Are all Dirac-harmonic maps uncoupled?

Dirac-harmonic maps $(f,\phi )$ consist of a map $f:M\to N$ and a twisted spinor $\phi \in \mathrm{\Gamma }(\mathrm{\Sigma }M\otimes f^{\ast }TN)$ and they are defined as critical points of the super-symmetric energy functional. A Dirac-harmonic map is called \emph{uncoupled}, if $f$ is a harmonic map. We show that under some minimality assumption Dirac-harmonic maps defined on a closed domain are uncoupled.