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Investigation of ferromagnetic resonance and damping properties of CoFeB
Accepted Manuscript Investigation of ferromagnetic resonance and damping properties of CoFeB E. Gokce Polat, C. Deger, F. Yildiz PII:
S1567-1739(19)30075-6
DOI:
https://doi.org/10.1016/j.cap.2019.03.002
Reference:
CAP 4938
To appear in:
Current Applied Physics
Received Date: 17 October 2018 Revised Date:
22 February 2019
Accepted Date: 1 March 2019
Please cite this article as: E. Gokce Polat, C. Deger, F. Yildiz, Investigation of ferromagnetic resonance and damping properties of CoFeB, Current Applied Physics (2019), doi: https://doi.org/10.1016/ j.cap.2019.03.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Investigation of ferromagnetic resonance and damping properties of CoFeB E. Gokce Polata, b*, C. Degerc and F. Yildizb
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Department of Engineering Physics, Istanbul Medeniyet University, Uskudar, Istanbul 34700, Turkey b
Department of Physics, Gebze Technical University, Kocaeli 41400, Turkey
c
Department of Physics, Marmara University 34722, Kadikoy, Istanbul, Turkey
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a
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Abstract
In this study, the influences of thin film thickness and post-annealing process on the magnetic properties of CoFeB thin films were investigated. The angular dependency and linewidth of the ferromagnetic resonance signal were used to explore the magnetic behavior of sputtered single-layer
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and trilayer thin film stacks of CoFeB. A micromagnetic simulation model was employed based on the metropolis algorithm comprising the demagnetizing field and in-plane induced uniaxial anisotropy terms with all relevant contributions. Our results reveal that the direction of magnetization changes
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from in-plane to out-of-plane as a result of the annealing process and induces a perpendicular magnetic anisotropy in the 1-nm thick CoFeB thin film. The ferromagnetic resonance (FMR) linewidth can be
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defined well by the intrinsic Gilbert damping effect and the magnetic inhomogeneity contribution in both as-grown and annealed samples. The difference between the linewidths of the single and trilayer film is mainly caused by the spin pumping effect on damping which is associated with the interface layers.
*
Corresponding author. E-mail address: [email protected]
ACCEPTED MANUSCRIPT Keywords: Magnetic thin films; Ferromagnetic resonance; Ferromagnetic resonance linewidth; Magnetic anisotropy; CoFeB.
1. Introduction
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The ferromagnetic alloy, cobalt-iron-boron (CoFeB) is a soft ferromagnetic material which is widely used in spintronic devices. When the CoFeB layer is thin enough, it shows a perpendicular magnetic anisotropy (PMA) and has potential applications for Magnetic Random Access Memories
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(MRAM)[1]. Ikeda et al. first identified the PMA in Ta/CoFeB/MgO stack, which has promising applications in STT devices[2]. CoFeB/MgO/CoFeB has become attractive for magnetic tunnel
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junctions (MTJs) due to high tunneling magnetoresistance (TMR) properties. In addition, this stack has aroused great interest for STT-MRAM owing to the high thermal stability, and magnetization switching speed [2–5].
The PMA of the Ta/CoFeB/MgO stack originates developing interfacial magnetic anisotropy because
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of the hybridization between Fe/Co 3d orbitals and Oxygen 2p orbitals at the CoFeB / MgO [6–8]. The under-layer of the CoFeB layer also has a significant influence on PMA [9,10]. Worledge et al. have reported that Ta / CoFeB interface plays an important role in CoFeB magnetization [4,11,12]. The
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practical use of such technologies requires the determination of physical mechanisms for
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magnetization and relaxation behaviors behind the magnetic thin films and multilayers, and studying the dynamic magnetic properties of structures continue to be important [13,14]. The understanding and the manipulation of the magnetic damping properties are crucial factors for the operation of CoFeBbased spintronic devices that function in the nanosecond range of magnetization switching [15,16]. Because of the decrease of the device size, the interface plays an important role in the characteristics [17,18]. Therefore, in thin films and multilayers, it is essential to explain the damping process which is caused by the magnetization energy losses due to surface or interface effects. The annealing process helps to improve the perpendicular magnetic anisotropy (PMA) which is required in some of these
ACCEPTED MANUSCRIPT applications. Miyakawa et al. reported that CoFe(B) crystallite formation at the CoFeB/MgO interface starts after annealing at 250 °C and the PMA starts to deteriorate at temperatures over 300 °C due to the diffusion of Ta atoms [19] .
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The FMR technique is used to investigate the magnetic properties of thin films [20–22]. This method is widely used to determine the magnetization, magnetic anisotropy constant, demagnetization field, gfactor, interlayer magnetic coupling and magnetocrystalline interaction for single and multilayer thin films [23]. The FMR linewidth in magnetic metallic thin films can provide the information about,
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magnetic relaxation, magnetic homogeneity and film quality [24]. The magnetic damping parameter
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(α) is well defined by the Landau-Lifshitz-Gilbert equation [5], and known as Gilbert damping. There are several reports in the literature to understand the basis of Gilbert damping in spin dynamics relaxation in single layer and multilayered magnetic thin films [25,26]. According to Lenz et al. [27] and Heinrich et al. [28] the intrinsic damping constant in a Ferromagnet (FM) / nonmagnet (NM)
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/ferromagnet (FM) trilayer system is enhanced due to spin pumping.
In this study, the angular behavior of resonance field and linewidth as functions of the CoFeB film thickness were investigated experimentally and the origins of magnetic damping in the CoFeB films
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were discussed. FMR linewidth the CoFeB/MgO/CoZrTa sample was also studied in this paper. The difference in the linewidths between the single and trilayer films is mainly caused by the variation of
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the spin pumping associated with the interfaces and indirectly observed as addition
to Gilbert
damping in ferromagnetic resonance experiment [29]. Our study offers important insights for the spin pumping and spin transfer torque for magnetic tunnel junction device applications which use MgO barriers. The obtained low damping constant shows that our structure can be an attractive candidate for low-speed current-requiring spintronic devices.
