  A three-dimensional self-consistent spin transport model is developed, which
includes both tunnelling transport, as well as metallic transport. Using the
spin accumulation computed either side of a tunnel barrier, spin torques are
obtained, and it is shown the model reproduces both damping-like and field-like
spin-transfer torques, with the expected sinusoidal angular dependence, and
inverse ferromagnetic layer thickness dependence. An explicit solution to the
drift-diffusion model is derived, which allows analysing the effect of both the
reference and free layer thickness on the spin-transfer torque polarization and
field-like coefficient. In particular, when the layers are thin, additional
spin-dependent scattering contributions due to incomplete absorption of
transverse spin components reduce both the damping-like and field-like spin
torques. It is shown the model developed here can be used to compute the
signal-to-noise ratio in realistic magnetic read-heads, where spin
torque-induced fluctuations and instabilities limit the maximum operating
voltage. The effect of metallic pinhole defects in the insulator layer is also
analysed, which results in a mixture of metallic and tunnelling transport, and
highly non-uniform charge and spin currents, requiring the full spin transport
model to compute the resulting magneto-resistance and spin torques. Increasing
the area covered by pinholes results in a rapid degradation of the
magneto-resistance, following an inverse dependence. Moreover, the spin torque
angular dependence becomes skewed, and the spin-transfer torque polarization
decreases. The same results are obtained when considering tunnel junctions with
a single pinhole defect, but decreasing cross-sectional area, showing that even
a single pinhole defect can significantly degrade the performance of tunnel
junctions and magnetic read-heads below the 40 nm node.
