Three-dimensional magnetic fields of nanoscale elements determined by electron-holographic tomography

In order to visualise the three-dimensional magnetic fields of nanoscale magnetic elements, we have combined off-axis electron holography (in which the measured phase image is related to the projection of two components of the magnetic induction) and electron tomography (used to reconstruct three-dimensional objects from two-dimensional projections taken at a series of sample tilts). Conventional 'scalar' tomography requires only a single tilt series whilst the reconstruction of a magnetic (vector) field in three dimensions would in principle require three tilt series with mutually perpendicular tilt axes, However, only two series are necessary as the third component of the magnetic field is constrained by Maxwell's equation del.B = 0. We have developed a holographic tomography method to reconstruct the three-dimensional magnetic fields of small magnetic elements. Such information is essential if the proposed use of nanoscale magnetic elements for the next generation of high-density data storage and memory is to be fully realised.