ACCEPTED MANUSCRIPT 2. Experimental The samples were fabricated using magnetron sputtering method at room temperature, with a base pressure of 5×10−9 Torr. The thin film stacks are as follows: Si/SiO2/ Ta(10)/ Co0.4Fe0.4B0.2 (t)/ MgO(1.5)/ Ta (3) (thicknesses in nm) where the thickness (t) of CoFeB was 1 nm, 1.5 nm, 2 nm, and 3
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nm and Si/ SiO2/ Ta(10)/ Co0.4Fe0.4B0.2 (1.5)/ MgO(1.5)/ Co91.5Zr4.0Ta4.5 (4)/ MgO(1.5)/ Ta (3) in the following referred to as S2. A 3-nm-thick layer of Ta as a capping layer was designed to protect the CoFeB from the oxidation. MgO layer thickness was chosen as 1.5 nm since the interface effect is very
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important for our study [30]. All the thickness values are nominal. These series were grown for the observation of the magnetic anisotropy orientation and the determination of the FMR linewidth
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broadening mechanism for different CoFeB thicknesses of as-grown state and the post-annealed state. An X-band JEOL JES-FA300 electron spin resonance spectrometer (ESR) was used for the FMR measurements. FMR measurements of all films have been performed at 9.8 GHz for various field orientations at room temperature. The angular dependence of FMR spectra in two geometries was
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measured. For the in-plane geometry (IPG) measurements, the film was rotated around the sample normal while the applied DC magnetic field was always in the film plane. For the application of the out-of-plane geometry (OPG), the film was rotated from the sample plane to the sample normal with
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respect to the applied the field. Samples were then annealed at 300°C for 30 min under vacuum above 10-8 Torr. A Rigaku Smart-Lab X-ray diffractometer was used for investigating the crystal structure
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and microstrucre of films as-grown and annealed state in out-of plane. 2.1 Theoretical Model
We start to construct our model by predicting of the energy Hamiltonian of the system. The Hamiltonian consists of three energy terms which are widely used to represent the magnetic behavior of the systems [31,32]. The energy terms are sorted below:
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(1)
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−MH cos(θ )cos(θ ) + sin(θ )sin(θ )cos(ϕ − ϕ ) H H H 2 4 H = +K eff cos (θ ) + K eff _ q cos (θ ) 2 2 −K ax sin (θ )cos (ϕ )
Where (θ, θH) and (φ, φH) are respectively the polar and azimuth angles for magnetization vector M
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and external DC field vector H with respect to the film plane. The first term of the Hamiltonian is the Zeeman energy of the film in the external DC field. The second term represents the magneto static energy due to demagnetizing field. The last term represents assumed in-plane-induced uniaxial anisotropy energy due to film preparation conditions. In Eq. (1) M, Keff , Keff_q and Kax are the
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effective magnetization, first order perpendicular anisotropy energy density, second order perpendicular anisotropy energy density and the axial anisotropy constant, respectively. External magnetic field is swept from 0 to 2 T to determine the field corresponding to the maximum value of
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χ2 which is called as the resonance field (Hres). Dynamic susceptibility spectra χ2
are calculated by
χ2
=
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using the following equation [33–35]:
40 2 + "
2
1 ∂2 2" ! 0 2 2 #2 $2
"
2 2
4"2
% #0 & − % # & ! − 4 2 # $2
(2)
ω0 is the precession frequency of the system, which can also be called Larmor frequency, k represents wave vector and D is equal to 2A/M0, where A is called as the exchange stiffness. E, γ, T2 and ω
ACCEPTED MANUSCRIPT represent energy density, gyromagnetic ratio, spin-spin relaxation time and frequency of microwave radiation, respectively. Then, Larmor frequency is calculated by the following equation (3) [36]:
)
"( ) 1 ∂) +,-./ 1 ∂) +,-./ 1 ∂) +,-./ ) 0 * + 0 − * 0 ! = * ) + # ( ) ( 123) 4) ( 123) 4
(3)
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While the external magnetic field is increasing, Larmor frequency is getting closer to the resonance frequency of microwave (ω). Then the dynamic susceptibility starts to increase as the values of ω and ω0 get closer. At ω = ω0, the corresponding external magnetic field is marked as a resonance field for
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both in-plane geometry (IPG) and out-of-plane geometry (OPG). All calculations were performed at room temperature to fit outputs of simulation with the experimental data. M, ω/γ, Keff, Keff_q and Kax
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were obtained by using the simulation model for all samples.
In general, the ferromagnetic linewidth (∆H) depends on two parameters: intrinsic contribution of magnetism and extrinsic contribution due to inhomogeneity of the material [37]. The total ∆H of the
∆ H = ∆ H G + ∆ H 2 mag + ∆ H in hom
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FMR can be written as
(4)
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The first term in the ∆H is the intrinsic damping known as the Gilbert damping (∆HG). ∆HG is caused by energy loss since the magnetization energy is directly transferred to the lattice as spin-orbit
∆H G =
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coupling [38]. 2 α ω 3γ Ξ
Ξ ≡ cos(θ H − θ M ) −
3H X + H Y H 0 sin 2 (θ H − θ M ) HY ( H X + HY )
(5)
(6)
∆HG contribution shows a linear change due to the frequency along the easy axis and the hard axis when the magnetization is parallel to the external magnetic field (θH=θM, Ξ=1) from Eq. (5) and (6).
ACCEPTED MANUSCRIPT However, since linewidth contribution should be formed by the deviation of the magnetization the effect of magnetic anisotropy at the intermediate angles, an addition from the angle of the external magnetic field. In the literature, this effect is called field dragging [39]. When external field and the magnetization become parallel, this effect is vanished (Eq. (6)). In Eq. (5), the extrinsic contribution
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contains two types of contribution, one of which is two-magnon scattering contribution (∆H2mag) because of weak inhomogeneity and the other is strong inhomogeneity contribution (∆Hinhom) caused by regional variations of the magnetization and the magnetic anisotropy field [15]. Two-magnon
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scattering (TMS) is a damping additive that includes nonuniformity of film magnetic properties. TMS is usually associated with surface / interface roughness and other film defects in thin films structures.
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The loss in the magnetization energy caused by the scattering of uniform spin modes into degenerate spin modes results in damping. The TMS contribution in the angle dependent measurements is compatible with the in-plane crystallographic orientation [40]. TMS contributions are activated by surface and interface anisotropy in ultra-thin films [1].
2 HX cos(2θ M ) Γ(H O ,θ H )sin−1 H X + M eff cos2 θ M 3
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∆H 2mag =
(7)
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Γ is the fitting function that changed with orientation of external field. It is apparent from the equation
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when θ M 〉π / 4 is, the root is negative and TMS contributions disappear. During FMR measurements of the thin film (going from the in-plane to out-of-plane), the TMS contribution is reduced from 0° to 90° in the perpendicular geometry and eventually this effect disappears when the angles are equal,
θM = θ H = 90° . In this case the perpendicular linewidth reaches a minimum value [40]. The strong inhomogeneity contribution to linewidth is given by
∆H in hom =
∂H ∂H ∆θ H + ∆ 4πM eff ∂θ H ∂ 4πM eff
(8)
ACCEPTED MANUSCRIPT Here, ∆θH represents variations in the direction which originate from the crystallographic axes of the particles and ∆4πMeff represents variations of the demagnetization field [37]. The direction of the magnetization does not follow the direction of the applied magnetic field. Inhomogeneity contribution is the major factor that is seen in polycrystalline multilayer or perpendicular surface anisotropy films.
is the sum of Gilbert and inhomogeneous contributions.
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3. Results and Discussion
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In such cases, the in-plane linewidth is smaller than the perpendicular linewidth [41] and the linewidth
The OPG angular dependence of FMR in as-grown and annealed CoFeB samples is showed in Fig.
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1(a) and (b), respectively. As the thickness of CoFeB increases, the large demagnetization field and inplane magnetic anisotropy (IMA) causes an increase of the resonance field (Hres) in the film normal (θH=90°) and a decrease of Hres in parallel geometry (θH=0°). KEFF is the effective anisotropy energy density which is used to characterize the magnetization orientation in magnetic thin films. KEFF is
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considered to be an approximate sum of a volume (67 − 28 ) ) and an interface contribution (Kint (Ks)/teff) of magnetic anisotropy. Positive sign of KEFF matches to the PMA while the negative sign of KEFF matches to IMA [1,42]. The simulation results show that KEFF for all of the as-grown samples is
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negative indicating these samples are IMA. As shown Table 1, the KEFF value decreases with
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increasing thickness of CoFeB layer due to the increase in the demagnetization field. Post-annealing treatment of the films causes KEFF to remain negative for thicker films and become positive for 1-nm thick CoFeB because of the increasing interface anisotropy. KEFF increases due to the enhancement in Fe/O bonding at the CoFeB/MgO interface [11]. This indicates the magnetic anisotropy changes from IMA to PMA in 1-nm CoFeB thin film (Fig. 1(b)). This behavior is similar to the results obtained by Liu et al. [10]. Due to the interfacial nature and nano-scale local differences of the perpendicular anisotropy at the CoFeB/MgO [43], a second-order perpendicular anisotropy occurs (Keff_q = 0.59 x 104 J/m3) for the annealed 1-nm-thick CoFeB. This can also be a possible result of non-uniform
ACCEPTED MANUSCRIPT mechanical stresses or strain due to an alteration of spin–orbital interaction or a crystallographic mismatch at the interfaces [43–45]. The demagnetization field is larger than the magnetic anisotropy field and thus the preferred direction of the magnetization is in-plane for thicker films. Our results demonstrate that the gyromagnetic ratio associated with the spin-orbital moments also increased with
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CoFeB thickness (Table 1).
