Magnetization dynamics and its scattering mechanism in thin CoFeB films with interfacial anisotropy

Atsushi Okada; Shikun He; Bo Gu; Shun Kanai; Anjan Soumyanarayanan; Sze Ter Lim; Michael Tran; Michiyasu Mori; Sadamichi Maekawa; Fumihiro Matsukura; Hideo Ohno; Christos Panagopoulos

doi:10.1073/pnas.1613864114

New Research In

Edited by J. M. D. Coey, Trinity College Dublin, Dublin, Ireland, and approved February 23, 2017 (received for review August 19, 2016)

Significance

Ferromagnetic resonance (FMR) is considered a standard tool in the study of magnetization dynamics, with an established analysis procedure. We show there is a missing piece of physics to consider to fully understand and precisely interpret FMR results. This physics manifests itself in the dynamics of magnetization and hence in FMR spectra of ferromagnets, where interfacial anisotropy is a fundamental term. Advances in ferromagnetic heterostructures enabled by developing cutting-edge technology now allow us to probe and reveal physics previously hidden in the bulk properties of ferromagnets.

Abstract

Studies of magnetization dynamics have incessantly facilitated the discovery of fundamentally novel physical phenomena, making steady headway in the development of magnetic and spintronics devices. The dynamics can be induced and detected electrically, offering new functionalities in advanced electronics at the nanoscale. However, its scattering mechanism is still disputed. Understanding the mechanism in thin films is especially important, because most spintronics devices are made from stacks of multilayers with nanometer thickness. The stacks are known to possess interfacial magnetic anisotropy, a central property for applications, whose influence on the dynamics remains unknown. Here, we investigate the impact of interfacial anisotropy by adopting CoFeB/MgO as a model system. Through systematic and complementary measurements of ferromagnetic resonance (FMR) on a series of thin films, we identify narrower FMR linewidths at higher temperatures. We explicitly rule out the temperature dependence of intrinsic damping as a possible cause, and it is also not expected from existing extrinsic scattering mechanisms for ferromagnets. We ascribe this observation to motional narrowing, an old concept so far neglected in the analyses of FMR spectra. The effect is confirmed to originate from interfacial anisotropy, impacting the practical technology of spin-based nanodevices up to room temperature.

The magnetization dynamics is determined by the combination of intrinsic and extrinsic effects. The intrinsic contribution is governed by the fundamental material parameter, damping constant α (1, 2). The extrinsic counterpart is due to inhomogeneity and magnon excitations (3 ⇓–5) and hence structure dependent, and is enhanced in magnets with small thickness and/or small lateral dimensions (4 ⇓⇓–7). The contribution from each effect is usually separated by the analysis of the linewidths of ferromagnetic resonance (FMR) spectra, in which the linewidth enhancement is caused by the distributions of magnitudes and directions of the effective magnetic anisotropy, and magnon excitations. In this work, we study the temperature and CoFeB thickness dependences of the FMR linewidths in CoFeB/MgO thin films, one of the most promising material systems for high-performance spintronics devices at the nanoscale. The system possesses sizable interfacial perpendicular magnetic anisotropy (8), whose effect on the FMR linewidth is the focus of this study.

Samples and Measurement Setups

We prepared thin Co_0.4Fe_0.4B_0.2 layers with thickness t ranging from 1.4 to 3.7 nm, sandwiched between 3-nm-thick MgO layers using magnetron sputtering. The thicknesses of the layers were calibrated by transmission electron microscopy. All of the samples studied in this work possess in-plane easiness for magnetization. FMR spectra were measured both by a vector-network analyzer (VNA-FMR) using a coplanar waveguide, and a conventional method using a TE₀₁₁ microwave cavity (cavity-FMR). The former technique enables us to measure the rf frequency f dependence of the spectra up to 26 GHz by applying an external magnetic field H either parallel (magnetic field angle θ_H = 90°) or perpendicular (θ_H = 0°) to the sample plane, and the spectra are obtained as the transmission coefficient S₂₁ (9). The latter technique measures the spectra at a fixed f of 9 GHz under H at various θ_H, and the spectra are obtained as the derivative of the microwave absorption with respect to H (10). The temperature dependence of spontaneous magnetization M_S was measured by a superconducting quantum interference device magnetometer.

VNA-FMR

Fig. 1A shows typical VNA-FMR at selected values of f for CoFeB with t = 1.5 nm at temperature T = 300 K and θ_H = 90°. We determine the resonance field H_R and linewidth (full width at half maximum) ΔH from the fitting of the modified Lorentz function (solid lines in Fig. 1A) to the VNA-FMR spectra (9). Fig. 1B shows the rf frequency dependence of H_R at θ_H = 0° and 90°, which we use to determine the effective perpendicular anisotropy fields H_K^eff from the resonance condition; f = μ₀γ(H_R + H_K^eff)/(2π) for θ_H = 0° and f = μ₀γ[H_R(H_R − H_K^eff)]^1/2/(2π) for θ_H = 90°. Here, μ₀ is the permeability in free space, and γ the gyromagnetic ratio. As shown in Fig. 1C, H_K^eff increases monotonically with decreasing t, indicative of interfacial perpendicular anisotropy at the CoFeB/MgO interface (8).

