Coarsening of Antiferromagnetic Domains: 
the Key Role of Magneto-crystalline Anisotropy 

M. Major, L. Bottyán, and D. L. Nagy 
KFKI Research Institute for Particle and Nuclear Physics, 
P.O.B. 49, H-1525 Budapest, Hungary

Experimental and theoretical study of the magnetic domain structure of an
antiferromagneticaly coupled
MgO(001)/[$^{57}$Fe(\unit{26}{\angstrom})/Cr(\unit{13}{\angstrom})]$_{20}$
superlattice is presented \cite{bsf3}. Synchrotron M\"ossbauer
reflectometric (SMR) and polarized neutron reflectometric (PNR) maps show
micrometer-size (\unit{2.6}{\micro\meter}) primary domain formation as the
external field decreases from full saturation ($H\gg
H_{\text{sat}}\approx\unit{0.9}{\tesla}$). From this primary domain state
a secondary domain state forms with majority presence of (order of
magnitude) larger\footnote{Due to the finite experimental resolution only
a lower limit can be given.} ($>\unit{16.5}{\micro\meter}$) and minority
presence of smaller ($\unit{2.6}{\micro\meter}$) domains when passing a
spin-flop transition\footnote{In remanence, the magnetization vectors of
the Fe layers in an antiferromagnetically coupled superlattice with
fourfold in-plane anisotropy point in an easy direction (Fe\{010\} or
Fe\{100\}). Releasing the external field from saturation along an easy
axis, the magnetizations settle solely in the perpendicular easy
direction. As observed by PNR \cite{21} and SMR \cite{22}, an irreversible
spin-flop transition takes place when a moderate magnetic field is applied
within the easy axis in which the layer magnetizations actually lay. At a
given spin-flop field $H_{\text{sf}}$, the layer magnetizations jump into
the perpendicular easy axis. This alignment is retained in remanence and
on further field cycles until the sample is turned with the magnetizations
parallel to the field. } ($H_{\text{sf}}=\unit{13}{\milli\tesla}$) from
field-parallel to field-perpendicular direction. This domain coarsening is
illustrated on Fig.~\ref{Fig.1} and Fig.~\ref{Fig.2} cited from
\cite{bsf3}.

A simple two dimensional Monte-Carlo calculation is presented in \cite{26}
on the transition from primary domain state to secondary domain state of
the multilayter. By applying simple first neighbour domain formation rules
both the primary and the secondary AF domain formation can be followed
with results being in fair accordance to already available
Kerr-microscopic results on Fe/Cr trilayers \cite{6}.

The presented model in accordance with the PNR and SMR measurements gives
a new insight into the nature of the domain transformation and lifts a
controversy in the literature by showing that the condition for domain
coarsening is not the equilibrium of the Zeeman energy with the
domain-wall energy, but {\it the equilibrium of the Zeeman energy with the
anisotropy energy}. It is only this equilibrium that permits the minute AF
domain-wall energy to shape the domain structure. Out of this equilibrium
the Zeeman energy or the anisotropy energy whichever is greater stabilizes
the actual domain structure.