We investigate the magnetic ground state and phase transitions in the frustrated three-dimensional system ${\mathrm{CaMn}}_2{\mathrm{P}}_2$ using first-principles calculations combined with spin-dynamics simulations. Our density functional theory (DFT) calculations, incorporating Hubbard $U$ corrections, reveal that ${\mathrm{CaMn}}_2{\mathrm{P}}_2$ exhibits an indirect gap semiconducting ground state with a localized ${\mathrm{Mn}}^{2+}$ ($3d^5$, $S=\frac{5}{2}$) electronic configuration and negligible spin-orbit coupling effects. The computed exchange interactions show that the magnetic behavior is well described by an isotropic Heisenberg Hamiltonian. In this model, there are two major couplings: The nearest-neighbor (NN) interaction $J_1$ couples the two Mn layers along the $c$ axis, and next-NN interaction $J_2$ is in the $a\text{−}b$ plane, where Mn ions form a hexagonal layer structure. Our results show that both $J_1$ and $J_2$ are antiferromagnetic in nature, and as a consequence, $J_2$ induces frustration owing to the in-plane triangular geometry of the Mn ions. $J_1$ is found to promote long-range antiferromagnetic order, while $J_2$ is responsible for spin canting and disorder. Our spin-wave analysis confirms that the system stabilizes a spin-spiral ground state with a propagation vector $q=(\frac{1}{6},\frac{1}{6},0)$, in agreement with neutron diffraction experiments. By tuning the $\frac{J_2}{J_1}$ ratio, we construct a phase diagram that reveals a transition from a collinear Néel antiferromagnetic state to spin-spiral phases with different propagation vectors and, eventually, to a disordered phase at large frustration. Atomistic spin dynamics simulations capture the temperature evolution of the magnetism and reproduce the experimentally measured magnetic specific heat as well as the transition temperature with good accuracy. Furthermore, for large $\frac{J_2}{J_1}$, we identify a low-temperature phase with slow spin relaxation and persistent fluctuations, suggesting a spin-liquid-like state. Our study provides a microscopic understanding of frustration-induced magnetism in ${\mathrm{CaMn}}_2{\mathrm{P}}_2$ and establishes it as a realization of the $J_1\text{−}{J}_2$ model in a three-dimensional lattice for exploring emergent magnetic phases.

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• Electronic structure
• First-principles calculations
• Magnetic interactions
• Magnetic phase transitions
• Magnetism
• Spin dynamics