Fig. 1.

VNA-FMR. (A) Typical spectra [real part of transmission coefficient Re(S₂₁) of coplanar waveguide] of CoFeB with thickness t = 1.5 nm as a function of rf frequency f obtained at magnetic–field angle θ_H = 90° and temperature T = 300 K. Solid lines are fits by the modified Lorentzian. (B) rf frequency f dependence of resonance field H_R obtained at θ_H = 0° and 90°. (C) Thickness t dependence of effective perpendicular anisotropy fields H_K^eff. rf frequency f dependence of the FMR linewidths ΔH obtained at θ_H = 0° as a function of (D) t at T = 300 K and as a function of (E) T for CoFeB with t = 1.5 nm. Solid lines in D and E are linear fits. (F and G) Same as D and E but at θ_H = 90°. Dashed lines in F and G are nonlinear fits based on two-magnon scattering. arb, arbitrary.

Fig. 1 D–G shows the frequency dependence of ΔH as a function of t and T. As shown in Fig. 1D, when H is applied perpendicular to the film (θ_H = 0°), ΔH obeys linear dependence, which is expressed as ΔH = ΔH_in + ΔH_inhom = (2hα/gμ₀μ_B)f + ΔH_inhom, where h is the Planck constant and μ_B is the Bohr magneton (9, 11). Here, ΔH_in is related to the intrinsic linewidth governed by α and ΔH_inhom is the extrinsic contribution due to inhomogeneity, such as the distribution of magnetic anisotropy. The value of α determines the slope in Fig. 1D and ΔH_inhom corresponds to the intercept on the vertical axis. Fig. 1D shows that α is nearly independent of t (α ∼ 0.004) and ΔH_inhom increases with decreasing t. As seen from Fig. 1E for CoFeB with t = 1.5 nm, α is also nearly independent of T, whereas ΔH_inhom increases with decreasing T. It is known that α depends on T through the change in resistivity with T (12 ⇓–14). The nearly temperature-independent α observed here may be due to the small temperature dependence of the resistivity of CoFeB (15). When H is in-plane (θ_H = 90°) (Fig. 1F), we observe a nonlinearity, which is enhanced with decreasing t. The nonlinearity, so far, is believed to be due to the contribution of two-magnon scattering (TMS) to the linewidth ΔH_TMS; TMS is known to be activated when the magnetization angle θ_M from the sample normal is greater than 45° (4 ⇓–6). The nonlinear frequency dependence of ΔH in Fig. 1F can be described in terms of TMS (dashed lines), assuming ΔH = ΔH_in + ΔH_inhom + ΔH_TMS. As depicted in Fig. 1G, the nonlinearity for CoFeB with t = 1.5 nm is enhanced strongly with decreasing T (nearly twice at 80 K compared with 300 K). This strong temperature dependence cannot be attributed to TMS, because the change in ΔH_TMS with T from 300 to 4 K is calculated to be ∼10% at most, using the measured T dependence of M_S and H_K^eff (4). Hence, it is imperative to consider an alternative mechanism for the nonlinearity, possibly related to the CoFeB/MgO-interface effect; notably, the nonlinearity is absent in thicker CoFeB with t = 3.7 nm (Fig. 1 F and G).

Cavity-FMR

Fig. 2A shows typical cavity-FMR spectra at T = 300 K for CoFeB with t = 1.5 nm. Fitting the derivative of the Lorentz function to the spectra gives H_R and ΔH (16). We fit the resonance condition to the magnetic-field angle dependence of H_R shown in Fig. 2B to obtain the magnitude of the effective first-order and second-order perpendicular anisotropy fields, H_K1^eff and H_K2, respectively, by following the procedure in ref. 10. Fig. 2C shows the CoFeB thickness dependence of H_K1^eff and H_K2 along with that of H_K^eff in Fig. 1C obtained from VNA-FMR. H_K2 is nearly independent of t and its strength is a few tens of millitesla at most. H_K1^eff increases with decreasing t, in agreement with H_K^eff obtained from VNA-FMR, confirming again the presence of perpendicular interfacial anisotropy at the CoFeB/MgO interface (8). In Fig. 2C, we plot also the values of H_K^eff obtained from magnetization measurements (8), which show good correspondence with those obtained from FMR measurements. Fig. 2D shows the magnetic-field angle dependence of ΔH as a function of t. For θ_M > 45°, where TMS is expected to be activated, ΔH is larger for CoFeB with smaller t. As shown in Fig. 2E, however, a nearly twice larger ΔH at lower T cannot be explained by the TMS contribution to ΔH. The results obtained from cavity-FMR are consistent with those from VNA-FMR, indicating that the unexpected T dependence of ΔH is not an artifact.

