  A non-Ohmic current that grows exponentially with the square root of applied
electric field is well known from thermionic field emission (the Schottky
effect), electrolytes (the second Wien effect) and semiconductors (the
Poole-Frenkel effect). It is a universal signature of the attractive Coulomb
force between positive and negative electrical charges, which is revealed as
the charges are driven in opposite directions by the force of an applied
electric field. Here we apply thermal quenches to spin ice to prepare
metastable populations of bound pairs of positive and negative emergent
magnetic monopoles at millikelvin temperatures. We find that the application of
a magnetic field results in a universal exponential-root field growth of
magnetic current, thus confirming the microscopic Coulomb force between the
magnetic monopole quasiparticles and establishing a magnetic analogue of the
Poole-Frenkel effect. At temperatures above 300 mK, gradual restoration of
kinetic monopole equilibria causes the non-Ohmic current to smoothly evolve
into the high field Wien effect for magnetic monopoles, as confirmed by
comparison to a recent and rigorous theory of the Wien effect in spin ice. Our
results extend the universality of the exponential-root field form into
magnetism and illustrate the power of emergent particle kinetics to describe
far-from equilibrium response in complex systems.
