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MgO (0 0 1) thin film
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
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Research articles
Strongly enhanced Gilbert damping anisotropy at low temperature in high quality single-crystalline Fe/MgO (0 0 1) thin film
T
Wei Zhanga,b, Yan Lia,b, Na Lia,b, Yang Lia,b, Zi-zhao Gonga,b, Xu Yanga,b, Zong-kai Xiea,b, ⁎ ⁎ Rui Suna,b, Xiang-qun Zhanga, Wei Hea, , Zhao-hua Chenga,b,c, a
State Key Laboratory of Magnetism and Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China b School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China c Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
ARTICLE INFO
ABSTRACT
Keywords: Gilbert damping Spin dynamics Magnetic devices
The anisotropic behavior of Gilbert damping provides a new dimension for controlling and tuning magnetization relaxation within the same magnetic device. The single-crystalline ferromagnetic metals with a high symmetry have been predicted to possess significantly anisotropic damping for one decade. By decreasing temperature down to T = 4.5 K, we found that the anisotropic damping factor Q, defined as the fractional difference of damping between easy and hard axis, can be approached to 60%–90% in Fe (15 nm)/MgO (0 0 1) without applied fields dependent behavior. It is much larger than Q = 10%–20% obtained at room temperature. Furthermore, it is followed by explanations on the basis of the breathing Fermi surface model giving around Q = 30%–40% when electron-phonon scattering rate is small enough. This discovery will enrich the understanding of damping mechanism, and can provide clues for searching strongly anisotropic damping within 3d transition metals and alloys.
Magnetic damping is a crucial parameter in spintronics because it describes the energy relaxation rate and the speed at which a device can be operated [1]. Controlling and tuning Gilbert damping is prerequisite for spintronic device optimization, since either a smaller or a larger damping is demanded in various devices. For instance, the thermally induced magnetization fluctuation noise (mag-noise) in the magnetoresistive (MR) sensors is proportional to the Gilbert damping [2]. As a result, small damping values are essential to guarantee the signal-tonoise ratio (SNR) in magnetic sensors. It is also required in minimizing power consumption in spin-torque-transfer (STT) based magnetic random access memory (MRAM) [3]. On the other hand, the currentperpendicular-to-the-plane giant magnetoresistance (CPP-GMR) device is susceptible to current-induced instability [4]. To improve the stability, a sufficiently large damping is preferred to increase the thermal coupling between magnetization and its host lattice. Therefore, tailoring Gilbert damping could facilitate the engineering of spintronic devices. It is hence desirable to discover Gilbert damping anisotropy in experiment followed by clarifying its microscopic mechanism. In principle, 3d transition metals or their alloys with a strong spinorbit coupling as well as the crystalline symmetry are good candidates
for exploring anisotropy Gilbert damping. In experiments, more convinced evidence is still required given a few attempts showing different results are outstanding. For instance, by changing the concentration of Si in FexSi1-x alloys, Barsukov et al. [5] tailored the spin-orbit coupling, and consequently the Gilbert damping. Although the electronic structure was varied by changing Si concentration, the Gilbert damping kept isotropy in experiment as well as in ab initial calculations. On the contrary, Li et al. [6] reported a giant Gilbert damping anisotropy in epitaxial Co50Fe50 thin film. It was ascribed to the variation of spin orbit coupling for different magnetization orientations induced by local tetragonal distortions. Because of the constrain that the damping anisotropy is structure sensitive behavior [7], Co25Fe75 thin film shows no evidently intrinsic anisotropy damping which was confirmed by Cheng et al. [8]. On the other hand, Chen et al. [9] discovered an anisotropic damping in the single element Fe ultrathin films due to robust interfacial spin-orbit field between Fe and GaAs substrate. However, the anisotropy factor Q defined as fractional difference between the damping with magnetization orientation along easy and hard axes around 20% induced by interfacial effect is too weak to be considered in practical applications. Similarly, the precise local tetragonal distortions
⁎ Corresponding authors at: State Key Laboratory of Magnetism and Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. E-mail addresses: [email protected] (W. He), [email protected] (Z.-h. Cheng).
https://doi.org/10.1016/j.jmmm.2019.165950 Received 23 September 2019; Received in revised form 3 October 2019; Accepted 4 October 2019 Available online 05 October 2019 0304-8853/ © 2019 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
W. Zhang, et al.
needed in Co50Fe50 resulting in anisotropy of spin-orbit coupling requires a complex deposited technique. Such strict condition also narrows its potential application in spintronic devices. Very recently, the presence of conductivity-like Gilbert damping was demonstrated in Fe (25 nm)/MgO at low temperatures by Khodadadi et al. [10]. And Gilmore et al. [11] predicted such kind of Gilbert damping should be anisotropic on the basis of first-principle calculations, while there has been no conclusive experimental evidence up to now. Here, our work aims at filling this gap. A giant anisotropy of damping with anisotropic factor Q = 120% was observed in a bare Fe (15 nm)/MgO by decreasing temperature down to 4.5 K. The reasons for selecting the bare Fe thin film are three-fold. Firstly, without capping layer, it would efficiently avoid extrinsic effect induced by interface, such as spin pumping [12]. Up to now, it is still not clear the Gilbert damping resulted from nonlocal spin pumping effect could be anisotropy or isotropy [13–16]. So it is better for us to avoid this effect temporary when we are interested in the intrinsic properties. Secondly, in order to achieve a much larger damping anisotropy that can be considered in applications, a thickness as large as 15 nm is necessary for utilizing its intrinsic bulk properties rather than the interface effect in Fe (1.3 nm)/GaAs [9]. Thirdly, unlike CoFe alloys, it is not necessary to care the needed local structure by controlling concentration precisely [6,7]. The loose of strict conditions makes Fe a more feasible candidate for exploring anisotropy damping. Fe film was epitaxially deposited on optically transparent singlecrystalline MgO(0 0 1) substrates in a molecular beam epitaxy chamber with a basic pressure 2 × 10 10 mbar [17]. Prior to Fe deposition, MgO (0 0 1) substrate was annealed at 700 0C for 2 h, and then 15 nm Fe film was deposited using electron-beam gun without capping layer. It allows us to focus on its intrinsic properties by avoiding the spin pumping effect at interface. The thickness of Fe layer was confirmed by x-ray reflection (XRR), while its crystal structure was measured by x-ray diffraction (XRD) with Cu Kα radiation. Fig. 1(a) shows the scan of xray reflectometry (XRR) curve with roughness around 0.1 nm, from which dFe = 15nm is given. In the θ-2θ XRD pattern [Fig. 1(b)], the (0 0 2) peaks of Fe indicate a good (0 0 2) out-of-plane texture. Meanwhile, the x-ray in-plane scans [Fig. 1(c)] display a fourfold symmetry
verifying the highly textured growth of Fe film in this study and confirm the epitaxial relationship of MgO (0 0 1)[1 0 0]//Fe (0 0 1)[1 1 0]. Furthermore, the atomic force microscopy (AFM) image shows a smooth surface of the epitaxial Fe film with a root-mean-square roughness of 0.12 nm. It is in consistent with the value obtained by XRR. Fig. 1(e) shows the normalized hysteresis loops of 15 nm Fe film along easy axis Fe [1 0 0] ( H = 00 ) and hard axis Fe [1 1 0] ( H = 450 ) by longitudinal 2K magneto-optical Kerr effect (MOKE). Based on the relation HK = M1 s
where HK is the saturated field in hysteresis loop when H = 450 , the value of in-plane magnetocrystalline is estimated as around K1 = 3 × 105erg/ cm3. The normalized remanence Mr/Ms in Fig. 1(e) indicates a good four-fold magnetocrystalline anisotropy [18]. The dynamical process of spin precession in Fe (15 nm)/MgO was measured by time-resolved magneto-optical Kerr effect (TRMOKE) [19]. A very low laser fluence 1 mJ/cm2 is used to avoid nonlinear spin dynamics induced by laser heating [20]. Even though its influence on spin dynamics is more pronounced at low temperature, it is independent of magnetization orientations. Therefore, the value of anisotropy factor Q could be independent of laser power. The scheme of TRMOKE experiment is illustrated in Fig. 2(a) where the external field was fixed at H = 150 with respect to film normal direction. In this case, the magnetization would be tilted far away from easy plane (0 0 1) when the applied field is large enough. For T = 300 K, Fig. 2(b) and (c) show the typical time evolution of the polar component of magnetization in the presence of external field H ranging from 3.9 kOe to 12.6 kOe with H = 00 and H = 450 , respectively. It is observed clearly that the spin precession process can be influenced significantly by magnetic fields for both cases. Interestingly, we have to address the dissimilarities in spin precession for different magnetization orientations. For instance, when H = 3.9 kOe, the precession of magnetization decays much faster with external field applied along hard axis ( H = 450 in Fig. 2(c)) than that along easy axis with H = 00 (Fig. 2(b)). With increasing magnetic fields, such differences are less pronounced. Similar behaviors are also shown in Fig. 2(d) (e) with T = 4.5 K. The exact values for f with various applied fields can be obtained using the damped harmonic function:
Fig. 1. Structure and morphology measurements for Fe (15 nm)/MgO as well as static magnetic property. (a) The scan of x-ray reflectivity gives the roughness of 0.1 nm and the layers thickness 15 nm for Fe thin film. (b) X-ray diffraction measurements of θ-2θ scan and (c) in-plane scan for Fe (15 nm)/MgO. (d) Atomic force microscopy image (2 × 2 μm2) of the Fe (15 nm) thin film. (e) Normalized hysteresis loops of Fe (15 nm)/MgO(0 0 1) with the in-plane applied magnetic field along Fe [1 0 0] (ϕH = 0°) and Fe [1 1 0] (ϕH = 45°). (f) Fourfold angular dependent remanence Mr/Ms. 2
