In-plane magnetic field effect on switching voltage and thermal stability in electric-field-controlled perpendicular magnetic tunnel junctions

Magnetic tunnel junctions (MTJs) exploiting voltage-controlled magnetic anisotropy (VCMA) have attracted interest for use in memory applications,^1–111. W. G. Wang, M. Li, S. Hageman, and C. L. Chien, Nat. Mater. 11(1), 64 (2012). https://doi.org/10.1038/nmat31712. Y. Shiota, T. Nozaki, F. Bonell, S. Murakami, T. Shinjo, and Y. Suzuki, Nat. Mater. 11(1), 39 (2012). https://doi.org/10.1038/nmat31723. J. G. Alzate, P. K. Amiri, P. Upadhyaya, S. S. Cherepov, J. Zhu, M. Lewis, R. Dorrance, J. A. Katine, J. Langer, K. Galatsis, D. Markovic, I. Krivorotov, and K. L. Wang, 2012 IEEE International Electron Devices Meeting (2012).4. S. Kanai, M. Yamanouchi, S. Ikeda, Y. Nakatani, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 101(12), 122403 (2012). https://doi.org/10.1063/1.47538165. K. L. Wang and P. Khalili Amiri, SPIN 02(03), 1240002 (2012). https://doi.org/10.1142/S20103247124000246. K. L. Wang, J. G. Alzate, and P. Khalili Amiri, Journal of Physics D: Appl. Phys. 46(7), 074003 (2013). https://doi.org/10.1088/0022-3727/46/7/0740037. P. Khalili Amiri, J. Alzate, X. Cai, F. Ebrahimi, Q. Hu, K. Wong, C. Grezes, H. Lee, G. Yu, X. Li, M. Akyol, Q. Shao, J. Katine, J. Langer, and B. Ocker, Magnetics, IEEE Transactions on Magnetics (99), 1 (2015). https://doi.org/10.1109/TMAG.2015.24431248. P. Khalili Amiri and K. L. Wang, IEEE Spectrum 52(7), 30 (2015). https://doi.org/10.1109/MSPEC.2015.71316929. Y. Shiota, S. Miwa, T. Nozaki, F. Bonell, N. Mizuochi, T. Shinjo, H. Kubota, S. Yuasa, and Y. Suzuki, Applied Physics Letters 101, 102406 (2012). https://doi.org/10.1063/1.475103510. W. G. Wang and C. L. Chien, J. Phys. D: Appl. Phys. 46, 074004 (2013). https://doi.org/10.1088/0022-3727/46/7/07400411. C. Grezes, F. Ebrahimi, J.G. Alzate, X. Cai, J.A Katine, J. Langer, B. Ocker, P. Khalili Amiri, and K.L Wang, Appl. Phys. Lett. 108, 012403 (2016). https://doi.org/10.1063/1.4939446 offering the potential for ultralow switching energy,^5–85. K. L. Wang and P. Khalili Amiri, SPIN 02(03), 1240002 (2012). https://doi.org/10.1142/S20103247124000246. K. L. Wang, J. G. Alzate, and P. Khalili Amiri, Journal of Physics D: Appl. Phys. 46(7), 074003 (2013). https://doi.org/10.1088/0022-3727/46/7/0740037. P. Khalili Amiri, J. Alzate, X. Cai, F. Ebrahimi, Q. Hu, K. Wong, C. Grezes, H. Lee, G. Yu, X. Li, M. Akyol, Q. Shao, J. Katine, J. Langer, and B. Ocker, Magnetics, IEEE Transactions on Magnetics (99), 1 (2015). https://doi.org/10.1109/TMAG.2015.24431248. P. Khalili Amiri and K. L. Wang, IEEE Spectrum 52(7), 30 (2015). https://doi.org/10.1109/MSPEC.2015.7131692 while employing conventional material combinations of stable MTJs with high tunneling magnetoresistance (TMR) ratios. Nanosecond bidirectional magnetization switching by the application of unipolar voltage pulses has been demonstrated,^1–41. W. G. Wang, M. Li, S. Hageman, and C. L. Chien, Nat. Mater. 11(1), 64 (2012). https://doi.org/10.1038/nmat31712. Y. Shiota, T. Nozaki, F. Bonell, S. Murakami, T. Shinjo, and Y. Suzuki, Nat. Mater. 11(1), 39 (2012). https://doi.org/10.1038/nmat31723. J. G. Alzate, P. K. Amiri, P. Upadhyaya, S. S. Cherepov, J. Zhu, M. Lewis, R. Dorrance, J. A. Katine, J. Langer, K. Galatsis, D. Markovic, I. Krivorotov, and K. L. Wang, 2012 IEEE International Electron Devices Meeting (2012).4. S. Kanai, M. Yamanouchi, S. Ikeda, Y. Nakatani, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 101(12), 122403 (2012). https://doi.org/10.1063/1.4753816 and switching energy down to 6fJ/bit has been achieved in VCMA-controlled CoFeB/MgO magnetic tunnel junctions with perpendicular anisotropy (p-MTJs).¹¹11. C. Grezes, F. Ebrahimi, J.G. Alzate, X. Cai, J.A Katine, J. Langer, B. Ocker, P. Khalili Amiri, and K.L Wang, Appl. Phys. Lett. 108, 012403 (2016). https://doi.org/10.1063/1.4939446 During the voltage pulse application, the two stable magnetization states of the free layer disappear in favor of in-plane easy axis and a precessional motion of the magnetization appears. The magnetization switching is achieved by timing of the pulse duration.