Fig. 2.

Cavity-FMR. (A) Typical spectra of CoFeB with thickness t of 1.5 nm as a function of magnetic-field angle θ_H at temperature T = 300 K. Solid lines are fits by the derivative of Lorentzian. (B) Angle θ_H dependence of resonance field H_R as a function of t. Solid lines are fitted lines by using the resonance condition. (C) Thickness t dependence of effective first-order perpendicular anisotropy field H_K1^eff and second-order anisotropy field H_K2 along with the results in Fig. 1C and from magnetization measurements. Angle θ_H dependence of the FMR linewidth ΔH obtained as a function of (D) t at T = 300 K and as a function of (E) T for CoFeB with t = 1.5 nm. Solid lines in D and E are fitted lines. (F) Double-logarithm plot of normalized magnetic anisotropy energy density K(T)/K(4K) versus normalized spontaneous magnetization M_S(T)/M_S(4 K). Solid line is a linear fit. (G) Calculated ΔH as a function of rf frequency f at different temperatures by using the parameters obtained from the analyses of cavity-FMR spectra. arb, arbitrary.

Discussion

Because the linewidth enhancement for θ_H = 90° is larger for thinner CoFeB (Figs. 1F and 2D), it is natural to consider that its mechanism is related to an interfacial effect in CoFeB/MgO. The most pronounced interfacial effect is the presence of interfacial perpendicular anisotropy as seen in Figs. 1C and 2C. Fig. 2F shows log(K(T)/K(4 K)) versus log(M_S(T)/M_S(4 K)) (Callen–Callen plot) (17), where M_S(T) is the measured spontaneous magnetization and K(T) the perpendicular magnetic anisotropy energy density determined from H_K1^eff and H_K2 using cavity-FMR (10); K = M_S(H_K1^eff − H_K2/2)/2 + M_S²/(2μ₀). The linear behavior in Fig. 2F gives a slope m of 2.16 [the exponent m in the Callen–Callen law of K(T)/K(0) = (M_S(T)/M_S(0))^m], consistent with the relationship between interfacial anisotropy energy density and M_S reported for CoFeB/MgO systems (18 ⇓–20). Hence, the temperature dependence of anisotropy in our CoFeB films is also governed by the interfacial anisotropy. Therefore, the linewidth broadening with decreasing t and T is expected to be due to random thermal fluctuation δH_i in the anisotropy field at interfacial site i of a magnetic atom. Indeed, phonons can induce thermal fluctuations of interfacial anisotropy through vibrations of interfacial atoms. Because δH_i is along the film normal (the in-plane component is expected to cancel out), it gives rise to a broader linewidth at larger θ_M, which is similar to the angular dependence of the TMS contribution. The T dependence of linewidths is also explained by the presence of δH_i. The value of δH_i fluctuates with time due to the thermal fluctuation of phonons, the frequency of which increases with increasing T, resulting in motional narrowing by averaging the randomness of δH_i, albeit an increase in its amplitude with increasing T (21).

To formulate the motional narrowing, we apply the Holstein–Primakov, Fourier, and Bogolyubov transformations to the spin-deviation Hamiltonian (22), and obtain H′ = −Σ_iδH_i·S_iz ∼ (S/2)^1/2sinθ_MΣ_kδH_−k(u_k + v_k)(α_k +α⁺_−k) (z direction along film normal) (Materials and Methods). H′ describes the coupling between local spin S_i and fluctuating field δH_i, which contributes to spin relaxation and thus FMR linewidth. Here, k is the wavevector of magnon; α_k, α⁺_−k, u_k, and v_k are the annihilation and creation operators for magnon and their coefficients after the Bogolyubov transformation; and S is the magnitude of spin. Adopting the Redfield theory to obtain the relationship between spin-relaxation time and δH_i (21), the linewidth ΔH_MN due to δH_i at k = 0 (Kittel mode) is expressed as ΔH_MN ∼ (S/2)(δH_k₌₀)²sin²θ_M(H₁/H₂)^1/2 with H₁ = H_Rcos(θ_H − θ_M)+H_K1^effcos²θ_M − H_K2cos⁴θ_M, H₂ = H_Rcos(θ_H − θ_M)+H_K1^effcos2θ_M −(H_K2/2)(cos2θ_M + cos4θ_M), and (δH_k₌₀)² = ∫dτδH_k₌₀(t₀)δH_k₌₀(t₀ + τ)e^−2iπfτ. Here, t₀ is the arbitrary time, and τ is the elapsed time from t₀. Writing the correlation function δH_k₌₀(t₀)δH_k₌₀(t₀ + τ) = (δH)²e^−|τ|/τ0, where τ₀ is the relaxation time of the random field δH_k=0, we obtainΔHMN≈(S/2)(δH)2τ0⁡sin2θM(H1/H2)1/2=Γ⁡sin2θM(H1/H2)1/2,[1]for 2πfτ₀ << 1.

