Introduction

Ever since it was discovered that magnetization dynamics can be controlled by spin transfer torque (STT)1,2, the approach has been widely studied and applied in data storage and memory applications, such as microwave-assisted magnetic recording (MAMR) in hard disk drives (HDDs) and magnetoresistive random access memory (MRAM)3,4,5,6,7,8. Recently, STO is also gathering expectations for neural networks applications9,10,11. While typical ferromagnetic transition metals show spin torque oscillation (STO) frequencies of several GHz12,13,14,15, antiferromagnets are presumed to have STO frequencies in the THz region; this assumption is in light of various theoretical studies, including those on magnetic resonance frequency16,17,18,19,20,21,22,23,24,25,26,27,28,29. However, usable STOs have never been achieved experimentally in antiferromagnets because of the strong exchange coupling between neighboring ions. Therefore, artificial magnetic structures such as synthetic antiferromagnetic coupling layers30,31,32 and quasi-antiferromagnets comprising biquadratic magnetic coupling33,34 have been proposed as an alternative to increase the STO frequency. On the other hand, an orthogonal magnetization multilayer comprising in-plane and perpendicular anisotropic magnetic layers was reported to have a high spin transfer efficiency that allows an STO to be excited easily, suggesting a spin transfer torque oscillator with high frequency and low power consumption35,36,37,38,39,40,41,42. The high efficiency of the STT originates from the small angle between the magnetizations of the two magnetic layers, which unfortunately reduces the current density range that shows a stable STO, considering magnetization switching occurs frequently. Therefore, a biquadratic magnetic coupling33,34,43,44,45,46,47,48,49,50,51,52,53,54,55 was introduced between the two magnetic layers in the orthogonal configuration to suppress complete magnetization switching, thereby improving the stability of the STO. Biquadratic magnetic coupling is an interlayer exchange interaction between two ferromagnetic (FM) layers separated by a thin spacer. In general, the magnetic coupling energy E is expanded to a higher-order equation by considering the quadratic term as E =  − A12M1∙M2 − B12 (M1∙M2)2, where M1 and M2 are the unit magnetizations in the first and second FM layers, respectively, and A12 and B12 are the bilinear and biquadratic coupling coefficients, respectively. A12 contributes to 0° or 180° magnetic coupling, whereas B12 contributes to + / − 90° magnetic coupling. Typically, + / − 90° coupling is realized under the conditions of |A12|< 2|B12| and B12 < 0, using a suitable layer as a spacer. The values of A12 and B12 depend on the spacer layer material and the magnetic material, respectively, and values of 0 erg/cm2 to –0.24 erg/cm2 for A12 and − 0.005 erg/cm2 to–2.0 erg/cm2 for B12 have been reported33,34,43,44,45,46,47,48,49,50,51,52,53,54,55. Previously, we reported that biquadratic coupling simply works as an effective field and increases the STO frequency in the quasi-antiferromagnet Co90Fe1033,34. However, the frequency was limited to 15 GHz under a realistic current density, using a multilayer with two in-plane magnetization layers. After that, we reported that a high frequency was obtained by applying biquadratic coupling to an orthogonal configuration, but there were still remained issues of frequency stability and long transient time42. In this study, we report a numerical experiment of STO behavior in an orthogonal magnetization configuration with biquadratic coupling. Additionally, we investigate the initial state to obtain a fast response with a short transient time before the stable STO occurs.

Methods

Calculation model

The magnetization dynamics were investigated by solving the Landau–Lifshitz–Gilbert (LLG) equation with an STT term, given by

$$\begin{array}{c}\frac{d\mathbf{m}}{dt}=-\gamma \left(\mathbf{m}\times {\mathbf{H}}_{\mathbf{e}\mathbf{f}\mathbf{f}}\right)+\alpha \left(\mathbf{m}\times \frac{d\mathbf{m}}{dt}\right)-\frac{g{\mu }_{B}Jp}{{M}_{s}{d}_{i}e}\left(\mathbf{m}\times \left({\mathbf{m}}_{\mathrm{p}}\times \mathbf{m}\right)\right)\end{array}$$
(1)

