“…According to the theory of thermally generated magnon-driven interfacial spin pumping mechanism, simultaneous application of a vertical ( z -axis) temperature gradient and an external transverse dc magnetic field ( x -axis) across the MgO/CoFeCrGa (95 nm)/Pt film gives rise to transverse spin current pumping from the CoFeCrGa layer into the Pt layer with the interfacial spin current density: at the CoFeCrGa/Pt interface, where G ↑↓ , ℏ, γ, M S , and V a are the interfacial spin-mixing conductance, the reduced Planck’s constant , the gyromagnetic ratio, the saturation magnetization of CoFeCrGa, and the magnon coherence volume, respectively. ,, The magnetic coherence volume is expressed as , where ζ is the Riemann Zeta function and D is the spin-wave stiffness constant. , This transverse spin current, , is then converted into charge current along the y -axis via the inverse spin Hall effect (ISHE), where e , θ SH Pt , and are the electron charge, the spin Hall angle of Pt, and the spin polarization vector, respectively. The corresponding voltage along the y -axis can be expressed as , where R y , L y , λ Pt , and t Pt are the electrical resistance between the voltage leads, the distance between the voltage leads, the spin diffusion length of Pt, and the thickness of the Pt layer (=5 nm), respectively. Since CoFeCrGa is a spin gapless semiconductor with soft ferromagnetic behavior, , concomitant application of the temperature gradient ( z -axis) and dc magnetic field ( x -axis) also generates a spin-polarized current in the CoFeCrGa layer along the y -axis due to ANE, which gives rise to an additional contribution ( V CoFeCRGa ANE ) to the total voltage signal measured across the Pt layer in the MgO/CoFeCrGa (95 nm)/Pt heterostructure.…”