(b)
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(a)
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Fig. 1. Angular dependency of resonance fields. a) as-grown and b) annealed CoFeB thin films. Symbols represent experimental data of the layers while lines represent the simulation outputs
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(experimental; ■: 1 nm, ▲:1.5 nm, ▼: 2 nm, ♦: 3 nm and theoretical; —).
Table 1. Summary of magnetic parameters of the samples obtained from the simulation results. The
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effective magnetization is represented with Meff, effective anisotropy energy density with KEFF, inplane uniaxial anisotropy constant with Kax and gyromagnetic ratio with Gamma (γ).
As-Grown State
Meff (MA/m)
KEFF (106 J/m3)
Kax (104 J/m3)
γ (1010 T-1 s-1)
1 nm
1.30
-0.028
-
2.46
1.5 nm
1.38
-0.104
-0.302
3.34
2 nm
1.39
-0.120
-0.188
3.44
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-0.159
-0.248
3.46
Annealed State
Meff (MA/m)
KEFF (106 J/m3)
Kax (104 J/m3)
γ (1010 T-1 s-1)
1 nm
1.35
0.160
-
3.59
1.5 nm
1.37
-0.088
-
3.05
2 nm
1.26
-0.140
0.216
3 nm
1.18
-0.161
0.247
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3 nm
3.44
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3.62
In the case of as-grown films, Meff slightly increases as the thickness of the film increases. After
general decrease in the Meff is observed.
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annealing, while 1-nm thick CoFeB film shows an increase in the Meff, for thicker CoFeB films, a
The boron atom has a very small size compared to Co, Fe and Ta atoms, therefore the diffusion of boron should be more facile than the diffusion of other atoms and hence it dominates the
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magnetization variation in the annealing treatment [46]. Consequently, the annealing causes boron diffusion from CoFeB into Ta. The saturation magnetization (Meff) and interface anisotropy increases as a result of boron reduction in the CoFeB/MgO interface. This result is similar to a behavior reported
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by Belmeguenai et al. [27]. For the CoFeB layer thickness larger than ∼2 nm, a general decrease in the
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Meff is observed. In accordance with the results of Sinha et al., in cases where CoFeB is thicker than critical thickness, boron diffusion is limited and extra Ta diffusion occurs. In the Ta/CoFeB interface, the Meff and interface anisotropy are decreased [12]. The XRD results and the X‐ray reflectivity (XRR) profile of 1-nm thick CoFeB film are displayed in Fig. 2. As shown in Fig. 2(a), we observed the formation of TaB2 in XRD results [48,49] suggesting boron diffusion towards the lower interface in the annealed samples (Fig. 2) which is in agreement with other studies [50]. Similarly, there are other spectroscopic reports which have shown that a thin TaB interface layer occurs upon annealing [51,52].
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(b)
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(a)
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Fig. 2. a) XRD result of 1-nm thick CoFeB as deposited and annealed, b) X‐ray reflectivity (XRR) profiles of 1-nm thick CoFeB after annealing. The red lines represent the experimental data, and the blue lines stand for the fitted results.
In order to find out the evolution of the individual functional film thicknesses and the interface
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roughness upon post annealing in the CoFeB layer, a detailed XRR study was carried out. The XRR results revealed that the thickness, roughness and density of the layers changed (Table 3). When 1 nm thick film was annealed, the thickness of CoFeB decreased and Ta thickness increased. This results
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confirms that there will be a diffusion of boron into Ta layer up to the critical thickness of CoFeB. As seen at 3 nm, the Ta thickness decreases due to diffusion of Ta into CoFeB above the critical thickness.
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While CoFeB/MgO interface roughness is minimized, Ta/ CoFeB interface roughness expands in the annealed states of samples.
Table 3. Summary of XRR best fitting parameters for the 1 nm and 3 nm thick CoFeB multilayers as deposited and post annealed.
Layer
Thickness (nm) As-grown
After Ann.
Density(gg/cc) As-grown
After Ann.
Interface roughness(nm) As-grown
After Ann.
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2.86
8.7
8.7
0.292
0.35
Ta
1.09
1.06
16.65
16.65
0.11
0.16
MgO
1.65
1.49
3.58
1.79
0.11
0.21
CoFeB
1.05
0.87
7.21
9.2
0.3
0.2
Ta
11.65
12.30
16.65
15.32
0.23
0.3
SiO2
-
-
-
-
-
-
Thickness (nm)
Density(gg/cc)
Interface roughness(nm)
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Layer
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TaO
After Ann.
As-grown
After Ann.
As-grown
After Ann.
TaO
2.61
2.67
8.7
8.7
0.33
0.22
Ta
1.07
1
16.65
19.9
0.26
0.1
MgO
1.6
1.53
3.58
1.34
0.25
0
CoFeB
3.02
3.07
7.21
9.3
0.25
0.19
Ta
10.5
7.10
16.65
20.2
0.30
0.41
-
-
-
-
-
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SiO2
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As-grown
To examine the effects of interaction between FM layers, Ta / CoFeB 1.5 nm / MgO (represented as S1)
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and the Ta / CoFeB 1.5 nm (FM1) / MgO / CoZrTa (FM2) / MgO (represented as S2) structures were grown. The interlayer interaction between layers results in the change of spin and orbital moments that
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causes an increase in γ-value of CoFeB (Table 2). The post-annealing treatment improves the interface anisotropy of CoFeB 1.5 nm, but not enough to switch for anisotropy direction. Surprisingly, after postannealing the magnetic parameters of CoFeB in S1 and S2 become almost equal. No changes were observed in the KEFF and γ-value of CoZrTa after the annealing process. This feature is an important advantage for observing the effect of spin pumping in our films. (a)
(b)
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Fig. 3. FMR results of a) as-grown and b) annealed states in S2. Symbols (■: as-grown and ●: annealed) represent the experimental results while lines represent the simulation outputs, respectively.
Meff (MA/m) 0.92
CoZrTa Annealed State
0.98
CoFeB 1.5 nm As-grown State
1.30 1.38
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CoFeB 1.5 nm Annealed State
KEFF (106J/m3)
Kax (104 J/m3)
γ (1010 T-1 s-1)
- 0.180
0.176
3.54
- 0.180
0.176
3.54
- 0.160
0.205
3.46
-
3.06
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CoZrTa As-grown State
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Table 2. Theoretical analyses of the FMR measurements for S2 stack structures.
