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Fe film plane
Journal of Magnetism and Magnetic Materials 451 (2018) 480–486
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Research articles
Anomalously large ferromagnetic resonance linewidth in the Gd/Cr/Fe film plane Li Sun a,⇑, Wen Zhang b,f, Ping Kwan Johnny Wong e, Yuli Yin b, Sheng Jiang c, Zhaocong Huang b, Ya Zhai b, Zhongyu Yao a, Jun Du d, Yunxia Sui d, Hongru Zhai d a
College of Physics and Electron Engineering, Hainan Normal University, Haikou 571158, China Department of Physics, Southeast University, Nanjing 211189, China Department of Materials and Nano Physics, School of Information and Communication Technology, Kista 16440, Sweden d National Laboratory of Solid Microstructures, Nanjing University, Nanjing 210093, China e NanoElectronics Group, MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands f Department of Physics, National University of Singapore, 2 Science Drive 3, 117542, Singapore b c
a r t i c l e
i n f o
Article history: Received 30 July 2017 Received in revised form 3 November 2017 Accepted 22 November 2017 Available online 23 November 2017 Keywords: Ferromagnetic resonance Linewidth Dampingconstant Two magnon scattering
a b s t r a c t As an important parameter for characterizing the magnetization dynamics, Gilbert damping constant a in a thin film or a multilayer is generally extracted from the linear fitting of the frequency-dependence of the ferromagnetic resonance linewidth, sometimes accompanied with a tiny deviation of the linewidth to a smaller value at the low-frequency or high-frequency region due to the two-magnon scattering with an in-plane-field configuration, in which an in-plane magnetic field H perpendicular to a microwave field h was applied in film plane during measurement. In contrast, here we report, in ultrathin Gd/Cr/Fe multilayers, an anomalously large linewidth in the film plane at the low-frequency region. For the first time, we have successfully extracted the Gilbert damping constant from perfect theoretical fitting to the experimental data, by considering the effective direction of the magnetization around in precession staying out of the film plane when the in-pane H at which the precession starts is below the saturation field. This magnetization deviation from the film plane is found to have an obvious contribution to the enhanced linewidth caused by two magnon scattering, while slightly reduce the intrinsic linewidth. Under the same resonance frequency, the deviation angle reaches the maximum values at tCr = 1.0 nm while decreases when tCr increases to 1.5 nm, which coincides with the trend of the surface perpendicular anisotropy constant K\. A reduced intrinsic damping constant a is obtained as the introduction of Gd layer and Cr layer as a result of the competition between the spin pumping effect and the interfacial effects at the Fe/Gd and Fe/Cr interfaces. While the decreasing a for film with Cr layer thickness increasing to 1.5 nm might means the contribution of the electron density of states at the Fermi energy n(EF). This study offers an effective way to accurately obtain the intrinsic damping constant of spintronic materials/devices, which is essential for broad applications in spintronics. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Gilbert damping constant a is an intrinsic parameter for characterizing the magnetization dynamics, which is in turn of crucial importance for current/future spintronic applications. For instance, a determines threshold current in spin-transfer-torque induced magnetization switching in magnetic tunnel junctions [1–3], plays critical roles for the performance of the readers in tunnel magnetoresistance readers as the free layer [4,5], and limits the steady-state oscillation excited in spin torque oscillator [6–8]. Ferromagnetic ⇑ Corresponding author. E-mail address: [email protected] (L. Sun). https://doi.org/10.1016/j.jmmm.2017.11.098 0304-8853/Ó 2017 Elsevier B.V. All rights reserved.
resonance (FMR) is one of the classic techniques to study the damping of magnetic thin films and multilayers by measuring their FMR linewidth [9,10]. Therefore, elucidate the mechanisms in linewidth which control the damping of spin motions is very important for study and developing spintronics devices. However, the linewidth is very sensitive to the structural and magnetic quality. Especially in ultrathin film, the contribution of two magnon scattering (TMS) play a not negligible role [11], in which accompanied with a tiny deviation of the linewidth to a smaller value at the lowfrequency and high-frequency region with in-plane-field configuration [12–14]. Here, a different deviation (to larger values) of the linewidth at lower frequencies with in-plane magnetic field was obtained in
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Gd/Cr/Fe film, which has higher saturation magnetization by employing a metal spacer layer (Cr) to mediate the antiferromagnetic coupling between Gd and Fe [15–17], simultaneously with modifying the intrinsic damping. The similar experimental results had also been obtained in ultrathin film with perpendicular magnetic anisotropy [18,19]. However, there has been no further numerical analysis on the magnetic illustration of such phenomenon but explained in terms of two-magnon scattering and low-field loss. In this paper, according to the theoretically report [20], we attribution this large linewidth to the two magnon scattering contribution in case of the effective direction of magnetization around during precession not parallel to the direction of inplane magnetic field. At the same time, the impact on the intrinsic linewidth was also studied. It is found the non-linear relationship between linewidth and microwave frequency were successfully fitted, and the magnetization deviation plays an important role in FMR linewidth.
at room temperature. Before deposition of Fe, a thin layer of Ta (5 nm) is first prepared as a buffer layer. The Cr thickness, tCr, varies as 0, 1.0, and 1.5. After deposition of Gd, all the samples are capped with 5-nm-thick Ta. For comparison, a pure Fe (5 nm) film, with 5-nm-thick Ta as both the capping and buffer layers, is also prepared. The base pressure of the sputtering chamber is 1.2 105 Pa, and the Ar working pressure is 0.5 Pa. For the Fe and Ta, a dc power of 30 W is used, while for the Gd and Cr, 15 W and 10 W are used, respectively. A magnetic field of 50 Oe is applied during sample preparation, which induces a small in-plane uniaxial magnetic anisotropy. Static magnetic properties are characterized using vibrating sample magnetometry (VSM), and dynamical magnetic properties are investigated by broadband ferromagnetic resonance (FMR) using a NanOsc Instruments Phase FMR with a 200-lm-wide coplanar waveguide. All the measurements are performed at room temperature.
