Dielectric constant of MgO tunnel barrier with epitaxial strain

Spintronics-based devices utilize the spin degree of freedom and have unique features such as nonvolatility, low power consumption, infinite endurance, and compatibility with CMOS-based technology. The demand for applications of spintronics, such as magnetic sensors and magnetoresistive random access memory (MRAM) is growing rapidly. Magnetic tunnel junctions (MTJs) based on MgO tunnel barriers are key components of spintronics and have been widely used in these applications^1,2. Recently, the voltage-controlled magnetic anisotropy (VCMA) effect^3,4,5,6,7 has attracted attention as a technology to realize low-power spintronics devices such as voltage-controlled MRAM^6,7,8. The VCMA effect was first demonstrated in a 3 d transition metal ferromagnetic layer using a liquid electrolyte³; it was then demonstrated in an all-solid structure with a MgO tunnel barrier^9,10. Currently, structures that use an MgO tunnel barrier as the dielectric layer are the main focus of research on the VCMA effect. However, further enhancement of the VCMA effect is necessary for device applications; this has motivated attempts to incorporate high-k dielectrics as tunnel barriers to obtain greater charge accumulation and thus an enhanced VCMA effect. To date, MgO/HfO₂^11,12,13, MgO/Pb(Zr_xTi_1-x)O₃/MgO¹⁴, SrTiO₃^15,16, and MgO/ZrO₂/MgO¹⁷ have been used as the high-k dielectrics. We experimentally demonstrated the enhancement of the VCMA coefficient through the enhancement of dielectric constant ε_r by establishing a technique to derive ε_r for thin and small tunnel barriers¹³. However, research on the ε_r of tunnel barriers in MTJs is still in the early stages. Even for the MgO tunnel barrier, which has been investigated most intensively, ε_r has not been measured experimentally, and was assumed to be equal to the bulk value. Moreover, we recently reported a large ε_r for the MgO tunnel barrier in an epitaxial MTJ¹⁷; however, the origin of this phenomenon has not yet been elucidated.

In this study, we investigated the ε_r of the MgO tunnel barrier in epitaxial stacks with varying MgO thicknesses. We reproduced a large ε_r for the MgO tunnel barrier in the epitaxial stack and observed a trend of increasing ε_r with decreasing MgO thickness. We interpreted this trend in terms of the epitaxial strain. We also confirmed that variation of ε_r directly affects the VCMA coefficient.

Multilayered epitaxial stacks consisting of MgO (0 or 5 nm)/Cr (50 nm)/Fe (t_Fe nm)/Ir (0.06 nm)/Co (0.1 nm)/MgO (t_MgO nm)/top electrodes were deposited on single-crystal MgO(001) substrates using a combination of molecular beam epitaxy (MBE) and magnetron sputtering techniques (Fig. 1a). Prior to deposition, the MgO substrate was cleaned by in situ annealing at 800 °C. The 5-nm-thick MgO seed layer was grown at 200 °C. The 50-nm-thick Cr buffer layer was grown at 200 °C by electron-beam evaporation or at room temperature (RT) by sputtering, followed by in situ annealing at 800 °C. Ultrathin Fe/Ir/Co layers were deposited at 150 °C, followed by in situ annealing at 250 °C. The MgO tunnel barrier was then deposited at RT and annealed in situ at 250 °C. Then, Cr (1 nm)/Pt (5 nm) or Pt (5 nm) cap layers were sputter-deposited on the MgO tunnel barrier at RT (MOKE stack) to evaluate the magnetic properties by vibrating sample magnetometry (VSM) and magneto-optical Kerr effect (MOKE), while a Fe (10 nm) reference layer and Ta (5 nm)/Ru (7 nm) cap layers were deposited by electron-beam evaporation and sputtering, respectively (MTJ stack), to measure the tunnel magnetoresistance (TMR) effect. Layers other than Cr, Pt, Ru, and Ta were deposited by electron-beam evaporation in the MBE chamber. For comparison, we also prepared a polycrystalline stack composed of Ta (5 nm)/Ru (10 nm)/Ta (5 nm)/Fe₈₀B₂₀ (t_FeB nm)/MgO (t_MgO nm)/top electrode on a thermally oxidized Si substrate. Prior to deposition, the thermally oxidized Si substrate was cleaned by in situ annealing at 400 °C. The Ta/Ru/Ta/Fe₈₀B₂₀ layers were deposited by sputtering at RT, while the MgO layer was deposited by electron-beam evaporation at RT, followed by in situ annealing at 260 °C. On the MgO tunnel barrier, Cr (1 nm)/Pt (5 nm) cap layers were sputter-deposited at RT (MOKE stack) to evaluate the magnetic properties, while Fe₈₀B₂₀ (10 nm)/Ta (5 nm)/Ru (7 nm) layers were sputter-deposited (MTJ stack) to measure the TMR effect. The method for the preparation of a similar polycrystalline stack was described in our previous study¹³. The sample was microfabricated into pillars and used for the capacitance, MOKE, and TMR measurements. We microfabricated pillars (devices) of multiple sizes (S) on one sample: devices with S = 36, 64, 100, and 144 μm² (MOKE device) or S = 22.5, 30, 62.5, and 90 μm² (MTJ device) were used for size-dependent capacitance measurements; S = 80 μm² was used for the MOKE measurements; and S = 10 μm² was used for the TMR measurements. For accurate evaluation of ε_r, we used relatively large device sizes. We note that the capacitance and MOKE or TMR measurements were performed for the same sample but different devices.

