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TiMn (=Al, Ga, In) compounds with CuHgTi-type structure are predicted to have the different width of band gap in two spin channels and exhibit a nearly spin gapless semiconductivity. There are different origins of the band gap in spin-up and spin-down channels. The width of the band gap can be adjusted by changing the lattice parameter or doping congeners. These compounds are completely-compensated ferrimagnets with a zero magnetic moment.


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