In practical situations however, an in-plane magnetic field (e.g. applied externally or provided by an in-plane fixed layer) is needed to ensure a single in-plane precessional axis,^9–119. Y. Shiota, S. Miwa, T. Nozaki, F. Bonell, N. Mizuochi, T. Shinjo, H. Kubota, S. Yuasa, and Y. Suzuki, Applied Physics Letters 101, 102406 (2012). https://doi.org/10.1063/1.475103510. W. G. Wang and C. L. Chien, J. Phys. D: Appl. Phys. 46, 074004 (2013). https://doi.org/10.1088/0022-3727/46/7/07400411. C. Grezes, F. Ebrahimi, J.G. Alzate, X. Cai, J.A Katine, J. Langer, B. Ocker, P. Khalili Amiri, and K.L Wang, Appl. Phys. Lett. 108, 012403 (2016). https://doi.org/10.1063/1.4939446 and hence modifies the energy landscape and switching behavior. The modification of the energy landscape affects the relevant parameters of the MTJs, including: (1) the thermal stability (Δ = E_b/k_BT, where E_b denotes the energy barrier that separates the two magnetization states, k_B is the Boltzmann constant, and T is the temperature), which characterizes the ability of the magnetization states to remain stable against thermal fluctuations, (2) the switching voltage (V_sw), which corresponds to the voltage required to switch between the two magnetization configurations, and (3) the switching time, equal to half the precession period. Recently, the effect of in-plane magnetic field on the period of the magnetization precession was studied in p-MTJs.^12,1312. S. Kanai, Y. Nakatani, M. Yamanouchi, S. Ikeda, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 103, 072408 (2013). https://doi.org/10.1063/1.481867613. S. Kanai, M. Yamanouchi, S. Ikeda, Y. Nakatani, F. Matsukura, and H. Ohno, IEEE Transactions on Magnetics (50), 1 (2014). In this Letter, we investigate the dependence of thermal stability and switching voltage on in-plane magnetic fields (H_in). We first provide a method for measuring the voltage-dependent energy barrier height E_b(V ), and gain insight into the energy landscape. We then apply the above method combined with switching experiments to reveal the effect of in-plane magnetic fields on the energy landscape and related MTJs parameters. Our results indicate that both Δ and V_sw decrease with the increase of H_in, with a dominant linear dependence. These observations are accurately reproduced by calculations of the energy landscape based on a macrospin model.