a Schematics of the epitaxial stack used in the present study. b Schematic of the equivalent circuit used for the analysis. c f dependence of Z’ (gray circles) and Z” (orange circles) for devices with t_MgO = 4.0 nm and S = 144 μm². d f dependence of −(Z”)⁻¹ for devices with t_MgO = 4.0 nm. The fitted lines are shown as black lines. e S dependence of C_p for devices with 4.0 ≤ t_MgO ≤ 10.0 nm. The colored closed circles represent C_p values obtained from the frequency dependence of Z” considering R_s. The black open circles represent C_p values obtained from the impedance at 1 MHz, ignoring R_s. f t_MgO dependence of ε_r for epitaxial MgO tunnel barriers with 4.0 ≤ t_MgO ≤ 10.0 nm.

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The capacitances of the microfabricated devices were measured using an impedance analyzer (Keysight, E4990A with a 42941 A impedance probe). In-plane X-ray diffraction (XRD) patterns were measured in the 2θ_χ/ϕ geometry using an X-ray diffractometer (Rigaku, SmartLab). The 2θ_χ/ϕscan was performed along the MgO (200) plane. The XRD measurements were performed for the same samples as those used for the capacitance and MOKE measurements. The VCMA effect was investigated by measuring the perpendicular magnetization curve with MOKE (wavelength = 408 nm) while applying a bias electric field, or by measuring the bias electric field dependence of the TMR effect under an in-plane magnetic field for MTJs with orthogonal magnetization configuration. The sign of the bias electric field was defined with respect to the top electrode: a positive (negative) bias induced electron accumulation (depletion) at the ferromagnetic layer/MgO interface. The value of the saturation magnetization of the sample was measured by VSM. All measurements were performed at RT.

Dielectric constant of MgO tunnel barriers

We investigated the ε_r of microfabricated devices of epitaxial stacks consisting of MgO (001) substrate/MgO (5 nm)/Cr (50 nm)/Fe (0.9 nm)/Ir (0.06 nm)/Co (0.1 nm)/MgO (t_MgO nm)/cap (2.0 ≤ t_MgO ≤ 10.0 nm) (MOKE device). We prepared two samples: a sample with four different MgO thicknesses (t_MgO = 4.0, 6.0, 8.0, and 10.0 nm) and a sample with a wedge-shaped MgO layer (2.0 ≤ t_MgO ≤ 3.0 nm). The former had a very thick MgO layer to investigate the thickness dependence of ε_r, the lattice parameter a, and the VCMA coefficient. The MgO thickness of the latter was comparable to that of a typical MTJ used for VCMA studies. Because the resistance change associated with the change in t_MgO is extremely large, we first ensured that an appropriate measurement method was used to evaluate the dependence of ε_r on t_MgO. After these verifications, we investigated the t_MgO dependence of ε_r. To evaluate the ε_r of the MgO tunnel barriers, we assumed the equivalent circuit shown in Fig. 1b, which considers the parallel resistance (R_p), series resistance (R_s), and parallel capacitance (C_p). Here, R_s corresponds mainly to the resistance of the electrode. In the equivalent circuit, the frequency (f) dependence of the real part (Z’) and imaginary part (Z”) of the impedance are expressed by the following equations:

