Carrier density and thickness-dependent proximity effect in doped-topological-insulator–metallic-ferromagnet bilayers

We use magnetoconductivity to study the magnetic proximity effect on surface states of doped topological insulators. Our bilayers consist of a layer of ${\mathrm{Fe}}_7{\mathrm{Se}}_8$, which is a metallic ferrimagnet, and a layer of ${\mathrm{Bi}}_{0.8}{\mathrm{Sb}}_{1.2}{\mathrm{Te}}_3$, which is a highly hole-doped topological insulator. Using transport measurements and a modified Hikami-Larkin-Nagaoka model, we show that the ferromagnet shortens significantly the effective coherence length of the surface states, suggesting that a gap is opened at the Dirac point. We show that the magnetically induced gap persists on surface states which are separated from the magnet by a topological insulator layer as thick as 170 nm. Furthermore, the size of the gap is found to be proportional to the magnetization that we extract from the anomalous Hall effect. Our results give information on the ties between carrier density, induced magnetization, and magnetically induced gap in topological-insulator–ferromagnet bilayers. This information is important both for a theoretical understanding of magnetic interactions in topological insulators and for the practical fabrication of such bilayers, which are the basis of various suggested technologies, such as spintronic devices, far-infrared detectors, etc.

Figure 1

(a) The bilayer scheme. (b) A time-of-flight secondary ion mass spectroscopy (TOF-SIMS) three-dimensional (3D) image of relative intensities of Bi (green) and Fe (red) atoms in 170-nm ${\text{Bi}}_{0.8}{\text{Sb}}_{1.2}{\text{Te}}_3$ on 12-nm ${\text{Fe}}_7{\text{Se}}_8$ on ${\text{Al}}_2{\text{O}}_3$. $X$ and $Y$ axes are spatial coordinates and $Z$ is etching time. The FM etching rate is $five$ times lower than the TI rate so the layer thicknesses are not scaled. The bottom transparent layer is the ${\text{Al}}_2{\text{O}}_3$ substrate. The image shows that the bilayer consists of two distinct phases with an interface volume much smaller than the sample volume.

Figure 2

Magnetoconductivity, $\mathrm{\Delta }{\sigma }_{xx}={\sigma }_{xx}\left(B\right)-{\sigma }_{xx}\left(0\right)$, of bare TI films (diamonds) and TI/FM-metal bilayers (solid circles) with a m-HLN model fit. The TI thicknesses are 17 nm (red), 73 nm (blue), and 170 nm (black). Inset: Conductivity vs magnetic field of a bilayer with 170-nm TI, with a Kohler quadratic fit in the high fields. The fit gives an upper limit on the TI bulk MC term, showing it is negligible at low fields.

Figure 3

(a) The bilayers' effective coherence length $l_{\varphi 1}$ vs TI layer thickness $\left(t^{\mathrm{TI}}\right)$, extracted by fitting the low field MC data (Fig. 2) using Eq. (1). (b) The bilayers' normalized magnetically induced energy gap $\tilde{\mathrm{\Delta }}=\mathrm{\Delta }/{\epsilon }_F$, obtained by fitting the low field MC data assuming the bilayers' coherence length $l_c$ is the same as in our bare TI films (blue), or one-fourth of this value (red). See main text for a discussion of this result. Error bars are from the fitting and thickness uncertainty. Note the inflection point around 73 nm which we discuss in the main text.

Figure 4

The bilayer TI layer carrier density vs TI layer thickness calculated using Eq. (3). The FM thickness is 12 nm.

Figure 5

(a) The bilayer (total) Hall resistivity symmetric part, which is the anomalous Hall effect, for bare ${\text{Fe}}_7{\text{Se}}_8$ (black, right $y$ axis) and bilayers with different TI thickness (left $y$ axis): 17 nm (red), 73 nm (green), and 102 nm (blue). Note the opposite sign of the ${\text{Fe}}_7{\text{Se}}_8$ and bilayer signals. The displayed data are for positive to negative magnetic field direction in the hysteresis curve. (b) The bilayer remnant magnetization vs thickness normalized by the minimal value to cancel unknown constants. As explained in main text, the signal arises mainly from the magnetization that the FM layer induces in the TI layer.

Figure 6

(a) The magnetic gap $\mathrm{\Delta }$ vs $t^{\mathrm{TI}}$ normalized by its minimal value, showing a similar thickness dependence as the magnetization and carrier density [Figs. 4 and 5]. We calculated $\mathrm{\Delta }$ assuming a parabolic band. Inset: The Fermi energies and $\mathrm{\Delta }$ values vs $t^{\mathrm{TI}}$. These are only rough estimates since there are some parameters we do not know such as the shift between the Dirac point and the valence band. However, different values of those parameters did not change the thickness dependence. (b) The magnetic gap $\mathrm{\Delta }$ vs the remnant bulk magnetization $\left(M_{\mathrm{rem}}\right)$. We normalized the values by the minimal value to cancel unknown constants. Importantly, the gap depends monotonically on the bulk magnetization.

Figure 7

(a) The magnetic interaction length $l_{\mathrm{int}}$ vs the TI layer thickness in our bilayers. See the text for the $l_{\mathrm{int}}$ definition. (b) The averaged magnetization $M_{av}$ of our model as defined in the main text vs the TI layer thickness.

Figure 8

(a) X-ray diffraction data in a $\theta -2\theta$ method of a 102-nm-thick bare TI film (black) and a bilayer with a 12-nm-thick FM layer and a 102-nm-thick TI layer (red). The $y$ axis is the counts per second root. We subtracted the background from both samples. The x-ray wavelength is 1.54 A. (b) A zoom-in of the TI [0,0,2] peak.