They are electrically charged, and so some of them get trapped in earth’s magnetic field forming the Van Allen belt. Others get pulled into the north and south magnetic poles. But do they form a magnetic field of their own? I don’t think so.
Moving charge creates a mag field. Faraday’s law. Or was it Maxwell?
Faraday. Maxwell’s is the relationship between E and M fields.
And in Earths atmosphere. The ionosphere. Charged particles flowing everywhere. Creating Mag fields and reacting to them. Would be interesting if someone modeled the whole system. Which is the cause and which is the effect?