"intellectual realms" is correct and usable in written English.
You can use this phrase to describe a subject of study or a field of expertise. For example, "My research focuses on the intellectual realms of critical thinking and problem solving."
Triumphant in the intellectual realm, the author quivers at, and makes great comedy of, physical danger.
It is this primal state of music that gives the work its consistent sensuality, yet the intellectual realm is not at all diminished.
The subjects in philosophy are preciously scarce, and the intellectual realm painfully small, so being forced to give up my dominion over them initially struck me as a bit of a cosmic injustice.
Caught between the physical world of their peers and the intellectual realm of adulthood, they mirror the feelings of not quite belonging one can experience as one gets older.
Above all, "Notes on an Appearance" (even the title is scintillatingly ironic) reflects a conflict-riddled, vigorously self-deluding intellectual realm where the ideal, grand-scale stakes bear the weight of immediate passion and the local, personal stakes remain disturbingly, bewilderingly remote.
In the intellectual realm, the path to truth is rocky, and errors are frequently the first result of reflection (Turgot 1750, 44; Condorcet 1795, 37 38).
In Twenty Years at Hull House, Addams talks about how the professor's lack of interest in matters of the "welfare of mankind" leaves behind the messy and chaotic experiential realm of student relationships for the more pure intellectual realm, which then left the students open to the influence of "charlatans" (1990 [1910], 247).
I challenge myself all the time in the intellectual realm, the career realm, the emotional realm, the interpersonal realm, and in just about any other realm, for that matter, except the physical realm.
Mostly, though, her assessments are astute and her characters well embedded in their intellectual and social realms.
