We address the branching of magnetic domains in a uniaxial ferromagnet. Our
thesis is that branching is required by energy minimization. To show this,
we consider the nonlocal, nonconvex variational problem of micromagnetics.
We identify the scaling law of the minimum energy by proving a rigorous lo
wer bound which matches the already-known upper bound. We further show that
any domain pattern achieving this scaling law must have average width of o
rder L-2/3, where L is the length of the magnet in the easy direction, Fina
lly we argue that branching is required, by considering the constrained var
iational problem in which branching is prohibited and the domain structure
is invariant in the easy direction, Its scaling law is different.