Interference between magnetism and surface roughness in coherent soft x-ray scattering

In coherent soft x-ray scattering from magnetically ordered surfaces there are contributions to the scattering from the magnetic domains, from the surface roughness, and from the diffraction associated with the pinhole aperture used as a coherence filter. In the present work, we explore the interplay between these contributions by analyzing speckle patterns in diffusely scattered x rays from the surface of magnetic thin films. Magnetic contrast from the surface of antiferromagnetically ordered LaFeO₃ films is caused by magnetic linear dichroism in resonant x-ray scattering. The samples studied possess two types of domains with their magnetic orientations perpendicular to each other. By tuning the x-ray energy from one of the two Fe-L₃ resonant absorption peaks to the other, the relative amplitudes of the x-ray scattering from the two domains is inverted which results in speckle pattern changes. A theoretical expression is derived for the intensity correlation between the speckle patterns with the magnetic contrast inverted and not inverted. The model is found to be in good agreement with the x-ray-scattering observations and independent measurements of the surface roughness. An analytical expression for the correlation function gives an explicit relation between the change in the speckle pattern and the roughness, and magnetic and aperture scattering. Changes in the speckle pattern are shown to arise from beating of magnetic scattering with the roughness scattering and diffraction from the aperture. The largest effect is found when the surface roughness scatter is comparable in intensity to the magnetic scatter.