-0.088
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(a)
Fig. 4. The angular dependent peak-to-peak FMR linewidth (∆H ) in OPG for different thickness of
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CoFeB samples a) as–grown state and b) annealed state (■: 1 nm, ●:1.5 nm, ▲: 2 nm, and ▼: 3 nm), respectively.
Fig. 4 shows the out-of-plane angular dependence of linewidths (∆H). ∆H is defined as the width between the negative and positive of FMR derivative curve. In Fig. 4(a), both the in-plane linewidth
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(∆HII, θH=0°) and the out-of-plane linewidth (∆H⊥, θH=90°) increase with decreasing CoFeB thickness. The ∆HII is inversely proportional with the CoFeB thickness since its mechanism is related to an interfacial effect in CoFeB/MgO [1]. Fig. 5 shows the out-of-plane angular dependence of FMR
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linewidth contributions in 1.5 nm-thick CoFeB in S1 in the as-grown state. Our data showed that the Gilbert contribution is insufficient to explain increase of ∆H at intermediate angles (Fig. 5), therefore
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the extrinsic contributions should be considered. Lindner et al. [40] identified angular dependence of the TMS contribution for the FMR linewidth switches from larger value to zero in parallel and perpendicular configuration, respectively. However, as it is seen in Fig. 5 ∆H⊥ is slightly larger than ∆HII. According to the theory developed by Arias and Mills [53], the increase in ∆H cannot be explained by TMS because the linewidth due to two-magnon scattering is zero around θH=90° [54] . For this reason, the contribution of two- magnon scattering is too small and could be unregarded in our films.
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in S1 structure in the as-grown state.
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Fig. 5. The out-of-plane angular dependence of FMR Linewidth contributions in 1.5 nm-thick CoFeB
The extra damping contribution is caused by strong inhomogeneities found in the samples. The magnetization direction does not follow the external field direction due to variations of effective magnetization from interface roughness. The magnetization of CoFeB films stays in-plane up to about
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θH=80°, a sharp change from in-plane to out-of-plane, then again to decreases to a minimum θH=90°, in this change causes two ∆H maximum points to form (Fig. 4). The maximum points of ∆H increase
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with the decrease in the CoFeB layer thickness, due to the increase in inhomogeneity contribution. For our films ∆θH contribution is dominant in intermediate angles as shown in Fig. 5. According to
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Mizukami et al. in ultra-thin film has regional planes of the FM from surface of the buffer layer is wavy, so ∆θH broadening becomes large with increasing roughness [55] . On the other hand, the CoFeB thickness increases, the films become continuous and the deviation in the effective magnetization angles decrease (∆θH) and as ∆H max points approach each other, so ∆θH contribution diminishes [55]. Therefore the max points of ∆H in intermediate (Fig. 4, 3-nm thick CoFeB film) become difficult to see the minimum point at 90 degrees. After post annealing, the inhomogeneity contribution of linewidth is reduced since the interface roughness, magnetic and structural inhomogeneities of samples is decreased. Spin orbit coupling increases due to interface diffusion and
ACCEPTED MANUSCRIPT the linewidth broadening is observed mainly due to the Gilbert damping, Gilbert field dragging contribution becomes dominant, in intermediate angles (Fig. 4(b)). (b)
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(a)
Fig. 6. a) The out-of-plane angular dependence of linewidths in as-grown state S2 structure b) The out-of-plane angular dependence of as-grown 1.5 nm thick CoFeB linewidth is compared in the S1 and
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S2 structures.
Although the intrinsic damping is mostly related to the intrinsic property of the material, there can also
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be contributions in multilayers due to spin pumping effect. The spin-pumping effect takes place when spin angular momentum is transferred from the FM into NM and then dissipated. This energy loss
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leads to an increase in damping. The spin current generated in the trilayer film can pass through the spacer layer followed by continuing to a second NM/FM2 interface or returning to the first FM1/NM interface [56]. ∆H of CoFeB becomes narrower line width (Fig. 6 (b)) in the S2 structure which indicates that a strong interlayer exchange coupling match between two FM layers over MgO is established. Since the magnetization components of CoFeB and CoZrTa are parallel to each other, the resonance fields are very close (Fig. 3(a)). In this case, the net spin currents across in the FM1/NM and NM/FM2 interfaces are zero, therefore there is no additional damping in this structure as in S1 [28]. But at 90 degrees the resonance fields become different with a reduction in the interlayer exchange
ACCEPTED MANUSCRIPT coupling. The FM1 stays in resonance with maximum precessional amplitude and thus the spin pump current for FM1 reaches its maximum while FM2, having a small precessional amplitude, stays off resonance and hence does not display a considerable spin current. Therefore, FM2 causes a non-local damping for FM1 by acting as a spin sink [28]. This energy loss causes additional contribution at ∆H⊥
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(Fig 6(b)). On the other hand, an increase in γ relative to a single layer can be seen in Table 2 and since the spin pumping amount is related to SOC, an decrease of the spin pumping is observed.
As a result of the analytical calculation using Eq. 5, the intrinsic damping constant (α) of the single 1.5
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nm thick CoFeB is determined to be close to 0.0041 in as-grown similar to the reported behavior by
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Liu et al. [3] and to 0.003 in post-annealed sample, respectively (Eq.5). In the post-annealed state, the Gilbert field dragging broadening became dominant because of the reducing roughness and increasing interface anisotropy [57]. The intrinsic damping of CoFeB in S2, α, is 0.0023 in the as-grown sample because of strong interlayer coupling while it becomes 0.003 in the post-annealed state because of because of spin pumping by coupling reduction. Such small a value of α is advantageous in STT-
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MRAM for reducing the spin-torque induced critical current. These results highlight the importance of
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magnetic systems as promising candidates for device applications that use MgO spacers [56].
Conclusions
We have studied the FMR spectra and the resonance linewidth in CoFeB thin layer and multilayer asgrown and annealed state. In the as-grown state, the in-plane linewidth is smaller than the perpendicular linewidth and the experimental results of the FMR linewidth can be explained by the intrinsic Gilbert damping and the inhomogeneity broadening. Our data show that as the thickness increases, the anisotropy increases; hence the linewidth decreases along with the inhomogeneity
ACCEPTED MANUSCRIPT contribution. The intrinsic damping decreases with increasing thickness, which confirms its interfacial origin. After the post annealing process, Gilbert field dragging becomes the dominant contribution to linewidth. When the single and multilayer states of the ferromagnetic layer are compared, the intrinsic damping changes due to the change of spin pumping, interlayer coupling between the layers and the γ-
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value from spin - orbital moments. This coupling could be great effects on magnetic relaxation and switching characteristic in hybrid structures and memory devices. When the resonance fields are away from each other, a significant increase in the resonance linewidth is seen, and when the resonance
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fields approach each other, a narrowing linewidth occurs due to the spin-pump mechanism. These results highlight the importance of magnetic systems as promising candidates for device applications
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that use MgO spacers.
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magnetic damping parameter Resolving the controversy of a possible relationship between perpendicular magnetic anisotropy and the magnetic damping parameter, 062406 (2014). doi:10.1063/1.4892532.
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Highlights The effect of CoFeB layer thickness on magnetization and linewidth were reported by using Ferromagnetic resonance technique.
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Micromagnetic simulation model was used for finding of magnetic parameters of the samples.
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The magnetization, magnetic anisotropy and line width changed as a result of the interlayer diffusion with the annealing treatment.
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After the post annealing process, Gilbert field dragging became the dominant contribution to linewidth.
