= Solution
The interface is material in <ideal magnetohydrodynamics>, so fluid on it remains on it. Its normal displacement $\xi_z$ must consequently be the same when approached from either side. Integrating normal momentum balance through an infinitesimal pillbox shows that the Lagrangian total-pressure traction is continuous. Because the equilibrium total pressure is constant on each side and continuous at $z=0$, this reduces to continuity of the Eulerian perturbation $\delta\Pi$. Hence
$$
\boxed{[\xi_z]_-^+=0,\qquad[\delta\Pi]_-^+=0}.
$$
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