We fitΔH=ΔHin(α,HK1eff,HK2)+ΔHinhom(ΔHK1eff,ΔHK2)+ΔHTMS(MS,HK1eff,HK2,AS,A,N)+ΔHMN(Γ,HK1eff,HK2),[2]to the magnetic-field angle dependence of the linewidths as a function of T in Fig. 2E (3, 10). Each contribution in the right-hand side of Eq. 2 is determined by the parameters in parentheses. The values of M_S, α, H_K1^eff, and H_K2 and their temperature dependence are determined experimentally; M_S from magnetization measurements, α obtained from VNA-FMR measurements at θ_H = 0° (Fig. 3A), and H_K1^eff and H_K2 from cavity-FMR measurements. We calculate ΔH_in from ΔH_in = α(H₁ + H₂)|dH_R/d[(H₁H₂)^1/2]| (3). The contribution from ΔH_inhom is expressed as ΔH_inhom = |dH_R/dH_K1^eff|ΔH_K1^eff+|dH_R/dH_K2|ΔH_K2, and ΔH_K1^eff and ΔH_K2 are adopted as fitting parameters (10). To describe the contribution from TMS, we adopt the expression in ref. 4. The TMS contribution at 300 K is determined from the best fit of Eq. 2 to the experimental result at 300 K with two defect-related fitting parameters, A and N, which reflect the size and density as well as the aspect ratio of the defects, respectively. The T dependence of TMS is calculated using the T dependence of M_S and H_K^eff, assuming the exchange stiffness constant A_S(T) ∝ [M_S(T)]² and T-independent A and N (20). As described before, the calculated TMS contribution changes by ∼10% at most with decreasing T from 300 to 4 K. For the ΔH_MN contribution, we adopt Γ as an adjustable parameter. The fit agrees with the experimental results as shown by the solid lines in Fig. 2E. Fig. 2G depicts the calculated linewidths as functions of f and T using parameters obtained from the analyses, reproducing the results in Fig. 1G. We note that the difference in the detected areas between VNA-FMR (∼0.1 mm²) and cavity-FMR (∼20 mm²) may result in the small difference observed in the magnitude of ΔH (compare Figs. 1G and 2G), due to inhomogeneity. The T dependence of Γ is shown in Fig. 3B. Although the observed functional form is unknown, it may be due to several contributions, such as the T dependence of the magnitude of δH_i and the magnon and phonon lifetimes (23). δH_i is expected to be determined by the T dependence of the thermal lattice expansion coefficient and the resultant lattice mismatch between CoFeB and MgO (24), whereas the magnon lifetime may be due to the exchange/stiffness constants at the interface (25, 26).

Fig. 3.

Temperature T and CoFeB thickness t dependences of damping constant α and linewidths Γ relating to motional narrowing. Temperature T dependence of (A) α and (B) Γ for CoFeB with t = 1.5 nm. Thickness t dependence of (C) α and (D) Γ. Filled symbols are determined from cavity-FMR and open symbols from VNA-FMR.

Furthermore, we fit Eq. 2 to the angle dependence of the linewidth for CoFeB with different t. Here, we treat α, ΔH_K1^eff, ΔH_K2, TMS parameters, and Γ as adjustable parameters. The CoFeB thickness dependence of α is shown in Fig. 3C. The magnitude of α is ∼0.004 independent of t (closed circles), and consistent with the values obtained from VNA-FMR spectra at θ_H = 0° (open circles). If we neglect ΔH_MN in the analyses of cavity-FMR linewidths, α increases with decreasing t (squares). It is therefore essential to include ΔH_MN in FMR analyses to obtain accurate values of α in thin CoFeB/MgO when θ_H ≠ 0°. Crucially, for the present CoFeB/MgO systems, we design the stacks to suppress the spin-pumping effect by sandwiching CoFeB by two MgO layers (27, 28). If we replace one or two sides of the adjacent MgO with Ta, α increases rapidly with decreasing t due to spin pumping (triangles and diamonds). The t dependence of Γ in Fig. 3D attests to its interfacial origin.

From systematic FMR studies, we have shown that interfacial anisotropy in thin-film CoFeB/MgO has a strong effect on the spectral linewidth. This effect is explained in terms of motional narrowing, which is commonly neglected in the analysis of FMR spectra. The present investigation demonstrates that great care must be taken in the study of FMR in magnetic architectures with interfacial anisotropy, a fundamental property for spin-based device applications. In addition, the result is expected to bring a new concept to spintronics devices using phonon–magnon coupling through the interfacial anisotropy (29, 30).

Materials and Methods

Sample Preparation.