2. Materials and methods
3. Results
A series of Gd(4 nm)/Cr(tCr)/Fe(5 nm) trilayers, as depicted in Fig. 1(a), are deposited on Si substrates by dc magnetron sputtering
Hysteresis loops, obtained by VSM, with the external magnetic field along the uniaxial easy axis (i.e., the direction of the small
Fig. 1. (a) Schematic diagram of the Gd/Cr/Fe trilayer structure. (b)–(e) In-plane hysteresis loops for the Fe and Gd/Cr/Fe films, with the magnetic field applied along the magnetization easy axis, measured by VSM. Insets: Enlarged area near the saturation field (HS) which is indicated by the arrow. The red dashed lines represent the linearly extrapolation from the high field magnetization. (f) tCr dependence of the coercivity. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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magnetic field applied during preparation) are shown in Fig. 1(b)– (e). The loops along the hard-axis direction are not shown, since they do not look much different from those in the figures due to the very small magnitude of the induced uniaxial anisotropy. The saturation magnetizations listed in Table 1 are determined by linearly extrapolation from the high field magnetization of hysteresis loops as shown the red dashed lines in Fig. 1. The saturation fields (HS) are also marked in the insets, which are important for the following analysis of FMR results. The values of the coercivity (HC) are summarized in Fig. 1(f): Upon insertion of the Gd layer, the HC becomes obviously larger than the Fe thin film, probably attributed to the antiferromagnetic coupling between Fe and Gd [21]; When Cr is inserted, HC increases with the increasing tCr, probably due to the introduction of two antiferromagnetic coupled interfaces of Fe/Cr and Cr/Gd, which has already been demonstrated by Sanyal et al. [15]. As shown in Table 1, the large saturation magnetization (MS) was obtained from the hysteresis loops which is similar to those reported in RE/Cr/TM trilayers [15–17,22,23], where Cr mediated the ferromagnetic coupling between Gd and Fe. FMR has been taken for all the samples with various frequencies ranging from 7 GHz to 25 GHz, with an in-plane-field configuration, in which an in-plane magnetic field H perpendicular to a microwave field h was applied along the uniaxial easy axis in film plane. Typical FMR spectra are shown in Fig. 2, from which we may see that at low frequencies such as 8 GHz, the resonance starts at a smaller magnetic field than the saturation field Hs, as marked by the arrows in Fig. 2 as well. Specifically, for the Fe film and Gd/Fe bilayer, this phenomenon happens with the frequency lower than 13 GHz; While for the Gd/Cr (1 nm)/Fe and Gd/Cr (1.5 nm)/Fe trilayers, it occurs lower than 14 GHz. Which results in the discrepancy, at the low frequency range, between the experimental data and the conventional numerical fitting involving intrinsic damping, TMS, inhomogeneous contributions, etc. Interestingly, the discrepancy disappears at high frequencies, such as 15 GHz, as the resonance starting at a larger magnetic field than Hs. To solve this discrepancy, below we try to find out a more common model than the conventional one, for the magnetization precession in these samples at the broad frequency range, by quantitative studies on the frequency-dependent resonance field, Hres, and linewidth, DH. 3.1. Fitting the dependences of resonance frequency on Hres First, we try to extract magnetic dynamical parameters by fitting the dependence of frequency (f) on the resonance field (Hres). By solving the Landau-Lifshitz-Gilbert (LLG) equation and minimizing the total free energy density, the Hres-dependence of f can be obtained from the equation below [24],
f ¼
c qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðHres þ Hk ÞðHres þ Hk þ 4pM eff Þ; 2p
ð1Þ
? where 4pM eff ¼ 4pMs 2K is the effective magnetization with the Ms
saturation magnetization (MS) and the perpendicular magnetic anisotropy constant (K\), Hk is the in-plane anisotropy field, and c is the gyromagnetic ratio. Here, the total free energy density of the system involves the Zeeman energy, demagnetizing energy, and the energy of perpendicular anisotropy and in-plane uniaxial aniso-
Fig. 2. Typical FMR spectra, taken from an in-plane-field configuration, with the microwave frequency ranging from 8 GHz to 15 GHz, as indicated by the numbers in the unit of GHz. The arrows point out the positions of Hs, corresponding to those in Fig. 1b–e.
