Croat n.

"type of neck-cloth worn usually by men," 1650s, from French cravate (17c.), from Cravate, literally "Croatian," from German Krabate, from Serbo-Croatian Hrvat "a Croat" (see Croat). Cravats came into fashion 1650s in imitation of linen scarves worn by the Croats or Crabats, 17th-century light cavalry forces who fought on the side of the Catholic League in the Thirty Years' War. The name in this context was not an ethnic label as much as a generic designation for light cavalry from the Hapsburg Military Frontier, which included  Croats, Hungarians, Serbs, Wallachians, Poles, Cossacks and Tatars.

When first introduced, it was commonly of lace, or of linen edged with lace. ... The modern cravat is rather a necktie, passed once round the neck, and tied in front in a bow, or, as about 1840 and earlier (when the cravat consisted of a triangular silk kerchief, usually black), twice round the neck, in imitation of the stock. Formerly, when starched linen cravats were worn, perfection in the art of tying them was one of the great accomplishments of a dandy. The cravat differs properly from the scarf, which, whether tied, or passed through a ring, or held by a pin, hangs down over the shirt front. [Century Dictionary, 1897]

from Modern Latin Croatia, from Croatian Hrvatska, probably related to Russian khrebet "mountain chain" (see Croat).