Films were deposited on a thermally oxidized Si substrate by ultrahigh-vacuum magnetron sputtering. The stack structure, from substrate side, is Ta (5)/ CuN (30)/ TaN (20)/ Ta (5)/ [CoFeB(0.6)/ Ru (3)]₂/ Ta (2)/ CoFeB (0.6)/ MgO (3)/ CoFeB(t = 1∼2.6)/ MgO (3)/ Ta (5)/ Ru (5)/ CuN (15), where numbers in parentheses are thickness in nanometers. The three 0.6-nm-thick CoFeB layers were inserted to improve the quality of the films above them (31, 32), and are expected to exhibit superparamagnetic behavior (33). We confirmed they do not affect the FMR spectra using a reference measurement on a stack in their absence. Because they are expected to exhibit very different anisotropy, due to different interfaces and thickness (compared with thick CoFeB, which is of interest here) their resonances are not detected in the temperature, frequency, and field range investigated. The FMR active layer is CoFeB sandwiched between two MgO layers. The CoFeB thickness t is varied from 1 to 2.6 nm over 8-inch wafer using wedged-film deposition. The actual thicknesses of CoFeB are calibrated from cross-sectional images obtained using a transmission electron microscope. We prepared also a reference sample with thick CoFeB namely, t = 3.7 nm.

VNA-FMR.

Most of the measurements were performed using a home-built instrument with applied magnetic fields up to 0.55 T (up to 1.4 T at 300 K) and frequencies up to 26 GHz. A separate home-built FMR dipper probe was used to measure the sample with t = 1.5 nm under a perpendicular magnetic field at temperatures down to 4.2 K. FMR spectra were acquired by sweeping the external magnetic field (9).

Cavity-FMR.

The sample was placed in a TE₀₁₁ microwave cavity, where microwave frequency f = 9 GHz was introduced. We measured the external magnetic-field H dependence of the FMR spectrum (derivative microwave absorption spectrum) by superimposing an ac magnetic field (1 mT and 100 kHz) for lock-in detection. The sample temperature was controlled from 4 to 300 K using a liquid He flow cryostat (10, 16).

Motional Narrowing.

The magnetic energy in the CoFeB film is described by a Heisenberg Hamiltonian H_H with anisotropy term D and external magnetic field H₀,HH=−J∑〈i,j〉Si⋅Sj−D∑iSiz2−H0⋅∑iSi.[3]

To study the linewidth in FMR due to the fluctuating field δH_i at interfaces, we consider the perturbation Hamiltonian,H′=−∑iδHiSiz,[4]

where we consider δH_i along the normal of the interfaces (z direction) because its in-plane components are expected to cancel out. We study the case for tilted magnetization direction to in-plane direction along x, and define the direction of magnetization M as the ζ-axis. By rotating by θ_M about the y axis, we convert x- and z axes of Cartesian coordinate system to ξ- and ζ-axes. In the ξ−ζ plane, the spin operator in the z direction is given bySiz=Siζ⁡cos⁡θM−Siξ⁡sin⁡θM,[5]

and Eq. 4 is rewritten asH′=−∑iδHi(Siζ⁡cos⁡θM−Siξ⁡sin⁡θM).[6]

Assuming a constant longitudinal spin component (along the ζ-direction) S_iζ, only the transverse spin component (along the ξ-direction) S_iξ contributes to FMR. Hence, a Hamiltonian contributing to FMR is expressed asH′ξ=sin⁡θM∑iδHiSiξ.[7]

By the Holstein–Primakoff transformation with the creation and annihilation operators a⁺_i and a_i, and the magnitude of spin S, the transverse component is written as (22, 34)Siξ=S2(ai+ai+),[8]

and Eq. 7 becomesH′ξ=S2sin⁡θM∑iδHi(ai+ai+).[9]

The Fourier transformation with wavevector k and number of interfacial sites N givesai=1N∑keik⋅riak,[10]δHi=1N∑keik⋅riδHk.[11]

Then, Eq. 9 is expressed asH′ξ=S2sin⁡θM∑kδH−k(ak+a−k+).[12]

Eq. 3 is diagonalized by the Bogolyubov transformation (22, 35),ak=ukαk+vkα-k+,[13]a-k=vkαk++ukα−k,[14]

and Eq. 12 transforms toH′ξ=S2sin⁡θM∑kδH−k(uk+vk)(αk+α−k+).[15]

Because we are interested in the FMR mode, we consider the k = 0 mode in Eq. 15,H′ξ(k=0)=S2sin⁡θMδHk=0(u0+v0)(αk=0+αk=0+).[16]

Adopting standard process to obtain the magnon dispersion, the coefficients in the Bogolyubov transformation in Eq. 16 are obtained as(u0+v0)2=H1H2,[17]

withH1≡H0⁡cos(θH−θM)+2DS⁡cos2θM,[18]H2≡H0⁡cos(θH−θM)+2DS⁡cos⁡2θM.[19]

According to Redfield theory (21, 36), the linewidth of FMR (k = 0) mode is proportional to the spectral density of fluctuating fields δH_k=0,ΔHMN≈S2sin2θM(u0+v0)2∫0∞δHk=0(t)δHk=0(t+τ)e−iωτdτ,[20]

where the time-correlation function of fluctuating field δH_k=0 at interfaces is given by (21)δHk=0(t)δHk=0(t+τ)=(δH)2e−|τ|/τ0.[21]