A schematic of the MTJ and measurement configuration used in this study is shown in Figure 1(a). The stack structure consists of a bottom 1.1 nm (t) thick Co₂₀Fe₆₀B₂₀ free layer, a 1.4 nm (t_d) thick MgO barrier layer, and top 1.4 nm thick Co₂₀Fe₆₀B₂₀ reference layer with a synthetic antiferromagnetic pinning layer. This is the same structure as that used in Ref. 1111. C. Grezes, F. Ebrahimi, J.G. Alzate, X. Cai, J.A Katine, J. Langer, B. Ocker, P. Khalili Amiri, and K.L Wang, Appl. Phys. Lett. 108, 012403 (2016). https://doi.org/10.1063/1.4939446. The film is processed into a circular MTJ of 50 nm (d) in junction diameter by using electron-beam lithography and dry etching techniques. Both CoFeB layers have perpendicular easy axes, and the magnetization direction of the CoFeB reference layer is fixed to the +z direction. A tilted external magnetic field (H) is applied with an angle θ_H from the film normal. The out-of-plane (H_oop) and in-plane (H_in) components of H correspond to Hcosθ_H and Hsinθ_H, respectively.

Figure 1(b) shows measurements of resistance R as a function of the out-of-plane component of the magnetic field H_oop under +10 mV dc bias for θ_H = 0°, 11°, and 26°. The junction resistance-area product is 650 Ω.μm², and the tunnel magnetoresistance ratio, defined as $\left({\mathrm{R}}_{\mathrm{AP}}-{\mathrm{R}}_{\mathrm{P}}\right)/{\mathrm{R}}_{\mathrm{P}}$ at θ_H = 0°, is 49%, where R_P and R_AP are the resistances at parallel (P) and antiparallel (AP) magnetization configurations, respectively. Increasing H_in is observed to decrease the coercivity of the free layer along the perpendicular axis, in agreement with previous studies in similar structures.^12,1312. S. Kanai, Y. Nakatani, M. Yamanouchi, S. Ikeda, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 103, 072408 (2013). https://doi.org/10.1063/1.481867613. S. Kanai, M. Yamanouchi, S. Ikeda, Y. Nakatani, F. Matsukura, and H. Ohno, IEEE Transactions on Magnetics (50), 1 (2014). The hysteresis curves are shifted at negative H_oop, due to stray fields from the fixed (i.e combined pinning and reference) layers acting on the CoFeB free layer. The shift is found to be independent of θ_H, which indicates that the directions of magnetization in the fixed layers are not tilted from the sample normal during the experiment. Hereafter, we present and compare results for various H_in, where the out-of-plane component of H is maintained near μ₀H_oop = μ₀H_s = − 142 mT, to compensate the stray field. Values of E_b and V_sw are determined from μ₀H_oop strictly fixed to μ₀H_s.

Energy barrier heights (E_b) are obtained by measuring the mean time for thermally activated switching (dwell time) under different applied magnetic fields.¹⁴14. W. Rippard, R. Heindl, M. Pufall, S. Russek, and A. Kos, Phys. Rev. B 84, 064439 (2011). https://doi.org/10.1103/PhysRevB.84.064439 The mean value at a particular magnetic field is determined from a total of 10² switching events, which are monitored by measuring the real-time voltage across the MTJ (Figure 2(a)–2(b)). The dwell times from P to AP (τ⁺) and AP to P (τ⁻) are then fitted using the Neel-Brown formula,¹⁵15. W. F. Brown, Jr., Phys. Rev. 130, 1677 (1963). https://doi.org/10.1103/PhysRev.130.1677

$${\displaystyle {\mathrm{\tau }}^{\pm }={\mathrm{\tau }}_{0}exp\left(\frac{{\mathrm{E}}_{\mathrm{b}}}{{\mathrm{k}}_{\mathrm{B}}\mathrm{T}}{\left(1\pm \frac{{\mathrm{H}}_{\mathrm{oop}}-{\mathrm{H}}_{\mathrm{s}}}{{\mathrm{H}}_{\mathrm{k,eff}}}\right)}^2\right),}$$

