If you want to keep these words, you have to say : "spiritus temp
oris" (in order to translate the "of the"). This would be correct grammatically.
But I would suggest you another vocabulary : maybe "aetas" instead of "tempus" (aetas is more long-scaled : a historical period, not just a moment) ; and maybe "animus" instead of "spiritus" (spiritus is actually a whisper).
So the result would be :
"animus aetatis"
or even better (in order to avoid confusions, because "aetas" can also mean the age of a man or woman) :
"animus huius aetatis" : the spirit of that time
or "animus nostrae aetatis" : the spirit of our time.
That's my suggestion : wait for other voices !
