Label-free biosensors enable the monitoring of biomolecular interactions in real-time, which is key to the analysis of the binding characteristics of biomolecules. While refractometric optical biosensors such as SPR [Surface Plasmon Resonance] are sensitive and well-established, they are susceptible to any change of the refractive index in the sensing volume caused by minute variations in composition of the sample buffer, temperature drifts and most importantly nonspecific binding to the sensor surface. Refractometric biosensors require reference channels as well as temperature stabilisation and their applicability in complex fluids such as blood is limited by nonspecific bindings. Focal molography does not measure the refractive index of the entire sensing volume but detects the diffracted light from a coherent assembly of analyte molecules. Thus, it does not suffer from the limitations of refractometric sensors since they stem from non-coherent processes and therefore do not add to the coherent molographic signal. The coherent assembly is generated by selective binding of the analyte molecules to a synthetic binding pattern -the mologram. Focal Molography has been introduced theoretically [C. Fattinger, Phys. Rev. X 4, 031024 (2014)] and verified experimentally Nat. Nanotechnol. 12, 1089 (2017)] in previous papers. However, further understanding of the underlying physics and a diffraction-limited readout is needed to unveil its full potential. This paper introduces refined theoretical models which can accurately quantify the amount of biological matter bound to the mologram from the diffracted intensity. In addition, it presents measurements of diffraction-limited molographic foci i.e. Airy discs. These improvements enabled us to demonstrate a resolution in real-time binding experiments comparable to the best SPR sensors, without the need of temperature stabilisation or drift correction and to detect low molecular weight compounds labelfree in an endpoint format. The presented experiments exemplify the robustness and sensitivity of the diffractometric sensor principle.

We show that the magnetic anisotropy in spinel-structure CoCr2O4 thin films exhibits a strain dependence in which compressive strain induces an out-of-plane magnetic easy axis and tensile strain an in-plane easy axis, exactly opposite to the behavior reported for the related compound CoFe2O4. We use density functional theory calculations within the LSDA+U approximation to reproduce and explain the observed behavior. Using second-order perturbation theory, we analyse the anisotropy tensor of the Co 2+ ions in both octahedral and tetrahedral coordination, allowing us to extend our results to spinels with general arrangements of Co 2+ ions. PACS numbers: 75.70.Ak, 75.80.+q, 75.30.Gw, 71.15.Mb Thin films with out-of-plane spontaneous magnetization, showing so-called perpendicular magnetic anisotropy, are of great interest for applications such as high density magnetic memories with fast switching 1 . Perpendicular magnetic anisotropy is also needed for spintronic applications, for example in magnetic tunnel junctions, and for low energy current-driven domain wall motion 2-5 .In a system of finite size, magnetic anisotropy is determined by the balance of magnetocrystalline and shape anisotropy. The former is a bulk property originating from spin-orbit interaction, while the latter originates from magnetic dipole-dipole interaction and depends on the geometry of the sample. For the case of thin films, where shape anisotropy always favors in-plane magnetization, it is interesting to understand how the strain affects the magnetocrystalline part. Indeed, the way in which epitaxial strain can affect the magnetocrystalline anisotropy has been the subject of intensive investigations 6-13 . A prominent example of such investigations is the spinel compound CoFe 2 O 4 , which has a strong magnetostriction coefficient 7,10,11,14 . In CoFe 2 O 4 thin films, it was shown that changing the sign of the strain leads from cooperation to competition of shape and magnetocrystalline anisotropies 7 .Compounds with spinel (MgAl 2 O 4 -type) structure have chemical formula AB 2 X 4 where A and B are cations and X represents the ligand anion (usually O, S or Se). In this structure, the cations occupy either the tetrahedrally coordinated 15 (T) site or the octahedrally coordinated (O) site. There are twice as many O sites as T sites. In a normal spinel, A and B cations occupy T and O sites, respectively, while in an inverse spinel, half of the B cations occupy the T sites and the remaining half occupy the O sites together with the A cations. In general, spinels can be characterised by the degree of inversion (i.e. the concentration of B cations occupying T sites).The bulk structure (unstrained case) of the inverse spinel CoFe 2 O 4 , with a disordered Co 2+ /Fe 3+ occu-pancy on the octahedrally coordinated sites, has cubic symmetry (space group F d3m). This enforces the quadratic magnetization terms in the magnetocrystalline anisotropy to vanish, leaving as lowest order terms the quartic ones, which are typically of smaller size, although ...

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