The pressure-induced spin crossover in divalent cobalt is studied. It is shown that the change in spin as a function of pressure and its effects on $K_{\beta }$ x-ray emission depend on the $3d$ spin-orbit interaction and local exchange fields, leading to a broadening of the spin-crossover transition as a function of octahedral crystal field or pressure. A detailed comparison is made with experimental data on ${\mathrm{Na}}_3{\mathrm{Co}}_2{\mathrm{SbO}}_6$ as a function of the octahedral field tuned by pressure. Additionally, the spectral weight of the $K_{{\beta }^{\prime }}$ feature is studied for transition metals, and the Tsutsumi rules [K. Tsutsumi, J. Phys. Soc. Jpn. 14, 1696 (1959); K. Tsutsumi and H. Nakamori, J. Phys. Soc. Jpn. 25, 1418 (1968); K. Tsutsumi et al., Phys. Rev. B 13, 929 (1976)] are reexamined.

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• Pressure effects
• Spin state transition
• Spin-orbit coupling
• Transition metals
• X-ray emission spectroscopy