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In this investigation, the low-frequency alternate-current (AC) magnetic susceptibility (χ_{ac}) and hysteresis loop of various MgO thickness in CoFeB/MgO/CoFeB magnetic tunneling junction (MTJ) determined coercivity (_{c}) and magnetization (_{s}) and correlated that with χ_{ac} maxima. The multilayer films were sputtered onto glass substrates and the thickness of intermediate barrier MgO layer was varied from 6 to 15 Å. An experiment was also performed to examine the variation of the highest χ_{ac} and maximum phase angle (θ_{max}) at the optimal resonance frequency (_{res}), at which the spin sensitivity is maximal. The results reveal that χ_{ac} falls as the frequency increases due to the relationship between magnetization and thickness of the barrier layer. The maximum χ_{ac} is at 10 Hz that is related to the maximal spin sensitivity and that this corresponds to a MgO layer of 11 Å. This result also suggests that the spin sensitivity is related to both highest χ_{ac} and maximum phase angle. The corresponding maximum of χ_{ac} is related to high exchange coupling. High coercivity and saturation magnetization contribute to high exchange-coupling χ_{ac} strength.

_{ac})

_{res})

Since 1995, the tunneling magnetoresistance (TMR) effect has been extensively discussed, and it has been exploited in much of our modern technology [_{ac}) has rarely been examined. The low field AC measurement at low frequencies is related to the spin sensitivity of MTJ devices [_{ac}) and hysteresis loop of CoFeB/MgO/CoFeB are worthwhile to study. This investigation focuses on the maximum χ_{ac}, the optimal resonance frequency (_{res}) and maximum phase angle (θ_{max}) for various MgO barrier thicknesses (6, 8, 11, 13, and 15 Å). The maximum χ_{ac} is 0.7 at the optimal resonant frequency of 10 Hz and the maximum phase angle is 228° at an MgO thickness of 11 Å. These values are larger than compared for Fe_{40}Pd_{40}B_{20}(_{ac} [_{ac} is due to the association between magnetic spin interactions [_{ac} value is corresponding to optimal resonance frequency, increasing spin sensitivity at optimal _{res}. It means that the optimal _{res} is associated with maximal spin sensitivity.

_{ac} amplitude of the CoFeB/MgO/CoFeB MTJ for different thicknesses of the MgO layer at frequencies in the range 10 to 25,000 Hz. The lowest measured frequency is 10 Hz and the smallest step frequency is 20 Hz at low frequencies for used χ_{ac} measurement. The maxima χ_{ac} at the optimal resonance frequency has the following physical meaning. At low frequencies, the resultant alternate-current (AC) magnetic dipole moment is contributed from the oscillation of volume magnetic dipole moment inside each domain. The applied AC magnetic field acts a driving force. The magnetic interactions among domains act restored. There exists a resonant frequency as a driving force acting to the system. Thus, the frequency of the peak of the low-frequency magnetic susceptibility corresponds to the resonant frequency of the oscillation of the magnetic dipole moment inside domains. The χ_{ac} peak indicates the spin exchange-coupling interaction and dipole moment of domain under frequency [_{ac} of the magnetic exchange-coupled signal, and as the frequency increases above 30 Hz, the χ_{ac} obtained from the signal declines, suggesting that the CoFeB/MgO/CoFeB MTJ is suited to use at low frequencies. The optimal maximum susceptibility, at frequencies in the range of 10 to 30 Hz, can be utilized in inductors and transformers [

Measured low-frequency alternate-current magnetic susceptibility (χ_{ac}) of CoFeB/MgO/CoFeB as a function of thickness of MgO barrier layer.

Briefly, the maximum χ_{ac} at the optimal resonant frequency (_{res}), _{res} corresponds to the maximum spin sensitivity. Therefore, _{ac} as a function of MgO thickness. The resonance peak of origin 10 Hz represents to initial spin exchange coupling status. The maximum χ_{ac} value at 6 Å is 0.44, at 8 Å is 0.52, at 11 Å is 0.71, at 13 Å is 0.27, and at 15 Å is 0.3. These findings are known to follow from indirect interactions of magnetic moment. The indirect interactions of magnetic moment mean the spin exchange interaction between free CoFeB and pinned CoFeB layers, which indicate a strong moment interactions can induce a high magnetic susceptibility [_{ac} peaks are corresponding to high exchange coupling.

Maximum χ_{ac} as a function of thickness of MgO barrier layer.

