Duke of Santa Cruz was a title of nobility of the Empire of Brazil created by Emperor Pedro I of Brazil, dated from 5 November 1829, for his brother-in-law, Prince Auguste de Beauharnais, brother of Pedro's second wife Empress Amélie.
Five years later, in December 1834, Auguste became (the late) Pedro I's son-in-law, when he was chosen to marry the Emperor's eldest daughter, Queen Maria II of Portugal.
The toponym associated to this title concerns Santa Cruz, today a neighborhood in Rio de Janeiro.
List of the Dukes
References
Duke of Santa Cruz Wikipedia(Text) CC BY-SA