  We propose a method to dynamically decouple every magnetically sensitive
hyperfine sublevel of a trapped ion from magnetic field noise, simultaneously,
using integrated circuits to adiabatically rotate its local quantization field.
These integrated circuits allow passive adjustment of the effective
polarization of any external (control or noise) field. By rotating the ion's
quantization direction relative to this field's polarization, we can perform
`passive' dynamical decoupling (PDD), inverting the linear Zeeman sensitivity
of every hyperfine sublevel. This dynamically decouples the entire ion, rather
than just a qubit subspace. Fundamentally, PDD drives the transition
$m_{F}\rightarrow -m_{F}$ for every magnetic quantum number $m_{F}$ in the
system--with only one operation--indicating it applies to qudits with constant
overhead in the dimensionality of the qudit. We show how to perform pulsed and
continuous PDD, weighing each technique's insensitivity to external magnetic
fields versus their sensitivity to diabaticity and control errors. Finally, we
show that we can tune the sinusoidal oscillation of the quantization axis to a
motional mode of the crystal in order to perform a laser-free two qubit gate
that is insensitive to magnetic field noise.
