  Polycrystalline samples of the quarter-doped manganites
$R_{0.75}$Ca$_{0.25}$MnO$_3$ ($R$ = Y, Tb, Dy, Ho, and Er) were studied by
X-ray diffraction and AC/DC susceptibility measurements. All five samples are
orthorhombic and exhibit similar magnetic properties: enhanced ferromagnetism
below $T_1$ ($\sim80$ K) and a spin glass (SG) state below $T_{SG}$ ($\sim30$
K). With increasing $R^{3+}$ ionic size, both $T_1$ and $T_{SG}$ generally
increase. The single crystal neutron diffraction results on
Tb$_{0.75}$Ca$_{0.25}$MnO$_3$ revealed that the SG state is mainly composed of
a short-range ordered version of a novel canted (i.e. noncollinear)
antiferromagnetic spin state. Furthermore, calculations based on the double
exchange model for quarter-doped manganites reveal that this new magnetic phase
provides a transition state between the ferromagnetic state and the
theoretically predicted spin-orthogonal stripe phase.
