Giant spin thermoelectric efficiency in ferromagnetic graphene nanoribbons with antidots

Thermoelectric effects in zigzag graphene nanoribbons with parallel alignment of the edge spin polarizations are investigated theoretically. Spin and charge thermopower, electrical and heat conductance, and charge and spin thermoelectric efficiency are calculated numerically for pristine nanoribbons as well as for nanoribbons with periodic one-dimensional lattice of structural defects in the form of antidots. It is shown that structural defects reduce thermal conductance due to phonons and open gaps in the corresponding electronic spectrum. This, in turn, leads to a significant enhancement of the Seebeck and spin Seebeck coefficients as well as of the thermoelectric efficiency. A giant enhancement appears in certain regions of chemical potential (controlled by doping or external gate) and survives at room temperatures.

Figure 1

Magnetic structure of pristine ferromagnetic zGNR (a) and of ferromagnetic zGNRs with antidots of the diameters $d=8$ Å (b), $d=12$ Å (c), and $d=15$ Å (d) for $N=10$. The red (black in print) dots indicate magnitude of the spin moments localized at the edge atoms of the nanoribbons.

Figure 2

Phonon heat conductance as a function of temperature for the pristine zGNR and for zGNRs with antidots of indicated diameter. The width of zGNRs corresponds to $N=10$ zigzag chains.

Figure 3

Band structure [(a)–(d)] and transmission functions [(e)–(h)] for the spin-up (dashed line) and spin-down (solid line) electrons in the pristine ferromagnetic zGNR [(a) and (e)] and in ferromagnetic zGNRs with antidots of the diameters $d=8$ Å [(b) and (f)], $d=12$ Å [(c) and (g)], and $d=15$ Å [(d) and (h)] for $N=10$. The other parameters as described in the text.

Figure 4

Electrical conductance $G$ as a function of chemical potential for spin-up (dashed line) and spin-down (solid line) channels, calculated for pristine [(a) and (e)] and defected zGNRs with the antidot diameters 8 Å [(b) and (f)], 12 Å [(c) and (g)], and 15 Å [(d) and (h)] at $T=100$ K (left panel) and $T=300$ K (right panel).

Figure 5

Spin current polarization $P$ as a function of chemical potential at $T=100$ K (dashed line) and $T=300$ K (solid line) for pristine (a) and defected zGNRs with diameters 8 Å (b), 12 Å (c), and 15 Å (d).

Figure 6

Electronic thermal conductance ${\kappa }_e$ as a function of chemical potential, calculated for $T=100$ K (dashed line) and $T=300$ K (solid line) for pristine (a) and defected zGNRs with the antidot diameters 8 Å (b), 12 Å (c), and 15 Å (d).

Figure 7

Charge (dotted line) and spin (solid line) thermopower as a function of chemical potential, calculated for pristine [(a) and (e)] and defected zGNRs with the antidot diameters 8 Å [(b) and (f)], 12 Å [(c) and (g)], and 15 Å [(d) and (h)] at $T=100$ K (left panel) and $T=300$ K (right panel).

Figure 8

Charge (dotted line) and spin (solid line) thermoelectric efficiency as a function of chemical potential calculated for pristine [(a) and (e)] and defected zGNRs with the antidot diameters 8 Å [(b) and (f)], 12 Å [(c) and (g)], and 15 Å [(d) and (h)] at $T=100$ K (left panel) and $T=300$ K (right panel).

Figure 9

(a) Transmission; (b) conductance $G_{\sigma }$ for spin-up (dashed line) and spin-down (solid line); (c) charge $S_c$ (dashed line) and spin $S_s$ (solid line) thermopower; (d) charge $Z{T}_c$ (dashed line) and spin $Z{T}_s$ (solid line) calculated as a function of $\mu$ for $T=100\text{K}$, $d=15\text{Å}$, and $N=16$.