Because only the z component of δH is relevant, we assume the single relaxation lifetime τ₀ of the fluctuating fields at interfaces. τ₀ is of the same order of the inverse of the phonon frequency––much larger than the resonance frequency ω, and thus ωτ₀ << 1. The integration over time τ is calculated as∫0∞e−|τ|/τ0e−iωτdτ=τ01+ω2τ02→ωτ0<<1τ0.[22]

Finally, we obtain the following linewidth for the FMR mode due to the fluctuating fields at interfaces:ΔHMN≈S2(δH)2τ0⁡sin2θM(H1/H2)1/2,[23]

which is Eq. 1 in the main text.

Acknowledgments

The work at Tohoku University was supported in part by Grants-in-Aid for Scientific Research from Ministry of Education, Culture, Sports, Science and Technology (MEXT) (26103002) and from JSPS (16H06081 and 16J05455), R&D project for Information and Communication Technology (ICT) Key Technology of MEXT, Impulsing Paradigm Change through Disruptive Technologies Program (ImPACT) program of Council for Science, Technology and Innovation (CSTI), Japan Society for the Promotion of Science (JSPS) Core-to-Core Program, as well as the Cooperative Research Projects of Research Institute of Electrical Communication (RIEC). The work in Singapore was supported by the Ministry of Education (MoE, Academic Research Fund Tier 2 Grant MOE2014-T2-1-050), the A*STAR Pharos Fund (1527400026), and the National Research Foundation (NRF), NRF-Investigatorship (NRFNRFI2015-04). The work at Japan Atomic Energy Agency was supported in part by Grants-in-Aid for Scientific Research from JSPS (Grants 26247063, 25287094, 15K05192, and 16H01082) and from MEXT (26103006 and 26247063).

Footnotes

↵¹A.O. and S.H. contributed equally to this work.
↵²To whom correspondence may be addressed. Email: f-matsu{at}wpi-aimr.tohoku.ac.jp or christos{at}ntu.edu.sg.

Author contributions: A.O.S.H., B.G., S.K., A.S., S.T.L., M.T., M.M., S.M., F.M., H.O., and C.P. performed research; A.O., S.H., A.S., B.G., F.M., and C.P. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.

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(2011) Origin of the collapse of tunnel magnetoresistance at high annealing temperature in CoFeB/MgO perpendicular magnetic tunnel junctions. Appl Phys Lett 99(25):252507.
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1. Alzate JG, et al.
(2014) Temperature dependence of the voltage-controlled perpendicular anisotropy in nanoscale MgO| CoFeB| Ta magnetic tunnel junctions. Appl Phys Lett 104(11):112410.
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1. Takeuchi Y,
2. Sato H,
3. Fukami S,
4. Matsukura F,
5. Ohno H
(2015) Temperature dependence of energy barrier in CoFeB-MgO magnetic tunnel junctions with perpendicular easy axis. Appl Phys Lett 107(15):152405.
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1. Slichter CP
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1. Kittel C
(1963) Quantum Theory of Solids (Wiley, New York), pp 49–52.
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1. Anand S,
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3. Jain K,
4. Abbi SC
(1996) Temperature dependence of optical phonon lifetimes in ZnSe. Physica B 226(4):331–337.
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1. Ong PV, et al.
(2015) Giant voltage modulation of magnetic anisotropy in strained heavy metal/magnet/insulator heterostructures. Phys Rev B 92(2):020407.
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OpenUrl
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1. Sakuma A,
2. Toga Y,
3. Tsuchiya H
(2009) Theoretical study on the stability of magnetic structures in the surface and interfaces of Heusler alloys, Co₂MnAl and Co₂MnSi. J Appl Phys 105(7):07C910.
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1. Miura Y,
2. Abe K,
3. Shirai M
(2011) Effects of interfacial noncollinear magnetic structures on spin-dependent conductance in Co₂MnSi/MgO/Co₂MnSi magnetic tunnel junctions: A first-principles study. Phys Rev B 83(21):214411.
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1. Mizukami S,
2. Ando Y,
3. Miyazaki T
(2002) Effect of spin diffusion on Gilbert damping for a very thin permalloy layer in Cu/permalloy/Cu/Pt films. Phys Rev B 66(10):104413.
.
OpenUrl
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1. Tserkovnyak Y,
2. Brataas A,
3. Bauer GEW
(2002) Enhanced Gilbert damping in thin ferromagnetic films. Phys Rev Lett 88(11):117601.
.
OpenUrl CrossRef PubMed
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1. Kittel C
(1958) Interaction of spin waves and ultrasonic waves in ferromagnetic crystals. Phys Rev 110(4):836.
.
OpenUrl CrossRef
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1. Ogawa N, et al.
(2015) Photodrive of magnetic bubbles via magnetoelastic waves. Proc Natl Acad Sci USA 112(29):8977–8981.
.
OpenUrl Abstract/FREE Full Text
↵
1. Hayakawa J,
2. Ikeda S,
3. Matsukura F,
4. Takahashi H,
5. Ohno H
(2005) Dependence of giant tunnel magnetoresistance of sputtered CoFeB/MgO/CoFeB magnetic tunnel junctions on MgO barrier thickness and annealing temperature. Jpn J Appl Phys 44(4L):L587–L589.
.
OpenUrl CrossRef
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1. Djayaprawira DD, et al.
(2005) 230% room-temperature magnetoresistance in CoFeB/ MgO/CoFeB magnetic tunnel junctions. Appl Phys Lett 86(9):092502.
.
OpenUrl CrossRef
↵
1. Jang Y, et al.
(2006) Magnetic field sensing scheme using CoFeB/MgO/CoFeB tunneling junction with superparamagnetic CoFeB layer. Appl Phys Lett 89(16):163119.
.
OpenUrl
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1. Holstein T,
2. Primakoff H
(1940) Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys Rev 58(12):1098–1113.
.
OpenUrl CrossRef
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1. Bogolibov N
(1947) On the theory of superfluidity. J Phys USSR 11(1):23–32.
.
OpenUrl
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1. Redfield AG
(1957) On the theory of relaxation processes. IBM J Res Develop 1(1):19–31.
.
OpenUrl