Based on the equivalent circuit, we considered an appropriate method to evaluate the C_p of the devices in the thick and thin t_MgO regions. In this study, to account for R_s, we evaluated C_p using the f dependence of the impedance. The C_p values were compared with those evaluated using our previous method^13,17,18, in which C_p was determined from the impedance at 1 MHz, ignoring R_s. Then, we evaluated the ε_r of the MgO tunnel barrier using the following equation:

Here, ε₀ is the permittivity of a vacuum (8.85 × 10⁻¹² F/m). To remove the nonnegligible parasitic capacitance^13,17,18, we measured the S dependence of C_p and then used the slope of C_p vs. S as C_p/S.

In thick MgO regions (4.0 ≤ t_MgO ≤ 10.0 nm), the resistance of the MgO tunnel barrier (R_p > 10⁸ Ω) exceeds the measurable resistance range of the impedance analyzer. Thus, we evaluated C_p based on the following approximated equations, assuming R_p >> (2πfC_p)⁻¹:

The equations indicate that Z’ converges to R_s with a weak f dependence, while |Z”| decreases with frequency and is inversely proportional to f. Figure 1c shows the f dependence of Z’ and Z” for devices with t_MgO = 4.0 nm and S = 144 μm². We confirmed that Z’ and Z” in Fig. 1c follow the trends of Eqs. (4) and (5), respectively. In this region, accurate evaluation of R_p is difficult. However, C_p can be evaluated from the f dependence of Z” using Eq. (5), which is independent of R_p. Figure 1d shows the f dependence of −(Z”)^-1 for devices with t_MgO = 4.0 nm as an example. By fitting the f dependence of −(Z”)^-1, we obtained the C_p of each device. The fitted lines are indicated by the black lines in Fig. 1d. Figure 1e shows the S dependence of C_p for devices with t_MgO = 4.0, 6.0, 8.0, and 10.0 nm using colored circles. We also plotted the C_p values evaluated using our previous method (determined from the impedance at 1 MHz, ignoring R_s) using open circles. The details of the evaluation method are described in Supplementary Information S1. As discussed in the Supplementary Information, the C_p evaluated using the f dependence of the impedance is more accurate than that evaluated using the impedance at 1 MHz. However, as shown in Fig. 1e, the C_p values evaluated using these two methods were almost identical, and we found that both methods could evaluate C_p with a certain accuracy. By fitting the S dependence of C_p evaluated using the f dependence of the impedance, we obtained C_p/S values of 0.0351, 0.0216, 0.0156, and 0.0120 F/m² for devices with t_MgO = 4.0, 6.0, 8.0, and 10.0 nm, respectively. Figure 1f shows the t_MgO dependence of ε_r for epitaxial MgO tunnel barriers with t_MgO = 4.0, 6.0, 8.0, and 10.0 nm. We found that ε_r tended to increase with decreasing t_MgO.

