Modulating magnetic anisotropy energy (MAE) by an electric field provides a powerful approach for advancing multiferroic materials and spintronic applications. In this work, we utilize first-principles calculations to investigate the electric field control of MAE in two-dimensional multiferroic materials ${\mathrm{CuCrP}}_2{\mathrm{S}}_6$ and ${\mathrm{CuMoP}}_2{\mathrm{S}}_6$, which belong to transition-metal thiophosphates (MTPs). Our results show a quasilinear relationship between MAE and the electric field, with the sign of induced changes in MAE varying based on the field's direction. This change in MAE is driven by two distinct and independent effects in the monolayer's response to the electric field: electronic and field-induced structural effects. Both effects on the MAE are enabled by the monolayer's asymmetry due to its ferroelectric nature. The electronic effect arises from the energy shifts of the $p$ states of the inequivalent (top and bottom) sulfur layers, which impact the density of states of the valence-band-edge majority-spin $d_{z^2}$ orbitals of the magnetic central atom, thereby modifying the MAE. The structural effect on the MAE is primarily attributed to the effect of an inverse-piezoelectric strain, which is manifested as a variation in the monolayer thickness. The trend of this induced strain is controlled by the difference in effective charges between the top and bottom sulfur layers. These findings offer insights into the tunability of MAE via electric fields, and they highlight potential MTP candidates for switching of MAE.

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• Density of states
• Electric field effects
• First-principles calculations
• Magnetic anisotropy
• Multiferroics