Among the $3d$ transition metal ions doped polar $\mathrm{N}{\mathrm{i}}_3\mathrm{Te}{\mathrm{O}}_6$, Mn-doped $\mathrm{N}{\mathrm{i}}_3\mathrm{Te}{\mathrm{O}}_6$ has stimulated great interest due to its high magnetic ordering temperature and complex magnetic phases, but the mechanism of magnetoelectric (ME) coupling is far from understood. Herein we report our systematic investigation of the chemical control of magnetism, metamagnetic transition, and ME properties of $\mathrm{N}{\mathrm{i}}_{3-x}\mathrm{M}{\mathrm{n}}_x\mathrm{Te}{\mathrm{O}}_6$ single crystals in high magnetic field ($H$) up to 52 T. We present a previously unreported weak ferromagnetic behavior appeared in the $ab$ plane below 9.5 K in addition to the incommensurate helical and commensurate collinear antiferromagnetic states. In the low-field region, a spin-flop-type metamagnetic transition without any hysteresis occurs at $H_{c1}$ for $H//c$, while another metamagnetic transition accompanied with a change in electric polarization is observed at $H_{c2}$ in the high-field region both for $H//c$ and $H//ab$ above 30 K, which can be attributed to the sudden rotation of magnetic moments at Ni2 sites. The ME measurements reveal that a first-order ME effect is observed in the low-$T$ and low-$H$ regions, while a second-order ME coupling term appears above 30 K in the magnetic field range of $H_{c1}<H<H_{c2}$ for $H//c$ and $H<H_{c2}$ for $H//ab$, both becoming significant with increasing temperature. Eventually, they are dominated by the second-order ME effect near the antiferromagnetic transition temperature. The present work demonstrates that $\mathrm{N}{\mathrm{i}}_{3-x}\mathrm{M}{\mathrm{n}}_x\mathrm{Te}{\mathrm{O}}_6$ is an exotic magnetoelectric material compared with $\mathrm{N}{\mathrm{i}}_3\mathrm{Te}{\mathrm{O}}_6$ and its derivatives, thereby providing insights to better understand the magnetism and ME coupling in $\mathrm{N}{\mathrm{i}}_3\mathrm{Te}{\mathrm{O}}_6$ and its derivatives.

• Received 25 September 2023
• Revised 18 March 2024
• Accepted 15 May 2024

DOI:https://doi.org/10.1103/PhysRevB.109.184112