Surface vs. Bulk Hysteresis Loops

Abstract

Very recently, it has been established that a large number of common magnetic materials exhibit hysteresis loops that depend on the probing depth of the magnetic measurement done at the surface. This indicates that important magnetic properties like the magnetic anisotropy K and the exchange energy JS1S2 where S1 and S2 are the spins of 2 neighboring atoms along a path perpendicular to the surface, may vary dramatically within a few lattice constants from the surface. The argument can be understood as follows: With bulk values for K and the exchange stiffness A = JS1S2/a where a is the distance of the atoms, the magnetization M will change in direction over distances of the order of \(\sqrt {A/K} \) which is the width of a magnetic domain wall. It typically amounts to 10–100 nm in materials like Fe or magnetite Fe3O4. Hence, if surface hysteresis loops are taken with techniques that differ in probing depth by 10 nm or less, we expect on the basis of the bulk constants that the hysteresis loops must be identical. However, M. Aeschlimann et al.1 showed that a hysteresis loop taken on Fe3O4 using the magneto-optic Kerr-effect with a probing depth of ~20nm shows a remanent magnetization as expected, whereas the magnetization curve taken with spin polarized photoelectrons with a probing depth of ~ 1nm exhibits no remanence at all. Even more dramatic differences between Kerr-effect and spin polarized photoemission occur with the magneto-optic recording materials FeTb and GdCo.2,3. Furthermore, Allenspach and coworkers4 reported that the shape of the hysteresis loops taken on Fe(100) by measuring the spin polarization of the secondary electrons depends on the energy ES of the secondaries. This must come about because the probing depth depends on ES.