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
W. Zhang, et al.
Fig. 2. Spin precession measured by TRMOKE for Fe (15 nm)/MgO as a function of temperature and magnetization orientations. (a) Schematic of the coordinate system for TRMOKE measurement in Fe (15 nm)/MgO. (b) spin precession for ϕH = 0°, T = 300 K. (c) spin precession for ϕH = 45°,T = 300 K. (d) spin precession for ϕH = 0°, T = 4.5 K. (e) spin precession for ϕH = 45°, T = 4.5 K. The red curves are the fitted results of the experimental data to Eq. (1).
K
= A + Bexp
t
sin(2 ft + )
The field dependence of frequency f extracted from the fitting procedure by Eq. (1) is shown in Fig. 3(a) for both T = 300 K and T = 4.5 K with H = 00 and H = 450 , respectively. We note that the experimental f-H relation can be described by Kittel Eq. (2) [21,22]:
(1)
where A is the background magnitudes, B, , f and φ are the magnetization precession amplitude, relaxation time, frequency and phase, respectively. 3
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
W. Zhang, et al.
Fig. 3. Spin dynamics for Fe(15 nm)/MgO by TRMOKE and VNA-FMR measurements. (a) The relation between frequency and applied fields as a function of temperature and magnetization orientations, respectively. (b) Effective Gilbert damping as a function of applied fields with ϕH = 0° and ϕH = 45° at room temperature. (c) Effective Gilbert damping as a function of applied fields with ϕH = 0° and ϕH = 45° at T = 4.5 K. (d) H as a function of frequency with the applied field along easy and hard axis.
2 f
=
1 Ms sin
With e
= 1.76 ×
H1· H2
M
eg
=
H3
is
the
2 107 Hz/Oe,
gyromagnetic
g = 2.09) ,
sin2 2 M (3sin2 M cos 2 M sin4 (cos H cos M + sin H sin M cos(
H2 =
2E 2 M
= 2K1sin4
and H3 =
2E M
M
The value of H is kept as 150 ± 10 in the fitting producer, while H and M are modified slightly within ± 20 due to the mismatch between applied field and easy or hard axis of the sample. The temperature dependent magnetocrystalline anisotropy [24] constant K1 = (5 ± 1) × 105erg / cm3 and K1 = (4 ± 1) × 105erg / cm3 were used to reproduce the f-H curves at T = 4.5 K and T = 300 K, respectively. The saturation magnetization Ms = 1.7 × 103erg / cm3 is kept as constant considering the measured temperature range is far away from the Curie temperature around 1000 K. This assumption is reasonable according to previous experiments [10,23]. During the fitting procedure, the constant value of out-of-plane magnetic anisotropy K out = 1 × 106erg / cm3 [25] gives rise to the demagnetization field Hd = 2 × 10 4 Oe [16] by 2K out Hd = 4 Ms . As is shown in Fig. 3(a), the field dependence of Ms frequency in experiment is reproduced well within theoretical calculations based on Kittle formula. The frequency differs largely for 0 0 H = 0 and H = 45 within the region of low applied fields due to the strong magnetocrystalline anisotropy in high quality single crystal sample. This fact has a large influence on the difference of damping in the case of H = 00and H = 450 at low applied fields as shown below. Furthermore, using the fitted values of τ from Eq. (1) we determine the effective Gilbert damping eff with Eq. (4) [22]:
(2)
M cos 4 M
= 2K1sin3
H1 =
M ) + 2(K out H ), M
+ sin
ratio 2E
2 M
+ HMs sin
Fe
= 2K1 cos 4
2 Ms2 ) cos 2
M sin H cos( M
M cos M sin 4 M
(for
M
[23] M
+ K1
+ HMs
H) H cos M sin( M
H ).
Here, K1 and K out are the in-plane magnetocrystalline and out-ofplane magnetic anisotropies of Fe films, respectively. M and M are polar and azimuthal equilibrium angles of magnetization with respect to the Fe [0 0 1] and Fe [1 0 0] directions respectively. Likewise, H and H are polar and azimuthal angles of the applied magnetic field H, respectively. The equilibrium angles of magnetization are determined via the following Eq. (3):
