As someone who listens to quite a bit of metal, I can tell you there are a bunch of bands that are dedicated wholly to Tolkien... or at least mostly... such as Blind Guardian... here are a few (I haven't checked all of them out - some are hard to come by... but here's a list I once had):
Akallabęth
Amon Din
Avathar
Battlelore
Black Jade
Cross Borns
Druad
Druadan Forest
Fashoht Stâz
Flying Nazgul
Gorthaur
Grimorc
Gurthang
Lugburz
Minas Morgul
Oberon
Ringwraith
Rivendell
Summoning
The Ring
Trollrath
Valar
Witchking
Zabiis
Other bands do mention Tolkien occasionally... such as the band Galadriel... GWAR even makes a Tolkien reference in the song Whargoul, and 3 Inches of Blood has the song Kill the Orcs (it is also rumoured that their latest album has many Tolkien references, although they are subtle and could potentially fit into various other fantasies) - not sure if you're looking for music for listening purposes or making a list of various bands/songs... since you mentioned a research paper. If you're not too fond of the sound of death metal, a lot of these bands might not be the most pleasurable listening experience...