Electrically Tunable Magnetism in Magnetic Topological Insulators

The external controllability of the magnetic properties in topological insulators would be important both for fundamental and practical interests. Here we predict the electric-field control of ferromagnetism in a thin film of insulating magnetic topological insulators. The decrease of band inversion by the application of electric fields results in a reduction of magnetic susceptibility, and hence in the modification of magnetism. Remarkably, the electric field could even induce the magnetic quantum phase transition from ferromagnetism to paramagnetism. We further propose a transistor device in which the dissipationless charge transport of chiral edge states is controlled by an electric field. In particular, the field-controlled ferromagnetism in a magnetic topological insulator can be used for voltage based writing of magnetic random access memories in magnetic tunnel junctions. The simultaneous electrical control of magnetic order and chiral edge transport in such devices may lead to electronic and spintronic applications for topological insulators.

Figure 1

Evolution of surface band structure upon increasing $V$ in TI thin films. The dashed line indicates the Fermi level $E_F$; BCB (BVB), bulk conduction (valence) band; DP, Dirac point. (a) $V=0$, upper and lower SSs are degenerate with a hybridization gap opened at the Dirac point. (b) $V=V_T^c$, upper and lower SSs move up and down in energy, respectively, and touch at a finite momentum $k_c=V_T^c/v_F$. (c) $V>V_T^c$, a band gap is reopened at $k_c$.

Figure 2

Band structure and magnetic properties. (a),(c) Band gap of 4 and 3 QL TIs, respectively, as a function of SIA $V$, calculated analytically from Eq. (1) (solid line) or numerically (symbols). The parameters are taken from Ref. [31] for $({\mathrm{Bi}}_{0.1}{\mathrm{Sb}}_{0.9}{)}_2{\mathrm{Te}}_3$. In (a), when $0\le V<V_T^c$, the band structure is inverted, resulting in a QSH with $Z_2$ index $\nu =1$; $V>V_T^c$, the band structure becomes normal. (b),(d) The calculated spin susceptibility vs $V$ for 4 and 3 QL TIs, respectively. $V_M^c\approx 0.13\mathrm{eV}$ [32].

Figure 3

The phase diagram of the thin films of MTIs for $m_0\ne 0$ with two variables: $\mathrm{\Delta }$ and $V$. Only $\mathrm{\Delta }\ge 0$ and $V\ge 0$ is shown. The parameters are taken from Table 1 for 4 QLs ${\mathrm{Cr}}_{0.15}({\mathrm{Bi}}_{0.1}{\mathrm{Sb}}_{0.9}{)}_{1.85}{\mathrm{Te}}_3$. Phase QSH is well defined only in the $\mathrm{\Delta }=0$ line. The phase boundary (navy solid lines) is the semimetal phase. The edge spectrum of points $A$ and $B$ is shown in Figs. 4 and 4, respectively.

Figure 4

(a) Schematic diagram of a proposed transistor device for using dual gates and an electric field to tune charge or spin transport. $V_{\text{tg}}$, top-gate voltage; $V_{\mathrm{bg}}$, back-gate voltage. (b) Without an electric field, the MTI film has FM order and is in a QAH phase, thus protected, chiral edge state (upper right). (c) Applying an electric field perpendicular to the film breaks the inversion symmetry, which drives the MTI to be PM and in a NI phase, thus no protected edge state (lower right).

Figure 5

Electric-field-assisted switching in a MTJ, which can be used as voltage based writing of MRAM. (a) Schematic drawing of a MTJ and the effect of electric field. (b) Dependence of $H_c$ for the top MTI and bottom FM layer on the bias voltage. The estimation of $H_c$ and working condition of the device are discussed in the Supplemental Material [32].