  For isolated vacancies in ordered local-moment antiferromagnets we show that
the magnetic-field linear-response limit is generically singular: The magnetic
moment associated with a vacancy in zero field is different from that in a
finite field h in the limit h->0. The origin is a universal and singular
screening cloud, which moreover leads to perfect screening as h->0 for magnets
which display spin-flop bulk states in the weak-field limit.
