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Ashani et al. Energy Mater. 2025, 5, 500111 https://dx.doi.org/10.20517/energymater.2025.10 Page 9 of 13

Figure 5. Electronic thermal conductivity along (A) x-direction and (B) y-direction for spin-up and spin-down at different temperatures
(red color for spin-up and blue color for spin-down); (C) The lattice thermal conductivity vs. temperature along x-direction (color black)
and y-direction (color red).

decreased with increasing temperature. This behavior agrees with the evolution law of K . For instance, at
L
-1
-1
-1
-1
100 K we obtained an isotropic K of 0.5 Wm K in both directions. This value decreased to 0.2 Wm K at
L
300 K. The low K at 300 K may be an indication of relatively stronger phonon-phonon interaction leading
L
to substantial anharmonic scattering. Due to this stronger scattering, the phonon mean free path will be
decreased, and this may result in low K . Overall, we found that the total thermal conductivity of the system
L
was mostly governed by the K . For comparison, we present the total thermal conductivity of the V S O
e
2 2
monolayer with other well-studied MoS in Supplementary Table 1.Finally, we evaluated the spin and
2
charge dimensionless figure of merit (ZT). We obtained the dimensionless ZT using the transport
parameters in the relations:
(14)
(15)

where σ = σ + σ , and K is the sum of the electronic part of the thermal conductivities of the spin-down
↑
↓
e
and spin-up carriers. Figure 6A-D reveals the computed results. Due to the directional spin-dependence of
the σ, we also obtained ZT Charge = ZT along the y and x directions. At 300 K, we obtained a maximum ZT
spin
of 0.86 in the hole-doped systems, while it became 0.63 in the electron-doped systems.
This carrier type dependent ZT feature comes from the electrical conductivity in which σ (σ ) is greater in
↑
↓
the hole-doped system along the y-direction (x-direction). Overall, the ZT is controlled by only one spin
component in each direction. Our findings may suggest that the V S O altermagnet system may be used for
2 2
potential pure spin current generation in spintronic and thermoelectricity.
CONCLUSIONS
We probed the spin-dependent transport properties of the altermagnet V S O monolayer using the
2 2
spin-polarized density functional theory and Boltzmann transport theory. This V S O monolayer had a
2 2
direct band gap of 1.15 eV and a uniform spin splitting of 0.51 eV at the X and Y points in the valence band
maximum. This band gap was determined by the spin-down (spin-up) channels at the X-point (Y-point).
We obtained a high critical temperature of about 746 K. Due to the directional spin-dependent feature in
the band structure, the Seebeck coefficients, electrical conductivity, effective spin and charge Seebeck
coefficients, electronic part of the thermal conductivity, and ZT are influenced by spin-down (spin-up)
carriers in the x-direction (y-direction). The electrical conductivity obtained in the hole-doped systems is