TY - JOUR
T1 - Domain branching in uniaxial ferromagnets
T2 - A scaling law for the minimum energy
AU - Choksi, Rustum
AU - Kohn, Robert V.
AU - Otto, Felix
PY - 1999
Y1 - 1999
N2 - 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 lower bound which matches the already-known upper bound. We further show that any domain pattern achieving this scaling law must have average width of order L2/3, where L is the length of the magnet in the easy direction. Finally we argue that branching is required, by considering the constrained variational problem in which branching is prohibited and the domain structure is invariant in the easy direction. Its scaling law is different.
AB - 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 lower bound which matches the already-known upper bound. We further show that any domain pattern achieving this scaling law must have average width of order L2/3, where L is the length of the magnet in the easy direction. Finally we argue that branching is required, by considering the constrained variational problem in which branching is prohibited and the domain structure is invariant in the easy direction. Its scaling law is different.
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U2 - 10.1007/s002200050549
DO - 10.1007/s002200050549
M3 - Article
AN - SCOPUS:0033450334
SN - 0010-3616
VL - 201
SP - 61
EP - 79
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
ER -