tropy. In the high frequency range, we find that the Hres are well fitted for the Gd/Cr/Fe films, from which 4pMeff, c, and K\ are extracted in Table 1. As expected, the obtained value of Hk from fitting is very small in all the samples, typically a few Oersteds, which is neglected in the following equations. Compared with the Fe film, c is significantly reduced with addition of the Gd layer, which may be attributed to the interaction between Fe and Gd with the quenched orbital magnetic moment [25]. Upon insertion of Cr, this interaction becomes weaker, and in turn the reduction of c becomes slower. Similarly, the effective magnetization 4pMeff is strongly increased by introduction of Gd probably due to the magnetic proximity effect [26,27], and then decreases with insertion of Cr. On the other hand, a similar enhancement K\ is obtained after adding Gd layer due to the increased interfaces as reported in Ref. [28] and weakened as the inserting of Cr layer. The perpendicular magnetic anisotropy constant is changed from positive to negative as the thickness of Cr layer increasing up to 1.5 nm, which coincide with the simulated values of deviation angles discussed later. Note that here the negative value of K\ represents the preferred alignment of the magnetization in the film plane, and a positive value corresponds to the magnetization staying out of the film plane. As we recently reported in Gd(Tb)/Cr/Ni80Fe20 system [23,29], the
Table 1 Extracted parameters for the Fe and Gd/Cr/Fe films from theoretical fitting. tCr (nm)
Ms (emu/m3)
4pMeff (104 Gs)
c
K\(105 erg/cm3)
DH0 (Oe)
a(1 0 2)
Fe film 0 1 1.5
1221 ± 102 1020 ± 183 1307 ± 131 1274 ± 127
1.452 ± 0.007 1.797 ± 0.032 1.604 ± 0.024 1.623 ± 0.023
1.885 ± 0.001 1.791 ± 0.004 1.810 ± 0.004 1.816 ± 0.004
5.0 ± 0.4 -26.3 ± 1.6 2.5 ± 1.2 -1.4 ± 1.1
85 87 106 120
1.173 ± 0.001 0.985 ± 0.002 1.057 ± 0.003 0.821 ± 0.002
(107 (Oes)1)
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perpendicular magnetic anisotropy, which is dependent on the exact nature of the interface (e.g., interface/surface roughness and adjacent materials), oscillates with the thickness of Cr layer, and the oscillation is related to the value of Ms. The dependences of f on Hres for all the samples are shown in Fig. 3c and e, from which we see that the numerical calculations (solid lines) do not fit the experimental data (dots) very well, in particular at the low frequencies as shown in Fig. 3c. This is because that Eq. (1) is obtained by assuming the magnetization processes around the direction of the external magnetic field, i. e. the effective direction Heff along the uniaxial easy axis in film plane as shown in Fig. 3a. Namely, in Eq. (1) we assume that the magnetization angles h = hH = 90° and u = uH = 0°, where h is the angle of the magnetization vectors in spherical coordinates with respect to the film normal, u is the in-plane angle of the magnetization vector with respect to the in-plane magnetization easy axis, while hH and uH are the angles of the magnetic-field relative to the film normal and the in-plane easy axis, respectively. Obviously, Eq. (1) cannot be used for numerical fitting at lower frequency range, where the magnetization cannot be saturated along the direction of the external applied field when resonance begins. Alternatively, we introduce a precession model, where the magnetization does not process around the external field while deviates with a small angle, 90°-h, from the external magnetic field or the in-plane easy axis, i. e. the effective direction Heff deviating from the external field, as shown in Fig. 3b. Accordingly, Eq. (1) can then be modified as below:
f ¼
c pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2p
HX H Y ;
HX ¼ Hres sin h 4pMeff cos2 h;
ð2Þ ð2aÞ
and
HY ¼ Hres sin h 4pMeff cos 2h:
ð2bÞ
Using the extracted parameters in Table 1, the experimental data at both low and high frequencies can be satisfactorily fitted, as shown in Fig. 3d and f. Note that this fitting is based on the fact that the magnetic anisotropy in the film plane is not large enough
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to influence the resonance field and linewidth, so that the in-plane projection of the magnetization in our thin films is supposed to be along the induced easy axis. 3.2. Fitting the frequency-dependences of DH Generally, the FMR linewidth, DH, is expressed as [30–32]
DHðf Þ ¼ DH0 þ DHintri þ DHTMS
ð3Þ
where the DH0 describes an inhomogeneous broadening due to sample imperfections which is assumed to be independent of f; DHintri is the intrinsic linewidth that is assumed to be linearly proportional to f in a perfect sample and can be expressed in terms of the Gilbert damping constant a [33,34]; and DHTMS represents the contribution of the two-magnon scattering here is necessary considering as the anomalously enhanced DH at low frequencies. Considering the magnetization deviates out of the film plane, the twomagnon scattering contribution to the linewidth [35] and the intrinsic linewidth [36] can be described as
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u½x2 þ ðx0 =2Þ2 1=2 x0 =2 ; DHTMS ðf ; hÞ ¼ CðHX ; HY ; qÞarsint 1=2 ½x2 þ ðx0 =2Þ2 þ x0 =2
ð4Þ
and
DHintri ðf ; hÞ ¼
2Gx c2 Ms
HX þ HY : ½ðHX þ HY Þ sin h þ ðHXh HY =HX þ HYh Þ cos h
ð5Þ
For Eq. (4), x0 = c4pMeff, x = 2pf, and the factor C is the strength of the two magnon scattering along the in-plane crystallographic direction, which is a function of h, as illustrated in Ref. [12]. As a result, DHTMS is not only as a function of frequency, but also depends on h. Eq. (5) is a simplified equation, by substituting hH = 90° and u = uH = 0° and assuming the external field parallel to the induced easy axis of the small in-plane magnetic anisotropy, where HXh and HYh represents the first partial derivatives of HX and HY, respectively.
Fig. 3. Resonance frequency f versus the resonance field (Hres). Symbols represent the experimental data, and the solid lines are the fits by Eq. (1) for (c) and (e) and Eq. (2) for (d) and (f), respectively. The precession of magnetization M around the effective direction Heff in case of lower frequencies are illustrated in (a) and (b). (a) for the effective direction (Heff) in the film plane; (b) for the direction out of the film plane.
