribution comes from surface anisotropy . Starting from (94) of AM model [5] and the approximation taken by Azevedo et al. [2] for thin magnetic films consisting of defects in the shape of rectangular parallelepipeds the total linewidth is given by [2], [5], and [8]
(1)
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is related to The geometrical factor the dimensions of the rectangular defects: height (b), width (c), length (a), and fraction of the surface covered by the defect (p). D is the stiffness constant. For a thin magnetic film, the effective anisotropy field has two contributions: i.e., . For ultrathin limit, the surface part often dominates. From the in-plane angular FMR measurements, we determine the anisotropy fields and found that a behavior is appropriate below 120 . In this case, the linewidth should be inversely proportional to square of sample thickness. Therefore, a fit of a function to is consistent with a two-magnon contribution to linewidth. We fit function to all the series studied here (solid line in the figures). The damping processes observed in bare Fe films (part A) and for Al/Fe/Al films (part function. Therefore, these series of samB) are best fit to a ples are consistent with the two-magnon relaxation processes. fit diverges away from the data of Cu, On the contrary, a plus a constant term fits well to the exTi, and Ta series. A perimental data. These results, thus, are not in agreement with the theory of two-magnon process. The presence of different metallic interfaces to Fe significantly changes the magnetization relaxation. To interpret these results, we considered a ferromagnetic film of thickness connected to two perfect nonmagnetic reservoirs, which support well-defined scattering states. The electrons incident on the ferromagnet are distributed according to the Fermi–Dirac statistics of the respective reservoir. The probability that an electron leaving the ferromagnet returns back with finite spin (phased memory) is extremely small. Such perfect spin sinks can be realized experimentally by attaching the ferromagnetic film to normal metal reservoir on either side. Coherent motion of magnetization, whose direction is given by the unit vector (t), leads to the emission of a spin current I into each normal-metal layer which acts as spin sinks. The Fe layer, therefore, acts as a spin-dependent scatterer between the two normal metals. The motion of a ferromagnetic spin excited by a radio frequency (RF) field in the FMR experiment (in a ferromagnetic sandwich structure with a large surface-to-volume ratio) pumps spins into adjacent reservoir. These spins damped by spin-flip scattering in the normal conductor lead to a Gilbert form of damping relaxation, which may dominate the intrinsic damping. The spin pumping theory [6] predicts a spin current proportional to the transverse component of the precessing magnetization. We rewrite the total Gilbert damping of [6, eq. (22)] in terms of total FMR linewidth : sum of bulk linewidth plus the spin-pumping contribution. A factor of was multiplied to both sides of (22) [6] to obtain linewidth. The total linewidth (using ) thus obtained is as follows: (2) Therefore, the spin pumping process based on conduction electron scattering at the interfaces of NM/Fe must induce a dependence to . In (2), ; is Plank’s constant, is the magnetization of Fe, is mixing conductance, and is the NM/Fe contact area. It was shown that complex mixing conductance is always nonnegative [6] so the correction to linewidth is always positive. Therefore, the spinpumping process always broadens linewidth, hence, enhancing
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Gilbert damping. The results of the Cu, Ti, and Ta series show ) for Ta/Fe/Ta structure is that the mixing conductance ( thrice and Ti/Fe/Ti structure is twice that of Cu/Fe/Cu structure. , We obtain mixing conductance (multiplied with which is constant) as 1.52 for Cu/Fe/Cu, 3.5 for Ti/Fe/Ti and [Ar] 3d 4S ) 4.4 for Ta/Fe/Ta series. In part “C,” Cu (Cu (relatively a light element with one outer most s-electron in the conduction band per atom) does not cause a large damping. On 4S ) in part “D” and Ta (Ta the other hand, Ti (Ti [Ar] [Xe] 4f 5d 6S ) in part “E” (which have unfilled d-electrons in the outermost shell), produce much larger linewidth. Ta being the heavier element (behaves as more efficient spin sinks) produced larger damping in comparison to Ti. With similar crystal structure for all the elements (Cu, Ti, and Ta), one expects the mixing conductance to be larger in Fe–Ti and Fe–Ta in comparison to Fe–Cu structure [6]. Therefore, Cu can be termed as poor spin sink for pumped spins from Fe. The spins pumped to Cu layer scattered back to Fe. In Ti/Fe/Ti and Ta/Fe/Ta structures, Ti/Ta film acts as good spin sink and, hence, the spins relax into the Ti/Ta layers are mostly absorbed. This results in large magnetization damping. For bare Fe series (part “A”), even though Fe is covered with Cu layer on top, does not enhance damping. This is because of negligible spin pumping due 5 . The case of Al (Al to extremely narrow layer of Cu [Ne] 3S 3p , with outer most unfilled p-electron) is tricky, because at Fe/Al interfaces, the intermixing is very high. The ( 200 Oe) for thinner Fe films in Ta, enhancements of Ti and even Al in comparison to Cu are related to their large Fermi level densities of states. In the spin-pumping formulation [6], the quantities determining the damping enhancement are not densities of states but transmission and reflection mixing conductances determined from the scattering matrix. The mixing conductance is usually obtained from the static measurement like angular dependence of magnetoresistance (MR) data. Here, we are providing mixing conductance from a dynamic measure-
IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 10, OCTOBER 2006
ment (FMR), by using the additional damping of the hybrid structures. IV. CONCLUSION We conclude that for the thinnest magnetic layers, the only effect of the spin pumping is to enhance the Gilbert damping. The correction is directly proportional to the mixing conductance (2) and is essentially an interface property. Our experimental results and their interpretation are in good agreement with the microscopic theories taking into account spin-current generated by the precession of magnetization in NM/Fe/NM (NM Cu, Ti, and Ta) films. ACKNOWLEDGMENT This work was supported in part by the U.S. US ARO under Grant DAAD19–02–1–0174 and the DOA under Grant W911NF-04–1–0247. REFERENCES [1] [2] [3] [4] [5] [6]
R. Urban et al., Phys. Rev. B, vol. 65, p. 20 402, 2002. A. Azevedo et al., Phys. Rev. B, vol. 62, p. 5331, 2000. W. Platow et al., Phys. Rev. B, vol. 58, p. 5611, 1998. S. Mizukami, J. Mag. Mag. Mater., pp. 226–230, 2001. 1640. R. Arias and D. L. Mills, Phys. Rev. B, vol. 60, p. 7395, 1999. Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Phys. Rev. B, vol. 66, p. 224 403, 2002. ˇ [7] E. Simánek and B. Heinrich, Phys. Rev. B, vol. 67, p. 144 418, 2003. [8] B. K. Kuanr, R. E. Camley, and Z. Celinski, J. Appl. Phys., vol. 95, p. 6610, 2004. [9] B. D. Cullity, Elements of X-Ray Diffraction, 2nd ed. Reading, MA: Addition-Wesley, 1978, ch. 9, p. 284.
Manuscript received March 12, 2006 (e-mail:
[email protected]).
