Spin-tunable thermoelectric performance in monolayer chromium pnictides

Historically, finding two-dimensional (2D) magnets is well known to be a difficult task due to the instability against thermal spin fluctuations. Metals are also normally considered poor thermoelectric (TE) materials. Combining intrinsic magnetism in two dimensions with conducting properties, one may expect to get the worst for thermoelectrics. However, we will show this is not always the case. Here, we investigate the spin-dependent TE properties of monolayer chromium pnictides ($\mathrm{Cr}X$, where $X=\text{P}$, As, Sb, and Bi) using first-principles calculations of electron- and phonon-energy dispersion, along with the Boltzmann transport formalism under an energy-dependent relaxation time approximation. All the $\mathrm{Cr}X$ monolayers are dynamically stable and they also exhibit half metallicity with ferromagnetic ordering. Using the spin-valve setup with an antiparallel spin configuration, the half metallicity and ferromagnetism in monolayer $\mathrm{Cr}X$ enable the manipulation of spin degrees of freedom to tune the TE figure of merit $\left(ZT\right)$. At an optimized chemical potential and operating temperature of 500 K, the maximum $ZT$ values ($\approx 0.22$, 0.12, and 0.09) with the antiparallel spin-valve setup in CrAs, CrSb, and CrBi improve up to almost twice the original values ($ZT\approx 0.12$, 0.08, and 0.05) without the spin-valve configuration. Only in CrP, which is the lightest species and less spin polarized among $\mathrm{Cr}X$, the maximum $ZT$ $(\approx 0.34)$ without the spin-valve configuration is larger than that $(\approx 0.19)$ with the spin-valve one. We also find that, at 500 K, all the $\mathrm{Cr}X$ monolayers possess exceptional TE power factors of about 0.02–0.08 W/m ${\mathrm{K}}^2$, which could be one of the best values among 2D conductors.

Figure 1

(a) Geometrical structure of 2D chromium pnictides with a honeycomb (hexagonal) lattice. (b) Spin-valve device setup with an antiparallel spin configuration.

Figure 2

Electronic structure (energy dispersion and density of states) of chromium pnictides: (a) CrP, (b) CrAs, (c) CrSb, (d) CrBi. The blue dashed (red solid) lines refer to spin-up (spin-down) states.

Figure 3

Thermoelectric quantities of CrP: (a)–(c) Electrical conductivity, (d)–(f) Seebeck coefficient, and (g)–(i) electron thermal conductivity of spin-up, spin-down, and total, respectively.

Figure 4

Phonon thermal conductivity ${\kappa }_{\text{ph}}$ as a function of temperature for different $\mathrm{Cr}X$ species. Indicated by boxes are ${\kappa }_{\text{ph}}$ values at 500 K.

Figure 5

(a)–(d) Power factors and (e), (f) figures of merit of CrP, CrAs, CrSb, and CrBi, respectively, as a function of chemical potential. In the PF plots, we show the contribution of spin-up states, spin-down states, and their total contribution to the PF values. In the $ZT$ plots, with $T=500\mathrm{K}$, we show a comparison of total $Z{T}^{\left(0\right)}$ [Eq. (6)] and $Z{T}^{\mathrm{sv}}$ that includes the spin-valve effect.

Figure 6

Maximum $Z{T}^{\left(0\right)}$ and $Z{T}^{\mathrm{sv}}$ (left axis) and the corresponding optimal chemical potential ${\mu }_{\mathrm{opt}}$ (right axis) for each $\mathrm{Cr}X$ species with $T=500\mathrm{K}$.