Correlation between rare-earth oscillator strengths and rare-earth–valence-band interactions in neodymium-doped $\mathrm{Y}M{\mathrm{O}}_4$ ($M=\mathrm{V},$ P, As), ${\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12},$ and ${\mathrm{LiYF}}_4$ matrices

${\mathrm{Nd}}^{3+}{:\mathrm{Y}\mathrm{V}\mathrm{O}}_4$ is one of the more promising laser hosts for micro and diode-pumped solid-state lasers. At room temperature, ${\mathrm{Nd}}^{3+}$ ions in this matrix exhibit strong absorption cross sections sixfold higher than in ${\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}.$ The neodymium oscillator strengths are measured in $\mathrm{Y}M{\mathrm{O}}_4$ ($M=\mathrm{V},$ P, As), ${\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12},$ and ${\mathrm{LiYF}}_4$ hosts, and they increase in the sequence ${\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}{<\mathrm{LiYF}}_4{<\mathrm{YAsO}}_4{<\mathrm{YPO}}_4{<\mathrm{YVO}}_4.$ This paper is an attempt to correlate these variations with covalent interactions between neodymium $4f,5d$ levels and valence-band levels. The strength of orbital interactions between $4f$ levels and valence-band states is estimated from the analysis of $3d$ x-ray photoemission spectra of ${\mathrm{Nd}}^{3+}$ ions. A two-step model is derived, in which $5d$ admixture into the $4f$ levels of the rare earth occurs via the valence-band levels. This model shows that the oscillator strengths increase with the Nd $4f$-valence-band interactions.