STT-Based Non-Volatile Logic-in-Memory Framework - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 182

When electrons flow from the fixed to the free layer inside the MTJ, their
spins are first polarized by the fixed layer. These spin polarized electrons travel
to the free layer and interacts with the local magnetization of the free layer. The
electrons then transfer their angular momentum to the electrons of the free layer.
This results in a spin transfer torque on the free layer that acts towards switching
the free layer towards logic 0 state. When electrons flow in the opposite direction
from the free to the fixed layer, they are first polarized by the free layer. The
electrons that are polarized in the same direction of the fixed layer pass through
it. Electrons with opposite polarization to the fixed layer are reflected back to the
free layer. These reflected electrons exert a torque on the free layer that tends to
switch it opposite to fixed layer, i.e. towards logic 1 state. The magnitude of the
spin transfer torque is proportion to the current through the MTJ. Depending
on the current direction, if the current magnitude exceeds a critical value (Eq. 6 ),
the spin transfer torque succeeds in switching the free layer to logic 0 or 1 state.
The LLG equation (Eq. 1 ) governs the magnetodynamics of the free layer from
spin transfer torque. We will assume that cells on an average take t w time to be
written, the numerical value of which is mentioned in Table 2 .
Clocking. For the chosen NML style computation in the free layers, we need to
clock the free layers for effective coupling. The advantage is that unlike NML,
we can now use spin transfer torque to clock the free layers, which is (i) low
power; and (ii) highly confined to individual cells rather than to a group of cells.
To elaborate the clocking we would first discuss the clocking mechanism and
principle and then go on to describe if any necessary MTJ configurations are
required to execute the spin transfer torque clock.
The intention of clocking is to take the MTJ free layers to a stationary state
along their hard axis. Here, instead of external fields we will take the help of
spin transfer torque to achieve the clocking mission. To reach the clocked state,
the torques from precession, damping and spin transfer should cancel each when
the magnetization of the free layer is along the hard axis. This condition can be
achieved with a clocking current I clk given by Eq. 7 . The current magnitude is
derived from Eq. 1 by taking the left hand side to a stationary state, i.e. dm/dt
= 0. Note, the clocking current scales with the device dimensions. Moreover, the
clocking current is also in the same order in magnitude as the switching cur-
rent (Eq. 6 ). This ensures a clocking power of one order less than field induced
clocking. For further details on the clocking, readers can refer to [ 30 ]. Clocking
procedure for MTJs with access transistors is same as writing into them. First the
required potential is applied across their bit and source lines. Next, their access
transistors are turned on to complete the path for current. For MTJs without
access transistors, clocking should be carried out by only applying the required
potential across the bit and source lines. We will assume that cells on an average
take t clk time to be clocked and t s time to settle down under neighbor coupling
from the instant the clock is released. Again t s <t clk is a condition to ensure
that cells in one clocking zone have completely settled before the clock in the