RKKY-type in-plane ferromagnetism in layered Mn1/4NbS2 single crystals

Placing the layers of the $3d$ magnetic elements in the van der Waals gap pulls the Nb/Ta-based transition metal dichalcogenides family from a nonmagnetic to a magnetic zone. However, the magnetic spectrum is strongly sensitive to the specific combination of host lattice and type of intercalated magnetic element and thus each combination needs a proper explicit study. In this context, we systematically investigate the magnetization of the Mn-intercalated layered ferromagnet ${\mathrm{Mn}}_{1/4}{\mathrm{NbS}}_{2}$ single crystal. Magnetization measurement revealed paramagnetic to ferromagnetic phase transition at around 105 K and an easy in-plane ($H\ensuremath{\perp}c$) significantly high magnetic anisotropy. The in-plane magnetic anisotropic energy (MAE) evaluated via the noncollinear first-principle approach is $\ensuremath{\sim}\ensuremath{-}600 \ensuremath{\mu}\mathrm{eV}$ per unit cell. The position of the Fermi level in between the spin-up and spin-down Mn states suppresses the positive contribution in the overall MAE, which lifts the overall MAE negative (in plane) with a larger size in ${\mathrm{Mn}}_{1/4}{\mathrm{NbS}}_{2}$. The comprehensive analysis of magnetization isotherms measured in the vicinity of ${T}_{c}$ with magnetic field $H$ applied parallel to the $ab$ plane ($H\ensuremath{\perp}c$) yields the asymptotic critical exponents $\ensuremath{\beta}=0.3251(2)$ and $\ensuremath{\gamma}=1.2(1)$, and $\ensuremath{\delta}=4.691(1)$. These critical exponents fulfill the scaling relation and scaling equation of the magnetic state predicted by the scaling theory. The determined critical exponents agree well with those obtained from the results of the renormalization group theory approach for a three-dimensional Ising system coupled with a long-range interaction between spins decaying as $J(r)\ensuremath{\approx}{r}^{\ensuremath{-}(d+\ensuremath{\sigma})}$ with $\ensuremath{\sigma}$ = 1.84. The Ising-type spin state in ${\mathrm{Mn}}_{1/4}{\mathrm{NbS}}_{2}$ is attributed to the higher size of MAE. Our theoretical analysis shows that indirect exchange interaction between Mn-Mn along the $c$ axis, mediated via spins' polarized conduction electrons of Nb atoms, a Ruderman-Kittel-Kasuya-Yoshida (RKKY) type ferromagnetic interaction, dominates over the direct in-plane Mn-Mn exchange interaction (less favorable due to large ${d}_{\text{Mn-Mn}}\ensuremath{\sim}6.67\phantom{\rule{4pt}{0ex}}\stackrel{\ifmmode \mathring{}\else \r{}\fi{}}{\mathrm{A}}$) and is thus responsible for the macroscopic magnetization in ${\mathrm{Mn}}_{1/4}{\mathrm{NbS}}_{2}$. The RKKY-type ferromagnetic interaction in ${\mathrm{Mn}}_{1/4}{\mathrm{NbS}}_{2}$ arises due to the large spin polarization of the conduction electrons associated with the Nb atoms at the Fermi energy and existence of unoccupied Mn $3d$ states well above the Fermi level.