Microwave Oscillators and Detectors Based …
7
observed. The first region (I) corresponds to the positive field, 100 < H ext ≤ 800 Oe;
here the FL and RL magnetizations are in an antiparallel (AP) configuration. In this
region, the frequencies of the modes increase with an external field. These modes
correspond to free layer excitations, labeled FLAP. The second region (II) corresponds to higher positive fields, H ext ≥ 800 Oe, where additional lower-frequency
modes appear with frequencies that decrease with H ext . These new modes are RL
modes. Finally, the third region (III) corresponds to the case of H ext < 100 Oe, with
the magnetization of the FL and RL in parallel (P) configuration, which is also an
FL mode, labeled FLP1.
By resolving these modes spatially, the region of the MTJ nanopillar that is excited
during oscillations at any particular mode can be extracted. It is observed that broadly
two kinds of spatial modes can be excited: (i) bulk modes and (ii) edge modes. With
bulk modes, the magnetization in the bulk (central region) of the ferromagnetic material moves in phase with each other and most of the output power (in the frequency
spectra) comes from this central region. The internal field is mostly homogeneous in
this region of the MTJ. In edge modes, the amplitude of magnetization oscillations
is significant mostly only around the edges, where the internal field is not homogeneous. Since spatial resolution of the frequencies is experimentally difficult, micromagnetic simulations utilizing the Landau–Lifshitz–Gilbert–Slonczewski (LLGS)
equation have been increasingly used for this purpose. The micromagnetic simulation results shown in Fig. 2b reproduces the experimental spin wave modes in all
the three regions. In Fig. 2c, d, spatially resolved plots of bulk spin wave modes
from free (at 400 Oe) and fixed (at 1000 Oe) layers are shown using micromagnetic
simulations. Several factors, such as the lateral size of MTJ and the current-induced
Oersted field, have also been reported to influence spin wave generation [41–43].
3 Bias Dependence of In-Plane and Field-Like Torques
Zhang et al. [44] have pointed out that spin torque not only has the in-plane component
predicted by Slonczewski [1] and Berger [2], but also possesses a perpendicular component. The in-plane torque (T IP ) is also referred to simply as the spin-transfer torque
(STT), τ , while the perpendicular or out-of-plane torque (T OOP ) is also referred to
as the field-like torque (FLT), τ ⊥ . The in-plane torque τ lies in the plane defined by
the magnetization of the fixed layer M fixed and the magnetization of the free layer
M free , while τ ⊥ points out of the plane defined by M fixed and M free , as shown in Fig. 1.
The FLT τ ⊥ is small in metallic systems such as spin valves [45–47], but much
larger (∼ 40% of τ ) in MTJs [48], where it significantly affects the magnetization
dynamics. In order to control the magnetization using spin-torque effects, the FLT
τ ⊥ needs to be known and understood. However, the magnitude of this component
is both difficult to calculate [49–51] and to measure.
The magnetization dynamics of the free layer, including both these torques, can
be described by the Landau–Lifshitz–Gilbert–Slonczewski (LLGS) equation:
7
observed. The first region (I) corresponds to the positive field, 100 < H ext ≤ 800 Oe;
here the FL and RL magnetizations are in an antiparallel (AP) configuration. In this
region, the frequencies of the modes increase with an external field. These modes
correspond to free layer excitations, labeled FLAP. The second region (II) corresponds to higher positive fields, H ext ≥ 800 Oe, where additional lower-frequency
modes appear with frequencies that decrease with H ext . These new modes are RL
modes. Finally, the third region (III) corresponds to the case of H ext < 100 Oe, with
the magnetization of the FL and RL in parallel (P) configuration, which is also an
FL mode, labeled FLP1.
By resolving these modes spatially, the region of the MTJ nanopillar that is excited
during oscillations at any particular mode can be extracted. It is observed that broadly
two kinds of spatial modes can be excited: (i) bulk modes and (ii) edge modes. With
bulk modes, the magnetization in the bulk (central region) of the ferromagnetic material moves in phase with each other and most of the output power (in the frequency
spectra) comes from this central region. The internal field is mostly homogeneous in
this region of the MTJ. In edge modes, the amplitude of magnetization oscillations
is significant mostly only around the edges, where the internal field is not homogeneous. Since spatial resolution of the frequencies is experimentally difficult, micromagnetic simulations utilizing the Landau–Lifshitz–Gilbert–Slonczewski (LLGS)
equation have been increasingly used for this purpose. The micromagnetic simulation results shown in Fig. 2b reproduces the experimental spin wave modes in all
the three regions. In Fig. 2c, d, spatially resolved plots of bulk spin wave modes
from free (at 400 Oe) and fixed (at 1000 Oe) layers are shown using micromagnetic
simulations. Several factors, such as the lateral size of MTJ and the current-induced
Oersted field, have also been reported to influence spin wave generation [41–43].
3 Bias Dependence of In-Plane and Field-Like Torques
Zhang et al. [44] have pointed out that spin torque not only has the in-plane component
predicted by Slonczewski [1] and Berger [2], but also possesses a perpendicular component. The in-plane torque (T IP ) is also referred to simply as the spin-transfer torque
(STT), τ , while the perpendicular or out-of-plane torque (T OOP ) is also referred to
as the field-like torque (FLT), τ ⊥ . The in-plane torque τ lies in the plane defined by
the magnetization of the fixed layer M fixed and the magnetization of the free layer
M free , while τ ⊥ points out of the plane defined by M fixed and M free , as shown in Fig. 1.
The FLT τ ⊥ is small in metallic systems such as spin valves [45–47], but much
larger (∼ 40% of τ ) in MTJs [48], where it significantly affects the magnetization
dynamics. In order to control the magnetization using spin-torque effects, the FLT
τ ⊥ needs to be known and understood. However, the magnitude of this component
is both difficult to calculate [49–51] and to measure.
The magnetization dynamics of the free layer, including both these torques, can
be described by the Landau–Lifshitz–Gilbert–Slonczewski (LLGS) equation: