In this work, we study the properties of single-flavor heavy baryons, ${\mathrm{\Omega }}_{\mathrm{ccc}}$ and ${\mathrm{\Omega }}_{\mathrm{bbb}}$, in a strong magnetic field. For that sake, we simply treat the baryons as quark–diquark two-body systems, and a systematic formalism is developed to deal with two-body Schrödinger equations in a magnetic field. It is found that (1) The orbital properties of ${\mathrm{\Omega }}_{\mathrm{bbb}}$ are almost not affected by the magnetic field, (2) ${\mathrm{\Omega }}_{\mathrm{ccc}}$ is more tightly bound in the presence of a magnetic field, and (3) the magnetic-spin effect dominates over the magnetic-orbital effect. Applying to peripheral heavy ion collisions, ${\mathrm{\Omega }}_{\mathrm{ccc}}$ is much better than ${\mathrm{\Omega }}_{\mathrm{bbb}}$ to explore the magnetic effect, and the discovery of ${\mathrm{\Omega }}_{\mathrm{ccc}}$ could be more promising.

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• Color confinement
• Jets & heavy flavor physics
• Relativistic heavy-ion collisions