As first pointed out by Bardeen and Ginzburg in the early sixties(1,2), the
amount of magnetic flux carried by vortices in superconducting materials d
epends on their distance from the sample edge, and can be smaller than one
flux quantum, phi(0) = h/2e (where h is Planck's constant and e is the elec
tronic charge). In bulk superconductors, this reduction of flux becomes neg
ligible at submicrometre distances from the edge, but in thin films the eff
ect may survive much farther into the material(3,4). But the effect has not
been observed experimentally, and it is often assumed that magnetic field
enters type II superconductors in units of f0. Here we measure the amount o
f flux introduced by individual vortices in a superconducting film, finding
that the flux always differs substantially from f0. We have observed vorti
ces that carry as little as 0.001 phi(0), as well as 'negative vortices', w
hose penetration leads to the expulsion of magnetic field. We distinguish t
wo phenomena responsible for non-quantized flux penetration: the finite-siz
e effect(1-4) and a nonlinear screening of the magnetic field due to the pr
esence of a surface barrier. The latter effect has not been considered prev
iously, but is likely to cause non-quantized penetration in most cases.