  We report a combined experimental and theoretical study on intriguing
magnetic properties of quasiferroelectric orthochromates. Large single crystals
of the family of RECrO$_3$ (RE = Y, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu)
compounds were successfully grown. Neutron Laue study indicates a good quality
of the obtained single crystals. Applied magnetic-field and temperature
dependent magnetization measurements reveal their intrinsic magnetic
properties, especially the antiferromagnetic (AFM) transition temperatures.
Density functional theory studies of the electronic structures were carried out
using the Perdew-Burke-Ernzerhof functional plus Hubbard $U$ method.
Crystallographic information and magnetism were theoretically optimized
systematically. When RE$^{3+}$ cations vary from Y$^{3+}$ and Eu$^{3+}$ to
Lu$^{3+}$ ions, the calculated $t$-$e$ orbital hybridization degree and
N\'{e}el temperature behave similarly to the experimentally-determined AFM
transition temperature with variation in cationic radius. We found that the
$t$-$e$ hybridization is anisotropic, causing a magnetic anisotropy of
Cr$^{3+}$ sublattices. This was evaluated with the nearest-neighbour
$J_1$-$J_2$ model. Our research provides a picture of the electronic structures
during the $t$-$e$ hybridization process while changing RE ions and sheds light
on the nature of the weak ferromagnetism coexisting with predominated
antiferromagnetism. The available large RECrO$_3$ single crystals build a
platform for further studies of orthochromates.

Strongly Correlated Electrons;Materials Science;Applied Physics;Computational Physics