Development of ferromagnetism in the doped topological insulator ${\text{Bi}}_{2-x}{\text{Mn}}_x{\text{Te}}_3$

The development of ferromagnetism in Mn-doped ${\text{Bi}}_2{\text{Te}}_3$ is characterized through measurements on a series of single crystals with different Mn content. Scanning tunneling microscopy analysis shows that the Mn substitutes on the Bi sites, forming compounds of the type ${\text{Bi}}_{2-x}{\text{Mn}}_x{\text{Te}}_3$, and that the Mn substitutions are randomly distributed, not clustered. Mn doping first gives rise to local magnetic moments with Curie-like behavior, but by the compositions ${\text{Bi}}_{1.96}{\text{Mn}}_{0.04}{\text{Te}}_3$ and ${\text{Bi}}_{1.91}{\text{Mn}}_{0.09}{\text{Te}}_3$, a second-order ferromagnetic transition is observed, with $T_C\sim 9–12\text{K}$. The easy axis of magnetization in the ferromagnetic phase is perpendicular to the ${\text{Bi}}_2{\text{Te}}_3$ basal plane. Thermoelectric power and Hall effect measurements show that the Mn-doped ${\text{Bi}}_2{\text{Te}}_3$ crystals are $p$-type. Angle-resolved photoemission spectroscopy measurements show that the topological surface states that are present in pristine ${\text{Bi}}_2{\text{Te}}_3$ are also present at 15 K in ferromagnetic Mn-doped ${\text{Bi}}_{2-x}{\text{Mn}}_x{\text{Te}}_3$ and that the dispersion relations of the surface states are changed in a subtle fashion.

Figure 1

(Color online) Zero-field cooled (ZFC) temperature-dependent dc magnetic susceptibility $\chi$ measured at 1 kOe applied magnetic field for the ${\text{Bi}}_{2-x}{\text{Mn}}_x{\text{Te}}_3$ crystals. The magnetic susceptibility in the region of 0 to 30 K is shown in the inset.

Figure 2

(Color online) Temperature dependence of the inverse susceptibility for $x=0.005$, 0.01, 0.02, 0.04, and 0.09 of ${\text{Bi}}_{2-x}{\text{Mn}}_x{\text{Te}}_3$.

Figure 3

(Color online) Temperature dependence of the inverse susceptibility per mole of Mn for $x=0.005$, 0.01, 0.02, 0.04, and 0.09 of ${\text{Bi}}_{2-x}{\text{Mn}}_x{\text{Te}}_3$. The effective magnetic moment per mole of Mn is shown in the inset.

Figure 4

(Color online) Arrott plots at various temperatures near $T_C$ for ${\text{Bi}}_{1.96}{\text{Mn}}_{0.04}{\text{Te}}_3$. The ferromagnetic transition is of second order at $T_C\sim 9\text{K}$.

Figure 5

(Color online) Arrott plots for ${\text{Bi}}_{1.91}{\text{Mn}}_{0.09}{\text{Te}}_3$ show the second-order ferromagnetic transition with a $T_C$ of about 12 K.

Figure 6

(Color online) Magnetic-field-dependent magnetization of a ${\text{Bi}}_{1.91}{\text{Mn}}_{0.09}{\text{Te}}_3$ crystal under the applied field parallel to the $c$ axis, $H\parallel c$, and perpendicular to the $c$ axis, $H\perp c$, at $T=1.8\text{K}$. Inset shows the hysteresis $MH$ loops of this ${\text{Bi}}_{1.91}{\text{Mn}}_{0.09}{\text{Te}}_3$ crystal for both field directions.

Figure 7

(Color online) Temperature-dependent resistivities for $x=0.005$, 0.02, and 0.09 of ${\text{Bi}}_{2-x}{\text{Mn}}_x{\text{Te}}_3$. Inset shows the resistivity of ${\text{Bi}}_{1.91}{\text{Mn}}_{0.09}{\text{Te}}_3$ crystal in 0 and 10 kOe applied magnetic fields.