(1)

where τ₀ is the inverse of the attempt frequency (assumed to be 1 ns), and H_k,eff is the effective magnetic anisotropy field. In the following, we restrict our measurements to E_b > 15k_BT to remain in the regime of high energy barriers (E_b ≫ k_BT) in which Eq. (1) is valid.¹⁶16. Z. Li and S. Zhang, Phys. Rev. B 69, 134416 (2004). https://doi.org/10.1103/PhysRevB.69.134416 Figure 2(c) shows a typical result of dwell time measurements for μ₀H_in = 0 mT under +1V dc bias. The measured dwell times are well fitted by Eq. (1), showing a symmetric behavior with respect to H_s. At μ₀H_oop = μ₀H_s, the relaxation times for the two states are equal ${\mathrm{\tau }}^{\pm }=\mathrm{\tau }={\mathrm{\tau }}_{0}exp\left({\mathrm{E}}_{\mathrm{b}}/{\mathrm{k}}_{\mathrm{B}}\mathrm{T}\right)$, and the energy barrier height E_b = 23.3 k_BT can be read directly at the intersection of the fits.

First, we focus on the voltage dependence of E_b in the absence of in-plane magnetic field. As shown in Figure 2(d), the energy barrier decreases linearly with positive voltage. This indicates a modulation of the perpendicular magnetic anisotropy by the applied voltage. The magnetic energy density S per unit volume is given by the sum of the densities of the Zeeman energy, demagnetizing energy, and magnetic anisotropy energy as

$${\displaystyle \mathrm{S}=\mathrm{K}{\sin }^{\mathrm{2}}\mathrm{\theta }+\frac{{\mathrm{M}}_{\mathrm{s}}^{\mathrm{2}}}{\mathrm{2}{\mathrm{\mu }}_{\mathrm{0}}}{\cos }^{\mathrm{2}}\mathrm{\theta }-{\mathrm{H}}_{\mathrm{in}}{\mathrm{M}}_{\mathrm{s}}\sin \mathrm{\theta }={\mathrm{K}}_{\mathrm{eff}}{\sin }^{\mathrm{2}}\mathrm{\theta }-{\mathrm{H}}_{\mathrm{in}}{\mathrm{M}}_{\mathrm{s}}\sin \mathrm{\theta }+\frac{{\mathrm{M}}_{\mathrm{s}}^{\mathrm{2}}}{\mathrm{2}{\mathrm{\mu }}_{\mathrm{0}}},}$$

(2)

where μ₀ is the permeability of vacuum, M_s is the free layer saturation magnetization, K is the first-order perpendicular magnetic anisotropy energy constant, and θ is the magnetization angle measured from the sample normal. We introduce the effective magnetic anisotropy energy ${\mathrm{K}}_{\mathrm{eff}}=\frac{{\mathrm{M}}_{\mathrm{s}}{\mathrm{H}}_{\mathrm{k,eff}}}{2}=\mathrm{K}-\frac{{\mathrm{M}}_{\mathrm{s}}^{\mathrm{2}}}{\mathrm{2}{\mathrm{\mu }}_{\mathrm{0}}}$, which corresponds to the difference in the magnetic energy densities between θ = 0° and θ = 90° at zero magnetic field. Note that, a more detailed analysis should also include the second-order magnetic anisotropy term K₂sin⁴θ. We neglect this in the following and find that this assumption adequately captures our experimental results, consistent with the recent experiments in CoFeB/MgO MTJs showing that K₂ is several time smaller than K.^17,1817. K. Mizunuma, M. Yamanouchi, H. Sato, S. Ikeda, S. Kanai, F. Matsukura, and H. Ohno, Appl. Phys. Express 6, 063002 (2013). https://doi.org/10.7567/APEX.6.06300218. A. Okada, S. Kanai, M. Yamanouchi, S. Ikeda, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 105, 052415 (2014). https://doi.org/10.1063/1.4892824 The energy barrier E_b can be calculated from Eq. (2) as the product of the difference between the maximum and minimum energy densities Δ S and the volume of the free layer V^* = A^*t (=tπ(d/2)² in the single domain case). In the absence of in-plane magnetic field, the maximum and minimum energy density for a perpendicular MTJ coincide with the hard (θ = 90°) and easy (θ = 0°) anisotropy axis, respectively, yielding E_b(H_in = 0) = K_effV^*. Assuming a linear dependence of the first-order anisotropy energy on voltage,^19,2019. T. Nozaki, Y. Shiota, M. Shiraishi, T. Shinjo, and Y. Suzuki, Appl. Phys. Lett. 96, 022506 (2010). https://doi.org/10.1063/1.327915720. J. Zhu, J. A. Katine, G. E. Rowlands, Y. Chen, Z. Duan, J. G. Alzate, P. Upadhyaya, J. Langer, P. Khalili Amiri, K. L. Wang, and I. N. Krivorotov, Phys. Rev. Lett. 108, 197203 (2012). https://doi.org/10.1103/PhysRevLett.108.197203 one can write K as $\mathrm{K(V\; )}={\mathrm{(K}}_{\mathrm{i}}-\frac{\mathrm{\xi }}{{\mathrm{t}}_{\mathrm{d}}}\mathrm{V\; )/t}$ (where K_i is the interfacial anisotropy energy density and ξ is the linear VCMA magnetoelectric coefficient) and express the voltage-dependent energy barrier (in the absence of in-plane magnetic field) as