where m and \({\mathbf{m}}_{\mathrm{p}}\) are the normalized magnetization of the top free layer and bottom pinned layer, respectively, γ is the gyromagnetic ratio, αis the damping constant, \(g\) is the gyromagnetic splitting factor, \({\mu }_{B}\) is the Bohr magneton, J is the current density, p is the polarity of current, Ms is the saturation magnetization of the top layer, di is the thickness of the top layer, and Heff is the effective field, which consists of the following fields: Heff = HK + Hexf + Hex + HST + Hbq + Hbl, where HK is the magnetic anisotropy field, Hexf is the external magnetic field, Hex is the exchange coupling field determined by the exchange stiffness constant A, HST is the stray field that depends on the saturation magnetization of the magnetic material, Hbq is the biquadratic exchange field determined by the biquadratic coefficient B12, and Hbl is the bilinear exchange field determined by the bilinear coefficient A12. When the two ferromagnetic (FM) layers, i and j, have normalized magnetizations mi and mj, respectively, the bilinear and biquadratic exchange fields Hbl and Hbq are given by56

$${\mathbf{H}}_{\mathrm{bl},i}=\frac{{A}_{12}}{{\mu }_{0}{{M}_{s}}_{,i}{d}_{i}}{\mathbf{m}}_{j}$$

and

$$\begin{array}{c}{\mathbf{H}}_{\mathrm{bq},i}=\frac{{2B}_{12}}{{{M}_{s}}_{,i}{d}_{i}}\left[\begin{array}{c}{m}_{i,x}{m}_{j,x}^{2}+{m}_{j,x}\left({m}_{i,y}{m}_{j,y}+{m}_{i,z}{m}_{j,z}\right)\\ {m}_{i,y}{m}_{j,y}^{2}+{m}_{j,y}\left({m}_{i,x}{m}_{j,x}+{m}_{i,z}{m}_{j,z}\right)\\ {m}_{i,z}{m}_{j,z}^{2}+{m}_{j,z}\left({m}_{i,x}{m}_{j,x}+{m}_{i,y}{m}_{j,y}\right)\end{array}\right]with\,i\ne j\end{array}$$
(2)

where Ms,i is the saturation magnetization of the magnetic material of the top layer. The xy plane and z-axis are the in-plane and perpendicular directions, respectively, as shown in Fig. 1.

Figure 1
figure 1

Calculation model with an orthogonal structure.

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In the orthogonal configuration, the top and bottom FM layers are assumed to be i and j with in-plane and perpendicular magnetic anisotropy, respectively. The bilinear exchange field Hbl,i is parallel to the magnetization mj, and the biquadratic exchange field Hbq,i becomes

$$\begin{array}{c}{\mathbf{H}}_{\mathrm{bq},i}=\frac{{2B}_{12}}{{{M}_{s}}_{,i}{d}_{i}}\left[\begin{array}{c}0\\ 0\\ {m}_{i,z}\end{array}\right]\end{array}$$
(3)

This indicates that Hbq is parallel to mj for B12 > 0 and antiparallel to mj for B12 < 0. Because the biquadratic magnetic coupling becomes apparent under the condition B12 < 0, the direction of Hbq is parallel or opposite to mj when the biquadratic exchange magnetic coupling is realized. Here, the STT term is parallel to mj in the LLG equation, so that the biquadratic exchange coupling Hbq is in the opposite direction to the STT. Considering that Hbq is dominant in the effective field Heff as well as HST, the biquadratic exchange coupling Hbq is important for suppressing the complete magnetization reversal from the in-plane to the perpendicular direction, resulting in a stable STO. The magnetic moment of the top layer is expected to exhibit a gyro motion around the z-axis.

In the proposed model, the orthogonal configuration consisted of FePt 2 nm/spacer 2 nm/Co90Fe10, Ni80Fe20, or Ni 2 nm. The device was disk-shaped with a diameter of 320 nm. The bottom layer of FePt had a perpendicular anisotropy, with Hk = 15,000 Oe and saturation magnetization Ms = 800 emu/cc57,58. The bottom FM layer (j) has the fixed magnetization by setting mj,x = mj,y = 0, and mj,z = 1 and as the current flows through its huge Hk to maintain perpendicular magnetization. The top layer had an in-plane magnetic anisotropy: Co90Fe10 had Hk = 35 Oe, Ms = 1450 emu/cc33 and a damping constant \(\mathrm{\alpha }\) of 0.035; Ni80Fe20 had Hk = 2 Oe, Ms = 825 emu/cc and a damping constant \(\mathrm{\alpha }\) of 0.00859; and Ni had Hk = 2 Oe, Ms = 510 emu/cc and a damping constant \(\mathrm{\alpha }\) of 0.008860. The bilinear coefficient A12 was set as 0 for simplicity and the biquadratic coefficient B12 was set to − 0.6, where B12 was reported in the experimental value of the spacer Fe-O33. Both A12 and B12 are realistic values from reports so far33,34,43,44,45,46,47,48,49,50,51,52,53,54,55. The magnetic unit cell size was 5 nm × 5 nm × 2 nm, and 64 × 64 × 3 cells were calculated. The exchange stiffness constant A was 1 × 10−6 erg/cm and the gyromagnetic ratio γ was 1.76 × 107 Oe−1 s−1. The calculation step dt was 10 fs.

