Microwave Oscillators and Detectors Based …
25
data. The inset of Fig. 13 shows that the excitation threshold decreases in the subthreshold region and reaches zero at I dc = 7 mA. In Ref. [117], it was also shown that
parametric synchronization favors single-mode oscillations in the case of multimode
excitation.
7.1 Time-Domain Stability of Parametric Synchronization
The thermal stability of any electronic device is a crucial issue. Although the synthetic antiferromagnetic structure gives good thermal stability to STNO devices, the
magnetization dynamics of the free layer are in general affected by thermal agitation, which can also affect parametric synchronization. The time-averaged spectrum
analyzer data cannot reveal the real-time dynamics of the signal generated by the
free layer precession. For this purpose, time-domain study is required. A study of the
effect of thermal noise is required to understand the coupling of STNOs in arrays.
George et al. [107] was the first to discuss and demonstrate the effects of thermal
Gaussian noise in injection-locked spin-valve-based STNO devices. According to
this work, thermal noise can weaken injection locking by affecting the range of locking bandwidth. On the other hand, in an another study based on micromagnetic simulation [119], injection-locked spin-valve-based STNOs were found to be quite stable
against thermal Gaussian noise. Recently, Lebrun et al. [120] described an experimental time-domain study of fractional synchronization under different conditions:
f e ∼ f 0 /2, f e ∼ f 0 , and f e ∼ 2f 0 , revealing that the power required for phase noise
squeezing (where 1/f
2 phase noise is completely suppressed) is different for different fractional synchronization conditions. In MTJ-STNO, a study of parametric synchronization [117] revealed that the frequency domain STNO spectra show a random
unlocking at low microwave power, which can be attributed to thermal fluctuation.
A recent time-domain study of parametric synchronization [121] by the authors
of this chapter revealed random unlocking at low RF power due to thermally driven
frequency stability, while the frequency-domain data show the expected synchronization of any STNO device. The instantaneous frequency calculated from the Hilbert
transform method reveals that the instantaneous frequency is not always inside the
locking bandwidth (32 MHz, shown by blue dotted line), as shown in Fig. 14a at
P rf = −11 dBm. At the high RF power value of −5 dBm, the instantaneous frequency is inside the locking bandwidth (107 MHz, shown by red dotted line) for the
total time of 5 μsec, as shown in Fig. 14a. However, even at −5 dBm, frequency
fluctuations are present, resulting in a phase noise that exceeds the injected signal.
We only observe phase slips of π , which, according to Ref. [120], is a signature of
phase locking with an injected signal at f rf = 2f 0 . These π phase slips still leads to
1/f
2 phase noise. To understand the random unlocking at low RF power, macrospin
simulations were performed by adding the thermal field to H eff by following Brown’s
approximation [122, 123]. The macrospin simulations reproduce the experimental
results and reveal that the random unlocking during synchronization is driven by
thermal fluctuations, as shown in Fig. 14b. Macrospin simulation further suggests
25
data. The inset of Fig. 13 shows that the excitation threshold decreases in the subthreshold region and reaches zero at I dc = 7 mA. In Ref. [117], it was also shown that
parametric synchronization favors single-mode oscillations in the case of multimode
excitation.
7.1 Time-Domain Stability of Parametric Synchronization
The thermal stability of any electronic device is a crucial issue. Although the synthetic antiferromagnetic structure gives good thermal stability to STNO devices, the
magnetization dynamics of the free layer are in general affected by thermal agitation, which can also affect parametric synchronization. The time-averaged spectrum
analyzer data cannot reveal the real-time dynamics of the signal generated by the
free layer precession. For this purpose, time-domain study is required. A study of the
effect of thermal noise is required to understand the coupling of STNOs in arrays.
George et al. [107] was the first to discuss and demonstrate the effects of thermal
Gaussian noise in injection-locked spin-valve-based STNO devices. According to
this work, thermal noise can weaken injection locking by affecting the range of locking bandwidth. On the other hand, in an another study based on micromagnetic simulation [119], injection-locked spin-valve-based STNOs were found to be quite stable
against thermal Gaussian noise. Recently, Lebrun et al. [120] described an experimental time-domain study of fractional synchronization under different conditions:
f e ∼ f 0 /2, f e ∼ f 0 , and f e ∼ 2f 0 , revealing that the power required for phase noise
squeezing (where 1/f
2 phase noise is completely suppressed) is different for different fractional synchronization conditions. In MTJ-STNO, a study of parametric synchronization [117] revealed that the frequency domain STNO spectra show a random
unlocking at low microwave power, which can be attributed to thermal fluctuation.
A recent time-domain study of parametric synchronization [121] by the authors
of this chapter revealed random unlocking at low RF power due to thermally driven
frequency stability, while the frequency-domain data show the expected synchronization of any STNO device. The instantaneous frequency calculated from the Hilbert
transform method reveals that the instantaneous frequency is not always inside the
locking bandwidth (32 MHz, shown by blue dotted line), as shown in Fig. 14a at
P rf = −11 dBm. At the high RF power value of −5 dBm, the instantaneous frequency is inside the locking bandwidth (107 MHz, shown by red dotted line) for the
total time of 5 μsec, as shown in Fig. 14a. However, even at −5 dBm, frequency
fluctuations are present, resulting in a phase noise that exceeds the injected signal.
We only observe phase slips of π , which, according to Ref. [120], is a signature of
phase locking with an injected signal at f rf = 2f 0 . These π phase slips still leads to
1/f
2 phase noise. To understand the random unlocking at low RF power, macrospin
simulations were performed by adding the thermal field to H eff by following Brown’s
approximation [122, 123]. The macrospin simulations reproduce the experimental
results and reveal that the random unlocking during synchronization is driven by
thermal fluctuations, as shown in Fig. 14b. Macrospin simulation further suggests