$${\displaystyle {\mathrm{E}}_{\mathrm{b}}({\mathrm{H}}_{\mathrm{in}}=0)={\mathrm{E}}_{\mathrm{b,s}}-\frac{\mathrm{\xi }{\mathrm{A}}^{*}}{{\mathrm{t}}_{\mathrm{d}}}\mathrm{V},}$$

(3)

where $\mathrm{\Delta }={\mathrm{E}}_{\mathrm{b,s}}/{\mathrm{k}}_{\mathrm{B}}\mathrm{T}=\left({\mathrm{K}}_{\mathrm{i}}-\frac{{\mathrm{M}}_{\mathrm{s}}^{\mathrm{2}}}{\mathrm{2}{\mathrm{\mu }}_{\mathrm{0}}}t\right){\mathrm{A}}^{*}/{\mathrm{k}}_{\mathrm{B}}\mathrm{T}$ is the standby thermal stability of the device. The fit to Eq. (3) yields Δ = 34.6 and ξ = 30.5 fJV⁻¹m⁻¹, with K_i = 0.24 mJm⁻² and M_s = 0.616 T (corresponding to a zero-voltage perpendicular anisotropy field ${{{\mathrm{\mu }}_{\mathrm{0}}\mathrm{H}}_{\mathrm{k,eff,0}}={\mathrm{\mu }}_{\mathrm{0}}\mathrm{H}}_{\mathrm{k,eff}}\left(\mathrm{V}=0\right)=268$ mT). Note that these values of K_i, M_s, μ₀H_k,eff,0 and ξ should be taken as lower limits, since sub-volume nucleation may exist in the CoFeB free layer,^21–2321. J. Z. Sun, R. P. Robertazzi, J. Nowak, P. L. Trouilloud, G. Hu, D. W. Abraham, M. C. Gaidis, S. L. Brown, E. J. O’Sullivan, W. J. Gallagher, and D. C. Worledge, Phys. Rev. B 84, 064413 (2011). https://doi.org/10.1103/PhysRevB.84.06441322. H. Sato, M. Yamanouchi, K. Miura, S. Ikeda, H. D. Gan, K. Mizunuma, R. Koizumi, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 99, 042501 (2011). https://doi.org/10.1063/1.361742923. H. Sato, E. C. I. Enobio, M. Yamanouchi, S. Ikeda, S. Fukami, S. Kanai, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 105, 062403 (2014). https://doi.org/10.1063/1.4892924 and hence an overestimated free layer area A^* would serve to lower the apparent values (see inset). Noteworthy, in the absence of in-plane field, the critical voltage V_c, defined as the voltage required to reduce the energy barrier to zero (E_b(V_c) = 0), can be estimated straightforwardly by linear extrapolation of the measured voltage-dependent energy barrier height, yielding V_c = 3.32 V.

