Magnetic dilution effect and topological phase transitions in (Mn1−xPbx)Bi2Te4

As the first intrinsic antiferromagnetic topological insulator, ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ has provided a material platform to realize various emergent phenomena arising from the interplay of magnetism and band topology. Here, by investigating (${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Pb}}_{x}){\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}\phantom{\rule{4pt}{0ex}}(0\ensuremath{\le}x\ensuremath{\le}0.82)$ single crystals via the x-ray, electrical transport, magnetometry and neutron measurements, chemical analysis, external pressure, and first-principles calculations, we reveal the magnetic dilution effect on the magnetism and band topology in ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$. With increasing $x$, both lattice parameters $a$ and $c$ expand linearly by around 2%. All samples undergo the paramagnetic to A-type antiferromagnetic transition with the $\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\text{e}}\mathrm{el}$ temperature decreasing lineally from 24 K at $x=0$ to 2 K at $x=0.82$. Our neutron data refinement of the $x=0.37$ sample indicates that the ordered moment is 4.3(1)${\ensuremath{\mu}}_{B}$/Mn at 4.85 K and the amount of the ${\mathrm{Mn}}_{\mathrm{Bi}}$ antisites is negligible within the error bars. Isothermal magnetization data reveal a slight decrease of the interlayer plane-plane antiferromagnetic exchange interaction and a monotonic decrease of the magnetic anisotropy due to diluting magnetic ions and enlarging the unit cell. For $x=0.37$, the application of external pressures enhances the interlayer antiferromagnetic coupling, boosting the $\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\text{e}}\mathrm{el}$ temperature at a rate of 1.4 K/GPa and the saturation field at a rate of 1.8 T/GPa. Furthermore, our first-principles calculations reveal that the band inversion in the two end materials, ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ and ${\mathrm{PbBi}}_{2}{\mathrm{Te}}_{4}$, occurs at the $\mathrm{\ensuremath{\Gamma}}$ and $Z$ point, respectively, while two gapless points appear at $x=$ 0.44 and $x=$ 0.66, suggesting possible topological phase transitions with doping.