  Platinum monatomic nanowires were predicted to spontaneously develop
magnetism, involving a sizable orbital moment via spin orbit coupling, and a
colossal magnetic anisotropy. We present here a fully-relativistic (spin-orbit
coupling included) pseudo-potential density functional calculation of
electronic and magnetic properties, and of Landauer ballistic conductance of Pt
model nanocontacts consisting of short nanowire segments suspended between Pt
leads or tips, reprented by bulk planes. Even if short, and despite the
nonmagnetic Pt leads, the nanocontact is found to be locally magnetic with
magnetization strictly parallel to its axis. Especially under strain, the
energy barrier to flip the overall spin direction is predicted to be tens of
meV high, and thus the corresponding blocking temperatures large, suggesting
the use of static Landauer ballistic electrical conductance calculations. We
carry out such calculations, to find that inclusion of spin-orbit coupling and
of magnetism lowers the ballistic conductance by about $15\div20$% relative to
the nonmagnetic case, yielding $ G\sim 2 G_0$ ($G_0=2e^2/h$), in good agreement
with break junction results. The spin filtering properties of this highly
unusual spontaneously magnetic nanocontact are also analysed.