Figure 3(a) shows the voltage dependence of the energy barrier height for various in-plane magnetic fields H_in. It is observed that E_b decreases (increases) linearly with increasing positive (negative) voltage, with a slope independent of H_in in the investigated region (E_b > 15k_BT). This behavior can be explained by considering again Eq. (2). For non-zero in-plane magnetic field, the two stable magnetizations states are no longer along the easy anisotropy axis (θ = 0°), but tilted from the sample normal with an angle θ₃ = sin⁻¹(H_in/H_k,eff) and θ₄ = π − sin⁻¹(H_in/H_k,eff) (fixed by the energy minimum conditions, ∂S/m∂θ = 0 and ∂²S/∂²θ > 0). The voltage-dependent energy barrier height ${\mathrm{E}}_{\mathrm{b}}=\left(\mathrm{S}\left({\mathrm{\theta }}_{\mathrm{1.2}}\right)-\mathrm{S}\left({\mathrm{\theta }}_{\mathrm{3,4}}\right)\right)V^{*}$ (with θ_1.2 = ± 90°, along the hard anisotropy axis) becomes

$${\displaystyle {\mathrm{E}}_{\mathrm{b}}=\left({\mathrm{K}}_{\mathrm{eff}}-{\mathrm{H}}_{\mathrm{in}}{\mathrm{M}}_{\mathrm{s}}+\frac{{\mathrm{M}}_{\mathrm{s}}^{\mathrm{2}}}{\mathrm{4}{\mathrm{K}}_{\mathrm{eff}}}{\mathrm{H}}_{\mathrm{in}}^{\mathrm{2}}\right)V^{*},}$$

(4)

with a third term $\frac{{\mathrm{M}}_{\mathrm{s}}^{\mathrm{2}}}{\mathrm{4}{\mathrm{K}}_{\mathrm{eff}}}{\mathrm{H}}_{\mathrm{in}}^{\mathrm{2}}{V}^{*}$ that results in nonlinearity both as a function of V and H_in. This non-linear term however is negligible when $\frac{{\mathrm{M}}_{\mathrm{s}}^{\mathrm{2}}}{\mathrm{4}{\mathrm{K}}_{\mathrm{eff}}}{\mathrm{H}}_{\mathrm{in}}^{\mathrm{2}}\ll {\mathrm{K}}_{\mathrm{eff}},{\mathrm{H}}_{\mathrm{in}}{\mathrm{M}}_{\mathrm{s}}$, conditions that reduce to H_in ≪ H_k,eff. In the experimental data shown in Figure 3, the condition H_in ≪ H_k,eff is always satisfied since we restrict our measurements to the regime where E_b > 15k_BT (as also shown below in Figure 5). The corresponding zero-voltage energy barrier height E_b,0 and VCMA coefficient ξ as a function of H_in are shown in Figure 3(b). It is observed that E_b,0 decreases almost linearly with H_in, a result well described by Eq. (4) for zero-voltage

$${\displaystyle {\mathrm{E}}_{\mathrm{b,0}}={\mathrm{E}}_{\mathrm{b,s}}-{\mathrm{H}}_{\mathrm{in}}{\mathrm{M}}_{\mathrm{s}}{V}^{*}+{\left({\mathrm{H}}_{\mathrm{in}}{\mathrm{M}}_{\mathrm{s}}{V}^{*}/2\right)}^2/{\mathrm{E}}_{\mathrm{b,s}},}$$

(5)

using the same values of E_b,s, M_s and V^* as in Eq. (3) (dashed-dotted line). This indicates that the nonlinearity in H_in arising from the third term in Eq. (5) is small, as expected for μ₀H_in ≤ 102 mT ≪μ₀H_k,eff,0. We note that Eq. (5) is independent of the switching mechanism used during writing, hence the above conclusions extend straightforwardly to field-driven and spin-transfer torque driven pMTJs. The VCMA coefficient, extracted from the slope as ${\mathrm{E}}_{\mathrm{b}}={\mathrm{E}}_{\mathrm{b,0}}-\frac{\mathrm{\xi }{\mathrm{A}}^{*}}{{\mathrm{t}}_{\mathrm{d}}}\mathrm{V}$, is found to be constant at 30 fJV⁻¹m⁻¹,confirming that the condition of negligible nonlinearity H_in ≪ H_k,eff is also satisfied for non-zero voltage.