In the first step, we calculated the magnetization relaxation after saturating the magnetization along the z- and y-axes. Then, the current was made to flow through the layers, from the top to the bottom layer. Because the required current density for the STO generally depends on the saturation magnetization Ms, we varied the current density from 8.0 × 107 A/cm2 to 20.0 × 107 A/cm2 for the Co90Fe10 top layer, and from 0.5 × 107 A/cm2 to 6.0 × 107 A/cm2 for the Ni80Fe20 and Ni top layers.

Results and discussion

Static and dynamic properties with z-axis magnetization saturation in initial state

First, we calculated the magnetization relaxation subject to the initial condition that the magnetization of the top layer was out-of-plane, i. e., in the z-axis, as shown in Fig. 2a. Figure 2b–d show the calculated magnetization maps after relaxation in the top layers of Co90Fe10, Ni80Fe20, and Ni, respectively. Figure 2e–g show the side views of the magnetization configuration of the top and bottom layers, which correspond to the areas surrounded by black lines in Fig. 2b–d, where all magnetizations in the y-direction were superimposed on each x position. Neither external fields nor electrical currents were applied here. In this case, the exchange stiffness energy acted equally on the magnetizations of adjacent cells, causing the relaxed state of the top layer to become a vortex state, as shown in Fig. 2b–d. The bottom layer of FePt exhibited perpendicular magnetization owing to the sufficiently high perpendicular anisotropy energy.

Figure 2
figure 2

[Top] Top views of the magnetization configuration of the top layers for (a) the initial state of z-axis magnetization saturation for Co90Fe10 2 nm, (b) the relaxed state of Co90Fe10 2 nm, (c) the relaxed state of Ni80Fe20 2 nm, and (d) the relaxed state of Ni 2 nm when A12 = 0 and B12 =  − 0.6. In the initial state, the configuration does not depend on the material of the top layer. [Bottom] Side views of the magnetization configuration in bottom FePt 2 nm/spacer 2 nm/top layer 2 nm when the top layer is (a) the Co90Fe10 2 nm in the initial state, (b) the relaxed state of Co90Fe10 2 nm, (c) the relaxed state of Ni80Fe20 2 nm, and (d) the relaxed state of Ni 2 nm, corresponding to the enclosed area in (e–h). The top and bottom arrows show the magnetization of the top and bottom layers, respectively. Magnetic moments in the y-direction are superimposed on each x position.

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In the next step, the current flowed through the device from the top to the bottom layers. Figure 3a–c show the [(i–iii)] time-domain magnetization precession, [(iv)-(vi)] Fast Fourier transform (FFT) spectra, and [(vii)-(ix)] side views of the magnetization configuration of the top and bottom layers at 20 ns after the current flow, when B12 is 0.0 or -0.6 for (a) Co90Fe10, (b) Ni80Fe20, and (c) Ni, respectively. The electrical current density was (i) 10 × 107 A/cm2, (ii) 15 × 107 A/cm2, and (iii) 20 × 107 A/cm2 for Co90Fe10 in Fig. 3a, and (i) 1.5 × 107 A/cm2, (ii) 3.5 × 107 A/cm2, (iii) and 6.0 × 107 A/cm2 for Ni80Fe20 and Ni in Fig. 3b,c. Furthermore, we tuned the current density to obtain the stable STO considering this depends on the top layer materials, as previously discussed. The calculated data under the wide current density, including Fig. 3, are also shown in Fig. S1, S2 and S3 in Supplementary material.