The phase angle (θ) has the following physical meaning. When a magnetic material is in an external magnetic field, the magnetic dipole moment tends to lie in the direction of the interaction of the magnetic moment with the external field. When an external AC magnetic field is applied, and the AC frequency is not too high compared to microwave frequencies, the magnetic dipole moment oscillates. The frequency of the applied AC magnetic field equals the frequency of oscillation of magnetic dipole. However, the direction of instantaneous magnetic dipole is not the same as the direction of the applied magnetic field. The phase angle denotes the difference [_{max}) between magnetic field and magnetization as a function of MgO thickness for maximal χ_{ac}. The high χ_{ac} ensures high spin sensitivity to an increase in the phase angle. Restated, by increasing the phase angle improved the sensitivity to detect the behavior of an electron spin. In summary, the results concerning the phase angle are consistent with trend of χ_{ac}.

Variation of maximum χ_{ac} with maximum phase angle (θ).

_{ac} of indirect exchange-coupling susceptibility of FM1 and FM2 is 0.7, corresponding to a resonant frequency of 10 Hz and a maximum phase angle of 228.5°. According to previous study, it indicates that susceptibility is associated with 1/f noise due to electron trap in the tunnel barrier [

Maximum χ_{ac} value, maximum phase angle, and corresponding optimal resonance frequency for various MgO barrier thicknesses.

MgO (Å) | Maximum χ_{ac} (a.u.) |
Maximun phase angle θ_{max} (degree) |
Highest χ_{ac} corresponding optimal resonance frequency _{res} (Hz) |
---|---|---|---|

6 Å | 0.44 | 142.24 | 30 Hz |

8 Å | 0.52 | 96.44 | 30 Hz |

11 Å | 0.71 | 228.59 | 10 Hz |

13 Å | 0.27 | 103.47 | 10 Hz |

15 Å | 0.30 | 155.44 | 10 Hz |

_{c} value of free CoFeB layer denotes (H2 + H4)/2. The _{c} value of pinned CoFeB layer is (H1 + H3)/2. The H_{c} value between two CoFeB layers initially increased at MgO thicknesses from 6 to 11 Å and decreased at MgO thicknesses from 11 to 15 Å. It can be reasonably concluded that high _{c} value means high exchange-coupling χ_{ac} strength. High _{c} strength requires a large external field to changing the spin arrangement. From _{c} of MTJ is varied by various MgO thicknesses. The result of _{ac} means a high magnetic exchange coupling between two CoFeB layers and induces a corresponding high _{c}. The saturation magnetization (_{s}) between two CoFeB layers is also shown the same trend to concave-down feature, which is shown in _{s} presents to high exchange-coupling χ_{ac} strength and high _{c} value.

The essential magnetic properties of magnetic tunneling junction are (

A multilayer MTJ was sputtered on a glass substrate by a DC and RF magnetron sputtering system. The chamber pressure was typically under 1 × 10^{−7} Torr and the Ar-working chamber pressure was 5 × 10^{−3} Torr. The MTJ structure was glass/CoFeB(75 Å)/MgO(_{2} with a mixing ratio of 9:16. The in-plane low-frequency alternate-current magnetic susceptibility (χ_{ac}) of MTJ was studied using an χ_{ac} analyzer (X_{ac}Quan, MagQu, Taiwan). First, the referenced standard sample is calibrated by an χ_{ac} analyzer with an external field. Then, the measured sample is inserted to χ_{ac} analyzer. The driving frequency ranged from 10 to 25,000 Hz. The minimum frequency step is 20 Hz and that the frequency minimum is 10 Hz. The χ_{ac} is determined through the magnetization measurement. All measured samples had the same shape and size to eliminate the demagnetization factor. The χ_{ac} valve is arbitrary unit (a.u.), because the χ_{ac} result is corresponding to referenced standard sample. It is a comparative valve. Moreover, the in-plane coercivity (_{c}) and saturation magnetization (_{s}) of the two CoFeB layers were obtained using a superconducting quantum interference device (SQUID, Quantum Design MPMS5, San Diego, CA, USA).

The MgO barrier layer thickness in CoFeB/MgO/CoFeB MTJs was varied to measure low-frequency alternate-current magnetic susceptibility and magnetic properties. The highest χ_{ac} was obtained at a thickness of 11 Å, corresponding to an optimal resonance frequency of 10 Hz and a maximum phase angle of 228.5°. The best resonance frequencies are from 10 to 30 Hz, and this range of frequencies is useful for transformers, sensors, and magnetic read heads. Additionally, the important low-frequency alternate-current susceptibility and magnetic results demonstrate that the indirect spin exchange coupling of top CoFeB and bottom CoFeB layers in CoFeB/MgO/CoFeB oscillates.

This work was supported by the National Science Council, under Grant No. NSC100-2112-M-214-001-MY3 and No. NSC 102-2815-C-214-009-M.

The authors declare no conflict of interest.

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