We focus now on the in-plane magnetic field dependence of the switching voltage. One can see in Figure 3(a) that the voltage at which the energy barrier is reduced to zero decreases with increasing H_in. In order to estimate this threshold, we performed electric-field induced switching measurements using voltage pulses of various lengths (t_pulse) and amplitudes (V_pulse) applied to the device. The measurement setup and procedure are identical to the ones of our previous study (Ref. 1111. C. Grezes, F. Ebrahimi, J.G. Alzate, X. Cai, J.A Katine, J. Langer, B. Ocker, P. Khalili Amiri, and K.L Wang, Appl. Phys. Lett. 108, 012403 (2016). https://doi.org/10.1063/1.4939446), and the switching probability precision is 0.05. Figure 4(a) shows the measured back and forth magnetization switching (P₀₁P₁₀) by two successive 1.9 V voltage pulses, as functions of pulse duration and out-of-plane (in-plane) component of the external magnetic field. The quantity P₀₁P₁₀ corresponds to the product of the probabilities of P to AP transition (P₁₀) and AP to P transition (P₀₁). An oscillatory dependence of the switching probability on the pulse duration is observed for the range of H_in investigated, which is a signature of the voltage-induced precessional motion of the magnetization. The period of the oscillations is seen to decreases with the increase of H_in magnitude. This indicates a reduction of the Larmor frequency with H_in, in good agreement with previous studies in similar voltage-controlled MTJs.^12,1312. S. Kanai, Y. Nakatani, M. Yamanouchi, S. Ikeda, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 103, 072408 (2013). https://doi.org/10.1063/1.481867613. S. Kanai, M. Yamanouchi, S. Ikeda, Y. Nakatani, F. Matsukura, and H. Ohno, IEEE Transactions on Magnetics (50), 1 (2014). The switching voltage is obtained by measuring the contrast of the first oscillation as a function of the pulse amplitude. To allow a comparison with the simulations, we introduce the threshold (switching) voltage V_sw at which the contrast exceed 50% (P₀₁P₁₀ > 0.25), the maximum switching errors induced by thermal fluctuations. Note that this definition does not necessarily correspond to the precessional critical voltage V_c as defined by E_b(V_c) = 0 since switching can occur also below V_c by thermal activation across the energy barrier during voltage pulse applications.²⁴24. P. Khalili Amiri, P. Upadhyaya, J. G. Alzate, and K. L. Wang, J. Appl. Phys. 113, 013912 (2013). https://doi.org/10.1063/1.4773342 The measured V_sw for μ₀H_in = 69, 82, 92 and 102 mT is shown in Figure 4(b). Its dependence on H_in is well reproduced by the simulations of V_c, obtained by resolving numerically the equation E_b(V_c) = 0, where E_b is given by Eq. (4).

In order to gain insight into the observed experimental characteristics, we show in Figure 5 the results of the calculations with our experimental parameters. The energy landscape in Figure 5(a) is obtained by calculating the magnetic energy SV^* of the CoFeB free layer from Eq. (2) for a set of magnetization angles θ and in-plane fields H_in. The stable magnetization states are observed to be shifted towards the hard anisotropy axis (θ = 90°) with increasing H_in (white dashed-lines). For H_in > H_k,eff,0, the easy axis is aligned with the direction of H_in (fully in-plane). Figure 5(b) shows the voltage dependence of the energy barrier height for various H_in values as determined from Eq. (4). The macrospin model reproduces quantitatively our experimental results shown in Figure 3(a). The remaining small discrepancy could be attributed to the effect of the second-order anisotropy and nonuniformity of the magnetization profile. Further study is needed to precisely understand the contributions of the higher order anisotropy in canted magnetization states and develop improved VCMA-based MTJs.²⁵25. Y. Shiota, T. Nozaki, S. Tamaru, K. Yakushiji, H. Kubota, A. Fukushima, S. Yuasa, and Y. Suzuki, Appl. Phys. Exp. 9, 1 (2015).

In conclusion, we have investigated the dependence of switching voltage and thermal stability on in-plane magnetic field in electric-field-controlled CoFeB/MgO perpendicular magnetic tunnel junctions. Both switching voltage and thermal stability factor decrease with the increase of in-plane magnetic field, with a behavior dominated by a linear dependence for H_in ≪ H_k,eff,0. These results are accurately reproduced by calculations based on a macrospin model, which indicates a tuning with H_in of the stable magnetization states towards the hard anisotropy axis.