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Fig. 4. Frequency-dependences of the FMR linewidth (DH). The black dots represent the experimental data (exp. data), and the black solid lines are theoretical fitting curves (cal.) involving the intrinsic contributions (intri., red stars), two-magnon scattering contributions (TMS, blue cross), and inhomogeneous broadening (inhom., pink intersects). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The fitting results are shown in Fig. 4, where the black solid lines represent the fitting curves, which fit the experimental data (black dots) satisfactorily. Three contributions, including the intrinsic linewidth, inhomogeneous linewidth, and two-magnon scattering, are shown as well. Among them, the intrinsic linewidth has been found to slightly decrease with decreasing frequency, while the two magnon scattering has an abrupt enhancement at the low frequency range resulting from the abovementioned deviation angles. Having a relatively slight contribution in the Fe film and Gd/Fe bilayer, the DHTMS, describing the defect mediated scattering of the uniform precession mode into nonuniform ones, presents stronger contribution in the Gd/Cr/Fe trilayers, nearly irrelevant to the Cr thickness. The inhomogeneous contribution, DH0 is also obtained from the fitting, as listed in Table 1, which increases as the inserting of ultrathin Cr layer. The increased contribution of DHTMS and DH0 as inserting of ultrathin Cr layer might mean the inhomogeneities in Cr layer as its thickness equal to or less than 1.5 nm [37,38]. The deviation angle (90°-h), as a function of frequency, is also obtained from the fitting, as shown in Fig. 5. They are almost linearly decreasing with increasing frequency for all the samples, among which the Gd/Cr (1.0 nm)/Fe trilayer has the highest values at the same frequencies and the slowest decreasing speed, which may be attributed to the fact of the positive K\, as shown in Table 1. The extracted Gilbert damping constants a are also shown in Table 1. Comparing to the Fe film, a is reduced in the bilayer and trilayers, which has also been demonstrated in the Gd-doped FeCo films and probably results from the strong influence of the quenched orbital moment in Gd at the interfaces [25]. After inserting the Cr layer, we found that a becomes larger than Fe/Gd bilayer, probably resulting from the spin-pumping effect in trilayers. In Gd/ Fe bilayer, the Fe spins can be scattered through the spin-orbit cou-
Fig. 5. Frequency-dependences of the deviation angles, i. e. 90°-h, with different tcr.
pling of Gd at the interface; while in Gd/Cr/Fe trilayers, the Fe spins do not interact with Gd directly and an additional mechanism, spin pumping effect, must be taken into account. Tserkovnyak et al. [39] showed that a magnetization precession can generate a spin current into an adjacent normal (NM) layer. Namely, in Gd/Cr/Fe film, the spin current injected by Fe into Cr, and some of which can also be absorbed by the Gd layer [40,41]. Moreover, accompanied by the decreasing of a, a smaller value of a in Gd/Cr/Fe film than that of Fe film was obtained, which implies more interfacial reasons might be taken into consideration other than the decreasing
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spin-pumping effect [23,42]. For example, the dependence of the interlayer coupling on spacer thickness can lead to an oscillations in damping constant [43,44], the spin-current in opposite directions across the Cr/Gd interface [45,46] and the inter-diffusion at the interface between Cr and Fe as reported in Ref. [27] can also reduce a. With the thickness of Cr layer increasing to 1.5 nm, the damping constant is decreasing while the gyromagnetic ratio is almost unchanged (see Table 1), which means other mechanism should be considered besides the spin–orbit interaction. Mankovsky et al. [47] theoretical predicted that the damping parameter can be proportional to the electron density of states at the Fermi energy n(EF) for samples with fixed c. And Schoen and colleagues [48] experimental proved it in metallic CoxFe1x films. We infer that n(EF) changed due to the intermixing at the interfaces of Gd/ Cr/Fe films might be the main origins of magnetic damping for the films with 1.5 nm Cr layer. To obtain a quantitative study of the origin of magnetic damping, more systematic and detailed investigations are necessary, both experimentally and theoretically.
4. Conclusions In summary, a method was proposed for successfully fitting the non-linear relationship between in-plane linewidth and frequency with anomalous large linewidths at lower frequencies in Gd/Cr/Fe films, with considering a deviating angle between the effective direction of magnetization precession and the film plane. It is proved that the alignment of the magnetization plays an important role in a determination and it points a method to accurately separating different mechanisms in linewidth. The obtained angles at the same frequency are the largest for films with 1.0 Cr layer which has positive K\, and go back to those of the Fe film with the increasing thickness of Cr layer as a result of the surface and interface effect. Compared with Fe film, the effective magnetization 4pMeff is improved in Gd/Fe bilayer resulting from the magnetic proximity effect at Gd/Fe interface, while the gyromagnetic ratio c and Gilbert damping constant a are reduced causing by the weakening spin-orbit coupling by adding Gd layer with the quenching of the orbital magnetic moment. Additionally, an inserting Cr layer reduces 4pMeff and makes c close to that of the Fe film from a lower value. Compared with Gd/Fe bilayer, a is increased as the inserting of 1.0 nm Cr layer by spin-pumping effect and decreasing with the increasing thickness of Cr layer to 1.5 nm. The smaller value of a in Gd/Cr (1.0 nm)/Fe film than that of Fe film suggests more interface reasons might be taken into consideration and the decreasing a for Gd/Cr (1.5 nm)/Fe film with nearly fixed c might means the contribution of the electron density of states at the Fermi energy n(EF). In this paper, both the fitting method on analyzing linewidth and the reducing damping constant a which can decrease the threshold current in spin-transfer-torque will have potential application for studying and developing spintronics devices. Acknowledgements This work is supported in part by the National Natural Science Foundation of China [Grant numbers 11364015, 51571062, 61427812, 11364014, 61306121, 11504047]; the Natural Science Foundation of Hainan Province of China [Grant numbers 117109, 114008, 113005]; and the Natural Science Foundation of Jiangsu Province of China [Grant number BK20141328). P.K.J.W. is financially supported by the EU FP7 Project SpinValley under Grant PIOF-GA-201.
