Electric-Field-Controlled MRAM: Physics and Applications
161
this implies that the effective slope should be calculated over this entire voltage range
instead. One extreme example of non-linear modulation of PMA is from the double
MgO free layer [66]. Here, the change in anisotropy follows a V-shape centered
with the minimal around 0 V. For both negative and positive voltages, the anisotropy
increases, making the MTJ harder to write regardless of the voltage polarity.
In the next section, we will discuss how VCMA and its related effects have been
utilized in MRAM.
3 Device Operation
3.1 MTJ Switching
Since the change in perpendicular anisotropy can be translated into a change in
magnetization direction, Shiota and Kanai et al. have utilized this to control the spin
dynamics of the MTJ [22, 32] via voltage resulting in precessional switching. The
basic principles are illustrated in Fig. 8.
As seen in Fig. 8a, the VCMA effect is used to reduce the magnetization component in the z-direction. An external magnetic field is then required in the x (or y)
direction to provide an axis about which the magnetization can precess. The dynamics
of this precessional effect is given by the Larmor frequency (or period τ) [23],
τ ≈ 2π/γ μ 0 H x
(9)
where γ is the gyromagnetic constant, μ 0 the permittivity of free space and H x the
field in the x-direction. Here, we have ignored the effect of the electric-field on the
reference layer but depending on the strength of the voltage this may be ignored [23].
We have also ignored the damping constant term α in Eq. 7 of Ref. [72] since this term
is small. Figure 9a and b show typical colormap plots of the switching probability
against both the field and the width of the electric-field pulse for magnetization
reversal from AP to P and from P to AP respectively. The ridges or regions where the
switching probability approaches 1, basically correspond to half a period τ defined
in Eq. 9. As shown in Fig. 8c, which is a typical cross-section of the plots in Fig. 9
at a certain H x , pulses equivalent to even multiples of half a period result in the
magnetization returning to its starting point while pulses which are odd multiples of
half a period corresponding to 180° rotation resulting in the switching of the initial
magnetization. This can also be understood from Fig. 8b. Two features can generally
be noted in Fig. 9a and b. First, along the contour given by Eq. 9 (i.e. assuming a
fixed number of precessional cycles), it can be seen that the probability is low when
the pulse width is high or the amplitude of H x is low. This can be understood as
follows. A high H x will cause the magnetization to settle in the H x direction. This
implies that the probability for both transitions tends to 0.5. This is shown by the
narrowing and gradually decreasing contour when H x is high. As for long pulses
161
this implies that the effective slope should be calculated over this entire voltage range
instead. One extreme example of non-linear modulation of PMA is from the double
MgO free layer [66]. Here, the change in anisotropy follows a V-shape centered
with the minimal around 0 V. For both negative and positive voltages, the anisotropy
increases, making the MTJ harder to write regardless of the voltage polarity.
In the next section, we will discuss how VCMA and its related effects have been
utilized in MRAM.
3 Device Operation
3.1 MTJ Switching
Since the change in perpendicular anisotropy can be translated into a change in
magnetization direction, Shiota and Kanai et al. have utilized this to control the spin
dynamics of the MTJ [22, 32] via voltage resulting in precessional switching. The
basic principles are illustrated in Fig. 8.
As seen in Fig. 8a, the VCMA effect is used to reduce the magnetization component in the z-direction. An external magnetic field is then required in the x (or y)
direction to provide an axis about which the magnetization can precess. The dynamics
of this precessional effect is given by the Larmor frequency (or period τ) [23],
τ ≈ 2π/γ μ 0 H x
(9)
where γ is the gyromagnetic constant, μ 0 the permittivity of free space and H x the
field in the x-direction. Here, we have ignored the effect of the electric-field on the
reference layer but depending on the strength of the voltage this may be ignored [23].
We have also ignored the damping constant term α in Eq. 7 of Ref. [72] since this term
is small. Figure 9a and b show typical colormap plots of the switching probability
against both the field and the width of the electric-field pulse for magnetization
reversal from AP to P and from P to AP respectively. The ridges or regions where the
switching probability approaches 1, basically correspond to half a period τ defined
in Eq. 9. As shown in Fig. 8c, which is a typical cross-section of the plots in Fig. 9
at a certain H x , pulses equivalent to even multiples of half a period result in the
magnetization returning to its starting point while pulses which are odd multiples of
half a period corresponding to 180° rotation resulting in the switching of the initial
magnetization. This can also be understood from Fig. 8b. Two features can generally
be noted in Fig. 9a and b. First, along the contour given by Eq. 9 (i.e. assuming a
fixed number of precessional cycles), it can be seen that the probability is low when
the pulse width is high or the amplitude of H x is low. This can be understood as
follows. A high H x will cause the magnetization to settle in the H x direction. This
implies that the probability for both transitions tends to 0.5. This is shown by the
narrowing and gradually decreasing contour when H x is high. As for long pulses