The analytical form of the magnetic pair distribution function (mPDF) is derived for the first time by computing the Fourier transform of the neutron scattering cross section from an arbitrary collection of magnetic moments. Similar to the atomic pair distribution function applied to the study of atomic structure, the mPDF reveals both short-range and long-range magnetic correlations directly in real space. This function is experimentally accessible and yields magnetic correlations even when they are only short-range ordered. The mPDF is evaluated for various example cases to build an intuitive understanding of how different patterns of magnetic correlations will appear in the mPDF.
Keywords: local structure; magnetic correlations; magnetic pair distribution function; magnetic short-range order; magnetic structure; neutron scattering; pair distribution function.