A magnetoresistive medium (1) includes a substrate (2) which has been treated to provide a miscut vicinal surface (3) in the form of terraces (4) and steps (5) of atomic and nanometer scale. There are discrete separated spacer nanowires (7) provided by an intermediate partial spacer film on each terrace (4) against each step (5). A further main film (11) provides main nanowires (10(a), 10(b)). A thin protective layer (15) covers the main nanowires (10(a), 10(b)) which form two separate subsets of main nanowires with different exchange interaction with the substrate and thus a different response to an external magnetic field. In use, when an external magnetic field (H) is applied the response of the main nanowires (10(a), 10(b)) changes as the exchange coupling with the substrate (2) varies and the magnetisation on the main nanowires (10(a), 10(b)) change. This is shown by the arrows while prior to the application of the external magnetic field, they might, for example, be aligned. Many different constructions of magnetoresistive media are described.