Invar effect of SrRu${\mathrm{O}}_3$: Itinerant electron magnetism of Ru $4d$ electrons

We have investigated the temperature dependence of the unit-cell parameters and volume of SrRu${\mathrm{O}}_3$ and CaRu${\mathrm{O}}_3$ with the Debye-Scherrer x-ray-diffraction technique in the temperature range from 12 to 300 K. The volume of SrRu${\mathrm{O}}_3$ is almost constant below the ferromagnetic transition temperature $T_c$ of 160 K. This represents a discovery of the Invar effect in transition-metal oxides, which is known to exist in $3d$ transition-metal itinerant magnets, e.g., Fe-Ni alloys. This fact suggests that the Ru $4d$ electrons, which cause ferromagnetism, have a Fermi surface and form a conduction band similar to that in $3d$ Invar alloys. On the other hand, the temperature dependence of the volume of CaRu${\mathrm{O}}_3$ can be well described by a Debye function, implying that thermal expansion is governed by phonons, and that magnetic ordering does not occur in this compound.