Figure 3
figure 3

STO performances for the top layer of (a) Co90Fe10, (b) Ni80Fe20, and (c) Ni in the orthogonal configuration with an out-of-plane initial state, namely the z-axis. (i–iii) Time-domain magnetization precessions Mx/Ms, (iv–vi) Fast Fourier transform spectra, and (vii)-(ix) side views of magnetization configuration. The light blue and orange lines denote the results for B12 = 0.0 and B12 =  − 0.6, respectively. For the time-domain magnetization precessions Mx/Ms, the electrical current density was (i) 10 × 107 A/cm2, (ii) 15 × 107 A/cm2, and (iii) 20 × 107 A/cm2 for Co90Fe10, and (i) 1.5 × 107 A/cm2, (ii) 3.5 × 107 A/cm2, and (iii) 6.0 × 107 A/cm2 for Ni80Fe20 and Ni.

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We now focus on the time domains when the current density is increased, as shown in Fig. 3b,c [(i)-(iii)]. For all top layers, an STO was observed with a B12 of either 0.0 or -0.6 at a relatively low current density, shown in (i). However, as shown in (ii) and (iii), as the current density increased, the stable STO with an almost immutable Mx/Ms is lost; in other words, the degradation of Mx/Ms when B12 = 0.0 is larger compared to when B12 = -0.6. This means that by introducing biquadratic magnetic coupling, we can expand the electric current region where the stable STO is realized. Therefore, the current density can be increased, which results in a high frequency in the STO. Additionally, the FFT spectra in (iv)-(vi) show that the STO frequency is higher for B12 = -0.6 than B12 = 0.0, even for the same current density. We also calculate the quality factor Q. The FFT curve was fitted with a Gaussian distribution while changing the standard deviation σ. The quality factor was derived from the FWHM of the fitting curve when the residual error between Gaussian distribution curve and FFT curve is minimum. Since the quality factor Q increased by introducing B12, the extrinsic disturbance decreased and the ideal frequency became evident, resulting a high STO frequency. This was supported by the side views of the magnetization in (vii–ix). The variation of magnetization precession angle of the top layer is larger when B12 = 0.0 than B12 = −0.6 for the same current density in the same top layer materials. Moreover, the variation of the precession angle led to a poor Q factor. The detail comparison of angle variation is shown in Supplementary material.

Changing the top layer from Co90Fe10 and Ni80Fe20 to Ni, Ms becomes a small value and the current density required to realize the STO can be reduced. The combination of biquadratic coupling and Ms reduction is another possible approach for improving the frequency, as reported in Ref.61.

In conclusion, we revealed the STO characteristics in an orthogonal magnetization sample with biquadratic coupling. We found that the transient time until the stable STO was approximately 5–15 ns, which is too long for oscillators to be ignored. Therefore, in the following, we find the optimal initial state for a short transient time.

Static and dynamic properties with y-axis magnetization saturation in initial state

Figure 4a shows the initial magnetization state before relaxation, where the magnetization of the top layer is saturated in-plane, i. e., the y-axis, by a sufficient external field. The calculated magnetization maps after relaxation in the top layers, Co90Fe10, Ni80Fe20, and Ni, are shown in Fig. 4b–d, respectively, when neither external fields nor electrical currents were applied. All layers exhibited typical magnetic domains with in-plane magnetization, i.e., a single domain or onion domain, with a domain wall where the magnetization gradually rotated. Technically, only the Co90Fe10 top layer had an onion domain; the Ni80Fe20 and Ni top layers exhibited a single domain with magnetization at an angle of 45° from the x-axis owing to the difference in the magnetostatic energy that varied with the saturation of the magnetization. On comparing Figs. 2 and 4, we see that the relaxed top layer magnetization structure depends on whether the magnetization was initially saturated on the z-axis or y-axis. The side views of the magnetization configuration of the top and bottom layers are shown in Fig. 4e–g. The magnetization of the bottom layers of the three materials were along the z-axis, and the magnetization of the top layers were oriented along the xy-plane, forming an orthogonal configuration. The orthogonal structure was regularly obtained regardless of the initial state prior to relaxation.

