Advanced materials characterization techniques with ever-growing data acquisition speed and storage capabilities represent a challenge in modern materials science, and new procedures to quickly assess and analyze the data are needed. Machine learning approaches are effective in reducing the complexity of data and rapidly homing in on the underlying trend in multi-dimensional data. Here, we show that by employing an algorithm called the mean shift theory to a large amount of diffraction data in high-throughput experimentation, one can streamline the process of delineating the structural evolution across compositional variations mapped on combinatorial libraries with minimal computational cost. Data collected at a synchrotron beamline are analyzed on the fly, and by integrating experimental data with the inorganic crystal structure database (ICSD), we can substantially enhance the accuracy in classifying the structural phases across ternary phase spaces. We have used this approach to identify a novel magnetic phase with enhanced magnetic anisotropy which is a candidate for rare-earth free permanent magnet.

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Using quantum mechanical perturbation theory (PT) we analyze how the energy of perturbation of different orders is renormalized in solids. We test the validity of PT analysis by considering a specific case of spin-orbit coupling as a perturbation. We further compare the relativistic energy and the magnetic anisotropy from the PT approach with direct density functional calculations in FePt, CoPt, FePd, MnAl, MnGa, FeNi, and tetragonally strained FeCo. In addition using decomposition of anisotropy into contributions from individual sites and different spin components we explain the microscopic origin of high anisotropy in FePt and CoPt magnets. The magnetocrystalline anisotropy is a central magnetic property for both fundamental and practical reasons.1-3 It can depend sensitively on many quantities such as dopants or small changes in lattice constant.4 While control of this sensitive quantity can be crucial in many applications, e.g. permanent magnetism 5 , magnetooptics 6 and magnetoresistive random-access memory devices 7 , it is often unclear what mechanisms are responsible for these anisotropy variations, even from a fundamental point of view. It was understood long ago 8,9 that the magnetic anisotropy energy (MAE) K in bulk materials is a result of simultaneous action of spin-orbit coupling (SOC) and crystal field (CF). While in general this statement is still valid, existing microscopic methods do not accurately describe K in the majority of materials. One can calculate MAE using ab-initio electronic structure methods based on density functional theory, however quantitative agreement is often rather poor. In any case such methods are usually not well equipped to resolve it into components that yield an intuitive understanding, to enable its manipulation and control. Sometimes K is analyzed in terms of SOC matrix elements of ξl·s, where ξ is the SOC constant. However, this perturbation also induces changes in other terms contributing the total energy, which can affect the MAE as well. Below we show how the actual atomic SOC is 'screened' in crystals and study spin decomposition of SOC and MAE in real world magnets.Let us write the total Hamiltonian of magnetic electronic system aswhere H 0 is the non-relativistic Hamiltonian (sum of kinetic and potential energies of electrons) and V = ξl·s is * Materials of this paper have been presented at the 58th Annual the SOC Hamiltonian. We assume that ξ is small relative to CF and spin splittings. The change in the total energy of the system when SOC is added (below we call it relativistic part of the total energy) can be written aswhere E so is the matrix element of SOC with full perturbed wavefunction and ∆E 0 is the induced energy change of the scalar-relativistic Hamiltonian ( sum of kinetic and potential energies) due to the SOC perturbation. Using standard quantum mechanical perturbation theory (PT) each quantity |φ = |n , E = E (n) and E so = V (n) (wave function, total energy and perturbation V ) can be expressed as a sum over orders n: V (n) is proportional to...

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