K1sin2 2
3 M sin M cos M
sin
H cos M cos( M
+
1 K1 sin 4 2 H)
M
+ (K out
+ HMs cos
2 Ms2 ) sin2
M cos H
=0
M
HMs (3) 4
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
W. Zhang, et al.
eff
=
extrinsic dephasing effect dominating at low field is reduced when the field is large enough. And only the intrinsic contributions to anisotropy damping is left. The consequence is the difference of damping between 0 0 H = 45 and H = 0 decreases. More interestingly, for T = 4.5 K, the lowest value of anisotropy factor Q reaches above 60% , even the largest value is around 120% as field increasing. It is much larger than Q = 15% in the case of T = 300 K at large enough field as is shown in the insert of Fig. 4, confirming the convinced enhancement of Gilbert damping anisotropy at low temperature. With applying larger external fields, the constant values of αeff at higher fields are therefore used to approximate the intrinsic Gilbert damping [27,28]. It is a general method to achieve the intrinsic Gilbert damping in TRMOKE experiment [29]. Therefore, the field-independent Q around 60%–90% is mainly considered from intrinsic contributions, rather than extrinsic ones. Even so, we prefer to discuss several possible contributions to damping anisotropy explicitly, including intrinsic and extrinsic effects. Among the extrinsic contributions, two-magnon scattering is famous for its anisotropy behavior within in-plane sample. Such extrinsic effect once leads to obstacle in identifying anisotropic Gilbert damping [30]. In particular, there is no capping layer to protect Fe film. In this case, the high quality of Fe would be destroyed at the surface by oxidation. As a result, there could be some two-magnon scattering events. However, we can exclude this effect based on the following reasons. Firstly, its strength is dependent on the magnetization orientation with respect to film normal [31]. Two-magnon scattering is only active for values of M > 450 , it shuts off for angles 0 M < 45 because there are no degenerate states available for this angular region. This limit condition could be fulfilled for external field closer to the film normal. Indeed, a value of H as small as 150 degree was selected in this study. In this case, the critical value of M = 450 is approached at high enough fields to reduce the two-magnon scattering as much as possible [32]. Secondly, previous demonstrations show that the two-magnon-scattering induced damping increases with precession frequency increasing because of the increased degeneracy of spin waves [33]. This disagrees with the fact here that the damping drops monotonously with field increasing shown in Fig. 3(b) and (c), indicating the minor contributions from two-magnon-scattering to Gilbert damping. Thirdly, this two-magnon process occurs when an excited spin-wave has degenerate states to relax by defects. And defects always cause more spin-wave scattering along easy axis than that along hard axis [34]. On the one hand, this is because the defects are preferred to being parallel to easy axis, which has been confirmed both in experiment by employing Mössbauer spectroscopy [35] as well as in first-principle calculations [36]. It makes the easy axis the stronger relaxation direction, hosting a larger damping from two-magnon scatterings. On the other hand, the two-magnon scattering is frequency dependent. The larger frequency obtained along easy axis would surely give rise to a stronger two-magnon scattering. Therefore, the anisotropy damping arising from two-magnon scattering will result in a negative Q rather than the positive one observed in this study. Above all, the two-magnon scattering induced damping always dominates in polycrystalline samples [31] as well as in exchange bias heterostructure [37] with a large amount of defects. A.Yu. Dobin et al. proposed that two-magnon scatterings is active for the roughness around 1.3 nm [38]. On the contrary, the high quality single-crystalline sample characterized by XRD and AFM with a roughness at atomic level of around 0.1 nm may suppress the twomagnon scattering in this study. Apart from two-magnon scatterings, the field-dragging effect in single-crystalline sample would also give rise to a damping anisotropy [9]. It results from the fact that the rotation of magnetization cannot follow closely with applied field due to the large magnetocrystalline anisotropy. In this study, we can not avoid this effect due to the misalignment between applied field and easy or hard axis. So, the anisotropy factor Q = 15% at room temperature maybe partly comes from field-dragging effect. However, there is no evidence on the enhancement of damping at low temperatures arising from field-dragging effect. Therefore, the enhancement of anisotropy
2 (H1 +
H2 ) sin2 M
(4)
As shown in Fig. 3(b) and (c), the effective damping constant eff are obtained for different magnetization orientations with T = 4.5 K and T = 300 K, respectively. In both cases, a nearly field-independent behavior of damping is observed when external field is along easy axis of Fe film with H = 00 , while there is a pronounced enhancement of damping with field decreasing when H = 450 . It gives rise to a quite larger damping for H = 450 at low fields, coming from a larger dephasing effect. Such dephasing effect [23] results from the variation of Fe spin orientation. As applied field decreasing, a much smaller frequency is obtained along H = 450 than that in H = 00 . It indicates a much weaker effective field along hard axis, and consequently a much larger variation of spin orientations there. Fortunately, such dephasing effect would be suppressed with field increasing. It is evidenced in Fig. 3(a) that the same frequency is approached for easy and hard configurations when applied field is large enough. In this case, the spin orientations are almost the same as they are determined by external applied field. It is unlike the case of low applied fields where the spin orientation is determined by effective fields. In addition, in-plane Vector Network Analyzer ferromagnetic resonance (VNA-FMR) [16] measurements have been performed at room temperature in Fig. 3(d) with applied field ranging from 0 Oe to 4000 Oe. The Gilbert damping for H = 450 and H = 00 could be obtained from the linearly fitted curves (red lines), based on the following equation [26]:
H = H0 +
2 f (5)
where is the geomagnetic ratio with the same value applied in Eq. (2) ° and H0 5Oe is the inhomogeneous broadening. The value of H = 45 ° obtained in VNA-FMR are around 0.0045 ± 0.0002 . This value and H =0 is consistent with that obtained using TRMOKE in Fig. 3(b). It suggests the reliability of our TRMOKE measurements carried out in this study. To quantify the anisotropy of the damping, we define Q in the following as an anisotropy factor [13]:
Q=
° H = 45
° H =0 H =0
°
(6)
It is the fractional difference between the damping with magnetization orientation along easy and hard axis. Applying this equation into Fig. 3(b) and (c), we can extract the value of Q for T = 300 K and T = 4.5 K, respectively. According to Fig. 4, the anisotropy factor drops as the applied field increasing for both temperatures. It is because the
Fig. 4. The variation of anisotropy damping factor Q with applied fields for T = 4.5 K and T = 300 K. Insert: anisotropy damping factor Q as a function of large applied fields. 5
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
W. Zhang, et al.
