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Page 4 of 13 Ashani et al. Energy Mater. 2025, 5, 500111 https://dx.doi.org/10.20517/energymater.2025.10

Figure 1. (A) Schematic illustration of top and side views of V S O monolayer. Magnetic configurations of (B) AFM-Neel, (C)
2 2
AFM-Stripy, and (D) AFM-Zigzag in a 2 × 2 × 1 supercell; (E) Band structure of monolayer V S O with First Brillouin zone with high
2 2
symmetry points as inset (red lines for spin-up and blue dashed-lines for spin-down); (F) Temperature-dependent sublattice
magnetization of V S O monolayer. AFM: Antiferromagnetic.
2 2
(4)

where m and N are the average magnetic moment and the number of magnetic atoms in the system.
Figure 1F shows the temperature-dependent sublattice magnetization curve. Overall, we obtained a Neel
temperature of 746 K for the V S O monolayer.
2 2

Now, we explore the spin-dependent transport properties such as spin-dependent Seebeck coefficients,
electrical conductivity, electronic thermal conductivity (K ), and lattice thermal conductivity (K ). First, the
e
L
spin-dependent Seebeck coefficient [S ] is obtained using:
(↑↓)
(5)

Here, q, T, and L are the elementary charge, the temperature, and the generalized linear spin-dependent
transport coefficient expressed as:

(6)

The conductivity tensor over the bands (i) and the k-points (k) can be expressed as σ (i,k) = e τi,kV ,
2
(↑↓)
2
where V represents group velocity. Figure 2 reveals the spin-dependent Seebeck coefficients for the spin-up
channel (S ) and spin-down channel (S ). In the x-direction, the Seebeck coefficient of the spin-down
↑
↓
channel comes first before the spin-up channel Seebeck coefficient in both doped systems. Meanwhile, in