  We investigate a large class of supersymmetric magnetic brane solutions
supported by U(1) gauge fields in AdS gauged supergravities. We obtain
first-order equations in terms of a superpotential. In particular, we find
systems which interpolate between AdS_{D-2}\times \Omega^2 (where \Omega^2=S^2
or H^2) in the horizon and AdS_D-type geometry in the asymptotic region, for
4\le D\le 7. The boundary geometry of the AdS_D-type metric is
Minkowski_{D-3}\times \Omega^2. This provides smooth supergravity solutions for
which the boundary of the AdS spacetime compactifies spontaneously. These
solutions indicate the existence of a large class of superconformal field
theories in diverse dimensions whose renormalization group flow runs from the
UV to the IR fixed point. We show that the same set of first-order equations
also admits solutions which are asymptotically AdS_{D-2}\times \Omega^2 but
singular at small distance. This implies that the stationary AdS_{D-2}\times
\Omega^2 solutions typically lie on the inflection points of the modulus space.