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by the spin pumping effect on damping.
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• The difference between the linewidths of the single and trilayer systems was observed
S1567-1739(19)30075-6
DOI:
https://doi.org/10.1016/j.cap.2019.03.002
Reference:
CAP 4938
To appear in:
Current Applied Physics
Received Date: 17 October 2018 Revised Date:
22 February 2019
Accepted Date: 1 March 2019
Please cite this article as: E. Gokce Polat, C. Deger, F. Yildiz, Investigation of ferromagnetic resonance and damping properties of CoFeB, Current Applied Physics (2019), doi: https://doi.org/10.1016/ j.cap.2019.03.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Investigation of ferromagnetic resonance and damping properties of CoFeB E. Gokce Polata, b*, C. Degerc and F. Yildizb
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Department of Engineering Physics, Istanbul Medeniyet University, Uskudar, Istanbul 34700, Turkey b
Department of Physics, Gebze Technical University, Kocaeli 41400, Turkey
c
Department of Physics, Marmara University 34722, Kadikoy, Istanbul, Turkey
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a
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Abstract
In this study, the influences of thin film thickness and post-annealing process on the magnetic properties of CoFeB thin films were investigated. The angular dependency and linewidth of the ferromagnetic resonance signal were used to explore the magnetic behavior of sputtered single-layer
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and trilayer thin film stacks of CoFeB. A micromagnetic simulation model was employed based on the metropolis algorithm comprising the demagnetizing field and in-plane induced uniaxial anisotropy terms with all relevant contributions. Our results reveal that the direction of magnetization changes
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from in-plane to out-of-plane as a result of the annealing process and induces a perpendicular magnetic anisotropy in the 1-nm thick CoFeB thin film. The ferromagnetic resonance (FMR) linewidth can be
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defined well by the intrinsic Gilbert damping effect and the magnetic inhomogeneity contribution in both as-grown and annealed samples. The difference between the linewidths of the single and trilayer film is mainly caused by the spin pumping effect on damping which is associated with the interface layers.
*
Corresponding author. E-mail address: [email protected]
ACCEPTED MANUSCRIPT Keywords: Magnetic thin films; Ferromagnetic resonance; Ferromagnetic resonance linewidth; Magnetic anisotropy; CoFeB.
1. Introduction
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The ferromagnetic alloy, cobalt-iron-boron (CoFeB) is a soft ferromagnetic material which is widely used in spintronic devices. When the CoFeB layer is thin enough, it shows a perpendicular magnetic anisotropy (PMA) and has potential applications for Magnetic Random Access Memories
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(MRAM)[1]. Ikeda et al. first identified the PMA in Ta/CoFeB/MgO stack, which has promising applications in STT devices[2]. CoFeB/MgO/CoFeB has become attractive for magnetic tunnel
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junctions (MTJs) due to high tunneling magnetoresistance (TMR) properties. In addition, this stack has aroused great interest for STT-MRAM owing to the high thermal stability, and magnetization switching speed [2–5].
The PMA of the Ta/CoFeB/MgO stack originates developing interfacial magnetic anisotropy because
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of the hybridization between Fe/Co 3d orbitals and Oxygen 2p orbitals at the CoFeB / MgO [6–8]. The under-layer of the CoFeB layer also has a significant influence on PMA [9,10]. Worledge et al. have reported that Ta / CoFeB interface plays an important role in CoFeB magnetization [4,11,12]. The
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practical use of such technologies requires the determination of physical mechanisms for
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magnetization and relaxation behaviors behind the magnetic thin films and multilayers, and studying the dynamic magnetic properties of structures continue to be important [13,14]. The understanding and the manipulation of the magnetic damping properties are crucial factors for the operation of CoFeBbased spintronic devices that function in the nanosecond range of magnetization switching [15,16]. Because of the decrease of the device size, the interface plays an important role in the characteristics [17,18]. Therefore, in thin films and multilayers, it is essential to explain the damping process which is caused by the magnetization energy losses due to surface or interface effects. The annealing process helps to improve the perpendicular magnetic anisotropy (PMA) which is required in some of these
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The FMR technique is used to investigate the magnetic properties of thin films [20–22]. This method is widely used to determine the magnetization, magnetic anisotropy constant, demagnetization field, gfactor, interlayer magnetic coupling and magnetocrystalline interaction for single and multilayer thin films [23]. The FMR linewidth in magnetic metallic thin films can provide the information about,
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magnetic relaxation, magnetic homogeneity and film quality [24]. The magnetic damping parameter
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(α) is well defined by the Landau-Lifshitz-Gilbert equation [5], and known as Gilbert damping. There are several reports in the literature to understand the basis of Gilbert damping in spin dynamics relaxation in single layer and multilayered magnetic thin films [25,26]. According to Lenz et al. [27] and Heinrich et al. [28] the intrinsic damping constant in a Ferromagnet (FM) / nonmagnet (NM)
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/ferromagnet (FM) trilayer system is enhanced due to spin pumping.
In this study, the angular behavior of resonance field and linewidth as functions of the CoFeB film thickness were investigated experimentally and the origins of magnetic damping in the CoFeB films
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were discussed. FMR linewidth the CoFeB/MgO/CoZrTa sample was also studied in this paper. The difference in the linewidths between the single and trilayer films is mainly caused by the variation of
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the spin pumping associated with the interfaces and indirectly observed as addition
to Gilbert
damping in ferromagnetic resonance experiment [29]. Our study offers important insights for the spin pumping and spin transfer torque for magnetic tunnel junction device applications which use MgO barriers. The obtained low damping constant shows that our structure can be an attractive candidate for low-speed current-requiring spintronic devices.
