Perrin and the Two Rivers

Min saw a flaring halo around his head, radiant in gold and blue. She compared the halo to a crown once, but did not say it was a crown, like the crowns she saw around Rand, Perrin, and Darlin. In other places she describes it as an aura. (See the Shadow rising, chapters 17 and 47, The Fires of Heaven, chapter 1, Crossroads of Twilight, chapter 24, and Knife of Dreams, chapter 18)

I do not think that Logain's glory is linked to the governmental crown of any nation. It does seem to be linked to him becoming leader of the Asha'man (see Egwene's Dream in A Crown of Swords, chapter 10)