A single crystal Mn-Zn based ferrite material contains 1-7 (preferably 3-5) wt.% nickel oxide based on the amount of Mn-Zn based ferrite which preferably has the composition 50-60 mol% iron oxide (including 0-10 mol% FeO), 5-30 mol% zinc oxide and 10-45 mol% manganese oxide. Also claimed is a magnetic core structure for use in a h.f. magnetic head, the structure comprising a gap material (15) between two spaced facing surfaces of two magnetic cores (11, 12) which are made of the above single crystal Mn-Zn based ferrite material.