Figure 8

(Color online) Hall resistivity ${\rho }_{yx}$ vs field $H$ in ${\text{Bi}}_{2-x}{\text{Mn}}_x{\text{Te}}_3$ with $x=0.04$ (upper panel) and $x=0.09$ (lower panel). ${\rho }_{yx}$ is holelike and displays a slight change of slope in the weak-field limit. The hole density $p=H/e{\rho }_{yx}$ inferred at 8 T and 20 K equals $5\times {10}^{18}{\text{cm}}^{-3}$ and $7\times {10}^{19}{\text{cm}}^{-3}$ for $x=0.04$ and 0.09, respectively.

Figure 9

(Color online) Quantum oscillations extracted from the derivative of the Hall resistivity $d{\rho }_{yx}/dH$ measured at 5 K in ${\text{Bi}}_{2-x}{\text{Mn}}_x{\text{Te}}_3$ with $x=0.04$. The period of the oscillations $\Delta \left(1/H\right)=0.046{\text{T}}^{-1}$ gives a (spherical) FS volume of wave vector $k_F=0.047{\text{Å}}^{-1}$, corresponding to a carrier density, $3.5\times {10}^{18}{\text{cm}}^{-3}$, slightly smaller than $p=H/e{\rho }_{yx}$.

Figure 10

(Color online) Temperature-dependent Seebeck coefficients for ${\text{Bi}}_{2-x}{\text{Mn}}_x{\text{Te}}_3$ crystals.

Figure 11

(Color online) STM topographic image of ${\text{Bi}}_{1.91}{\text{Mn}}_{0.09}{\text{Te}}_3$, identifying the atomic substitutional site of Mn dopants, and the absences of Mn clustering. (a) STM topograph ($+250\text{meV}$, 40 pA) of the ${\text{Bi}}_{1.91}{\text{Mn}}_{0.09}{\text{Te}}_3$ (001) surface over a $1000\times 1000{\text{Å}}^2$ area. Substitutional Mn atoms appear as triangular suppressions of the LDOS. [(b) and (c)] Zoom-in topographies over Mn dopants in an area of $30\times 30{\text{Å}}^2$ for unoccupied ($+500\text{mV}$, 30 pA) and filled states ($-500\text{mV}$, 30 pA). The positions of top Te layer, Bi layer, and substitutional Mn are shown by blue, magenta, and green circles on the topographies. (d) Study of the possibility of clustering by calculating the probability of correlation between Mn pairs in different locations. For a randomly chosen pair of Mn, $P\left(<r\right)$ gives the probability of the pair having a separation less than $r$. The calculated probability scales very close to $r^2$ (solid line) for an extended range of distances, demonstrating the uncorrelated distribution of Mn dopants.

Figure 12

(Color online) Comparison of the LDOS for pristine ${\text{Bi}}_2{\text{Te}}_3$ [blue (darker) line] and ${\text{Bi}}_{1.96}{\text{Mn}}_{0.04}{\text{Te}}_3$ [red (lighter) line] as measured by STM at 4.2 K. Valence band (V.B.) and conduction band (C.B.) states are seen at the low and high bias values and surface states (S.S.) are seen in the band gap at intermediate bias conditions. The chemical potential is shifted by about 150 mV toward the valence band in the Mn-doped sample, indicating the $p$-type character of the Mn dopants. The surface states are present in Mn-doped ${\text{Bi}}_2{\text{Te}}_3$ below its bulk ferromagnetic $T_C$.

Figure 13

(Color online) (a) Fermi surface of the surface states of undoped ${\text{Bi}}_2{\text{Te}}_3$ is shown, with a complete map of momentum space in the inset revealing only $\sim 0.001$ conducting electrons in the surface Brillouin zone. [(b) and (c)] Energy-resolved ARPES measurements show that the chemical potential of ${\text{Bi}}_{1.91}{\text{Mn}}_{0.09}{\text{Te}}_3$ (“${\mu }_{\text{Mn}}$”) is lowered by approximately 180 meV compared to undoped ${\text{Bi}}_2{\text{Te}}_3$ (“${\mu }_0$”), resulting in some changes to the surface states and a transition from electronlike to holelike charge carriers $\left(\sim 0.001\text{holes}/\text{BZ}\right)$ in the surface states. Data were taken approximately 30 min after cleavage.