In thin MgO regions (2.0 ≤ t_MgO ≤ 3.0 nm), we evaluated C_p using Eqs. (1) and (2). Here, the ε_r of the epitaxial MgO tunnel barrier with t_MgO = 3.0 nm was evaluated from the C_p/S obtained from the S dependence of C_p (Fig. 2d). On the other hand, the ε_r values of epitaxial MgO tunnel barriers with 2.2 ≤ t_MgO ≤ 3.0 nm were evaluated from the C_p of one device size (80 μm²) by assuming the parasitic capacitance such that the ε_r of these MgO tunnel barriers is consistent with those with t_MgO = 3.0 nm. Figure 2a–c show the f dependence of Z’ and Z” for devices with t_MgO = 2.2, 2.6, and 3.0 nm. The results presented in these figures are highly consistent with Eqs. (1) and (2). In Fig. 2c, Z” exhibits a minimum at the resonant frequency f_R = (2π)^-1(R_pC_p)^-1/2 (~0.7 MHz). At sufficiently low frequencies, Z’ converges to R_p + R_s, while at sufficiently high frequencies, Z’ converges to R_s. As t_MgO (and thus R_p) decreases, f_R shifts to a higher frequency and finally surpasses the measured frequency range (above 100 MHz for devices with t_MgO < 2.2 nm). C_p and R_p can be evaluated by fitting the f dependence of the Z’ or Z” plot. By fitting the f dependence of the Z’ plot according to Eq. (1), we can evaluate R_s in addition to C_p and R_p. We obtain R_s of ~24 Ω by fitting Z’ for several devices using Eq. (1). However, for appropriate fitting using Eq. (1), the fitted data should include the full transition of Z’ from R_p + R_s to R_s, as shown in Fig. 2b, c. When the transition is incomplete, such as in Fig. 2a, R_s cannot be evaluated correctly, resulting in inaccurate evaluation of C_p and R_p. On the other hand, by fitting the f dependence of the Z” plot according to Eq. (2), we can evaluate C_p and R_p with greater accuracy if the fitted plot includes the minimum of Z” at f_R, as shown in Fig. 2a–c. See Supplementary Information S2 for a more detailed consideration of the fitting accuracy. Therefore, we determined the C_p values of devices with t_MgO ≥ 2.2 nm from the fitting of the f dependence of Z” according to Eq. (2). The fitting curves are indicated by the black lines in Fig. 2a–c. Figure 2d shows the S dependence of C_p for devices with t_MgO = 3.0 nm (red closed squares). We also plotted the C_p values evaluated using our previous method (determined from the impedance at 1 MHz, ignoring R_s) as open squares. The C_p values evaluated using these two methods were almost identical, indicating that the influence of R_s was negligible. By fitting the S dependence of C_p evaluated using the f dependence of the impedance, we obtained the C_p/S of 0.0469 F/m² for the devices with t_MgO = 3.0 nm. Figure 2e shows the t_MgO dependence of ε_r for the epitaxial MgO tunnel barriers with 2.2 ≤ t_MgO ≤ 3.0 nm (blue closed circles). We found that ε_r tended to increase as t_MgO decreased, even in the range of 2.2 ≤ t_MgO ≤ 3.0 nm. We observed a large ε_r of 15.9–17.5 for the epitaxial MgO tunnel barriers with 2.2 ≤ t_MgO ≤ 3.0 nm, which is more than 50% greater than that of the MgO bulk (ε_r ~ 10). In Fig. 2e, we also plot ε_r evaluated by our previous method (determined from the impedance at 1 MHz, ignoring R_s) using open circles. We found that the ε_r values obtained by our previous method are smaller than those evaluated from the f dependence of the impedance for devices with t_MgO < 2.4 nm. In other words, our previous method underestimated ε_r for the thin MgO region. Neglecting R_s in Eq. (1) results in an overestimation of R_p and thus an underestimation of C_p and ε_r. We found that the influence of the neglect of R_s in the evaluation of ε_r was obvious for devices with t_MgO < 2.4 nm, where R_p < 1 kΩ (Fig. 2f). Figure 2f shows the t_MgO dependence of R_p for devices with 2.2 ≤ t_MgO ≤ 3.0 nm (left axis). The RA values, which are the product of R_p and S (=80 μm²), are also shown on the right axis. R_p increases exponentially with increasing t_MgO because of the nature of the tunnel conductance. We confirmed that the RA values in this study are similar to those reported in previous reports^19,20,21. In other words, the MgO layer thickness in this study is almost the same as those in previous reports.

a–c f dependence of Z’ (gray circles) and Z” (orange circles) for devices with t_MgO = 2.2, 2.6, and 3.0 nm. The black lines indicate the fitting curves obtained using Eq. (2). d S dependence of C_p for the epitaxial MgO tunnel barrier with t_MgO = 3.0 nm. The red closed squares represent C_p values obtained from the frequency dependence of Z” considering R_s. The open squares represent C_p values obtained from the impedance at 1 MHz, ignoring R_s. e t_MgO dependence of ε_r for epitaxial MgO tunnel barriers with 2.2 ≤ t_MgO ≤ 3.0 nm obtained by fitting the f dependence of Z” (blue closed circles) and obtained from the impedance at 1 MHz (open circles). ε_r of the polycrystalline MgO tunnel barrier with t_MgO = 2.2 nm is also represented by the black triangle. f t_MgO dependence of R_p (left axis) and RA (right axis) for epitaxial MgO tunnel barriers with 2.2 ≤ t_MgO ≤ 3.0 nm.

