  The crystal and magnetic structures of the spinel compounds ZnCr$_2$S$_4$ and
ZnCr$_2$Se$_4$ were investigated by high resolution powder synchrotron and
neutron diffraction. ZnCr$_2$Se$_4$ exhibits a first order phase transition at
$T_N=21$ K into an incommensurate helical magnetic structure. Magnetic
fluctuations above $T_N$ are coupled to the crystal lattice as manifested by
negative thermal expansion. Both, the complex magnetic structure and the
anomalous structural behavior can be related to magnetic frustration.
Application of an external magnetic field shifts the ordering temperature and
the regime of negative thermal expansion towards lower temperatures. Thereby,
the spin ordering changes into a conical structure. ZnCr$_2$S$_4$ shows two
magnetic transitions at $T_{N1}=15$ K and $T_{N2}=8$ K that are accompanied by
structural phase transitions. The crystal structure transforms from the cubic
spinel-type (space group $Fd$\={3}$m$) at high temperatures in the paramagnetic
state, via a tetragonally distorted intermediate phase (space group $I4_1$ /
$amd$) for $T_{N2} < T < T_{N1}$ into a low temperature orthorhombic phase
(space group $I m m a$) for $T < T_{N2}$. The cooperative displacement of
sulfur ions by exchange striction is the origin of these structural phase
transitions. The low temperature structure of ZnCr$_2$S$_4$ is identical to the
orthorhombic structure of magnetite below the Verwey transition. When applying
a magnetic field of 5 T the system shows an induced negative thermal expansion
in the intermediate magnetic phase as observed in ZnCr$_2$Se$_4$.
