Modulation of ferromagnetism in $(\mathrm{In},\mathrm{Fe})\mathrm{As}$ quantum wells via electrically controlled deformation of the electron wave functions

We demonstrate electrical control of ferromagnetism in field-effect transistors with a trilayer quantum well (QW) channel containing an ultrathin n-type ferromagnetic semiconductor $(\mathrm{In},\mathrm{Fe})\mathrm{As}$ layer. A gate voltage is applied to control the electron wave functions ${\phi }_i$ in the QW, such that the overlap of ${\phi }_i$ and the $(\mathrm{In},\mathrm{Fe})\mathrm{As}$ layer is modified. The Curie temperature is largely changed by 42%, whereas the change in sheet carrier concentration is two to three orders of magnitude smaller than that of previous gating experiments. This result provides an approach for versatile, low power, and ultrafast manipulation of magnetization.

Figure 1

(a) Schematic illustration of the two methods: Controlling $T_{\mathrm{C}}$ by carrier density as in previous works (top panel) and by carrier wave function as in the present study (bottom panel). Unlike 3D cases, in ferromagnetic QW, $T_{\mathrm{C}}$ does not change monotonically with the carrier density, which is due to the steplike change of the density of states. (b) Sample structures of device A (left panel) and device B (right panel). In both samples, the QW is the top $\mathrm{InAs}/(\mathrm{I}{\mathrm{n}}_{0.94},\mathrm{F}{\mathrm{e}}_{0.06})\mathrm{As}/\mathrm{InAs}$ trilayer structure. The Fe concentration is fixed at 6%. In device B, the bottom 5-nm InAs layer in the QW is doped with $\mathrm{Si}(5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3})$. (c) Schematic structure of the FET device with electrolyte (DEME-TFSI) between the gate (G), the reference electrode (R), and the trilayer QW. The source (S) and drain (D) electrodes and the electrodes numbered 1, 2, and 3 are used for transport measurements. (d) Anomalous Hall resistance (AHR) of device A at various temperatures. The inset shows the temperature dependence of the remanent AHR, which indicates a $T_{\mathrm{C}}$ of 24 K.

Figure 2

(a) Temperature dependence of the $R_{13}$ of device A at various gate voltage $V_{\mathrm{G}}$ values. (b) $n_{\mathrm{sheet}}$ values of device A (red circles) and device B (blue circles) at $4.2\mathrm{K}$ as functions of $V_{\mathrm{G}}$.

Figure 3

(a), (c) Evolution of the AHR of device A measured at 15 K when adjusting $V_{\mathrm{G}}$ as follows: $0\mathrm{V}\to 0.5\mathrm{V}\to 6\mathrm{V}\to 0\mathrm{V}$ and $0\mathrm{V}\to -3\mathrm{V}\to 0\mathrm{V}$, respectively. The insets present the AHR data near the origin, which exhibit clear changes in hysteresis characteristics. (b), (d) Temperature dependence of the remanent AHR of device A at various $V_{\mathrm{G}}$ values. The colored arrows indicate the $T_{\mathrm{C}}$ values of device A at each $V_{\mathrm{G}}$. (e) Evolution of the AHR of device B measured at 25 K when adjusting $V_{\mathrm{G}}:0\mathrm{V}\to 2\mathrm{V}\to 0\mathrm{V}$. The inset presents the AHR data near the origin. (f) Temperature dependence of the remanent AHR of device B at various $V_{\mathrm{G}}$ values. The colored arrows indicate the $T_{\mathrm{C}}$ values of device B at each $V_{\mathrm{G}}$.

Figure 4

(a) Experimental $T_{\mathrm{C}}$ values of device A (black circles) and device B (blue circles), respectively, as functions of $V_{\mathrm{G}}$. Red squares and green diamonds represent the $T_{\mathrm{C}}^{2\mathrm{D}}$ values calculated using the 2D mean-field Zener model for device A and B, respectively, which exhibit good agreement with the experimental results. (b) Calculated potential profiles (blue curves), electron wave functions (yellow shapes), and electron-density distributions (red curves, with arrows pointing to the corresponding right-hand vertical axes) of the QW of device A at $V_{\mathrm{G}}=0,6$, and $-3\mathrm{V}$, from top to bottom. The Fermi levels (green dashed lines) and quantized energy levels (black lines, in the eV unit) in the trilayer QWs are shown. (c) Calculated evolution of the electron-density distribution in the trilayer QW of device A at $4.2\mathrm{K}$ when $V_{\mathrm{G}}$ is varied from $-3\mathrm{V}$ to $6\mathrm{V}$. The reddish regions correspond to the $(\mathrm{In},\mathrm{Fe})\mathrm{As}$ layer.