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We also investigated ε_r for devices with a polycrystalline MgO tunnel barrier composed of Ta (5 nm)/Ru (10 nm)/Ta (5 nm)/Fe₈₀B₂₀ (1.6 nm)/MgO (2.2 nm)/cap (MOKE device) and obtained ε_r = 11.8 for the polycrystalline MgO tunnel barrier with t_MgO = 2.2 nm. The ε_r of the polycrystalline MgO tunnel barrier is indicated by the black triangle in Fig. 2e. See Supplementary Information S3 for further details. The value of ε_r = 11.8 is slightly larger than that of the MgO bulk (~10.0), but it is smaller than that of the epitaxial MgO tunnel barriers (15.9–17.5), indicating the importance of the epitaxial stack in obtaining large ε_r values.

Evaluation of epitaxial strain of MgO tunnel barriers

Here, we focus on the effect of the epitaxial strain of the MgO tunnel barrier as the origin of the variation in ε_r, as shown in Figs. 1f and 2e. The strain-induced increase in ε_r in rocksalt oxides has previously been investigated both theoretically^22,23,24 and experimentally^25,26. When the c-axis is stretched due to compressive strain, the electron orbital overlap between cations and anions in the c-direction decreases. Softening of the optical phonon mode then occurs, resulting in an increase in ε_r. Such compressive strain can occur in the epitaxial stack due to lattice mismatch, as the (sqrt{2}a) of the Cr buffer layer (4.08 Å) is much smaller than the a of MgO (4.21 Å). Thus, we investigated the changes in the lattice constant, a, of the MgO tunnel barrier of the samples with respect to t_MgO. Figure 3a shows the in-plane XRD patterns of samples with t_MgO = 4.0, 6.0, 8.0, and 10.0 nm. The dashed black line and blue arrows indicate the MgO (002) peak positions of the MgO substrate and MgO tunnel barriers, respectively. The (002) peak of the MgO tunnel barriers exists at a higher angle than that of the MgO substrate, indicating a smaller a. With increasing t_MgO, the peak position shifts to a lower angle. Figure 3b shows the t_MgO dependence of a of the MgO tunnel barriers. The a value of the 4-nm-thick MgO is 4.15 Å, which is between the (sqrt{2}a) values of Cr and bulk MgO. This indicates that the MgO tunnel barrier is tetragonally compressed because of restraint from the underlying layers, such as the Cr buffer layer. With increasing t_MgO, the a of the MgO tunnel barrier increases and approaches that of bulk MgO. This trend may reflect the lattice relaxation of the MgO tunnel barrier with the introduction of misfit dislocations. The detection depth of the in-plane XRD measurements is greater than t_MgO. Therefore, the obtained a value represents the mean value throughout the MgO tunnel barrier. We deduce that the a of the MgO tunnel barrier changes gradually along the film thickness direction with the introduction of misfit dislocations, resulting in a change in the mean a value with t_MgO. Figure 3c shows a plot of the ε_r of the MgO tunnel barriers against the mean a. The lattice strain, Δa, is also shown on the upper axis. We find that as a decreases, corresponding to larger compressive strain, ε_r increases. This result demonstrates the increase in ε_r of the MgO tunnel barrier due to epitaxial strain. Based on previous reports^22,23,25, as compressive strain is applied to rocksalt oxide, softening of the optical phonon mode occurs, and the phonon frequency decreases. When a critical strain is applied and the phonon frequency becomes imaginary, the inversion symmetry along the c-axis is removed, and the rocksalt oxide becomes ferroelectric. The ε_r value increases with increasing compressive strain and diverges at the critical strain. The critical strain for MgO is estimated to be −7.4%²², which is greater than the strain of the 4.0-nm-thick MgO tunnel barrier in this study (−1.5%). Therefore, Fig. 3c may represent a nonlinear increase in ε_r toward the critical strain. On the other hand, as previously discussed, the increase in ε_r was smaller for the MgO tunnel barrier in the polycrystalline stack. In the polycrystalline stack, because the MgO (001) plane preferentially grows on the amorphous Fe₈₀B₂₀ layer, the MgO tunnel barrier may receive less lattice strain from the underlying layer. The smaller ε_r value of the polycrystalline MgO tunnel barrier ensures the dominant contribution of the epitaxial strain in enhancing the ε_r of the epitaxial MgO tunnel barriers.

a In-plane 2θ_χ/ϕ XRD patterns of samples with t_MgO = 4.0, 6.0, 8.0, and 10.0 nm along the MgO (200) plane. b MgO thickness dependence of the lattice parameter a of the MgO tunnel barrier. c Variation in ε_r of the MgO tunnel barrier with respect to the lattice parameter a (lower axis) and lattice strain Δa (upper axis).

