  We propose a $\sigma_z\otimes \sigma_z$ laser-free entangling gate which uses
the intrinsic J-coupling of ions in a static magnetic gradient. Dephasing of
the interaction is suppressed by means of continuous dynamical decoupling using
pairs of microwave fields. The gate is virtually insensitive to common
amplitude noise of the microwave fields and enables high fidelities despite
qubit frequency fluctuations, while the J-coupling interaction's inherent
robustness to motional decoherence is retained. Errors far below the
fault-tolerant threshold can be achieved at high initial temperatures, negating
the requirement of sideband cooling below the Doppler temperature. By adjusting
the powers of the continuous microwave fields, the J-coupling interaction can
be tuned and can be used to implement parallel entangling gates within an ion
chain.