factor Q at low temperature is mainly resulted from intrinsic effect as shown below. This also holds for excluding mosaicity effect [39]. Here, the field-independent damping anisotropy factor Q = 60%–90% at T = 4.5 K is ascribed to the competition between conductivity-like and resistivity-like damping with decreasing temperature. Based on the breathing Fermi-surface model [11], the electrons scatterings from intraband contribution (conductivity-like damping) maintains damping anisotropy for all scattering rates. The scattering rates are dependent on temperature in experiment. In contrast, the interband contribution (resistivity-like damping) exhibits these anisotropies only at small scattering rates (low temperature) and becomes increasingly isotropic with temperature increasing. Therefore, the experiments carried out at room temperature show an almost isotropic behavior for damping. For instance, as is reported by Zhai et al. [40], an isotropy Gilbert damping of Fe film can be used to fit anisotropy linewidth in FMR measurements because interband contribution to electrons scatterings dominates at room temperature. Similarly, the damping of hard and easy axis are almost the same in Fe (1.14 nm 2.3 nm)/InAs at room temperature reported by Meckenstock et al. [41]. Very recently, Khodadadi et al. [10] reported an isotropic Gilbert damping in Fe (25 nm)/MgO at room temperature, stating the resistivity-like Gilbert damping dominates there. Although anisotropic electronic structure has been predicted in single-crystalline ferromagnetic metals, such as bulk Fe, Co and Ni, the anisotropic damping can be dramatically reduced due to smearing of the energy bands with electron scattering. Up to now, it makes experimental observation of the anisotropic damping in bulk materials difficult at room temperature. By decreasing temperature, the strength of electron scattering could be decreased. As a result, the isotropy resistivity-like damping could be suppressed largely and only the anisotropy part could be left at low temperature. In this case, the maximum damping anisotropy factor Q = 120% at T = 4.5 K is observed. Even the lowest value Q = 60% is larger than Q = 30% in the theoretical prediction based on the breathing Fermi-surface model [11]. We address that it is much larger than Q = 20% induced by interfacial spin orbit coupling between ultrathin Fe film and GaAs substrate [9]. Moreover, it has the same magnitude order with the value Q = 300% obtained in Co50Fe50 but with a more feasible deposited method. In this study, we proposed that Gilbert damping in pure 3d transition metal Fe exhibits anisotropic behavior by decreasing temperature. At low temperature, the isotropy resistivity-like damping is suppressed largely. In contrary, at room temperature the anisotropic electronic structure can be dramatically reduced due to the enhanced electron scattering. This is the main reason that very few convinced experiments demonstrating the anisotropic Gilbert damping in pure 3d metals at room temperature were reported. Following the line of suppressing isotropy resistivity-like damping, we can expect ferromagnetic half metals would show an obvious anisotropic Gilbert damping. In this kind of materials, the isotropic resistivity-like damping is blocked and so the damping can be dominated by the anisotropic contributions. Improving the Q factor in ferromagnetic materials at room temperature would facilitate the engineering of spintronic devices. Half metals such as Heusler alloys should be noted as the potential candidates to show a large Q factor at room temperature. In summary, the high quality single crystal Fe film provides an ideal platform for exploring spin dynamics especially for anisotropy damping. A considerable damping anisotropy with Q larger than 60% is observed at T = 4.5 K. It is much larger than that at T = 300 K with Q is around 15%. We show that the enhancement of damping anisotropy at low temperature can be explained based on the breathing Fermi surface model. In this model, the resistivity-like damping from interband scattering is isotropic at sufficiently high temperatures and it can be suppressed largely by decreasing temperature. Thereafter, only conductivity-like damping from intraband scattering dominates which shows anisotropic behavior with various magnetization orientations. Our results open up a new avenue to tailor the Gilbert damping in
metallic ferromagnets by changing temperature, which are important for optimizing dynamic properties of future magnetic devices. Acknowledgements This work is supported by the National Key Research Program of China (Grant Nos. 2015CB921403, 2016YFA0300701, and 2017YFB0702702), the National Natural Sciences Foundation of China (Grant Nos. 1187411, 51427801, and 51671212) and the Key Research Program of Frontier Sciences, CAS (Grant Nos. QYZDJ-SSW-JSC023, KJZD-SW-M01 and ZDYZ2012-2). References [1] Y.S. Hou, R.Q. Wu, Phys. Rev. Appl. 11 (2019) 054032. [2] N. Smitha, P. Arnett, Appl. Phys. Lett. 78 (2001) 1448. [3] A.V. Khvalkovskiy, D. Apalkov, S. Watts, R. Chepulskii, R.S. Beach, A. Ong, X. Tang, A. DriskillSmith, W.H. Butler, D. Lottis, E. Chen, V. Nikitin, M. Krounbi, J. Phys. D: Appl. Phys. 46 (2013) 139601. [4] K. Nagasaka, J. Magn. Magn. Mater. 321 (2009) 508. [5] I. Barsukov, S. Mankovsky, A. Rubacheva, R. Meckenstock, D. Spoddig, J. Lindner, N. Melnichak, B. Krumme, S.I. Makarov, H. Wende, H. Ebert, M. Farle, Phys. Rev. B. 84 (2011) 180405(R). [6] Y. Li, F.L. Zeng, Steven S.-L. Zhang, H. Shin, H. Saglam, V. Karakas, O. Ozatay, J.E. Pearson, O.G. Heinonen, Y.Z. Wu, A. Hoffmann, W. Zhang, Phys. Rev. Lett. 122 (2019) 117203. [7] Y.W. Zhao, Y. Liu, H.M. Tang, H.H. Jiang, Z. Yuan, K. Xia, Phys. Rev. B. 98 (2018) 174412. [8] Y. Cheng, A.J. Lee, J.T. Brangham, S.P. White, W.T. Ruane, P.C. Hammel, F.Y. Yang, Appl. Phys. Lett. 113 (2018) 262403. [9] L. Chen, S. Mankovsky, S. Wimmer, M.A.W. Schoen, H.S. Körner, M. Kronseder, D. Schuh, D. Bougeard, H. Ebert, D. Weiss, C.H. Back, Nat. Phys. 14 (2018) 490. [10] B. Khodadadi, A. Rai, A. Sapkota, A. Srivastava, B. Nepal, Y.M. Lim, D. A. Smith, C. Mewes, S. J. Budhathoki, A. J. Hauser, M. Gao, J. F. Li, D. D. Viehland, Z. J. Jiang, J. J. Heremans, P. V. Balachandran, T. Mewes, S. Emori, arXiv:1906.10326, 2019. [11] K. Gilmore, M.D. Stiles, J. Seib, D. Steiauf, M. Fähnle, Phys. Rev. B 81 (2010) 174414. [12] Y. Liu, Z. Yuan, R.J.H. Wesselink, A.A. Starikov, P.J. Kelly, Phys. Rev. Lett. 113 (2014) 207202. [13] W. Cao, L. Yang, S. Auffret, W.E. Bailey, Phys. Rev. B. 99 (2019) 094406. [14] K. Chen, S. Zhang, Phys. Rev. Lett. 114 (2015) 126602. [15] A.A. Baker, A.I. Figueroa, C.J. Love, S.A. Cavill, T. Hesjedal, G. van der Laan, Phys. Rev. Lett. 116 (2016) 047201. [16] Y. Li, Y. Li, Q. Liu, Z. Yuan, W. He, H. L. Liu, K. Xia, W. Yu, X. Q. Zhang and Z. H. Cheng, arXiv:1809.11020, 2018. [17] Z.H. Cheng, W. He, X.Q. Zhang, D.L. Sun, H.F. Du, Q. Wu, Y.P. Fang, H.L. Liu, Chin. Phys. B. 24 (2015) 077505. [18] Q.F. Zhan, S. Vandezande, K. Temst, C.V. Haesendonck, Phys. Rev. B. 80 (2009) 094416. [19] W. Zhang, W. He, X.Q. Zhang, Z.H. Cheng, J. Teng, M. Fähnle, Phys. Rev. B. 96 (2017) 220415(R). [20] W. He, B. Hu, Q.F. Zhan, X.Q. Zhang, Z.H. Cheng, Appl. Phys. Lett. 104 (2014) 142405. [21] T.L. Gilbert, Phys. Rev. 100 (1955) 1243. [22] G.M. Müller, M. Münzenberg, G.X. Miao, A. Gupta, Phys. Rev. B. 77 (2008) 020412. [23] Y. Fan, X. Ma, F. Fang, J. Zhu, Q. Li, T.P. Ma, Y.Z. Wu, Z.H. Chen, H.B. Zhao, G. Lupke, Phys. Rev. B. 89 (2014) 094428. [24] C. Zener, Phys. Rev. 96 (1954) 1335. [25] B. Heinrich, K.B. Urquhart, A.S. Arrott, J.F. Cochran, K. Myrtle, S.T. Purcell, Phys. Rev. Lett. 59 (1987) 1756. [26] Y.L. Zhao, Q. Song, S.H. Yang, T. Su, W. Yuan, S.S.P. Parkin, J. Shi, W. Han, Sci. Rep. 6 (2016) 22890. [27] T. Kato, Y. Matsumoto, S. Okamoto, N. Kikuchi, O. Kitakami, N. Nishizawa, S. Tsunashima, S. Iwata, I.E.E.E. Trans, Magn. 78 (2011) 3036. [28] X. Ma, L. Ma, P. He, H.B. Zhao, S.M. Zhou, G. Lupke, Phys. Rev. B 91 (2015) 014438. [29] S. Mizukami, F. Wu, A. Sakuma, J. Walowski, D. Watanabe, T. Kubota, X. Zhang, H. Naganuma, M. Oogane, Y. Ando, T. Miyazaki, Phys. Rev. Lett. 106 (2011) 117201. [30] H. Kurebayashi, T.D. Skinner, K. Khazen, K. Olejnık, D. Fang, C. Ciccarelli, R.P. Campion, B.L. Gallagher, L. Fleet, A. Hirohata, A.J. Ferguson, Appl. Phys. Lett. 102 (2013) 062415. [31] J. Lindner, I. Barsukov, C. Raeder, C. Hassel, O. Posth, R. Meckenstock, P. Landeros, D.L. Mills, Phys. Rev. B. 80 (2009) 224421. [32] Y. Li, W. Zhang, N. Li, R. Sun, J. Tang, Z.Z. Gong, Y. Li, X. Yang, Z.K. Xie, Q. Gul, X.Q. Zhang, W. He, Z.H. Cheng, J. Phys.: Condens. Matter. 31 (2019) 305802. [33] H. Moradi, G.A. Gehring, J. Magn. Magn. Mater. 256 (2003) 3. [34] K. Lenz, H. Wende, W. Kuch, K. Baberschke, K. Nagy, A. Jánossy, Phys. Rev. B. 73 (2006) 144424. [35] B. Sepiol, G. Vogl, Phys. Rev. Lett. 71 (1993) 731 and references therein. [36] S. Dennler, J. Hafner, Phys. Rev. B. 73 (2006) 174303.
