There is a difference between what you describe in the question, a 'white' skinned European enslaving a darker skinned African, and racial slavery.

As an institution slavery has existed throughout most of recorded history and was practiced by many groups globally. For example, in the Roman Empire 'white' Romans owned dark skinned Nubians. But they also owned other 'white' Europeans, people enslaved in North Africa, the Baltics, the Middle East, etc. So we wouldn't call Roman slavery racial.

If we jump ahead to the 13-15th c. slavery had diminished in importance in Europe but most parts of Mediterranean Europe still had some slaves and still acquired slaves from various sources in Europe, Africa, and the Middle East. The shift to a racialized slavery really began when North Africans and the Portuguese began to trade with sub-Saharan Africa and began to import slaves from sub-Saharan Africa to North Africa, Europe and eventually the Americas. Overtime, it became easier and cheaper to acquire slaves there than from earlier markets. As it became more and more normal to have 'black' slaves, slavery became associated with blackness and eventually, the perception shifted so that blacks were perceived to be only suited for slavery because blacks were slaves.

For some good works on slavery and its evolution see:

Blackburn, Robin. The Making of New World Slavery: From the Baroque to the Modern, 1492-1800. London ; New York: Verso, 1997.

———. "The Old World Background to European Colonial Slavery." The William and Mary Quarterly 54, no. 1 (1997): 65-102.

Davis, David Brion. Inhuman Bondage: The Rise and Fall of Slavery in the New World. Oxford, England ; New York: Oxford University Press, 2006.

Jordan, Winthrop D. White over Black: American Attitudes Toward the Negro, 1550-1812. New York: Norton, 1977.

Phillips, William D. Slavery from Roman Times to the Early Transatlantic Trade. Minneapolis: University of Minnesota Press, 1985.

———. Slavery in Medieval and Early Modern Iberia. Philadelphia: University of Pennsylvania Press, 2013.

Sweet, James H. "The Iberian Roots of American Racist Thought." The William and Mary Quarterly 54, no. 1 (1997): 143-66.

Thornton, John K. Africa and Africans in the Making of the Atlantic World, 1400-1800. 2nd ed. Cambridge ; New York: Cambridge University Press, 1998.