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Research articles
Anomalously large ferromagnetic resonance linewidth in the Gd/Cr/Fe film plane Li Sun a,⇑, Wen Zhang b,f, Ping Kwan Johnny Wong e, Yuli Yin b, Sheng Jiang c, Zhaocong Huang b, Ya Zhai b, Zhongyu Yao a, Jun Du d, Yunxia Sui d, Hongru Zhai d a
College of Physics and Electron Engineering, Hainan Normal University, Haikou 571158, China Department of Physics, Southeast University, Nanjing 211189, China Department of Materials and Nano Physics, School of Information and Communication Technology, Kista 16440, Sweden d National Laboratory of Solid Microstructures, Nanjing University, Nanjing 210093, China e NanoElectronics Group, MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands f Department of Physics, National University of Singapore, 2 Science Drive 3, 117542, Singapore b c
a r t i c l e
i n f o
Article history: Received 30 July 2017 Received in revised form 3 November 2017 Accepted 22 November 2017 Available online 23 November 2017 Keywords: Ferromagnetic resonance Linewidth Dampingconstant Two magnon scattering
a b s t r a c t As an important parameter for characterizing the magnetization dynamics, Gilbert damping constant a in a thin film or a multilayer is generally extracted from the linear fitting of the frequency-dependence of the ferromagnetic resonance linewidth, sometimes accompanied with a tiny deviation of the linewidth to a smaller value at the low-frequency or high-frequency region due to the two-magnon scattering with an in-plane-field configuration, in which an in-plane magnetic field H perpendicular to a microwave field h was applied in film plane during measurement. In contrast, here we report, in ultrathin Gd/Cr/Fe multilayers, an anomalously large linewidth in the film plane at the low-frequency region. For the first time, we have successfully extracted the Gilbert damping constant from perfect theoretical fitting to the experimental data, by considering the effective direction of the magnetization around in precession staying out of the film plane when the in-pane H at which the precession starts is below the saturation field. This magnetization deviation from the film plane is found to have an obvious contribution to the enhanced linewidth caused by two magnon scattering, while slightly reduce the intrinsic linewidth. Under the same resonance frequency, the deviation angle reaches the maximum values at tCr = 1.0 nm while decreases when tCr increases to 1.5 nm, which coincides with the trend of the surface perpendicular anisotropy constant K\. A reduced intrinsic damping constant a is obtained as the introduction of Gd layer and Cr layer as a result of the competition between the spin pumping effect and the interfacial effects at the Fe/Gd and Fe/Cr interfaces. While the decreasing a for film with Cr layer thickness increasing to 1.5 nm might means the contribution of the electron density of states at the Fermi energy n(EF). This study offers an effective way to accurately obtain the intrinsic damping constant of spintronic materials/devices, which is essential for broad applications in spintronics. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Gilbert damping constant a is an intrinsic parameter for characterizing the magnetization dynamics, which is in turn of crucial importance for current/future spintronic applications. For instance, a determines threshold current in spin-transfer-torque induced magnetization switching in magnetic tunnel junctions [1–3], plays critical roles for the performance of the readers in tunnel magnetoresistance readers as the free layer [4,5], and limits the steady-state oscillation excited in spin torque oscillator [6–8]. Ferromagnetic ⇑ Corresponding author. E-mail address: [email protected] (L. Sun). https://doi.org/10.1016/j.jmmm.2017.11.098 0304-8853/Ó 2017 Elsevier B.V. All rights reserved.
resonance (FMR) is one of the classic techniques to study the damping of magnetic thin films and multilayers by measuring their FMR linewidth [9,10]. Therefore, elucidate the mechanisms in linewidth which control the damping of spin motions is very important for study and developing spintronics devices. However, the linewidth is very sensitive to the structural and magnetic quality. Especially in ultrathin film, the contribution of two magnon scattering (TMS) play a not negligible role [11], in which accompanied with a tiny deviation of the linewidth to a smaller value at the lowfrequency and high-frequency region with in-plane-field configuration [12–14]. Here, a different deviation (to larger values) of the linewidth at lower frequencies with in-plane magnetic field was obtained in
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Gd/Cr/Fe film, which has higher saturation magnetization by employing a metal spacer layer (Cr) to mediate the antiferromagnetic coupling between Gd and Fe [15–17], simultaneously with modifying the intrinsic damping. The similar experimental results had also been obtained in ultrathin film with perpendicular magnetic anisotropy [18,19]. However, there has been no further numerical analysis on the magnetic illustration of such phenomenon but explained in terms of two-magnon scattering and low-field loss. In this paper, according to the theoretically report [20], we attribution this large linewidth to the two magnon scattering contribution in case of the effective direction of magnetization around during precession not parallel to the direction of inplane magnetic field. At the same time, the impact on the intrinsic linewidth was also studied. It is found the non-linear relationship between linewidth and microwave frequency were successfully fitted, and the magnetization deviation plays an important role in FMR linewidth.
at room temperature. Before deposition of Fe, a thin layer of Ta (5 nm) is first prepared as a buffer layer. The Cr thickness, tCr, varies as 0, 1.0, and 1.5. After deposition of Gd, all the samples are capped with 5-nm-thick Ta. For comparison, a pure Fe (5 nm) film, with 5-nm-thick Ta as both the capping and buffer layers, is also prepared. The base pressure of the sputtering chamber is 1.2 105 Pa, and the Ar working pressure is 0.5 Pa. For the Fe and Ta, a dc power of 30 W is used, while for the Gd and Cr, 15 W and 10 W are used, respectively. A magnetic field of 50 Oe is applied during sample preparation, which induces a small in-plane uniaxial magnetic anisotropy. Static magnetic properties are characterized using vibrating sample magnetometry (VSM), and dynamical magnetic properties are investigated by broadband ferromagnetic resonance (FMR) using a NanOsc Instruments Phase FMR with a 200-lm-wide coplanar waveguide. All the measurements are performed at room temperature.