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Journal of Magnetism and Magnetic Materials 496 (2020) 165950
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Z. Frait, Phys. Rev. B 76 (2007) 104416. [40] Y. Zhai, C. Ni, Y. Xu, Y.B. Xu, J. Wu, H.X. Lu, H.R. Zhai, J. Appl. Phys 101 (2007) 09D120. [41] R. Meckenstocka, D. Spoddiga, Z. Fraitb, V. Kamberskyb, J. Pelzl, J. Magn. Magn. Mater. 272 (2004) 1203.
7
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Research articles
Strongly enhanced Gilbert damping anisotropy at low temperature in high quality single-crystalline Fe/MgO (0 0 1) thin film
T
Wei Zhanga,b, Yan Lia,b, Na Lia,b, Yang Lia,b, Zi-zhao Gonga,b, Xu Yanga,b, Zong-kai Xiea,b, ⁎ ⁎ Rui Suna,b, Xiang-qun Zhanga, Wei Hea, , Zhao-hua Chenga,b,c, a
State Key Laboratory of Magnetism and Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China b School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China c Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
ARTICLE INFO
ABSTRACT
Keywords: Gilbert damping Spin dynamics Magnetic devices
The anisotropic behavior of Gilbert damping provides a new dimension for controlling and tuning magnetization relaxation within the same magnetic device. The single-crystalline ferromagnetic metals with a high symmetry have been predicted to possess significantly anisotropic damping for one decade. By decreasing temperature down to T = 4.5 K, we found that the anisotropic damping factor Q, defined as the fractional difference of damping between easy and hard axis, can be approached to 60%–90% in Fe (15 nm)/MgO (0 0 1) without applied fields dependent behavior. It is much larger than Q = 10%–20% obtained at room temperature. Furthermore, it is followed by explanations on the basis of the breathing Fermi surface model giving around Q = 30%–40% when electron-phonon scattering rate is small enough. This discovery will enrich the understanding of damping mechanism, and can provide clues for searching strongly anisotropic damping within 3d transition metals and alloys.
Magnetic damping is a crucial parameter in spintronics because it describes the energy relaxation rate and the speed at which a device can be operated [1]. Controlling and tuning Gilbert damping is prerequisite for spintronic device optimization, since either a smaller or a larger damping is demanded in various devices. For instance, the thermally induced magnetization fluctuation noise (mag-noise) in the magnetoresistive (MR) sensors is proportional to the Gilbert damping [2]. As a result, small damping values are essential to guarantee the signal-tonoise ratio (SNR) in magnetic sensors. It is also required in minimizing power consumption in spin-torque-transfer (STT) based magnetic random access memory (MRAM) [3]. On the other hand, the currentperpendicular-to-the-plane giant magnetoresistance (CPP-GMR) device is susceptible to current-induced instability [4]. To improve the stability, a sufficiently large damping is preferred to increase the thermal coupling between magnetization and its host lattice. Therefore, tailoring Gilbert damping could facilitate the engineering of spintronic devices. It is hence desirable to discover Gilbert damping anisotropy in experiment followed by clarifying its microscopic mechanism. In principle, 3d transition metals or their alloys with a strong spinorbit coupling as well as the crystalline symmetry are good candidates
for exploring anisotropy Gilbert damping. In experiments, more convinced evidence is still required given a few attempts showing different results are outstanding. For instance, by changing the concentration of Si in FexSi1-x alloys, Barsukov et al. [5] tailored the spin-orbit coupling, and consequently the Gilbert damping. Although the electronic structure was varied by changing Si concentration, the Gilbert damping kept isotropy in experiment as well as in ab initial calculations. On the contrary, Li et al. [6] reported a giant Gilbert damping anisotropy in epitaxial Co50Fe50 thin film. It was ascribed to the variation of spin orbit coupling for different magnetization orientations induced by local tetragonal distortions. Because of the constrain that the damping anisotropy is structure sensitive behavior [7], Co25Fe75 thin film shows no evidently intrinsic anisotropy damping which was confirmed by Cheng et al. [8]. On the other hand, Chen et al. [9] discovered an anisotropic damping in the single element Fe ultrathin films due to robust interfacial spin-orbit field between Fe and GaAs substrate. However, the anisotropy factor Q defined as fractional difference between the damping with magnetization orientation along easy and hard axes around 20% induced by interfacial effect is too weak to be considered in practical applications. Similarly, the precise local tetragonal distortions
⁎ Corresponding authors at: State Key Laboratory of Magnetism and Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. E-mail addresses: [email protected] (W. He), [email protected] (Z.-h. Cheng).
https://doi.org/10.1016/j.jmmm.2019.165950 Received 23 September 2019; Received in revised form 3 October 2019; Accepted 4 October 2019 Available online 05 October 2019 0304-8853/ © 2019 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
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needed in Co50Fe50 resulting in anisotropy of spin-orbit coupling requires a complex deposited technique. Such strict condition also narrows its potential application in spintronic devices. Very recently, the presence of conductivity-like Gilbert damping was demonstrated in Fe (25 nm)/MgO at low temperatures by Khodadadi et al. [10]. And Gilmore et al. [11] predicted such kind of Gilbert damping should be anisotropic on the basis of first-principle calculations, while there has been no conclusive experimental evidence up to now. Here, our work aims at filling this gap. A giant anisotropy of damping with anisotropic factor Q = 120% was observed in a bare Fe (15 nm)/MgO by decreasing temperature down to 4.5 K. The reasons for selecting the bare Fe thin film are three-fold. Firstly, without capping layer, it would efficiently avoid extrinsic effect induced by interface, such as spin pumping [12]. Up to now, it is still not clear the Gilbert damping resulted from nonlocal spin pumping effect could be anisotropy or isotropy [13–16]. So it is better for us to avoid this effect temporary when we are interested in the intrinsic properties. Secondly, in order to achieve a much larger damping anisotropy that can be considered in applications, a thickness as large as 15 nm is necessary for utilizing its intrinsic bulk properties rather than the interface effect in Fe (1.3 nm)/GaAs [9]. Thirdly, unlike CoFe alloys, it is not necessary to care the needed local structure by controlling concentration precisely [6,7]. The loose of strict conditions makes Fe a more feasible candidate for exploring anisotropy damping. Fe film was epitaxially deposited on optically transparent singlecrystalline MgO(0 0 1) substrates in a molecular beam epitaxy chamber with a basic pressure 2 × 10 10 mbar [17]. Prior to Fe deposition, MgO (0 0 1) substrate was annealed at 700 0C for 2 h, and then 15 nm Fe film was deposited using electron-beam gun without capping layer. It allows us to focus on its intrinsic properties by avoiding the spin pumping effect at interface. The thickness of Fe layer was confirmed by x-ray reflection (XRR), while its crystal structure was measured by x-ray diffraction (XRD) with Cu Kα radiation. Fig. 1(a) shows the scan of xray reflectometry (XRR) curve with roughness around 0.1 nm, from which dFe = 15nm is given. In the θ-2θ XRD pattern [Fig. 1(b)], the (0 0 2) peaks of Fe indicate a good (0 0 2) out-of-plane texture. Meanwhile, the x-ray in-plane scans [Fig. 1(c)] display a fourfold symmetry
