Scanning tunnelling spectroscopy (STS) of thin Fe films on W(l 10) shows that the electronic structures of magnetic domains and domain walls are different. This experimental result is explained on the basis of first-principles calculations. A detailed analysis reveals that the spin-orbit induced mixing between minority d(xy+xz) and minority d(z2) spin states depends on the magnetization direction and changes the local density of states in the vacuum detectable by STS. The effect scales in second or fourth order with the magnetization angle relative to the easy axis. Our finding implies that nanometre-scale magnetic structure information can be obtained even by using non-magnetic probe tips. Magnetization dependent measurements show that the canting of adjacent spins has no major influence on the electronic structure of the sample.