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We consider E 6 GUT model in F-theory approach where E 6 is broken via trinification to the Standard Model (SM) gauge group using non-abelian fluxes. Including the gauge singlet wave function we found hierarchically small values for both the μ term as well as Dirac neutrino masses.

The ab initio study of electronic, magnetic properties and Curie temperature of AlAs doped by single and double impurities is investigated using LDA–KKR–CPA method. It is shown that the Al substituted by V and/or Ti induces a half-metallic character and ferromagnetism in the system for different concentrations except co-doping by x[Formula: see text]=[Formula: see text]y[Formula: see text]=[Formula: see text]0.035. The stability of magnetism between the ferromagnetic and DLM states as well as the mechanism of exchange interaction are discussed. The density of states are plotted in the energy diagram for different concentrations of dopants. The co-doping with (V, Ti) increases Curie temperature in AlAs with respect to single substituant. The finding of this work confirms that the new compounds have a great potential for spintronic devices.

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