  We study the temperature dependence of the optical conductivity of rare-earth
nickelate films of varying composition and strain close to the
antiferromagnetic ordering temperature, TN. Two prominent peaks at 0.6 and 1.3
eV, which are characteristic of the insulating phase, display a small but
significant increase in intensity when the material passes from para- to
antiferromagnetic. This observation indicates the presence of a positive
feedback between antiferromagnetic (AF) and bond disproportionation (BD) order.
By analyzing the temperature dependence near TN, and using a Landau-type
free-energy expression for BD and AF order, we infer that BD order is a
necessary condition for the AF phase to appear, and that the antiferromagnetism
contributes to stabilization of the bond disproportionation. This model also
explains why hysteresis is particularly strong when the transition into the
insulating state occurs simultaneously with antiferromagnetic order.
