  Magnetic remanence - found in bar magnets or magnetic storage devices - is
probably the oldest and most ubiquitous phenomenon underpinning technological
applications of magnetism. It is a macroscopic non-equilibrium phenomenon: a
remanent magnetisation appears when a magnetic field is applied to an initially
unmagnetised ferromagnet, and then taken away. Here, we present an inverted
magnetic hysteresis loop in the pyrochlore compound Nd$_2$Hf$_2$O$_7$: the
remanent magnetisation points in a direction opposite to the applied field.
This phenomenon is exquisitely tunable as a function of the protocol in field
and temperature, and it is reproducible as in a quasi-equilibrium setting. We
account for this phenomenon in considerable detail in terms of the properties
of non-equilibrium population of domain walls which exhibit a magnetic moment
between domains of an ordered antiferromagnetic state which itself has zero net
magnetisation. Properties and (non-equilibrium) dynamics of topological defects
play an important role in modern spintronics, and our study adds an instance
where a uniform field couples selectively to domain walls rather than the bulk.
