La_{1-x} Ca_{x}MnO_{3} perovskites show semiconducting properties in the paramagnetic range. The gap is reduced near x=0.33, where ferromagnetic ordering is observed. The ferromagnetic ordering then induces a semiconductor-metal transition, and gives rise to a giant magnetoresistance effect. The ground state electronic structure calculations were done with KKR-CPA method for hypothetical cubic and ferromagnetic LaMnO_{3} and CaMnO_{3} compounds, as well as for disordered La_{1-x}Ca_{x}MnO_{3} (x=0.33, 0.4, 0.5) alloys with real crystal data. As a result, we get a magnetic moment per formula 4.00μ_{B} and 3.00μ_{B} and half-metallic behaviour for end-compounds, respectively. In the ferromagnetic region a linear decrease in the magnetic moment of La_{1-x}Ca_{x}MnO_{3} is observed, together with the decrease in the gap width for spin-down carriers, if doping Ca in La_{1-x}Ca_{x}MnO_{3}. A simple model is developed, which describes magnetic and transport properties as resulting from an exchange-induced band-crossing semiconductor-metal transition, as for instance in EuO.
In this work, some relations between crystal structure and magnetic ordering in CrCoFeNiAl HEAs are discussed in view of the KKR-CPA calculations. Remarkably, it is noticed that the transition between fcc and bcc phases in the analysed CrCoFeNi_{x}Al and CrCoFeNiAl_{x} alloys is closely related to change in ordering of the local magnetic moments, namely the magnetic moment on Cr is either parallel (ferromagnetic) or antiparallel (ferrimagnetic) to the magnetic moments of other atoms (Co, Fe and Ni). On the whole, the theoretical diagram showing the fcc-bcc phase preference and their coexistence vs. alloy composition well corroborates with available experimental data.
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