  We present a type IIB supergravity solution dual to a spatially anisotropic
$\mathcal{N}=4$ super Yang-Mills plasma at finite $U(1)$ chemical potential and
finite temperature. The effective five-dimensional gravitational theory is a
consistent Einstein-Maxwell-dilaton-Axion truncation of the gauged
supergravity. We obtain the solutions both numerically and analytically. We
study the phase structure and thermodynamic instabilities of the solution, and
find new instabilities independent of the renormalization scheme.