verifying the highly textured growth of Fe film in this study and confirm the epitaxial relationship of MgO (0 0 1)[1 0 0]//Fe (0 0 1)[1 1 0]. Furthermore, the atomic force microscopy (AFM) image shows a smooth surface of the epitaxial Fe film with a root-mean-square roughness of 0.12 nm. It is in consistent with the value obtained by XRR. Fig. 1(e) shows the normalized hysteresis loops of 15 nm Fe film along easy axis Fe [1 0 0] ( H = 00 ) and hard axis Fe [1 1 0] ( H = 450 ) by longitudinal 2K magneto-optical Kerr effect (MOKE). Based on the relation HK = M1 s
where HK is the saturated field in hysteresis loop when H = 450 , the value of in-plane magnetocrystalline is estimated as around K1 = 3 × 105erg/ cm3. The normalized remanence Mr/Ms in Fig. 1(e) indicates a good four-fold magnetocrystalline anisotropy [18]. The dynamical process of spin precession in Fe (15 nm)/MgO was measured by time-resolved magneto-optical Kerr effect (TRMOKE) [19]. A very low laser fluence 1 mJ/cm2 is used to avoid nonlinear spin dynamics induced by laser heating [20]. Even though its influence on spin dynamics is more pronounced at low temperature, it is independent of magnetization orientations. Therefore, the value of anisotropy factor Q could be independent of laser power. The scheme of TRMOKE experiment is illustrated in Fig. 2(a) where the external field was fixed at H = 150 with respect to film normal direction. In this case, the magnetization would be tilted far away from easy plane (0 0 1) when the applied field is large enough. For T = 300 K, Fig. 2(b) and (c) show the typical time evolution of the polar component of magnetization in the presence of external field H ranging from 3.9 kOe to 12.6 kOe with H = 00 and H = 450 , respectively. It is observed clearly that the spin precession process can be influenced significantly by magnetic fields for both cases. Interestingly, we have to address the dissimilarities in spin precession for different magnetization orientations. For instance, when H = 3.9 kOe, the precession of magnetization decays much faster with external field applied along hard axis ( H = 450 in Fig. 2(c)) than that along easy axis with H = 00 (Fig. 2(b)). With increasing magnetic fields, such differences are less pronounced. Similar behaviors are also shown in Fig. 2(d) (e) with T = 4.5 K. The exact values for f with various applied fields can be obtained using the damped harmonic function:
Fig. 1. Structure and morphology measurements for Fe (15 nm)/MgO as well as static magnetic property. (a) The scan of x-ray reflectivity gives the roughness of 0.1 nm and the layers thickness 15 nm for Fe thin film. (b) X-ray diffraction measurements of θ-2θ scan and (c) in-plane scan for Fe (15 nm)/MgO. (d) Atomic force microscopy image (2 × 2 μm2) of the Fe (15 nm) thin film. (e) Normalized hysteresis loops of Fe (15 nm)/MgO(0 0 1) with the in-plane applied magnetic field along Fe [1 0 0] (ϕH = 0°) and Fe [1 1 0] (ϕH = 45°). (f) Fourfold angular dependent remanence Mr/Ms. 2
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
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Fig. 2. Spin precession measured by TRMOKE for Fe (15 nm)/MgO as a function of temperature and magnetization orientations. (a) Schematic of the coordinate system for TRMOKE measurement in Fe (15 nm)/MgO. (b) spin precession for ϕH = 0°, T = 300 K. (c) spin precession for ϕH = 45°,T = 300 K. (d) spin precession for ϕH = 0°, T = 4.5 K. (e) spin precession for ϕH = 45°, T = 4.5 K. The red curves are the fitted results of the experimental data to Eq. (1).
K
= A + Bexp
t
sin(2 ft + )
The field dependence of frequency f extracted from the fitting procedure by Eq. (1) is shown in Fig. 3(a) for both T = 300 K and T = 4.5 K with H = 00 and H = 450 , respectively. We note that the experimental f-H relation can be described by Kittel Eq. (2) [21,22]:
(1)
where A is the background magnitudes, B, , f and φ are the magnetization precession amplitude, relaxation time, frequency and phase, respectively. 3
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
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Fig. 3. Spin dynamics for Fe(15 nm)/MgO by TRMOKE and VNA-FMR measurements. (a) The relation between frequency and applied fields as a function of temperature and magnetization orientations, respectively. (b) Effective Gilbert damping as a function of applied fields with ϕH = 0° and ϕH = 45° at room temperature. (c) Effective Gilbert damping as a function of applied fields with ϕH = 0° and ϕH = 45° at T = 4.5 K. (d) H as a function of frequency with the applied field along easy and hard axis.
2 f
=
1 Ms sin
With e
= 1.76 ×
H1· H2
M
eg
=
H3
is
the
2 107 Hz/Oe,
gyromagnetic
g = 2.09) ,
sin2 2 M (3sin2 M cos 2 M sin4 (cos H cos M + sin H sin M cos(
H2 =
2E 2 M
= 2K1sin4
and H3 =
2E M
M
The value of H is kept as 150 ± 10 in the fitting producer, while H and M are modified slightly within ± 20 due to the mismatch between applied field and easy or hard axis of the sample. The temperature dependent magnetocrystalline anisotropy [24] constant K1 = (5 ± 1) × 105erg / cm3 and K1 = (4 ± 1) × 105erg / cm3 were used to reproduce the f-H curves at T = 4.5 K and T = 300 K, respectively. The saturation magnetization Ms = 1.7 × 103erg / cm3 is kept as constant considering the measured temperature range is far away from the Curie temperature around 1000 K. This assumption is reasonable according to previous experiments [10,23]. During the fitting procedure, the constant value of out-of-plane magnetic anisotropy K out = 1 × 106erg / cm3 [25] gives rise to the demagnetization field Hd = 2 × 10 4 Oe [16] by 2K out Hd = 4 Ms . As is shown in Fig. 3(a), the field dependence of Ms frequency in experiment is reproduced well within theoretical calculations based on Kittle formula. The frequency differs largely for 0 0 H = 0 and H = 45 within the region of low applied fields due to the strong magnetocrystalline anisotropy in high quality single crystal sample. This fact has a large influence on the difference of damping in the case of H = 00and H = 450 at low applied fields as shown below. Furthermore, using the fitted values of τ from Eq. (1) we determine the effective Gilbert damping eff with Eq. (4) [22]:
(2)
M cos 4 M
= 2K1sin3
H1 =
M ) + 2(K out H ), M
+ sin
ratio 2E
2 M
+ HMs sin
Fe
= 2K1 cos 4
2 Ms2 ) cos 2
M sin H cos( M
M cos M sin 4 M
(for
M
[23] M
+ K1
+ HMs
H) H cos M sin( M
H ).