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Influence of the variation in the dielectric constant on the VCMA effect

Finally, we examined the effect of the ε_r variation on the VCMA coefficient. The VCMA effect was investigated by measuring the perpendicular magnetization curve using MOKE while a bias electric field was applied. We designed the epitaxial stacks such that the ferromagnetic layer exhibited moderate in-plane magnetic anisotropy to investigate the change in the magnetic anisotropy induced by a bias electric field from the perpendicular magnetization curve. Figure 4a, b show the perpendicular magnetization curves under a bias electric field for devices with t_MgO = 4.0 and 10.0 nm, respectively. For both devices, a clear increase in the saturation magnetic field, H_k, was observed upon the application of a positive electric field (orange and red curves), whereas a decrease in H_k was observed upon the application of a negative electric field (light blue and blue curves). Based on the perpendicular magnetization curves measured by MOKE and the saturation magnetization values measured by VSM, we evaluated the effective magnetic anisotropy energy, K_eff, using the same procedure as that in our previous reports^13,27,28. Figure 4c shows the bias electric field dependence of K_efft_FM for the devices with t_MgO = 4.0 and 10.0 nm, where t_FM denotes the total thickness of the Fe/Ir/Co ferromagnetic layers, i.e., 1.06 nm. All samples exhibited a linear magnetic anisotropy change under the bias electric field. The slope represents the VCMA coefficient. The evaluated VCMA coefficients were −255 and −212 fJ/Vm for the devices with t_MgO = 4.0 and 10.0 nm, respectively. Figure 4d shows the t_MgO dependence of the VCMA coefficient for the devices with 4.0 ≤ t_MgO ≤ 10.0 nm. The VCMA coefficient tended to increase with decreasing t_MgO. This trend is the same as that for the ε_r variation shown in Fig. 1f. In other words, we confirmed the increase in the VCMA coefficient through epitaxial strain-induced ε_r enhancement. Figure 4e shows the VCMA coefficient plotted versus ε_r for devices with t_MgO = 4.0, 6.0, 8.0, and 10.0 nm. The VCMA coefficient increases almost proportionally with increasing ε_r; comparing devices with t_MgO = 4.0 and 10.0 nm, it is observed that the VCMA coefficient increases by 1.2 times (−216.5 to −256.0 fJ/Vm), and ε_r increases by 1.2 times (13.6 to 15.9). Figure 4f shows the t_MgO dependence of the VCMA coefficient for the devices with 2.2 ≤ t_MgO ≤ 3.0 nm. An increasing trend in the VCMA coefficient with decreasing t_MgO is observed for devices with t_MgO ≥ 2.4 nm, taking the relatively large measurement dispersion of the VCMA coefficient into account (blue closed circles). On the other hand, for t_MgO < 2.4 nm, VCMA deviates from the increasing trend and gradually decreases with decreasing t_MgO (blue open circles). This deviation may be due to the influence of the voltage drop at the electrode as the resistance of the MgO tunnel barrier approaches the resistance of the electrode. From the capacitance measurements, we estimated R_p of the 2.2-nm-thick MgO tunnel barrier to be approximately 300 Ω (Fig. 2f), whereas the resistance of the electrode (R_s) was 24 Ω. The resistance of the probe also contributes to the voltage drop. Considering these resistance values, a voltage drop of approximately 10%, and thus a decrease of approximately 10% in the VCMA coefficient, is expected to occur for devices with t_MgO = 2.2 nm. Note that the relatively large device size of the MOKE devices (80 μm²) reduced R_p, leading to an obvious voltage drop at the electrode for the device with t_MgO = 2.2 nm. Because the typical MTJ size is several orders of magnitude smaller, such a voltage-drop effect is not visible until the MgO film becomes much thinner.

a, b Perpendicular magnetization curves under an electric field for devices with t_MgO = 4.0 and 10.0 nm measured by MOKE. c Electric field dependence of K_efft_FM for devices with t_MgO = 4.0 and 10.0 nm. d, e t_MgO and ε_r dependence of the VCMA coefficient for devices with 4.0 ≤ t_MgO ≤ 10.0 nm. f t_MgO dependence of the VCMA coefficient for devices with 2.2 ≤ t_MgO ≤ 3.0 nm.

