  To tune the magnetic properties of hexagonal ferrites, a family of
magnetoelectric multiferroic materials, by atomic-scale structural engineering,
we studied the effect of structural distortion on the magnetic ordering
temperature (TN). Using the symmetry analysis, we show that unlike most
antiferromagnetic rare-earth transition-metal perovskites, a larger structural
distortion leads to a higher TN in hexagonal ferrites and manganites, because
the K3 structural distortion induces the three-dimensional magnetic ordering,
which is forbidden in the undistorted structure by symmetry. We also revealed a
near-linear relation between TN and the tolerance factor and a power-law
relation between TN and the K3 distortion amplitude. Following the analysis, a
record-high TN (185 K) among hexagonal ferrites was predicted in hexagonal
ScFeO3 and experimentally verified in epitaxially stabilized films. These
results add to the paradigm of spin-lattice coupling in antiferromagnetic
oxides and suggests further tunability of hexagonal ferrites if more lattice
distortion can be achieved.
