The two-dimensional $M{A}_2{Z}_4$ material family has emerged as a research frontier in condensed matter physics and materials science due to its excellent stability and tunable electronic properties. While recent investigations have focused predominantly on their valley- and spin-related physical characteristics, exploration of their orbital Hall effect remains relatively insufficient. In this work, we systematically investigate the band structure and spin/orbital transport properties of monolayer ${\mathrm{MoSi}}_2{\mathrm{P}}_4$ through first-principles calculations and effective $k$·$p$ model analysis. The results show that ${\mathrm{MoSi}}_2{\mathrm{P}}_4$ exhibits an intrinsic orbital Hall effect. It demonstrates a pronounced orbital Hall conductivity near the Fermi level while maintaining relatively weak spin Hall conductivity. We further find a finite orbital Nernst response. Strain engineering studies on monolayer ${\mathrm{MoSi}}_2{\mathrm{P}}_4$ reveal that biaxial strain can induce a transition from a direct to an indirect bandgap. Despite this band structure change, the orbital Hall effect demonstrates remarkable robustness within a certain strain range. More importantly, the total orbital Nernst conductivity exhibits sign-tunable behavior under strain modulation, while the $\mathrm{\Gamma }$-region contribution is strongly enhanced when tensile strain shifts the valence band maximum to $\mathrm{\Gamma }$.

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• Hall effect
• Nernst effect
• First-principles calculations
• k dot p method