ACCEPTED MANUSCRIPT 2. Experimental The samples were fabricated using magnetron sputtering method at room temperature, with a base pressure of 5×10−9 Torr. The thin film stacks are as follows: Si/SiO2/ Ta(10)/ Co0.4Fe0.4B0.2 (t)/ MgO(1.5)/ Ta (3) (thicknesses in nm) where the thickness (t) of CoFeB was 1 nm, 1.5 nm, 2 nm, and 3
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nm and Si/ SiO2/ Ta(10)/ Co0.4Fe0.4B0.2 (1.5)/ MgO(1.5)/ Co91.5Zr4.0Ta4.5 (4)/ MgO(1.5)/ Ta (3) in the following referred to as S2. A 3-nm-thick layer of Ta as a capping layer was designed to protect the CoFeB from the oxidation. MgO layer thickness was chosen as 1.5 nm since the interface effect is very
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important for our study [30]. All the thickness values are nominal. These series were grown for the observation of the magnetic anisotropy orientation and the determination of the FMR linewidth
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broadening mechanism for different CoFeB thicknesses of as-grown state and the post-annealed state. An X-band JEOL JES-FA300 electron spin resonance spectrometer (ESR) was used for the FMR measurements. FMR measurements of all films have been performed at 9.8 GHz for various field orientations at room temperature. The angular dependence of FMR spectra in two geometries was
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measured. For the in-plane geometry (IPG) measurements, the film was rotated around the sample normal while the applied DC magnetic field was always in the film plane. For the application of the out-of-plane geometry (OPG), the film was rotated from the sample plane to the sample normal with
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respect to the applied the field. Samples were then annealed at 300°C for 30 min under vacuum above 10-8 Torr. A Rigaku Smart-Lab X-ray diffractometer was used for investigating the crystal structure
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and microstrucre of films as-grown and annealed state in out-of plane. 2.1 Theoretical Model
We start to construct our model by predicting of the energy Hamiltonian of the system. The Hamiltonian consists of three energy terms which are widely used to represent the magnetic behavior of the systems [31,32]. The energy terms are sorted below:
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(1)
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−MH cos(θ )cos(θ ) + sin(θ )sin(θ )cos(ϕ − ϕ ) H H H 2 4 H = +K eff cos (θ ) + K eff _ q cos (θ ) 2 2 −K ax sin (θ )cos (ϕ )
Where (θ, θH) and (φ, φH) are respectively the polar and azimuth angles for magnetization vector M
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and external DC field vector H with respect to the film plane. The first term of the Hamiltonian is the Zeeman energy of the film in the external DC field. The second term represents the magneto static energy due to demagnetizing field. The last term represents assumed in-plane-induced uniaxial anisotropy energy due to film preparation conditions. In Eq. (1) M, Keff , Keff_q and Kax are the
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effective magnetization, first order perpendicular anisotropy energy density, second order perpendicular anisotropy energy density and the axial anisotropy constant, respectively. External magnetic field is swept from 0 to 2 T to determine the field corresponding to the maximum value of
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χ2 which is called as the resonance field (Hres). Dynamic susceptibility spectra χ2
are calculated by
χ2
=
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using the following equation [33–35]:
40 2 + "
2
1 ∂2 2" ! 0 2 2 #2 $2
"
2 2
4"2
% #0 & − % # & ! − 4 2 # $2
(2)
ω0 is the precession frequency of the system, which can also be called Larmor frequency, k represents wave vector and D is equal to 2A/M0, where A is called as the exchange stiffness. E, γ, T2 and ω
ACCEPTED MANUSCRIPT represent energy density, gyromagnetic ratio, spin-spin relaxation time and frequency of microwave radiation, respectively. Then, Larmor frequency is calculated by the following equation (3) [36]:
)
"( ) 1 ∂) +,-./ 1 ∂) +,-./ 1 ∂) +,-./ ) 0 * + 0 − * 0 ! = * ) + # ( ) ( 123) 4) ( 123) 4
(3)
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While the external magnetic field is increasing, Larmor frequency is getting closer to the resonance frequency of microwave (ω). Then the dynamic susceptibility starts to increase as the values of ω and ω0 get closer. At ω = ω0, the corresponding external magnetic field is marked as a resonance field for
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both in-plane geometry (IPG) and out-of-plane geometry (OPG). All calculations were performed at room temperature to fit outputs of simulation with the experimental data. M, ω/γ, Keff, Keff_q and Kax
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were obtained by using the simulation model for all samples.
In general, the ferromagnetic linewidth (∆H) depends on two parameters: intrinsic contribution of magnetism and extrinsic contribution due to inhomogeneity of the material [37]. The total ∆H of the
∆ H = ∆ H G + ∆ H 2 mag + ∆ H in hom
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FMR can be written as
(4)
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The first term in the ∆H is the intrinsic damping known as the Gilbert damping (∆HG). ∆HG is caused by energy loss since the magnetization energy is directly transferred to the lattice as spin-orbit
∆H G =
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coupling [38]. 2 α ω 3γ Ξ
Ξ ≡ cos(θ H − θ M ) −
3H X + H Y H 0 sin 2 (θ H − θ M ) HY ( H X + HY )
(5)
(6)
∆HG contribution shows a linear change due to the frequency along the easy axis and the hard axis when the magnetization is parallel to the external magnetic field (θH=θM, Ξ=1) from Eq. (5) and (6).
ACCEPTED MANUSCRIPT However, since linewidth contribution should be formed by the deviation of the magnetization the effect of magnetic anisotropy at the intermediate angles, an addition from the angle of the external magnetic field. In the literature, this effect is called field dragging [39]. When external field and the magnetization become parallel, this effect is vanished (Eq. (6)). In Eq. (5), the extrinsic contribution
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contains two types of contribution, one of which is two-magnon scattering contribution (∆H2mag) because of weak inhomogeneity and the other is strong inhomogeneity contribution (∆Hinhom) caused by regional variations of the magnetization and the magnetic anisotropy field [15]. Two-magnon
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scattering (TMS) is a damping additive that includes nonuniformity of film magnetic properties. TMS is usually associated with surface / interface roughness and other film defects in thin films structures.
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The loss in the magnetization energy caused by the scattering of uniform spin modes into degenerate spin modes results in damping. The TMS contribution in the angle dependent measurements is compatible with the in-plane crystallographic orientation [40]. TMS contributions are activated by surface and interface anisotropy in ultra-thin films [1].
2 HX cos(2θ M ) Γ(H O ,θ H )sin−1 H X + M eff cos2 θ M 3
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∆H 2mag =
(7)
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Γ is the fitting function that changed with orientation of external field. It is apparent from the equation
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when θ M 〉π / 4 is, the root is negative and TMS contributions disappear. During FMR measurements of the thin film (going from the in-plane to out-of-plane), the TMS contribution is reduced from 0° to 90° in the perpendicular geometry and eventually this effect disappears when the angles are equal,
θM = θ H = 90° . In this case the perpendicular linewidth reaches a minimum value [40]. The strong inhomogeneity contribution to linewidth is given by
∆H in hom =
∂H ∂H ∆θ H + ∆ 4πM eff ∂θ H ∂ 4πM eff
(8)
ACCEPTED MANUSCRIPT Here, ∆θH represents variations in the direction which originate from the crystallographic axes of the particles and ∆4πMeff represents variations of the demagnetization field [37]. The direction of the magnetization does not follow the direction of the applied magnetic field. Inhomogeneity contribution is the major factor that is seen in polycrystalline multilayer or perpendicular surface anisotropy films.
is the sum of Gilbert and inhomogeneous contributions.
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3. Results and Discussion
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In such cases, the in-plane linewidth is smaller than the perpendicular linewidth [41] and the linewidth
The OPG angular dependence of FMR in as-grown and annealed CoFeB samples is showed in Fig.
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1(a) and (b), respectively. As the thickness of CoFeB increases, the large demagnetization field and inplane magnetic anisotropy (IMA) causes an increase of the resonance field (Hres) in the film normal (θH=90°) and a decrease of Hres in parallel geometry (θH=0°). KEFF is the effective anisotropy energy density which is used to characterize the magnetization orientation in magnetic thin films. KEFF is
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considered to be an approximate sum of a volume (67 − 28 ) ) and an interface contribution (Kint (Ks)/teff) of magnetic anisotropy. Positive sign of KEFF matches to the PMA while the negative sign of KEFF matches to IMA [1,42]. The simulation results show that KEFF for all of the as-grown samples is
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negative indicating these samples are IMA. As shown Table 1, the KEFF value decreases with
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increasing thickness of CoFeB layer due to the increase in the demagnetization field. Post-annealing treatment of the films causes KEFF to remain negative for thicker films and become positive for 1-nm thick CoFeB because of the increasing interface anisotropy. KEFF increases due to the enhancement in Fe/O bonding at the CoFeB/MgO interface [11]. This indicates the magnetic anisotropy changes from IMA to PMA in 1-nm CoFeB thin film (Fig. 1(b)). This behavior is similar to the results obtained by Liu et al. [10]. Due to the interfacial nature and nano-scale local differences of the perpendicular anisotropy at the CoFeB/MgO [43], a second-order perpendicular anisotropy occurs (Keff_q = 0.59 x 104 J/m3) for the annealed 1-nm-thick CoFeB. This can also be a possible result of non-uniform
ACCEPTED MANUSCRIPT mechanical stresses or strain due to an alteration of spin–orbital interaction or a crystallographic mismatch at the interfaces [43–45]. The demagnetization field is larger than the magnetic anisotropy field and thus the preferred direction of the magnetization is in-plane for thicker films. Our results demonstrate that the gyromagnetic ratio associated with the spin-orbital moments also increased with
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CoFeB thickness (Table 1).