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Proceedings of the National Academy of Sciences: 114 (15)

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Article Classifications

Physical Sciences
Applied Physical Sciences

[1] ↵
Gilbert TL
(2004) A phenomenological theory of damping in ferromagnetic materials. IEEE Trans Magn 40(6):3443–3449.
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[2] Gilbert TL

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Miyazaki T
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[6] Mizukami S,

[7] Ando Y,

[8] Miyazaki T

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Mills D
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Zhang W,
Carter MJ,
Xiao G
(2011) Ferromagnetic resonance and damping properties of CoFeB thin films as free layers in MgO-based magnetic tunnel junctions. J Appl Phys 110(3):033910.
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[15] Liu X,

[16] Zhang W,

[17] Carter MJ,

[18] Xiao G

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Hirayama E,
Kanai S,
Sato H,
Matsukura F,
Ohno H
(2015) Ferromagnetic resonance in nanoscale CoFeB/MgO magnetic tunnel junctions. J Appl Phys 117(17):17B708.
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[20] Hirayama E,

[21] Kanai S,

[22] Sato H,

[23] Matsukura F,

[24] Ohno H

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Ikeda S, et al.
(2010) A perpendicular-anisotropy CoFeB-MgO magnetic tunnel junction. Nat Mater 9(9):721–724.
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He S,
Panagopoulos C
(2016) A broadband ferromagnetic resonance dipper probe for magnetic damping measurements from 4.2 K to 300 K. Rev Sci Instrum 87(4):043110.
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[28] He S,

[29] Panagopoulos C

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Okada A, et al.
(2014) Electric-field effects on magnetic anisotropy and damping constant in Ta/CoFeB/MgO investigated by ferromagnetic resonance. Appl Phys Lett 105(5):052415.
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(2006) Two-magnon scattering and viscous Gilbert damping in ultrathin ferromagnets. Phys Rev B 73(14):144424.
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Lubitz P
(1974) Temperature variation of ferromagnetic relaxation in the 3d transition metals. Phys Rev B 10:179–185.
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[36] Lubitz P

[37] ↵
Kuneš J,
Kamberský V
(2002) First-principles investigation of the damping of fast magnetization precession in ferromagnetic 3d metals. Phys Rev B 65(21):212411.
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[38] Kuneš J,

[39] Kamberský V

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Kamberský V
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[42] ↵
Okuno T, et al.
(2016) Temperature dependence of spin Hall magnetoresistance in W/CoFeB bilayer. Jpn J Appl Phys 55(8):080308.
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[43] Okuno T, et al.

[44] ↵
Chen L,
Matsukura F,
Ohno H
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[45] Chen L,

[46] Matsukura F,

[47] Ohno H

[48] ↵
Callen HB,
Callen E
(1966) The present status of the temperature dependence of magnetocrystalline anisotropy, and the l(l+1) power law. J Phys Chem Solids 27(8):1271–1285.
.
OpenUrl

[49] Callen HB,

[50] Callen E

[51] ↵
Gan HD, et al.
(2011) Origin of the collapse of tunnel magnetoresistance at high annealing temperature in CoFeB/MgO perpendicular magnetic tunnel junctions. Appl Phys Lett 99(25):252507.
.
OpenUrl

[52] Gan HD, et al.

[53] ↵
Alzate JG, et al.
(2014) Temperature dependence of the voltage-controlled perpendicular anisotropy in nanoscale MgO| CoFeB| Ta magnetic tunnel junctions. Appl Phys Lett 104(11):112410.
.
OpenUrl

[54] Alzate JG, et al.