Figure 4
figure 4

[Top] Top views of the magnetization configuration of the top layers for (a) the initial state of y-axis magnetization saturation for Co90Fe10 2 nm, (b) the relaxed state of Co90Fe10 2 nm, (c) the relaxed state of Ni80Fe20 2 nm, and (d) the relaxed state of Ni 2 nm when A12 = 0 and B12 =  − 0.6. In the initial state, the configuration does not depend on the material of the top layer. [Bottom] Side views of magnetization configuration in bottom FePt 2 nm/spacer 2 nm/top layer 2 nm when the top layer is (a) the Co90Fe10 2 nm in the initial state, (b) the relaxed state of Co90Fe10 2 nm, (c) the relaxed state of Ni80Fe20 2 nm, and (d) the relaxed state of Ni 2 nm, corresponding to the enclosed area in (e–h). The top and bottom arrows show the magnetization of the top and bottom layers, respectively. Magnetic moments in the y-direction are superimposed on each x position.

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Next, we considered the dynamics when the current flows through the device from the top to the bottom layers, similar to the case of initial state with z-axis magnetization saturation in the previous section. Figure 5a–c show the [(i–iii)] time-domain magnetization precession, [(iv–vi)] Fast Fourier transform (FFT) spectra, and [(vii–ix)] side view snapshots of the magnetization configuration of the top and bottom layers at 10 ns after the current flow, with B12 is 0.0 or −0.6, for (a) Co90Fe10, (b) Ni80Fe20, and (c) Ni. The electrical current densities were set as the same values as those for the z-axis saturation at the initial state in the previous section. The calculated data under the wide current density, including Fig. 5, are also shown in Fig. S4, S5 and S6 in Supplementary material. The common tendencies were obtained in both initial states of y-axis and z-axis saturation; the sample with B12 = −0.6 exhibited a more stable STO with an almost immutable Mx/Ms, a higher quality factor Q, and higher frequency than that with B12 = 0.0. We found that the biquadratic coupling is effective for increasing the frequency, regardless of the initial state.

Figure 5
figure 5

STO performances for the top layer of (a) Co90Fe10, (b) Ni80Fe20, and (c) Ni in the orthogonal configuration with an out-of-plane initial state, namely the y-axis. (i–ii) Time-domain magnetization precessions Mx/Ms, (iv–vi) the Fast Fourier transform spectra, and (vii–ix) side views of magnetization configuration. The light blue and orange lines denote the results for B12 = 0.0 and B12 =  − 0.6, respectively. For the time-domain magnetization precessions Mx/Ms, the electrical current density was (i) 10 × 107 A/cm2, (ii) 15 × 107 A/cm2, and (iii) 20 × 107 A/cm2 for Co90Fe10, and (i) 1.5 × 107 A/cm2, (ii) 3.5 × 107 A/cm2, and (iii) 6.0 × 107 A/cm2 for Ni80Fe20 and Ni.

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However, there is a clear difference in the transient time between the initial state with y-axis and z-axis magnetization saturation. For the initial state with z-axis saturation magnetization, the transient times were 5.5, 8.9, and 11.2 ns for Co90Fe10, Ni80Fe20, and Ni, respectively, as shown in Fig. 3. In contrast, for the initial state with y-axis saturation magnetization, the transient times were 0.7, 1.2, and 1.0 ns for Co90Fe10, Ni80Fe20, and Ni, respectively, as shown in Fig. 5. Therefore, the transient time was significantly reduced by changing the initial magnetization state. As an example, we have provided a video of the magnetic moment dynamics for the Ni layer under 3.0 × 107 A/cm2 for the initial states of z-axis and y-axis saturation (see the Supplementary material).

Notably, we can see a long period fluctuation in the time domain of the STO in Figs. 3a–c and 5a and b. This explains the overlapping of several STO modes, as shown in the [(iv–vi)] FFT spectra and [(vii–ix)] side views of the magnetization. For the Ni top layer only, there was one peak in the FFT and the magnetization amplitude was relatively uniform because of its small Ms.

Once the STO was obtained, the effect of the initial state on the STO frequency was found to be insignificant. However, for Ni only, the magnitude of Mx/Ms was increased from 0.084 to 0.800 by changing the initial state from z-axis saturation to y-axis saturation, as shown in Figs. 3c and 5c. This indicates that the initial magnetization state affects the transient time as well as the STO intensity when the top layer is Ni. To determine the reason for the large change in Mx/Ms only for Ni, we compared the side view snapshots of the magnetization between the two different the initial states in Figs. 3c and 5c. In Fig. 3c, the magnetization directions of the top Ni layer disperse in the xy-plane, which indicates that the trajectory of magnetization is not uniform in the film, which decreases the total intensity Mx/Ms. On the other hand, as shown in Fig. 5c, the magnetization directions of the top layer maintain the same direction, leading to a large total intensity Mx/Ms. We observed that the magnetization directions disperse in the xy-plane, but the z component of the total magnetization does not depend on the initial magnetization state, which will be explained in the followings.

