  Pyrochlore iridates A2Ir2O7 (A = rare earth elements, Y or Bi) hold great
promise for realizing novel electronic and magnetic states owing to the
interplay of spin-orbit coupling, electron correlation and geometrical
frustration. A prominent example is the formation of all-in/all-out
(AIAO)antiferromagnetic order in the Ir4+ sublattice that comprises of
corner-sharing tetrahedra. Here we report on an unusual magnetic phenomenon,
namely a cooling-field induced shift of magnetic hysteresis loop along
magnetization axis, and its possible origin in pyrochlore iridates with
non-magnetic Ir defects (e.g. Ir3+). In a simple model, we attribute the
magnetic hysteresis loop to the formation of ferromagnetic droplets in the AIAO
antiferromagnetic background. The weak ferromagnetism originates from canted
antiferromagnetic order of the Ir4+ moments surrounding each non-magnetic Ir
defect. The shift of hysteresis loop can be understood quantitatively based on
an exchange-bias like effect in which the moments at the shell of the FM
droplets are pinned by the AIAO AFM background via mainly the Heisenberg (J)
and Dzyaloshinsky-Moriya (D) interactions. The magnetic pinning is stable and
robust against the sweeping cycle and sweeping field up to 35 T, which is
possibly related to the magnetic octupolar nature of the AIAO order.
