Magnetoelectric Switching of Magnetic Order in Rhombohedral Graphene

Abstract

A finite Hall conductance under zero magnetic field implies time reversal symmetry (TRS) breaking due to magnetic order. In rhombohedral stacked multilayer graphene, the angular momentum that breaks TRS can result from the orbital degree of freedom at the $K$ and $K'$ valleys. This leads to valley polarization and occupation-dependent anomalous Hall resistance (AHR) due to the chirality in Berry curvature at the valleys. We report magnetoelectric control of orbital magnetic order in crystalline rhombohedral hexalayer graphene (R6G), achieved without the introduction of a moiré superlattice. At moderate displacement fields and low carrier densities, we observe a non-volatile and hysteretic AHR that can be electrically toggled by sweeping either the carrier density or the displacement field. Upon the application of small perpendicular magnetic fields, the system reveals a characteristic double sign reversal of the AHR, indicating a competition between distinct magnetic ground states. This interplay between valley polarization and electric and magnetic field tuning demonstrates the rich multiferroic behavior of R6G. Our findings present crystalline R6G as a minimal, tunable platform for studying symmetry-breaking phases and magnetic order in flat-band systems, offering insights into the coupling between electronic structure and magnetoelectric response.

Figures (13)

• Figure 1: Device structure and electronic transport characteristics. a, Schematic drawing of the device. R6G is fully encapsulated between two flakes of hBN. Dual graphite gates (top and bottom) enable independent control over the vertical electric displacement field $D$ and carrier density $n$. The displacement field is defined to be positive when directed from the top gate to the bottom gate. b, Optical microscope image of the fabricated device. Electrical contacts to the top gate (TG) and bottom gate (BG) are labeled. Scale bar: 10 $\upmu$m. c, 2D color map of the longitudinal resistance $R_{\text{xx}}$ as a function of carrier density $n$ and displacement field $D$ at zero magnetic field. Two distinct regions of interest characterized by tunable multiferroic behavior emerge at moderate positive and negative values of $D$, and are highlighted in green and red, respectively. d, Zoomed-in 2D color map of the transverse resistance $R_{\text{xy}}$ in the green region as highlighted in panel c. e, Zoomed-in 2D color map of the transverse resistance $R_{\text{xy}}$ in the red region as highlighted in panel c.
• Figure 1: a, Plot of the 2D interlayer vibrational Raman mode that can be used to identify regions with RH stacking ordering. The ratio of the left-to-right shoulder peak is greater than unity for RH stacking (red line) and smaller than unity for Bernal stacking (blue line). b, The stacking order of the entire flake can be mapped by scanning the Laser along the surface. c, A sufficiently large region of the flake with RH ordering is cut out via anodic oxidation using an AFM. The isolation helps to increase the likelihood that the region remains in RH stacking during fabrication. d, The intensity in arbitrary gray value units (a.u.) plotted against the distance in pixels along the black dashed line in panel c for the green color channel of the optical microscope CCD camera. The optical microscope settings are calibrated against AFM measurements so that 8 a.u. correspond to a single layer of graphene. The 48 a.u. across the graphene multilayer flake corresponds to six layers.
• Figure 2: Electric switching of magnetic order and orbital magnetization phase diagram. a--d, 2D color maps of the transverse resistance $R_{\text{xy}}$ as a function of carrier density $n$ and electric displacement field $D$ at zero magnetic field, shown for the positive displacement field region. Black arrows indicate the direction and axis of the fast parameter sweep. Independent control of the AHR is achieved by sweeping either the carrier density or the displacement field. This tunability is robust against variations in the preparation of the zero-field state and is independent of the direction of the slow sweeping axis. While sweeping the carrier density induces a sign reversal in $R_{\text{xy}}$ over most of the AHR wing, the tunability via the displacement field is more localized near charge neutrality and diminishes at higher doping levels. In the negative $D$ region, the behavior mirrors that of the positive side, with a reversed sign of the transverse resistance. e--h, Calculated phase diagram of the orbital magnetization for R6G in the $n$--$D$-plane. The sign of the orbital magnetization order parameter depends on the direction of the sweeping of the carrier density or the displacement field. Gray areas denote regions where the Landau free-energy model is inapplicable due to a negative quartic coefficient $c$.
• Figure 2: a, 2D color map of the transverse resistance $R_{\text{xy}}$ as a function of carrier density $n$ and perpendicular magnetic field $B$, measured at a fixed displacement field $D/\varepsilon_\text{0} = -0.16$ V/nm. The carrier density is swept in the direction indicated by the white arrow. b, c, 2D color maps of the longitudinal and transverse resistance $R_{\text{xx}}$ and $R_{\text{xy}}$, respectively, as a function of carrier density $n$ and perpendicular magnetic field $B$, measured at a fixed displacement field $D/\varepsilon_\text{0}$ = 0.15 V/nm. The carrier density is swept in the direction indicated by the black arrows. d--f, The same as in panels a--c, but with the reverse sweeping direction of the fast axis. Panels a and d show analogous behavior of the system as in Figure \ref{['fig: figure4']}a, b when exposed to a negative displacement field. The positions of the Dirac point in panels b, c, e, and f were used to correct for the sweeping direction-dependent small absolute offset in the carrier density during the hysteretic measurements.
• Figure 3: Magnetic-field dependence of electric tunability in the anomalous Hall response. a--d, 2D color maps of the transverse resistance $R_{\text{xy}}$ as a function of carrier density $n$ and electric displacement field $D$ at a small magnetic field $B = +20$ mT shown for the positive displacement field region. e--h, Equivalent maps for the negative displacement field region. Black arrows indicate the direction and axis of the fast parameter sweep. The tunability of the ground state with carrier density and displacement field persists in the positive displacement field region, albeit with a sign change in the transverse resistance, making it behave like the state in the negative displacement field region at zero magnetic field. The situation is different in the negative displacement field region shown in panels e--h. The AHR remains positive on the electron-doped side, with a sign switch to negative values across the CNP along a diagonal white line in the $n$--$D$-space.