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The tunneling conductance in the half-metal/conical magnet/superconductor(HM/CM/SC) is investigated by the use of the combined Blonder-Tinkham-Klapwijk(BTK) formalism and the Bogoliubov-de Gennes (BdG) equations. We show that theconductance calculated self-consistently differs significantly from the onecalculated in the non-self-consistent framework. The use of the self-consistentprocedure ensures that the charge conservation is satisfied. Due to the spinband separation in the HM, the conductance in the subgap region is mainlydetermined by the anomalous Andreev reflection the probability of whichstrongly depends on the spin transmission in the CM layer. We show that thespin of electron injected from the HM can be transmitted through the CM to theSC adiabatically or non-adiabatically depending on the period of the exchangefield modulation. We find that the conductance in the subgap region oscillatesas a function of the CM layer thickness wherein the oscillations transform fromirregular, in the non-adiabatic regime, to regular in the adiabatic case. Inthe non-adiabatic regime the decrease of the exchange field amplitude in the CMleads to the emergence of the conductance peak for one particular CM thicknessin agreement with experiment [J.W.A Robinson, J. D. S Witt and M. G. Blamire,Science 329, 5987]. For both transport regimes the conductance is analyzed overa broad range of parameters determining the spiral magnetization in the CM.

Tunneling conductance in half-metal/conical magnet/superconductor junctions in the adiabatic and non-adiabatic regime: self-consistent calculations