2. Materials and methods
3. Results
A series of Gd(4 nm)/Cr(tCr)/Fe(5 nm) trilayers, as depicted in Fig. 1(a), are deposited on Si substrates by dc magnetron sputtering
Hysteresis loops, obtained by VSM, with the external magnetic field along the uniaxial easy axis (i.e., the direction of the small
Fig. 1. (a) Schematic diagram of the Gd/Cr/Fe trilayer structure. (b)–(e) In-plane hysteresis loops for the Fe and Gd/Cr/Fe films, with the magnetic field applied along the magnetization easy axis, measured by VSM. Insets: Enlarged area near the saturation field (HS) which is indicated by the arrow. The red dashed lines represent the linearly extrapolation from the high field magnetization. (f) tCr dependence of the coercivity. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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magnetic field applied during preparation) are shown in Fig. 1(b)– (e). The loops along the hard-axis direction are not shown, since they do not look much different from those in the figures due to the very small magnitude of the induced uniaxial anisotropy. The saturation magnetizations listed in Table 1 are determined by linearly extrapolation from the high field magnetization of hysteresis loops as shown the red dashed lines in Fig. 1. The saturation fields (HS) are also marked in the insets, which are important for the following analysis of FMR results. The values of the coercivity (HC) are summarized in Fig. 1(f): Upon insertion of the Gd layer, the HC becomes obviously larger than the Fe thin film, probably attributed to the antiferromagnetic coupling between Fe and Gd [21]; When Cr is inserted, HC increases with the increasing tCr, probably due to the introduction of two antiferromagnetic coupled interfaces of Fe/Cr and Cr/Gd, which has already been demonstrated by Sanyal et al. [15]. As shown in Table 1, the large saturation magnetization (MS) was obtained from the hysteresis loops which is similar to those reported in RE/Cr/TM trilayers [15–17,22,23], where Cr mediated the ferromagnetic coupling between Gd and Fe. FMR has been taken for all the samples with various frequencies ranging from 7 GHz to 25 GHz, with an in-plane-field configuration, in which an in-plane magnetic field H perpendicular to a microwave field h was applied along the uniaxial easy axis in film plane. Typical FMR spectra are shown in Fig. 2, from which we may see that at low frequencies such as 8 GHz, the resonance starts at a smaller magnetic field than the saturation field Hs, as marked by the arrows in Fig. 2 as well. Specifically, for the Fe film and Gd/Fe bilayer, this phenomenon happens with the frequency lower than 13 GHz; While for the Gd/Cr (1 nm)/Fe and Gd/Cr (1.5 nm)/Fe trilayers, it occurs lower than 14 GHz. Which results in the discrepancy, at the low frequency range, between the experimental data and the conventional numerical fitting involving intrinsic damping, TMS, inhomogeneous contributions, etc. Interestingly, the discrepancy disappears at high frequencies, such as 15 GHz, as the resonance starting at a larger magnetic field than Hs. To solve this discrepancy, below we try to find out a more common model than the conventional one, for the magnetization precession in these samples at the broad frequency range, by quantitative studies on the frequency-dependent resonance field, Hres, and linewidth, DH. 3.1. Fitting the dependences of resonance frequency on Hres First, we try to extract magnetic dynamical parameters by fitting the dependence of frequency (f) on the resonance field (Hres). By solving the Landau-Lifshitz-Gilbert (LLG) equation and minimizing the total free energy density, the Hres-dependence of f can be obtained from the equation below [24],
f ¼
c qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðHres þ Hk ÞðHres þ Hk þ 4pM eff Þ; 2p
ð1Þ
? where 4pM eff ¼ 4pMs 2K is the effective magnetization with the Ms
saturation magnetization (MS) and the perpendicular magnetic anisotropy constant (K\), Hk is the in-plane anisotropy field, and c is the gyromagnetic ratio. Here, the total free energy density of the system involves the Zeeman energy, demagnetizing energy, and the energy of perpendicular anisotropy and in-plane uniaxial aniso-
Fig. 2. Typical FMR spectra, taken from an in-plane-field configuration, with the microwave frequency ranging from 8 GHz to 15 GHz, as indicated by the numbers in the unit of GHz. The arrows point out the positions of Hs, corresponding to those in Fig. 1b–e.
