Spin reorientation, magnetization reversal, and negative thermal expansion observed in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi><mml:mi mathvariant="normal">F</mml:mi><mml:msub><mml:mi mathvariant="normal">e</mml:mi><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:msub><mml:mi mathvariant="normal">r</mml:mi><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>perovskites<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mi>Lu</mml:mi><mml:mo>,</mml:mo><mml:mi>Yb</mml:mi><mml:mo>,</mml:mo><mml:mi>Tm</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>

Three members of the perovskite family $R\mathrm{F}{\mathrm{e}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5}{\mathrm{O}}_{3}$ ($R=\mathrm{Lu},\mathrm{Yb}$, and Tm) have been synthesized and characterized. A systematic study of the crystal and magnetic structures was performed by neutron powder diffraction combined with magnetization measurements. All these compounds crystallize in a Pbnm orthorhombic unit cell and they are already antiferromagnetic at room temperature. The study of the magnetic structure vs temperature showed the occurrence of a progressive spin reorientation from ${\mathrm{\ensuremath{\Gamma}}}_{4}^{\text{TM}}$ to ${\mathrm{\ensuremath{\Gamma}}}_{2}^{\text{TM}}$ for the transition metal sublattice, and in the Tm-based sample, a long-range magnetic order of the $\mathrm{T}{\mathrm{m}}^{3+}$ sublattice was found $({\mathrm{\ensuremath{\Gamma}}}_{8}^{R})$. These results are in excellent agreement with the magnetic susceptibility measurements. No spin reorientation is observed in the Lu-based sample for which a magnetization reversal at a compensation temperature ${T}_{\mathrm{comp}}=225\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ was detected. A clear magnetostrictive effect was observed in the samples with $R=\mathrm{Yb}$ and Tm associated with a negative thermal expansion and was assigned to a magnetoelastic effect produced by repulsion between the magnetic moments of neighboring transition metal ions.