Spin thermoelectric properties of the $\text{ Al}_{12} \text{ N}_{12}$ molecule

Abstract

In this paper, the effect of the direction of a magnetic field has been studied in leads (electrodes with limited width) on thermoelectric properties of $\text{ Al}_{12} \text{ N}_{12}$ cage with and without considering inelastic electron–phonon interactions. Results showed that the biggest (smallest) value of total conductivity is observed in the case of the maximum value of elastic conductivity ($G_{\sigma , {\sigma }'}^{M}$) with respect to the direction of the magnetic field for antiparallel ($\uparrow \downarrow \mathrm {or}\downarrow \uparrow )$, parallel configurations ($\downarrow \downarrow \mathrm {or}\uparrow \uparrow )$ for the left ($\sigma =\uparrow \downarrow )$ and the right (${\sigma }'=\uparrow \downarrow )$ lead spins, i.e., $G_{\downarrow ,\uparrow }^{M}\,(G_{\uparrow ,\uparrow }^{M})$. The maximum number of conduction heights was seen for $\sigma =\downarrow$ and ${\sigma }'=\uparrow$. With respect to the direction of magnetic field in the leads, the maximum value of electronic thermal conductance $(K_{e,\sigma {\sigma }'}^{\max } )$ can be arranged in the following order: $K_{e,\downarrow \uparrow }^{\max }>K_{e,\downarrow \downarrow }^{\max }>K_{e,\uparrow \downarrow }^{\max } >K_{e,\uparrow \uparrow }^{\max }$. The direction of the magnetic field in the leads affects the numbers, height and width peaks and valleys of the first derivative of thermopower (TP). We observe the highest (deepest) peak (valley) when $\sigma =\uparrow$ and ${\sigma }'=\downarrow$ ($\sigma =\uparrow$ and ${\sigma }'=\uparrow$). Also, the effect of temperature on current and tunnel magnetoresistance (TMR) was considered in this paper.