Awarded a scholarship, Hayward went on to pursue a Ph.D. degree, also at University of Canterbury, again under the supervision of Vincent Orange. His topic was an analysis of German air operations during the eastern campaigns of World War II, based on unpublished German archival sources. In 1994, the U.S. Air Force Historical Research Agency, located within the Air University at Maxwell Air Force Base, Alabama, awarded him a research fellowship to conduct research for his dissertation in its archives. He subsequently received a research fellowship from the Federal Government of Germany which enabled him to conduct primary research in the German Military Archives in Freiburg, Germany. became the basis of his first book, "Stopped at Stalingrad: The Luftwaffe and Hitler’s Defeat in the East 1942-1943.", which was acclaimed upon its publication in 1998.