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In the thick MgO region (4.0 ≤ t_MgO ≤ 10.0 nm), ε_r, lattice strain, and VCMA coefficient show consistent tends, confirming the reliable evaluation of ε_r. On the other hand, in the thin MgO region, since the thickness-dependent trend of the VCMA coefficient deviates from that of ε_r, the reliability of the ε_r evaluations is unclear. Therefore, we investigated the VCMA effect and ε_r of MTJ stacks with smaller device sizes and compared their thickness-dependent trends. We prepared a sample of an epitaxial MTJ stack consisting of MgO (001) substrate/Cr (50 nm)/Fe (0.5 nm)/Ir (0.06 nm)/Co (0.1 nm)/MgO (t_MgO nm)/Fe (10 nm)/cap with three different MgO thicknesses (t_MgO = 2.0, 2.5, and 3.0 nm), as shown in Fig. 5a. In this stack, the top 10 nm-thick Fe acted as a reference layer with an in-plane magnetic easy axis, resulting in an orthogonal magnetization configuration with the bottom Fe/Ir/Co perpendicular free layers under zero magnetic field. The application of an in-plane magnetic field tilted the magnetization of the Fe/Ir/Co free layers to the in-plane direction, which can be observed through the TMR effect. By investigating the bias electric field dependence of the TMR effect, we investigated the VCMA effect using the same procedure as that in our previous report²⁹. The measurement procedures are described in detail in Supplementary Information S4. Figure 5b shows the t_MgO dependence of the VCMA coefficient for the epitaxial MTJ devices with t_MgO = 2.0, 2.5, and 3.0 nm. At each t_MgO, the VCMA coefficients of more than 10 devices were measured. The error bars account for the variation in the VCMA coefficient for each device as well as the variation in t_MgO within the sample (3%). Note that the nonlinear uncertainty of the VCMA coefficient caused by the variation in the free layer thickness is not included in the error bars. The VCMA coefficient remains almost constant or increases slightly with decreasing t_MgO from 3.0 to 2.0 nm, taking the error bars into consideration. By measuring MTJs with a small device size, we confirmed that the VCMA coefficient does not decrease even when t_MgO is reduced to 2.0 nm. Figure 5c shows the t_MgO dependence of ε_r for MTJ devices with t_MgO = 2.0, 2.5, and 3.0 nm. The error bars account for the variation in C_p for each device as well as the variation in t_MgO within the sample (3%). For devices with t_MgO = 2.0 nm, the uncertainty of the fitting f dependence of Z” (1%), as discussed in Supplementary Information S2, is also considered. We obtained a thickness-dependent trend consistent with the VCMA coefficient; ε_r also remains almost constant or increases slightly with decreasing t_MgO, taking the error bars into consideration. Note that the rate of increase in ε_r in the range of 4.0 ≤ t_MgO ≤ 10.0 nm is as small as 3% per nm. While it is difficult to determine whether ε_r increases at this rate in the range of 2.0 ≤ t_MgO ≤ 3.0 nm, it is confirmed that the ε_r is at least maintained at t_MgO = 2.0 nm. We also investigated the VCMA effect and ε_r of MTJ devices with polycrystalline MgO tunnel barriers for the same t_MgO range (t_MgO = 2.0, 2.5, and 3.0 nm) and confirmed that the changes in the VCMA coefficient and ε_r in this range are within the error bars (see Supplementary Information S5). Finally, from the perspective of practical application, we would like to comment on the ε_r of devices with lower t_MgO and smaller device sizes. With respect to lower t_MgO, if we consider the origin of the variation in the lattice strain shown in Fig. 3b as lattice relaxation accompanied by the introduction of misfit dislocations, the lattice strain becomes unchanged below a certain critical thickness. According to the transmission electron microscopy (TEM) image of the epitaxial MgO tunnel barrier fabricated by electron-beam evaporation technique in a previous report³⁰, misfit dislocations are rarely observed in the 2.3 nm-thick MgO layer, except at the interface. This suggests that the lattice strain and thus the ε_r of the epitaxial MgO tunnel barrier will not increase significantly below this thickness. We assume that even when the t_MgO decreases further, such a lattice strain-induced increase in ε_r is maintained, and ε_r converges to approximately 17−18. On the other hand, independent of the lattice strain, if an interfacial layer with a lower ε_r is formed, the ε_r of the dielectric film decreases with decreasing film thickness. In this study, such a decrease in ε_r was not clearly observed at t_MgO = 2.0 nm, indicating the absence of an apparent interfacial layer at the high-quality interface of epitaxial MgO-MTJs. Another theory indicates that even in the absence of an interfacial layer, ε_r of the dielectric film may decrease with thickness due to the intrinsic size effect^31,32. However, the size effect is remarkable when the bulk ε_r of the dielectric film is very large (e.g., ε_r > 100). Our estimation based on ref. ³² indicated that a decrease in ε_r of only ~8% will occur for a 1.0-nm-thick dielectric film when the bulk ε_r is 10 (see Supplementary Information S6). Since the epitaxial MgO tunnel barrier has a relatively large ε_r of ~18, we assume that a 10−20% decrease in ε_r may occur for 1.0-nm-thick MgO. With regard to device size, since lattice strain is introduced during the epitaxial growth of the MgO tunnel barrier, the lattice strain is not relieved during the subsequent microfabrication process. While there may be other factors that affect ε_r in addition to the lattice strain, generally, ε_r is considered to be less sensitive to device size. In addition, past size-dependent VCMA coefficient measurements suggested that the VCMA coefficient does not decrease with decreasing device size down to 50 nmϕ ^33,34. Therefore, we believe that ε_r does not decrease with decreasing device size; however, further verification is required.