(b)
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(a)
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Fig. 1. Angular dependency of resonance fields. a) as-grown and b) annealed CoFeB thin films. Symbols represent experimental data of the layers while lines represent the simulation outputs
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(experimental; ■: 1 nm, ▲:1.5 nm, ▼: 2 nm, ♦: 3 nm and theoretical; —).
Table 1. Summary of magnetic parameters of the samples obtained from the simulation results. The
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effective magnetization is represented with Meff, effective anisotropy energy density with KEFF, inplane uniaxial anisotropy constant with Kax and gyromagnetic ratio with Gamma (γ).
As-Grown State
Meff (MA/m)
KEFF (106 J/m3)
Kax (104 J/m3)
γ (1010 T-1 s-1)
1 nm
1.30
-0.028
-
2.46
1.5 nm
1.38
-0.104
-0.302
3.34
2 nm
1.39
-0.120
-0.188
3.44
ACCEPTED MANUSCRIPT 1.39
-0.159
-0.248
3.46
Annealed State
Meff (MA/m)
KEFF (106 J/m3)
Kax (104 J/m3)
γ (1010 T-1 s-1)
1 nm
1.35
0.160
-
3.59
1.5 nm
1.37
-0.088
-
3.05
2 nm
1.26
-0.140
0.216
3 nm
1.18
-0.161
0.247
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3 nm
3.44
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3.62
In the case of as-grown films, Meff slightly increases as the thickness of the film increases. After
general decrease in the Meff is observed.
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annealing, while 1-nm thick CoFeB film shows an increase in the Meff, for thicker CoFeB films, a
The boron atom has a very small size compared to Co, Fe and Ta atoms, therefore the diffusion of boron should be more facile than the diffusion of other atoms and hence it dominates the
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magnetization variation in the annealing treatment [46]. Consequently, the annealing causes boron diffusion from CoFeB into Ta. The saturation magnetization (Meff) and interface anisotropy increases as a result of boron reduction in the CoFeB/MgO interface. This result is similar to a behavior reported
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by Belmeguenai et al. [27]. For the CoFeB layer thickness larger than ∼2 nm, a general decrease in the
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Meff is observed. In accordance with the results of Sinha et al., in cases where CoFeB is thicker than critical thickness, boron diffusion is limited and extra Ta diffusion occurs. In the Ta/CoFeB interface, the Meff and interface anisotropy are decreased [12]. The XRD results and the X‐ray reflectivity (XRR) profile of 1-nm thick CoFeB film are displayed in Fig. 2. As shown in Fig. 2(a), we observed the formation of TaB2 in XRD results [48,49] suggesting boron diffusion towards the lower interface in the annealed samples (Fig. 2) which is in agreement with other studies [50]. Similarly, there are other spectroscopic reports which have shown that a thin TaB interface layer occurs upon annealing [51,52].
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(b)
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(a)
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Fig. 2. a) XRD result of 1-nm thick CoFeB as deposited and annealed, b) X‐ray reflectivity (XRR) profiles of 1-nm thick CoFeB after annealing. The red lines represent the experimental data, and the blue lines stand for the fitted results.
In order to find out the evolution of the individual functional film thicknesses and the interface
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roughness upon post annealing in the CoFeB layer, a detailed XRR study was carried out. The XRR results revealed that the thickness, roughness and density of the layers changed (Table 3). When 1 nm thick film was annealed, the thickness of CoFeB decreased and Ta thickness increased. This results
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confirms that there will be a diffusion of boron into Ta layer up to the critical thickness of CoFeB. As seen at 3 nm, the Ta thickness decreases due to diffusion of Ta into CoFeB above the critical thickness.
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While CoFeB/MgO interface roughness is minimized, Ta/ CoFeB interface roughness expands in the annealed states of samples.
Table 3. Summary of XRR best fitting parameters for the 1 nm and 3 nm thick CoFeB multilayers as deposited and post annealed.
Layer
Thickness (nm) As-grown
After Ann.
Density(gg/cc) As-grown
After Ann.
Interface roughness(nm) As-grown
After Ann.
ACCEPTED MANUSCRIPT 2.74
2.86
8.7
8.7
0.292
0.35
Ta
1.09
1.06
16.65
16.65
0.11
0.16
MgO
1.65
1.49
3.58
1.79
0.11
0.21
CoFeB
1.05
0.87
7.21
9.2
0.3
0.2
Ta
11.65
12.30
16.65
15.32
0.23
0.3
SiO2
-
-
-
-
-
-
Thickness (nm)
Density(gg/cc)
Interface roughness(nm)
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Layer
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TaO
After Ann.
As-grown
After Ann.
As-grown
After Ann.
TaO
2.61
2.67
8.7
8.7
0.33
0.22
Ta
1.07
1
16.65
19.9
0.26
0.1
MgO
1.6
1.53
3.58
1.34
0.25
0
CoFeB
3.02
3.07
7.21
9.3
0.25
0.19
Ta
10.5
7.10
16.65
20.2
0.30
0.41
-
-
-
-
-
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SiO2
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As-grown
To examine the effects of interaction between FM layers, Ta / CoFeB 1.5 nm / MgO (represented as S1)
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and the Ta / CoFeB 1.5 nm (FM1) / MgO / CoZrTa (FM2) / MgO (represented as S2) structures were grown. The interlayer interaction between layers results in the change of spin and orbital moments that
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causes an increase in γ-value of CoFeB (Table 2). The post-annealing treatment improves the interface anisotropy of CoFeB 1.5 nm, but not enough to switch for anisotropy direction. Surprisingly, after postannealing the magnetic parameters of CoFeB in S1 and S2 become almost equal. No changes were observed in the KEFF and γ-value of CoZrTa after the annealing process. This feature is an important advantage for observing the effect of spin pumping in our films. (a)
(b)
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ACCEPTED MANUSCRIPT
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Fig. 3. FMR results of a) as-grown and b) annealed states in S2. Symbols (■: as-grown and ●: annealed) represent the experimental results while lines represent the simulation outputs, respectively.
Meff (MA/m) 0.92
CoZrTa Annealed State
0.98
CoFeB 1.5 nm As-grown State
1.30 1.38
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CoFeB 1.5 nm Annealed State
KEFF (106J/m3)
Kax (104 J/m3)
γ (1010 T-1 s-1)
- 0.180
0.176
3.54
- 0.180
0.176
3.54
- 0.160
0.205
3.46
-
3.06
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CoZrTa As-grown State
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Table 2. Theoretical analyses of the FMR measurements for S2 stack structures.
-0.088
ACCEPTED MANUSCRIPT (b)
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(a)
Fig. 4. The angular dependent peak-to-peak FMR linewidth (∆H ) in OPG for different thickness of
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CoFeB samples a) as–grown state and b) annealed state (■: 1 nm, ●:1.5 nm, ▲: 2 nm, and ▼: 3 nm), respectively.
