Table 1 Nearest- and third-neighbor exchange interactions from ab-initio calculation results (in meV)

		In-plane first nearest-neighbor exchange interactions (in meV)
	A1	B1	C1	A2	B2	C2	A3	B3	C3	Total
J₁	−1.085	0.468	0.776	0.066	5.481	−2.603	0.027	−4.171	0	−1.040
K₁	0.559	−1.652	0	0.196	−3.117	0	−0.278	2.085	0	−2.207
Г₁	−0.243	0	0	0	0	0	0	0	0	−0.243


J₃	−0.036	1.681	-	-	-	-	-	-	1.664
K₃	0.015	0	-	-	-	-	-	-	0.015
Г₃	−0.011	0	-	-	-	-	-	-	−0.011

Here J, K, and Γ denote the isotropic Heisenberg, anisotropic Kitaev, and the symmetric anisotropy interaction terms, respectively. The numerals 1, 2, and 3 denotes intersite, two-hole, and cyclic exchange processes, respectively. A, B, and C refers t_2g - t_2g, t_2g - e_g, and e_g - e_g exchange processes, respectively²⁵. The on-site Coulomb potential on Co d- and O p-orbitals, Hund’s coupling on Co d- and O p-orbitals, and the crystal-field splitting within the Co d-orbitals were chosen to be 6 eV, 4 eV, 1.2 eV, 1 eV, and 1.022 eV, respectively. The parameters were specifically set to match the calculated optically excited energies with the experimental observations. The hopping parameters employed here are listed in the Supplementary information (Supplementary Note 1).

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