Microwave Oscillators and Detectors Based …
23
ments of the line width can then provide a direct measurement of the mode-hopping
rate λ. Under the assumption that mode-hopping events obey an Arrhenius distribution, the energy barrier E that must be overcome by thermal agitation in order to
produce a mode-hopping event can then be obtained from
E(I dc ) = k B T log
f a
λ
.
(15)
Here, we have indicated that the energy barrier δE(I dc ) depends sensitively on the
dc current I dc ; the frequency f a is an attempt frequency. k B is the Boltzmann constant
and T is the temperature. Using a simple assumption that the attempted frequency is
twice the relaxation frequency and be extracting E(I dc ) from a single measurement,
Iacocca et al. [98] obtained good quantitative and qualitative agreement between
theory and experiment [96] for the linewidth as a function of temperature.
7 Parametric Synchronization
Injection locking is a phenomenon in oscillators where one oscillator can synchronize
with the other when operating at nearby frequencies. In case of STNOs, injection
locking [105–109] is useful in understanding the synchronization behavior of an
STNO to an external RF source. Furthermore, injection locking is useful for understanding the mutual synchronization [71, 83–85, 110–112] of multiple STNO, which
is essential for improving the power of STNOs. In addition to injection locking, an
external RF source operating at a fraction or harmonic of the STNO eigenfrequency
can also synchronize the STNO. In particular, parametric synchronization [113–118],
in which the external RF source frequency (f e ) is twice the STNO operating frequency
(f 0 ), allows the synchronization of an STNO without interference from the external
RF signal.
Parametric excitation is a related phenomena that was first reported by Urazhdin et
al. [113] in a nanocontact-based STNO at the very low temperature of 5 K. Urazhdin
et al. [113] applied a microwave field via a separately fabricated strip line on top of the
STNO. They applied a frequency f e , equal to twice the resonance frequency f 0 of the
STNO, and parametrically induced oscillations at a DC current below the oscillation
threshold. The first room-temperature measurement of parametric excitation was
performed by Bortolotti et al. [90] in vortex-based MTJ-STNOs using RF currents
instead of an RF magnetic field. In this work, the Oersted or orthoradial field due to
the RF current was used to parametrically excite the vortex gyration.
Both parametric excitation and parametric synchronization have been demonstrated in MTJ-based STNOs in Ref. [117], as shown in Fig. 13. At a current of
I dc = 4 mA , well below the threshold current I th = 6.3 mA, parametric excitation
was observed, while at a high current of I dc = 7 mA, parametric synchronization
was observed. In the case of parametric excitation, the total integrated power around
the STNO single mode increases, unlike in the case of injection locking, where the
23
ments of the line width can then provide a direct measurement of the mode-hopping
rate λ. Under the assumption that mode-hopping events obey an Arrhenius distribution, the energy barrier E that must be overcome by thermal agitation in order to
produce a mode-hopping event can then be obtained from
E(I dc ) = k B T log
f a
λ
.
(15)
Here, we have indicated that the energy barrier δE(I dc ) depends sensitively on the
dc current I dc ; the frequency f a is an attempt frequency. k B is the Boltzmann constant
and T is the temperature. Using a simple assumption that the attempted frequency is
twice the relaxation frequency and be extracting E(I dc ) from a single measurement,
Iacocca et al. [98] obtained good quantitative and qualitative agreement between
theory and experiment [96] for the linewidth as a function of temperature.
7 Parametric Synchronization
Injection locking is a phenomenon in oscillators where one oscillator can synchronize
with the other when operating at nearby frequencies. In case of STNOs, injection
locking [105–109] is useful in understanding the synchronization behavior of an
STNO to an external RF source. Furthermore, injection locking is useful for understanding the mutual synchronization [71, 83–85, 110–112] of multiple STNO, which
is essential for improving the power of STNOs. In addition to injection locking, an
external RF source operating at a fraction or harmonic of the STNO eigenfrequency
can also synchronize the STNO. In particular, parametric synchronization [113–118],
in which the external RF source frequency (f e ) is twice the STNO operating frequency
(f 0 ), allows the synchronization of an STNO without interference from the external
RF signal.
Parametric excitation is a related phenomena that was first reported by Urazhdin et
al. [113] in a nanocontact-based STNO at the very low temperature of 5 K. Urazhdin
et al. [113] applied a microwave field via a separately fabricated strip line on top of the
STNO. They applied a frequency f e , equal to twice the resonance frequency f 0 of the
STNO, and parametrically induced oscillations at a DC current below the oscillation
threshold. The first room-temperature measurement of parametric excitation was
performed by Bortolotti et al. [90] in vortex-based MTJ-STNOs using RF currents
instead of an RF magnetic field. In this work, the Oersted or orthoradial field due to
the RF current was used to parametrically excite the vortex gyration.
Both parametric excitation and parametric synchronization have been demonstrated in MTJ-based STNOs in Ref. [117], as shown in Fig. 13. At a current of
I dc = 4 mA , well below the threshold current I th = 6.3 mA, parametric excitation
was observed, while at a high current of I dc = 7 mA, parametric synchronization
was observed. In the case of parametric excitation, the total integrated power around
the STNO single mode increases, unlike in the case of injection locking, where the