  We use the solution generating technique, the TsT transformation, to obtain
new solutions in type II string theory as well as in M-theory. We explicitly
work out examples starting with rotating D3 and M2 branes as well as D1-D5-p
system. Among a variety of solutions, we find many of them have asymptotic
Schr\"odinger symmetry. We also device a new method of deriving free energy of
black brane systems, which is more efficient than the Euclidean action
procedure. We test our method on known examples before applying it to new
asymptotically Schr\"odinger backgrounds. We study phase structure of these
backgrounds by analysing the free energy thus derived.
