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A brief survey of experimental and theoretical studies of half-metallicferromagnets (HMFs) and spin gapless semiconductors is given, the possiblecandidates being the X$_2$YZ (X = Mn, Fe, Co; Y = Ti, V, Cr, Mn, Fe, Co, Ni; Z= Al, Si, Ga, Ge, In, Sn, Sb) Heusler alloys. The data on the electricalresistivity, normal and anomalous Hall Effect, and magnetic properties arepresented. It is shown that the Co$_2$FeZ alloys demonstrate properties ofconventional ferromagnets, the HMF properties being also manifested at thevariation of the Z-component. The Fe$_2$YAl and Mn$_2$YAl alloys show at thevariation of the Y-component both metallic and semiconducting electroniccharacteristics, the magnetic properties, changing from the ferromagnetic tocompensated ferrimagnetic state. The HMF and spin gapless semiconductor statesare supposed to exist in these Heusler alloys systems.

Peculiarities of electronic transport and magnetic state in half-metallic ferromagnetic and spin gapless semiconducting Heusler alloys