Here, K1 and K out are the in-plane magnetocrystalline and out-ofplane magnetic anisotropies of Fe films, respectively. M and M are polar and azimuthal equilibrium angles of magnetization with respect to the Fe [0 0 1] and Fe [1 0 0] directions respectively. Likewise, H and H are polar and azimuthal angles of the applied magnetic field H, respectively. The equilibrium angles of magnetization are determined via the following Eq. (3):
K1sin2 2
3 M sin M cos M
sin
H cos M cos( M
+
1 K1 sin 4 2 H)
M
+ (K out
+ HMs cos
2 Ms2 ) sin2
M cos H
=0
M
HMs (3) 4
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
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eff
=
extrinsic dephasing effect dominating at low field is reduced when the field is large enough. And only the intrinsic contributions to anisotropy damping is left. The consequence is the difference of damping between 0 0 H = 45 and H = 0 decreases. More interestingly, for T = 4.5 K, the lowest value of anisotropy factor Q reaches above 60% , even the largest value is around 120% as field increasing. It is much larger than Q = 15% in the case of T = 300 K at large enough field as is shown in the insert of Fig. 4, confirming the convinced enhancement of Gilbert damping anisotropy at low temperature. With applying larger external fields, the constant values of αeff at higher fields are therefore used to approximate the intrinsic Gilbert damping [27,28]. It is a general method to achieve the intrinsic Gilbert damping in TRMOKE experiment [29]. Therefore, the field-independent Q around 60%–90% is mainly considered from intrinsic contributions, rather than extrinsic ones. Even so, we prefer to discuss several possible contributions to damping anisotropy explicitly, including intrinsic and extrinsic effects. Among the extrinsic contributions, two-magnon scattering is famous for its anisotropy behavior within in-plane sample. Such extrinsic effect once leads to obstacle in identifying anisotropic Gilbert damping [30]. In particular, there is no capping layer to protect Fe film. In this case, the high quality of Fe would be destroyed at the surface by oxidation. As a result, there could be some two-magnon scattering events. However, we can exclude this effect based on the following reasons. Firstly, its strength is dependent on the magnetization orientation with respect to film normal [31]. Two-magnon scattering is only active for values of M > 450 , it shuts off for angles 0 M < 45 because there are no degenerate states available for this angular region. This limit condition could be fulfilled for external field closer to the film normal. Indeed, a value of H as small as 150 degree was selected in this study. In this case, the critical value of M = 450 is approached at high enough fields to reduce the two-magnon scattering as much as possible [32]. Secondly, previous demonstrations show that the two-magnon-scattering induced damping increases with precession frequency increasing because of the increased degeneracy of spin waves [33]. This disagrees with the fact here that the damping drops monotonously with field increasing shown in Fig. 3(b) and (c), indicating the minor contributions from two-magnon-scattering to Gilbert damping. Thirdly, this two-magnon process occurs when an excited spin-wave has degenerate states to relax by defects. And defects always cause more spin-wave scattering along easy axis than that along hard axis [34]. On the one hand, this is because the defects are preferred to being parallel to easy axis, which has been confirmed both in experiment by employing Mössbauer spectroscopy [35] as well as in first-principle calculations [36]. It makes the easy axis the stronger relaxation direction, hosting a larger damping from two-magnon scatterings. On the other hand, the two-magnon scattering is frequency dependent. The larger frequency obtained along easy axis would surely give rise to a stronger two-magnon scattering. Therefore, the anisotropy damping arising from two-magnon scattering will result in a negative Q rather than the positive one observed in this study. Above all, the two-magnon scattering induced damping always dominates in polycrystalline samples [31] as well as in exchange bias heterostructure [37] with a large amount of defects. A.Yu. Dobin et al. proposed that two-magnon scatterings is active for the roughness around 1.3 nm [38]. On the contrary, the high quality single-crystalline sample characterized by XRD and AFM with a roughness at atomic level of around 0.1 nm may suppress the twomagnon scattering in this study. Apart from two-magnon scatterings, the field-dragging effect in single-crystalline sample would also give rise to a damping anisotropy [9]. It results from the fact that the rotation of magnetization cannot follow closely with applied field due to the large magnetocrystalline anisotropy. In this study, we can not avoid this effect due to the misalignment between applied field and easy or hard axis. So, the anisotropy factor Q = 15% at room temperature maybe partly comes from field-dragging effect. However, there is no evidence on the enhancement of damping at low temperatures arising from field-dragging effect. Therefore, the enhancement of anisotropy
2 (H1 +
H2 ) sin2 M
(4)
As shown in Fig. 3(b) and (c), the effective damping constant eff are obtained for different magnetization orientations with T = 4.5 K and T = 300 K, respectively. In both cases, a nearly field-independent behavior of damping is observed when external field is along easy axis of Fe film with H = 00 , while there is a pronounced enhancement of damping with field decreasing when H = 450 . It gives rise to a quite larger damping for H = 450 at low fields, coming from a larger dephasing effect. Such dephasing effect [23] results from the variation of Fe spin orientation. As applied field decreasing, a much smaller frequency is obtained along H = 450 than that in H = 00 . It indicates a much weaker effective field along hard axis, and consequently a much larger variation of spin orientations there. Fortunately, such dephasing effect would be suppressed with field increasing. It is evidenced in Fig. 3(a) that the same frequency is approached for easy and hard configurations when applied field is large enough. In this case, the spin orientations are almost the same as they are determined by external applied field. It is unlike the case of low applied fields where the spin orientation is determined by effective fields. In addition, in-plane Vector Network Analyzer ferromagnetic resonance (VNA-FMR) [16] measurements have been performed at room temperature in Fig. 3(d) with applied field ranging from 0 Oe to 4000 Oe. The Gilbert damping for H = 450 and H = 00 could be obtained from the linearly fitted curves (red lines), based on the following equation [26]:
H = H0 +
2 f (5)
where is the geomagnetic ratio with the same value applied in Eq. (2) ° and H0 5Oe is the inhomogeneous broadening. The value of H = 45 ° obtained in VNA-FMR are around 0.0045 ± 0.0002 . This value and H =0 is consistent with that obtained using TRMOKE in Fig. 3(b). It suggests the reliability of our TRMOKE measurements carried out in this study. To quantify the anisotropy of the damping, we define Q in the following as an anisotropy factor [13]:
Q=
° H = 45
° H =0 H =0
°
(6)
It is the fractional difference between the damping with magnetization orientation along easy and hard axis. Applying this equation into Fig. 3(b) and (c), we can extract the value of Q for T = 300 K and T = 4.5 K, respectively. According to Fig. 4, the anisotropy factor drops as the applied field increasing for both temperatures. It is because the
Fig. 4. The variation of anisotropy damping factor Q with applied fields for T = 4.5 K and T = 300 K. Insert: anisotropy damping factor Q as a function of large applied fields. 5
Journal of Magnetism and Magnetic Materials 496 (2020) 165950
