  The magnetic bipolar transistor (MBT) is a bipolar junction transistor with
an equilibrium and nonequilibrium spin (magnetization) in the emitter, base, or
collector. The low-injection theory of spin-polarized transport through MBTs
and of a more general case of an array of magnetic {\it p-n} junctions is
developed and illustrated on several important cases. Two main physical
phenomena are discussed: electrical spin injection and spin control of current
amplification (magnetoamplification). It is shown that a source spin can be
injected from the emitter to the collector. If the base of an MBT has an
equilibrium magnetization, the spin can be injected from the base to the
collector by intrinsic spin injection. The resulting spin accumulation in the
collector is proportional to $\exp(qV_{be}/k_BT)$, where $q$ is the proton
charge, $V_{be}$ is the bias in the emitter-base junction, and $k_B T$ is the
thermal energy. To control the electrical current through MBTs both the
equilibrium and the nonequilibrium spin can be employed. The equilibrium spin
controls the magnitude of the equilibrium electron and hole densities, thereby
controlling the currents. Increasing the equilibrium spin polarization of the
base (emitter) increases (decreases) the current amplification. If there is a
nonequilibrium spin in the emitter, and the base or the emitter has an
equilibrium spin, a spin-valve effect can lead to a giant magnetoamplification
effect, where the current amplifications for the parallel and antiparallel
orientations of the the equilibrium and nonequilibrium spins differ
significantly. The theory is elucidated using qualitative analyses and is
illustrated on an MBT example with generic materials parameters.