a Schematics of the epitaxial MTJ stack used in the present study. b t_MgO dependence of the VCMA coefficient for epitaxial MgO MTJ devices with t_MgO = 2.0, 2.5, and 3.0 nm. c t_MgO dependence of ε_r for epitaxial MgO MTJ devices with t_MgO = 2.0, 2.5, and 3.0 nm (blue closed circles). The ε_r of epitaxial MgO MOKE devices are also shown by open circles.

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In this study, we demonstrated an increase in the ε_r of MgO tunnel barriers owing to lattice strain and an associated increase in the VCMA coefficient in epitaxial stacks, which is smaller in polycrystalline stacks. To date, large VCMA coefficients exceeding −300 fJ/Vm have been observed only in epitaxial MTJs^19,35,36,37, whereas VCMA coefficients of up to approximately −100 fJ/Vm have been observed in polycrystalline stacks^{38,39,40,41,42}. This difference mainly be due to the difference in the ferromagnetic layers. In epitaxial MTJs, a large VCMA coefficient has been realized through precise subnanometer-scale control of the thickness of ferromagnetic and heavy metal layers. It has also been reported that the presence of B, which is commonly used in polycrystalline MTJs, suppresses the increase in the VCMA coefficient caused by heavy metal doping³⁸. On the other hand, this study clarified the nonnegligible influence of the differences in the ε_r of MgO tunnel barriers on the VCMA coefficient. Our study provides a new perspective that the strain-induced ε_r enhancement of the MgO tunnel barrier is another effective approach to increase the VCMA coefficient, in addition to the development of ferromagnetic materials. Strain engineering makes simple rocksalt tunnel barriers more attractive.

In this study, we systematically investigated the dielectric constant (ε_r), lattice parameter (a), and VCMA coefficient of MgO tunnel barriers in epitaxial stacks. We observed a trend of increasing ε_r of the MgO tunnel barrier with decreasing MgO thickness. We obtained much larger ε_r values of approximately 17 for epitaxial MgO tunnel barriers with 2.0 ≤ t_MgO ≤ 3.0 nm than for bulk MgO (~10). We also observed an increase in the VCMA coefficient associated with the increase in ε_r with decreasing MgO thickness. In-plane XRD measurements revealed that the mean a value decreased with decreasing MgO thickness, indicating the presence of tetragonal compression of the MgO tunnel barrier due to epitaxial strain. We concluded that tetragonal compression enhanced the ε_r of the MgO tunnel barrier and thus the VCMA coefficient in the epitaxial stacks. The strain-induced increase in ε_r was maintained at t_MgO = 2.0 nm. Strain engineering is an effective approach to improve the characteristics of simple rocksalt tunnel barriers.