[55] ↵
Takeuchi Y,
Sato H,
Fukami S,
Matsukura F,
Ohno H
(2015) Temperature dependence of energy barrier in CoFeB-MgO magnetic tunnel junctions with perpendicular easy axis. Appl Phys Lett 107(15):152405.
.
OpenUrl

[56] Takeuchi Y,

[57] Sato H,

[58] Fukami S,

[59] Matsukura F,

[60] Ohno H

[61] ↵
Slichter CP
(1990) Principles of Magnetic Resonance (Springer Science & Business Media, New York), pp 206–215.
.

[62] Slichter CP

[63] ↵
Kittel C
(1963) Quantum Theory of Solids (Wiley, New York), pp 49–52.
.

[64] Kittel C

[65] ↵
Anand S,
Verma P,
Jain K,
Abbi SC
(1996) Temperature dependence of optical phonon lifetimes in ZnSe. Physica B 226(4):331–337.
.
OpenUrl

[66] Anand S,

[67] Verma P,

[68] Jain K,

[69] Abbi SC

[70] ↵
Ong PV, et al.
(2015) Giant voltage modulation of magnetic anisotropy in strained heavy metal/magnet/insulator heterostructures. Phys Rev B 92(2):020407.
.
OpenUrl

[71] Ong PV, et al.

[72] ↵
Sakuma A,
Toga Y,
Tsuchiya H
(2009) Theoretical study on the stability of magnetic structures in the surface and interfaces of Heusler alloys, Co₂MnAl and Co₂MnSi. J Appl Phys 105(7):07C910.
.
OpenUrl CrossRef

[73] Sakuma A,

[74] Toga Y,

[75] Tsuchiya H

[76] ↵
Miura Y,
Abe K,
Shirai M
(2011) Effects of interfacial noncollinear magnetic structures on spin-dependent conductance in Co₂MnSi/MgO/Co₂MnSi magnetic tunnel junctions: A first-principles study. Phys Rev B 83(21):214411.
.
OpenUrl

[77] Miura Y,

[78] Abe K,

[79] Shirai M

[80] ↵
Mizukami S,
Ando Y,
Miyazaki T
(2002) Effect of spin diffusion on Gilbert damping for a very thin permalloy layer in Cu/permalloy/Cu/Pt films. Phys Rev B 66(10):104413.
.
OpenUrl

[81] Mizukami S,

[82] Ando Y,

[83] Miyazaki T

[84] ↵
Tserkovnyak Y,
Brataas A,
Bauer GEW
(2002) Enhanced Gilbert damping in thin ferromagnetic films. Phys Rev Lett 88(11):117601.
.
OpenUrl CrossRef PubMed

[85] Tserkovnyak Y,

[86] Brataas A,

[87] Bauer GEW

[88] ↵
Kittel C
(1958) Interaction of spin waves and ultrasonic waves in ferromagnetic crystals. Phys Rev 110(4):836.
.
OpenUrl CrossRef

[89] Kittel C

[90] ↵
Ogawa N, et al.
(2015) Photodrive of magnetic bubbles via magnetoelastic waves. Proc Natl Acad Sci USA 112(29):8977–8981.
.
OpenUrl Abstract/FREE Full Text

[91] Ogawa N, et al.

[92] ↵
Hayakawa J,
Ikeda S,
Matsukura F,
Takahashi H,
Ohno H
(2005) Dependence of giant tunnel magnetoresistance of sputtered CoFeB/MgO/CoFeB magnetic tunnel junctions on MgO barrier thickness and annealing temperature. Jpn J Appl Phys 44(4L):L587–L589.
.
OpenUrl CrossRef

[93] Hayakawa J,

[94] Ikeda S,

[95] Matsukura F,

[96] Takahashi H,

[97] Ohno H

[98] ↵
Djayaprawira DD, et al.
(2005) 230% room-temperature magnetoresistance in CoFeB/ MgO/CoFeB magnetic tunnel junctions. Appl Phys Lett 86(9):092502.
.
OpenUrl CrossRef

[99] Djayaprawira DD, et al.

[100] ↵
Jang Y, et al.
(2006) Magnetic field sensing scheme using CoFeB/MgO/CoFeB tunneling junction with superparamagnetic CoFeB layer. Appl Phys Lett 89(16):163119.
.
OpenUrl

[101] Jang Y, et al.

[102] ↵
Holstein T,
Primakoff H
(1940) Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys Rev 58(12):1098–1113.
.
OpenUrl CrossRef

[103] Holstein T,

[104] Primakoff H

[105] ↵
Bogolibov N
(1947) On the theory of superfluidity. J Phys USSR 11(1):23–32.
.
OpenUrl

[106] Bogolibov N

[107] ↵
Redfield AG
(1957) On the theory of relaxation processes. IBM J Res Develop 1(1):19–31.
.
OpenUrl

[108] Redfield AG

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