tropy. In the high frequency range, we find that the Hres are well fitted for the Gd/Cr/Fe films, from which 4pMeff, c, and K\ are extracted in Table 1. As expected, the obtained value of Hk from fitting is very small in all the samples, typically a few Oersteds, which is neglected in the following equations. Compared with the Fe film, c is significantly reduced with addition of the Gd layer, which may be attributed to the interaction between Fe and Gd with the quenched orbital magnetic moment [25]. Upon insertion of Cr, this interaction becomes weaker, and in turn the reduction of c becomes slower. Similarly, the effective magnetization 4pMeff is strongly increased by introduction of Gd probably due to the magnetic proximity effect [26,27], and then decreases with insertion of Cr. On the other hand, a similar enhancement K\ is obtained after adding Gd layer due to the increased interfaces as reported in Ref. [28] and weakened as the inserting of Cr layer. The perpendicular magnetic anisotropy constant is changed from positive to negative as the thickness of Cr layer increasing up to 1.5 nm, which coincide with the simulated values of deviation angles discussed later. Note that here the negative value of K\ represents the preferred alignment of the magnetization in the film plane, and a positive value corresponds to the magnetization staying out of the film plane. As we recently reported in Gd(Tb)/Cr/Ni80Fe20 system [23,29], the
Table 1 Extracted parameters for the Fe and Gd/Cr/Fe films from theoretical fitting. tCr (nm)
Ms (emu/m3)
4pMeff (104 Gs)
c
K\(105 erg/cm3)
DH0 (Oe)
a(1 0 2)
Fe film 0 1 1.5
1221 ± 102 1020 ± 183 1307 ± 131 1274 ± 127
1.452 ± 0.007 1.797 ± 0.032 1.604 ± 0.024 1.623 ± 0.023
1.885 ± 0.001 1.791 ± 0.004 1.810 ± 0.004 1.816 ± 0.004
5.0 ± 0.4 -26.3 ± 1.6 2.5 ± 1.2 -1.4 ± 1.1
85 87 106 120
1.173 ± 0.001 0.985 ± 0.002 1.057 ± 0.003 0.821 ± 0.002
(107 (Oes)1)
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perpendicular magnetic anisotropy, which is dependent on the exact nature of the interface (e.g., interface/surface roughness and adjacent materials), oscillates with the thickness of Cr layer, and the oscillation is related to the value of Ms. The dependences of f on Hres for all the samples are shown in Fig. 3c and e, from which we see that the numerical calculations (solid lines) do not fit the experimental data (dots) very well, in particular at the low frequencies as shown in Fig. 3c. This is because that Eq. (1) is obtained by assuming the magnetization processes around the direction of the external magnetic field, i. e. the effective direction Heff along the uniaxial easy axis in film plane as shown in Fig. 3a. Namely, in Eq. (1) we assume that the magnetization angles h = hH = 90° and u = uH = 0°, where h is the angle of the magnetization vectors in spherical coordinates with respect to the film normal, u is the in-plane angle of the magnetization vector with respect to the in-plane magnetization easy axis, while hH and uH are the angles of the magnetic-field relative to the film normal and the in-plane easy axis, respectively. Obviously, Eq. (1) cannot be used for numerical fitting at lower frequency range, where the magnetization cannot be saturated along the direction of the external applied field when resonance begins. Alternatively, we introduce a precession model, where the magnetization does not process around the external field while deviates with a small angle, 90°-h, from the external magnetic field or the in-plane easy axis, i. e. the effective direction Heff deviating from the external field, as shown in Fig. 3b. Accordingly, Eq. (1) can then be modified as below:
f ¼
c pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2p
HX H Y ;
HX ¼ Hres sin h 4pMeff cos2 h;
ð2Þ ð2aÞ
and
HY ¼ Hres sin h 4pMeff cos 2h:
ð2bÞ
Using the extracted parameters in Table 1, the experimental data at both low and high frequencies can be satisfactorily fitted, as shown in Fig. 3d and f. Note that this fitting is based on the fact that the magnetic anisotropy in the film plane is not large enough
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to influence the resonance field and linewidth, so that the in-plane projection of the magnetization in our thin films is supposed to be along the induced easy axis. 3.2. Fitting the frequency-dependences of DH Generally, the FMR linewidth, DH, is expressed as [30–32]
DHðf Þ ¼ DH0 þ DHintri þ DHTMS
ð3Þ
where the DH0 describes an inhomogeneous broadening due to sample imperfections which is assumed to be independent of f; DHintri is the intrinsic linewidth that is assumed to be linearly proportional to f in a perfect sample and can be expressed in terms of the Gilbert damping constant a [33,34]; and DHTMS represents the contribution of the two-magnon scattering here is necessary considering as the anomalously enhanced DH at low frequencies. Considering the magnetization deviates out of the film plane, the twomagnon scattering contribution to the linewidth [35] and the intrinsic linewidth [36] can be described as
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u½x2 þ ðx0 =2Þ2 1=2 x0 =2 ; DHTMS ðf ; hÞ ¼ CðHX ; HY ; qÞarsint 1=2 ½x2 þ ðx0 =2Þ2 þ x0 =2
ð4Þ
and
DHintri ðf ; hÞ ¼
2Gx c2 Ms
HX þ HY : ½ðHX þ HY Þ sin h þ ðHXh HY =HX þ HYh Þ cos h
ð5Þ
For Eq. (4), x0 = c4pMeff, x = 2pf, and the factor C is the strength of the two magnon scattering along the in-plane crystallographic direction, which is a function of h, as illustrated in Ref. [12]. As a result, DHTMS is not only as a function of frequency, but also depends on h. Eq. (5) is a simplified equation, by substituting hH = 90° and u = uH = 0° and assuming the external field parallel to the induced easy axis of the small in-plane magnetic anisotropy, where HXh and HYh represents the first partial derivatives of HX and HY, respectively.
Fig. 3. Resonance frequency f versus the resonance field (Hres). Symbols represent the experimental data, and the solid lines are the fits by Eq. (1) for (c) and (e) and Eq. (2) for (d) and (f), respectively. The precession of magnetization M around the effective direction Heff in case of lower frequencies are illustrated in (a) and (b). (a) for the effective direction (Heff) in the film plane; (b) for the direction out of the film plane.