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factor Q at low temperature is mainly resulted from intrinsic effect as shown below. This also holds for excluding mosaicity effect [39]. Here, the field-independent damping anisotropy factor Q = 60%–90% at T = 4.5 K is ascribed to the competition between conductivity-like and resistivity-like damping with decreasing temperature. Based on the breathing Fermi-surface model [11], the electrons scatterings from intraband contribution (conductivity-like damping) maintains damping anisotropy for all scattering rates. The scattering rates are dependent on temperature in experiment. In contrast, the interband contribution (resistivity-like damping) exhibits these anisotropies only at small scattering rates (low temperature) and becomes increasingly isotropic with temperature increasing. Therefore, the experiments carried out at room temperature show an almost isotropic behavior for damping. For instance, as is reported by Zhai et al. [40], an isotropy Gilbert damping of Fe film can be used to fit anisotropy linewidth in FMR measurements because interband contribution to electrons scatterings dominates at room temperature. Similarly, the damping of hard and easy axis are almost the same in Fe (1.14 nm 2.3 nm)/InAs at room temperature reported by Meckenstock et al. [41]. Very recently, Khodadadi et al. [10] reported an isotropic Gilbert damping in Fe (25 nm)/MgO at room temperature, stating the resistivity-like Gilbert damping dominates there. Although anisotropic electronic structure has been predicted in single-crystalline ferromagnetic metals, such as bulk Fe, Co and Ni, the anisotropic damping can be dramatically reduced due to smearing of the energy bands with electron scattering. Up to now, it makes experimental observation of the anisotropic damping in bulk materials difficult at room temperature. By decreasing temperature, the strength of electron scattering could be decreased. As a result, the isotropy resistivity-like damping could be suppressed largely and only the anisotropy part could be left at low temperature. In this case, the maximum damping anisotropy factor Q = 120% at T = 4.5 K is observed. Even the lowest value Q = 60% is larger than Q = 30% in the theoretical prediction based on the breathing Fermi-surface model [11]. We address that it is much larger than Q = 20% induced by interfacial spin orbit coupling between ultrathin Fe film and GaAs substrate [9]. Moreover, it has the same magnitude order with the value Q = 300% obtained in Co50Fe50 but with a more feasible deposited method. In this study, we proposed that Gilbert damping in pure 3d transition metal Fe exhibits anisotropic behavior by decreasing temperature. At low temperature, the isotropy resistivity-like damping is suppressed largely. In contrary, at room temperature the anisotropic electronic structure can be dramatically reduced due to the enhanced electron scattering. This is the main reason that very few convinced experiments demonstrating the anisotropic Gilbert damping in pure 3d metals at room temperature were reported. Following the line of suppressing isotropy resistivity-like damping, we can expect ferromagnetic half metals would show an obvious anisotropic Gilbert damping. In this kind of materials, the isotropic resistivity-like damping is blocked and so the damping can be dominated by the anisotropic contributions. Improving the Q factor in ferromagnetic materials at room temperature would facilitate the engineering of spintronic devices. Half metals such as Heusler alloys should be noted as the potential candidates to show a large Q factor at room temperature. In summary, the high quality single crystal Fe film provides an ideal platform for exploring spin dynamics especially for anisotropy damping. A considerable damping anisotropy with Q larger than 60% is observed at T = 4.5 K. It is much larger than that at T = 300 K with Q is around 15%. We show that the enhancement of damping anisotropy at low temperature can be explained based on the breathing Fermi surface model. In this model, the resistivity-like damping from interband scattering is isotropic at sufficiently high temperatures and it can be suppressed largely by decreasing temperature. Thereafter, only conductivity-like damping from intraband scattering dominates which shows anisotropic behavior with various magnetization orientations. Our results open up a new avenue to tailor the Gilbert damping in
metallic ferromagnets by changing temperature, which are important for optimizing dynamic properties of future magnetic devices. Acknowledgements This work is supported by the National Key Research Program of China (Grant Nos. 2015CB921403, 2016YFA0300701, and 2017YFB0702702), the National Natural Sciences Foundation of China (Grant Nos. 1187411, 51427801, and 51671212) and the Key Research Program of Frontier Sciences, CAS (Grant Nos. QYZDJ-SSW-JSC023, KJZD-SW-M01 and ZDYZ2012-2). References [1] Y.S. Hou, R.Q. Wu, Phys. Rev. Appl. 11 (2019) 054032. [2] N. Smitha, P. Arnett, Appl. Phys. Lett. 78 (2001) 1448. [3] A.V. Khvalkovskiy, D. Apalkov, S. Watts, R. Chepulskii, R.S. Beach, A. Ong, X. Tang, A. DriskillSmith, W.H. Butler, D. Lottis, E. Chen, V. Nikitin, M. Krounbi, J. Phys. D: Appl. Phys. 46 (2013) 139601. [4] K. Nagasaka, J. Magn. Magn. Mater. 321 (2009) 508. [5] I. Barsukov, S. Mankovsky, A. Rubacheva, R. Meckenstock, D. Spoddig, J. Lindner, N. Melnichak, B. Krumme, S.I. Makarov, H. Wende, H. Ebert, M. Farle, Phys. Rev. B. 84 (2011) 180405(R). [6] Y. Li, F.L. Zeng, Steven S.-L. Zhang, H. Shin, H. Saglam, V. Karakas, O. Ozatay, J.E. Pearson, O.G. Heinonen, Y.Z. Wu, A. Hoffmann, W. Zhang, Phys. Rev. Lett. 122 (2019) 117203. [7] Y.W. Zhao, Y. Liu, H.M. Tang, H.H. Jiang, Z. Yuan, K. Xia, Phys. Rev. B. 98 (2018) 174412. [8] Y. Cheng, A.J. Lee, J.T. Brangham, S.P. White, W.T. Ruane, P.C. Hammel, F.Y. Yang, Appl. Phys. Lett. 113 (2018) 262403. [9] L. Chen, S. Mankovsky, S. Wimmer, M.A.W. Schoen, H.S. Körner, M. Kronseder, D. Schuh, D. Bougeard, H. Ebert, D. Weiss, C.H. Back, Nat. Phys. 14 (2018) 490. [10] B. Khodadadi, A. Rai, A. Sapkota, A. Srivastava, B. Nepal, Y.M. Lim, D. A. Smith, C. Mewes, S. J. Budhathoki, A. J. Hauser, M. Gao, J. F. Li, D. D. Viehland, Z. J. Jiang, J. J. Heremans, P. V. Balachandran, T. Mewes, S. Emori, arXiv:1906.10326, 2019. [11] K. Gilmore, M.D. Stiles, J. Seib, D. Steiauf, M. Fähnle, Phys. Rev. B 81 (2010) 174414. [12] Y. Liu, Z. Yuan, R.J.H. Wesselink, A.A. Starikov, P.J. Kelly, Phys. Rev. Lett. 113 (2014) 207202. [13] W. Cao, L. Yang, S. Auffret, W.E. Bailey, Phys. Rev. B. 99 (2019) 094406. [14] K. Chen, S. Zhang, Phys. Rev. Lett. 114 (2015) 126602. [15] A.A. Baker, A.I. Figueroa, C.J. Love, S.A. Cavill, T. Hesjedal, G. van der Laan, Phys. Rev. Lett. 116 (2016) 047201. [16] Y. Li, Y. Li, Q. Liu, Z. Yuan, W. He, H. L. Liu, K. Xia, W. Yu, X. Q. Zhang and Z. H. Cheng, arXiv:1809.11020, 2018. [17] Z.H. Cheng, W. He, X.Q. Zhang, D.L. Sun, H.F. Du, Q. Wu, Y.P. Fang, H.L. Liu, Chin. Phys. B. 24 (2015) 077505. [18] Q.F. Zhan, S. Vandezande, K. Temst, C.V. Haesendonck, Phys. Rev. B. 80 (2009) 094416. [19] W. Zhang, W. He, X.Q. Zhang, Z.H. Cheng, J. Teng, M. Fähnle, Phys. Rev. B. 96 (2017) 220415(R). [20] W. He, B. Hu, Q.F. Zhan, X.Q. Zhang, Z.H. Cheng, Appl. Phys. Lett. 104 (2014) 142405. [21] T.L. Gilbert, Phys. Rev. 100 (1955) 1243. [22] G.M. Müller, M. Münzenberg, G.X. Miao, A. Gupta, Phys. Rev. B. 77 (2008) 020412. [23] Y. Fan, X. Ma, F. Fang, J. Zhu, Q. Li, T.P. Ma, Y.Z. Wu, Z.H. Chen, H.B. Zhao, G. Lupke, Phys. Rev. B. 89 (2014) 094428. [24] C. Zener, Phys. Rev. 96 (1954) 1335. [25] B. Heinrich, K.B. Urquhart, A.S. Arrott, J.F. Cochran, K. Myrtle, S.T. Purcell, Phys. Rev. Lett. 59 (1987) 1756. [26] Y.L. Zhao, Q. Song, S.H. Yang, T. Su, W. Yuan, S.S.P. Parkin, J. Shi, W. Han, Sci. Rep. 6 (2016) 22890. [27] T. Kato, Y. Matsumoto, S. Okamoto, N. Kikuchi, O. Kitakami, N. Nishizawa, S. Tsunashima, S. Iwata, I.E.E.E. Trans, Magn. 78 (2011) 3036. [28] X. Ma, L. Ma, P. He, H.B. Zhao, S.M. Zhou, G. Lupke, Phys. Rev. B 91 (2015) 014438. [29] S. Mizukami, F. Wu, A. Sakuma, J. Walowski, D. Watanabe, T. Kubota, X. Zhang, H. Naganuma, M. Oogane, Y. Ando, T. Miyazaki, Phys. Rev. Lett. 106 (2011) 117201. [30] H. Kurebayashi, T.D. Skinner, K. Khazen, K. Olejnık, D. Fang, C. Ciccarelli, R.P. Campion, B.L. Gallagher, L. Fleet, A. Hirohata, A.J. Ferguson, Appl. Phys. Lett. 102 (2013) 062415. [31] J. Lindner, I. Barsukov, C. Raeder, C. Hassel, O. Posth, R. Meckenstock, P. Landeros, D.L. Mills, Phys. Rev. B. 80 (2009) 224421. [32] Y. Li, W. Zhang, N. Li, R. Sun, J. Tang, Z.Z. Gong, Y. Li, X. Yang, Z.K. Xie, Q. Gul, X.Q. Zhang, W. He, Z.H. Cheng, J. Phys.: Condens. Matter. 31 (2019) 305802. [33] H. Moradi, G.A. Gehring, J. Magn. Magn. Mater. 256 (2003) 3. [34] K. Lenz, H. Wende, W. Kuch, K. Baberschke, K. Nagy, A. Jánossy, Phys. Rev. B. 73 (2006) 144424. [35] B. Sepiol, G. Vogl, Phys. Rev. Lett. 71 (1993) 731 and references therein. [36] S. Dennler, J. Hafner, Phys. Rev. B. 73 (2006) 174303.
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