Fig. 4 shows the out-of-plane angular dependence of linewidths (∆H). ∆H is defined as the width between the negative and positive of FMR derivative curve. In Fig. 4(a), both the in-plane linewidth
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(∆HII, θH=0°) and the out-of-plane linewidth (∆H⊥, θH=90°) increase with decreasing CoFeB thickness. The ∆HII is inversely proportional with the CoFeB thickness since its mechanism is related to an interfacial effect in CoFeB/MgO [1]. Fig. 5 shows the out-of-plane angular dependence of FMR
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linewidth contributions in 1.5 nm-thick CoFeB in S1 in the as-grown state. Our data showed that the Gilbert contribution is insufficient to explain increase of ∆H at intermediate angles (Fig. 5), therefore
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the extrinsic contributions should be considered. Lindner et al. [40] identified angular dependence of the TMS contribution for the FMR linewidth switches from larger value to zero in parallel and perpendicular configuration, respectively. However, as it is seen in Fig. 5 ∆H⊥ is slightly larger than ∆HII. According to the theory developed by Arias and Mills [53], the increase in ∆H cannot be explained by TMS because the linewidth due to two-magnon scattering is zero around θH=90° [54] . For this reason, the contribution of two- magnon scattering is too small and could be unregarded in our films.
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ACCEPTED MANUSCRIPT
in S1 structure in the as-grown state.
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Fig. 5. The out-of-plane angular dependence of FMR Linewidth contributions in 1.5 nm-thick CoFeB
The extra damping contribution is caused by strong inhomogeneities found in the samples. The magnetization direction does not follow the external field direction due to variations of effective magnetization from interface roughness. The magnetization of CoFeB films stays in-plane up to about
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θH=80°, a sharp change from in-plane to out-of-plane, then again to decreases to a minimum θH=90°, in this change causes two ∆H maximum points to form (Fig. 4). The maximum points of ∆H increase
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with the decrease in the CoFeB layer thickness, due to the increase in inhomogeneity contribution. For our films ∆θH contribution is dominant in intermediate angles as shown in Fig. 5. According to
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Mizukami et al. in ultra-thin film has regional planes of the FM from surface of the buffer layer is wavy, so ∆θH broadening becomes large with increasing roughness [55] . On the other hand, the CoFeB thickness increases, the films become continuous and the deviation in the effective magnetization angles decrease (∆θH) and as ∆H max points approach each other, so ∆θH contribution diminishes [55]. Therefore the max points of ∆H in intermediate (Fig. 4, 3-nm thick CoFeB film) become difficult to see the minimum point at 90 degrees. After post annealing, the inhomogeneity contribution of linewidth is reduced since the interface roughness, magnetic and structural inhomogeneities of samples is decreased. Spin orbit coupling increases due to interface diffusion and
ACCEPTED MANUSCRIPT the linewidth broadening is observed mainly due to the Gilbert damping, Gilbert field dragging contribution becomes dominant, in intermediate angles (Fig. 4(b)). (b)
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(a)
Fig. 6. a) The out-of-plane angular dependence of linewidths in as-grown state S2 structure b) The out-of-plane angular dependence of as-grown 1.5 nm thick CoFeB linewidth is compared in the S1 and
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S2 structures.
Although the intrinsic damping is mostly related to the intrinsic property of the material, there can also
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be contributions in multilayers due to spin pumping effect. The spin-pumping effect takes place when spin angular momentum is transferred from the FM into NM and then dissipated. This energy loss
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leads to an increase in damping. The spin current generated in the trilayer film can pass through the spacer layer followed by continuing to a second NM/FM2 interface or returning to the first FM1/NM interface [56]. ∆H of CoFeB becomes narrower line width (Fig. 6 (b)) in the S2 structure which indicates that a strong interlayer exchange coupling match between two FM layers over MgO is established. Since the magnetization components of CoFeB and CoZrTa are parallel to each other, the resonance fields are very close (Fig. 3(a)). In this case, the net spin currents across in the FM1/NM and NM/FM2 interfaces are zero, therefore there is no additional damping in this structure as in S1 [28]. But at 90 degrees the resonance fields become different with a reduction in the interlayer exchange
ACCEPTED MANUSCRIPT coupling. The FM1 stays in resonance with maximum precessional amplitude and thus the spin pump current for FM1 reaches its maximum while FM2, having a small precessional amplitude, stays off resonance and hence does not display a considerable spin current. Therefore, FM2 causes a non-local damping for FM1 by acting as a spin sink [28]. This energy loss causes additional contribution at ∆H⊥
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(Fig 6(b)). On the other hand, an increase in γ relative to a single layer can be seen in Table 2 and since the spin pumping amount is related to SOC, an decrease of the spin pumping is observed.
As a result of the analytical calculation using Eq. 5, the intrinsic damping constant (α) of the single 1.5
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nm thick CoFeB is determined to be close to 0.0041 in as-grown similar to the reported behavior by
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Liu et al. [3] and to 0.003 in post-annealed sample, respectively (Eq.5). In the post-annealed state, the Gilbert field dragging broadening became dominant because of the reducing roughness and increasing interface anisotropy [57]. The intrinsic damping of CoFeB in S2, α, is 0.0023 in the as-grown sample because of strong interlayer coupling while it becomes 0.003 in the post-annealed state because of because of spin pumping by coupling reduction. Such small a value of α is advantageous in STT-
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MRAM for reducing the spin-torque induced critical current. These results highlight the importance of
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magnetic systems as promising candidates for device applications that use MgO spacers [56].
Conclusions
We have studied the FMR spectra and the resonance linewidth in CoFeB thin layer and multilayer asgrown and annealed state. In the as-grown state, the in-plane linewidth is smaller than the perpendicular linewidth and the experimental results of the FMR linewidth can be explained by the intrinsic Gilbert damping and the inhomogeneity broadening. Our data show that as the thickness increases, the anisotropy increases; hence the linewidth decreases along with the inhomogeneity
ACCEPTED MANUSCRIPT contribution. The intrinsic damping decreases with increasing thickness, which confirms its interfacial origin. After the post annealing process, Gilbert field dragging becomes the dominant contribution to linewidth. When the single and multilayer states of the ferromagnetic layer are compared, the intrinsic damping changes due to the change of spin pumping, interlayer coupling between the layers and the γ-
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value from spin - orbital moments. This coupling could be great effects on magnetic relaxation and switching characteristic in hybrid structures and memory devices. When the resonance fields are away from each other, a significant increase in the resonance linewidth is seen, and when the resonance
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fields approach each other, a narrowing linewidth occurs due to the spin-pump mechanism. These results highlight the importance of magnetic systems as promising candidates for device applications
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that use MgO spacers.
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magnetic damping parameter Resolving the controversy of a possible relationship between perpendicular magnetic anisotropy and the magnetic damping parameter, 062406 (2014). doi:10.1063/1.4892532.
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Highlights The effect of CoFeB layer thickness on magnetization and linewidth were reported by using Ferromagnetic resonance technique.
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Micromagnetic simulation model was used for finding of magnetic parameters of the samples.
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The magnetization, magnetic anisotropy and line width changed as a result of the interlayer diffusion with the annealing treatment.
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After the post annealing process, Gilbert field dragging became the dominant contribution to linewidth.
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by the spin pumping effect on damping.
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• The difference between the linewidths of the single and trilayer systems was observed