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We have successfully grown centimeter-sized layered $R$SrNiO$_4$ singlecrystals under high oxygen pressures of 120 bar by the floating zone technique.This enabled us to perform neutron scattering experiments where we observeclose to quarter-integer magnetic peaks below $\sim$77 K that are accompaniedby steep upwards dispersing spin excitations. Within the high-frequency Ni-Obond stretching phonon dispersion, a softening at the propagation vector for acheckerboard modulation can be observed. Together with our spin wavesimulations these observations reveal that this Ni$^{3+}$ system exhibitscharge disproportionation with charges segregating into a checkerboard patternwithin a nano phase separation scenario rather than showing a Jahn-Tellereffect.

Charge disproportionation and nano phase separation in $R$SrNiO$_4$