Hi Hester, again!
There are Logie all over Scotland and it's a reasonably popular surname.
They have their own Clan website ( sited in NY of course)
Try it here http://www.cnyscots.com/logan.html
There's actually a site with a bit more info here http://www.rampantscotland.com/clans/blclanlogan.htm
I think that the word Logie probably originated with the tendency in the Scottish east coast dialect to add "ie" onto many words.
Hence Lag (lagan-plural) would become Lagie.
Can't think of such a song just know although I'm sure there are many. Try, however, Bogie's Bonny Belle. It has a similar theme and Archie Fisher does a superb version