We present a first-principles computational study of the nature and origin of ferromagnetism in Co-doped $\mathrm{Ti}{\mathrm{O}}_2$. We calculate the magnetic ordering and electronic properties as a function of the concentration and distribution of Co dopants and oxygen vacancies. We find that Co atoms prefer to substitute on neighboring sites of the Ti lattice, and show, using the well-established Goodenough-Kanamori-Anderson rules, that this leads to a ferromagnetic superexchange. We propose other semiconductor hosts in which the superexchange mechanism should lead to ferromagnetic coupling between the magnetic moments of neighboring transition metal dopants.

The influence of the interstitial impurities B, C, N, O, and H on the interfacial cohesion and structure of grain boundaries in body-centered cubic transition metals is investigated by means of the local-density-functional theory (LDFT), using the mixed-basis pseudopotential approach. $\Sigma 5$ (310) [001] symmetrical tilt grain boundaries (STGB) in Nb and Mo are chosen for this theoretical case study. The analysis of interface energies and geometric translation states, site-projected densities of states and bonding electron densities yields the following systematic trends: B and C form angle-dependent covalentlike bonds with the nearest host-metal neighbors, strengthen the interfacial cohesion by inducing covalent metal-metal bonds across the interface, and favor a mirror-symmetric configuration of the STGB, while N and O as well as H form isotropic polarlike bonds, cause interfacial embrittlement, and break the mirror symmetry of the STGB. The ab initio LDFT results for energetical trends concerning cohesion of boundaries and embrittlement by segregation support the qualitative validity of empirical models of Cottrell and of Rice and Wang for bcc transition metals. In addition, structural trends are derived, which relate the geometrical translation state of the STGB to the type of bonding of the impurity with the host metal at the interface.