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Fig. 4. Frequency-dependences of the FMR linewidth (DH). The black dots represent the experimental data (exp. data), and the black solid lines are theoretical fitting curves (cal.) involving the intrinsic contributions (intri., red stars), two-magnon scattering contributions (TMS, blue cross), and inhomogeneous broadening (inhom., pink intersects). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The fitting results are shown in Fig. 4, where the black solid lines represent the fitting curves, which fit the experimental data (black dots) satisfactorily. Three contributions, including the intrinsic linewidth, inhomogeneous linewidth, and two-magnon scattering, are shown as well. Among them, the intrinsic linewidth has been found to slightly decrease with decreasing frequency, while the two magnon scattering has an abrupt enhancement at the low frequency range resulting from the abovementioned deviation angles. Having a relatively slight contribution in the Fe film and Gd/Fe bilayer, the DHTMS, describing the defect mediated scattering of the uniform precession mode into nonuniform ones, presents stronger contribution in the Gd/Cr/Fe trilayers, nearly irrelevant to the Cr thickness. The inhomogeneous contribution, DH0 is also obtained from the fitting, as listed in Table 1, which increases as the inserting of ultrathin Cr layer. The increased contribution of DHTMS and DH0 as inserting of ultrathin Cr layer might mean the inhomogeneities in Cr layer as its thickness equal to or less than 1.5 nm [37,38]. The deviation angle (90°-h), as a function of frequency, is also obtained from the fitting, as shown in Fig. 5. They are almost linearly decreasing with increasing frequency for all the samples, among which the Gd/Cr (1.0 nm)/Fe trilayer has the highest values at the same frequencies and the slowest decreasing speed, which may be attributed to the fact of the positive K\, as shown in Table 1. The extracted Gilbert damping constants a are also shown in Table 1. Comparing to the Fe film, a is reduced in the bilayer and trilayers, which has also been demonstrated in the Gd-doped FeCo films and probably results from the strong influence of the quenched orbital moment in Gd at the interfaces [25]. After inserting the Cr layer, we found that a becomes larger than Fe/Gd bilayer, probably resulting from the spin-pumping effect in trilayers. In Gd/ Fe bilayer, the Fe spins can be scattered through the spin-orbit cou-
Fig. 5. Frequency-dependences of the deviation angles, i. e. 90°-h, with different tcr.
pling of Gd at the interface; while in Gd/Cr/Fe trilayers, the Fe spins do not interact with Gd directly and an additional mechanism, spin pumping effect, must be taken into account. Tserkovnyak et al. [39] showed that a magnetization precession can generate a spin current into an adjacent normal (NM) layer. Namely, in Gd/Cr/Fe film, the spin current injected by Fe into Cr, and some of which can also be absorbed by the Gd layer [40,41]. Moreover, accompanied by the decreasing of a, a smaller value of a in Gd/Cr/Fe film than that of Fe film was obtained, which implies more interfacial reasons might be taken into consideration other than the decreasing
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spin-pumping effect [23,42]. For example, the dependence of the interlayer coupling on spacer thickness can lead to an oscillations in damping constant [43,44], the spin-current in opposite directions across the Cr/Gd interface [45,46] and the inter-diffusion at the interface between Cr and Fe as reported in Ref. [27] can also reduce a. With the thickness of Cr layer increasing to 1.5 nm, the damping constant is decreasing while the gyromagnetic ratio is almost unchanged (see Table 1), which means other mechanism should be considered besides the spin–orbit interaction. Mankovsky et al. [47] theoretical predicted that the damping parameter can be proportional to the electron density of states at the Fermi energy n(EF) for samples with fixed c. And Schoen and colleagues [48] experimental proved it in metallic CoxFe1x films. We infer that n(EF) changed due to the intermixing at the interfaces of Gd/ Cr/Fe films might be the main origins of magnetic damping for the films with 1.5 nm Cr layer. To obtain a quantitative study of the origin of magnetic damping, more systematic and detailed investigations are necessary, both experimentally and theoretically.
4. Conclusions In summary, a method was proposed for successfully fitting the non-linear relationship between in-plane linewidth and frequency with anomalous large linewidths at lower frequencies in Gd/Cr/Fe films, with considering a deviating angle between the effective direction of magnetization precession and the film plane. It is proved that the alignment of the magnetization plays an important role in a determination and it points a method to accurately separating different mechanisms in linewidth. The obtained angles at the same frequency are the largest for films with 1.0 Cr layer which has positive K\, and go back to those of the Fe film with the increasing thickness of Cr layer as a result of the surface and interface effect. Compared with Fe film, the effective magnetization 4pMeff is improved in Gd/Fe bilayer resulting from the magnetic proximity effect at Gd/Fe interface, while the gyromagnetic ratio c and Gilbert damping constant a are reduced causing by the weakening spin-orbit coupling by adding Gd layer with the quenching of the orbital magnetic moment. Additionally, an inserting Cr layer reduces 4pMeff and makes c close to that of the Fe film from a lower value. Compared with Gd/Fe bilayer, a is increased as the inserting of 1.0 nm Cr layer by spin-pumping effect and decreasing with the increasing thickness of Cr layer to 1.5 nm. The smaller value of a in Gd/Cr (1.0 nm)/Fe film than that of Fe film suggests more interface reasons might be taken into consideration and the decreasing a for Gd/Cr (1.5 nm)/Fe film with nearly fixed c might means the contribution of the electron density of states at the Fermi energy n(EF). In this paper, both the fitting method on analyzing linewidth and the reducing damping constant a which can decrease the threshold current in spin-transfer-torque will have potential application for studying and developing spintronics devices. Acknowledgements This work is supported in part by the National Natural Science Foundation of China [Grant numbers 11364015, 51571062, 61427812, 11364014, 61306121, 11504047]; the Natural Science Foundation of Hainan Province of China [Grant numbers 117109, 114008, 113005]; and the Natural Science Foundation of Jiangsu Province of China [Grant number BK20141328). P.K.J.W. is financially supported by the EU FP7 Project SpinValley under Grant PIOF-GA-201.
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