  Giant or tunneling magnetoresistance are physical phenomena used for reading
information in commercial spintronic devices. The effects rely on a conserved
spin current passing between a reference and a sensing ferromagnetic electrode
in a multilayer structure. Recently, we have proposed that these fundamental
spintronic effects can be realized in collinear antiferromagnets with staggered
spin-momentum exchange interaction, which generates conserved spin currents in
the absence of a net equilibrium magnetization. Here we elaborate on the
proposal by presenting archetype model mechanisms for the antiferromagnetic
giant and tunneling magnetoresistance effects. The models are based,
respectively, on anisotropic and valley-dependent forms of the non-relativistic
staggered spin-momentum interaction. Using first principles calculations we
link these model mechanisms to real antiferromagnetic materials and predict a
$\sim$100\% scale for the effects. We point out that besides the GMR/TMR
detection, our models directly imply the possibility of spin-transfer-torques
excitation of the antiferromagnets.
