Nonvolatile Switching of Magnetism via Gate-Induced Sliding in Tetralayer Graphene

Abstract

Interlayer sliding degrees of freedom often determine the physical properties of two-dimensional (2D) materials. In graphene, for instance, the metastable rhombohedral stacking arrangement hosts correlated and topological electronic phases, which are absent in conventional Bernal stacking. Here, we demonstrate a sliding-induced first-order structural phase transition between Bernal and rhombohedral tetralayer graphene driven by gate voltages. Through transport measurement, we observe bistable switching between a Bernal-dominant state and a rhombohedral-Bernal mixed state across a wide space of the gate-voltage phase diagram. The structural phase transition results in nonvolatile switching between a paramagnet and a ferromagnet accompanied by the anomalous Hall effect. The sign reversal of the anomalous Hall effect under opposite displacement fields suggests that it may originate from domain boundaries between the Bernal and rhombohedral regions. Our discovery paves the way for on-demand toggling of quantum phases based on the sliding phase transition of 2D materials and offers a playground to explore unconventional physics at the stacking domain boundaries.

Figures (4)

• Figure 1: Doping-induced sliding phase transition between rhombohedral and Bernal tetralayer graphene.a, Crystal structures of Bernal (ABAB) and rhombohedral (ABCA) tetralayer graphene drawn with VESTA momma_vesta_2011. The two structures are related by an interlayer sliding between the second and the third layers of graphene. b, Kelvin probe force microscopy (KPFM) image of mixed Bernal (B, light) and rhombohedral (R, dark) domains. The Bernal regions is larger in area than the rhombohedral regions because of the lower energy of Bernal stacking. c, Longitudinal resistance $R_{xx}$ measured versus forward (red) and backward (blue) scan directions of carrier density $n$ at a constant displacement field of $D/\varepsilon_0 = -0.067 \ \mathrm{V/nm}$, where $\varepsilon_0$ is the vacuum permittivity. Abrupt changes in the resistance appear at $-4.1 \times 10^{12}\ \mathrm{cm}^{-2}$ and $-15.5 \times 10^{12}\ \mathrm{cm}^{-2}$ for the forward and backward scans, respectively, as highlighted by the black triangles. d, (Top) $R_{xx}$ measured versus time $t$. The high and low resistance regions correspond to the RB-mixed and B-dominant states, respectively. (Bottom) $n$ versus $t$ controlled under $D/\varepsilon_0 = -0.067 \ \mathrm{V/nm}$.
• Figure 2: Determination of switching boundary.a, Schematic of the measurement procedure for determining the switching boundary between the RB-mixed and B-dominant states. We repeated Steps 1-4 at different values of $V_t$ to obtain b and c. b,$R_{xx}$ measured by sweeping $V_b$ in the increasing direction, $R_{xx}^F$. c,$R_{xx}$ measured by sweeping $V_b$ in the decreasing direction, $R_{xx}^B$. d, The difference, $\Delta R_{xx} = (R_{xx}^F - R_{xx}^B)$, over the average resistance, $\bar{R}_{xx} = (R_{xx}^F + R_{xx}^B) / 2$. The black dashed line corresponds to the switching boundary from RB-mixed to B-dominant state. e-h, The same as a-d with flipped $V_b$ and $V_t$.
• Figure 3: Phase Diagram. a, The sum of Fig. \ref{['fig2']}d and \ref{['fig2']}h. The left side of the black dashed boundary indicates the area of phase space accessible to the RB-mixed state. The blue dashed lines indicate other equipotential contours that are extracted from another contact configuration (see Extended Data Fig. 7). The black boxes indicate the areas measured in Fig. \ref{['fig4']}. b, The calculated energy difference, $\Delta U$, between the two structures. Overlaid are the contour lines extracted from the experimental data.
• Figure 4: Nonvolatile control of the anomalous Hall effect. RB-mixed measurements were taken by first going to the largest hole density corner and then going along the edge of the gate boundary, similar to the measurement in Fig. \ref{['fig2']}, for each line. B-dominant measurements were taken by first going to $V_t = V_b = 0$ V, before scanning for each line. a,b,$R_{yx}$ measured at $B = 0.03$ T in the positive $D$ and small positive $n$ region (black box in Fig. \ref{['fig3']}a), in the RB-mixed (a) and B-dominant state (b), respectively. Large negative $R_{yx}$ appears exclusively in the RB-mixed state, indicating an anomalous Hall effect (AHE). c,d,$R_{yx}$ measured at $T=$ 1.5 K as a function of $B$ in both the forward (red) and backward (blue) directions for the RB-mixed (c) and B-dominant state (d), respectively. A nonzero $R_{yx}$ at $B=0$ T and the hysteresis appears only in the RB-mixed state. Note that both of these data are taken at exactly the same gate voltages as highlighted at the diamond position in a and b. e,f, The same as a and b measured in the negative $D$ region. A large positive AHE (and a negative AHE in the smaller $n$ region) appears only in the RB-mixed state. g,h,$R_{yx}$ measured at $T=$ 1.5 K at the star position in the RB-mixed (g) and B-dominant state (h), respectively. i,j,$R_{yx}$ measured at $T=$ 1.5 K at the pentagon position in the RB-mixed (i) and B-dominant state (j), respectively. Nonlinearity in $R_{yx}$ indicates a weak, but finite AHE.