Effect of initial state and biquadratic coupling on the STO

Figure 6 shows the STO frequency, intensity Mx/Ms, and transient time as a function of the current density for the initial states of z-axis and y-axis saturation. The Mx/Ms intensity over 0.1 is plotted. The solid circle and triangle denote the results for the initial states of y-axis saturation when B12 is −0.6 and 0.0, respectively. The open square and diamond denote the calculated results for the initial states of z-axis saturation when B12 is −0.6 and 0.0, respectively. In both cases, the critical current density for realizing the STO decreases and the frequency increases by changing the top layer from Co90Fe10 to Ni80Fe20 and Ni, depending on their Ms. Provided the saturation magnetization does not change, the intensity Mx/Ms decreases with an increase in current density. Whether the top layer is Ni, Ni80Fe20, or Co90Fe10, the current density region realizing the stable STO is widened by using B12 = −0.6 instead of B12 = 0. In particular, the biquadratic coupling effect is most obvious in the top layer of Ni, whose saturation magnetization is small when the initial state is y-axis saturation. There appears to be no significant difference in the frequencies and intensity of Mx/Ms dependencies on the current density between the two initial states, except for Ni, which is consistent with the comparison results between Figs. 3c and 5c. In contrast to the frequency and intensity, a large discrepancy is observed in the transient times between the two initial states, as shown in Fig. 6c. Regardless of the current flow in any of the top layers, the initial state with y-axis saturation demonstrated a much smaller transient time than in the initial state with z-axis saturation. This tendency is particularly pronounced in the Ni80Fe20 and Ni top layers with an Ms smaller than that of Co90Fe10. We noted that the transient time did not change as the current density changed for an initial state of y-axis saturation; however, it varied widely for an initial state of z-axis saturation. This large variation in the transient time can be attributed to the dispersion of the magnetization directions in the xy-plane, as shown in the side views.

Figure 6
figure 6

Current density dependences of (a) frequency, (b) intensity Mx/Ms, and (c) transient time in an orthogonal configuration. The solid circles and triangles denote the calculated results for the initial states of y-axis saturation when B12 is −0.6 or 0.0, respectively. The open squares and diamonds denote the calculated results for the initial states of z-axis saturation when B12 is −0.6 or 0.0, respectively.

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Finally, to confirm the effect of biquadratic coupling on STO performance, we compare the frequency, intensity, and transient time between the system with and without biquadratic coupling, namely between B12 = -0.6 and B12 = 0, highlighted by solid triangles and open diamonds in Fig. 6, respectively. The biquadratic coupling clearly increases the STO frequency for the same current density. However, more importantly, the current density region for which the STO was realized was expanded by the biquadratic coupling, resulting in the possibility that the maximum value of the frequency could be increased.

Conclusion

In summary, we carried out a numerical investigation on spin torque oscillation in the magnetic multilayer FePt/spacer/Co90Fe10, Ni80Fe20, or Ni with an orthogonal magnetization configuration by introducing biquadratic magnetic coupling. The frequency and current density region were increased by introducing the biquadratic coupling, leading to 37 GHz, 40 GHz, and 58 GHz in the Co90Fe10, Ni80Fe20 and Ni layer at a current density of 18 × 107 A/cm2, 4 × 107 A/cm2, and 5.5 × 107 A/cm2, respectively. In addition, we determined that two types of initial magnetic state, z-axis saturation and y-axis saturation, result in a vortex structure and in-plane onion magnetic structure after relaxation, respectively. The transient time before the stable STO was reduced from 0.5 to 1.8 ns by changing the initial state from z-axis saturation to y-axis saturation. The vortex structure is more stable than the onion structure, which is considered to be the reason for the difference in the transient time. By combining the orthogonal configuration, the biquadratic magnetic coupling, and the initial state with in-plane magnetic saturation, a stable STO with several tens of GHz frequency was obtained, which is advantageous for STO applications.