I'm not looking for words like "freshness" for example, but a word that is used exclusively to denote this specific smell.
While not explicitly limited to morning, the phrase new-mown hay is often associated with early morning smells, as in this folk song
As I strolled out one bright new morn,
All under the new mown hay, O,
I there did espy a fair pretty maid,
Under the new-mown hay, O, under the new-mown hay.