Observation of Orbital Resonance Hall Effect in ${(\mathrm{TMTSF})}_2{\mathrm{ClO}}_4$

We report the observation of a Hall effect driven by orbital resonance in the quasi-1-dimensional (q1D) organic conductor ${(\mathrm{TMTSF})}_2{\mathrm{ClO}}_4$. Although a conventional Hall effect is not expected in this class of materials due to their reduced dimensionality, we observed a prominent Hall response at certain orientations of the magnetic field $B$ corresponding to lattice vectors of the constituent molecular chains, known as the magic angles (MAs). We show that this Hall effect can be understood as the response of conducting planes generated by an effective locking of the orbital motion of the charge carriers to the MA driven by an electron-trajectory resonance. This phenomenon supports a class of theories describing the rich behavior of MA phenomena in q1D materials based on altered dimensionality. Furthermore, we observed that the effective carrier density of the conducting planes is exponentially suppressed in large $B$, which indicates possible density wave formation.

Figure 1

The transverse resistivity in the conducting plane ${\rho }_{xy}$ is plotted as a function of the angle $\theta$ of the applied magnetic field $B$ at 12.5 T, 14.0 T, and 14.8 T. The magnetic field is rotated in the $yz$ plane, and $\theta$ is measured from the $z$ axis (inset right; visible contact areas shown in gold). The signals show a resonating structure that changes sign at the magic angles, shown as dashed lines with index $p$. Magic-angle representation is depicted in inset left for $p=4$.

Figure 2

(a) Transverse resistivity in the vicinity of Lebed resonance $\mathrm{\Delta }{\rho }_{xy}$ ($p=3$ and 4) and the $y$ axis as a function of the angular deviation $\mathrm{\Delta }\theta$. (b) Definition of $B_{\perp }$ and $B_{//}$ for a small $\mathrm{\Delta }\theta$ about $p=2$ (other $p$ also shown) for the blue quasi-1-dimensional conducting chains (circles). (c) $\mathrm{\Delta }{\rho }_{xy}$ plotted against $B_{\perp }$ for $B=12.5\mathrm{T}$; all data collapse onto a single curve. (d) When the 2-dimensional conducting planes are dominant in the Hall response, the effective magnetic field depends on $\theta$, and the response is proportional to $B\cos \theta$. (e) When MA-formed conducting planes are dominant in conduction, the effective magnetic field in the Hall response is $B_{\perp }=B\mathrm{\Delta }\theta$, consistent with the observations herein.

Figure 3

Intensity plot of transverse resistivity against the magnetic field strength (vertical) and the magnetic field angle (horizontal; scale bar at right). The structure in the vicinity of the Lebed resonance appears as a nondispersing vertical line in an increasing magnetic field. In contrast, the field-induced spin-density wave (FISDW) transition shows a dispersive angular dependence in an increasing magnetic field (dashed lines).

Figure 4

(a) Transverse resistivity in the vicinity of the Lebed resonance $\mathrm{\Delta }{\rho }_{xy}$ as a function of $B_{\perp }$ for different total $B$ at all $p$ indices. (b) The coefficient ${\rho }_{\mathrm{co}}$ as determined by the slope of $\mathrm{\Delta }{\rho }_{xy}(B_{\perp })$ at each fixed $B$ is plotted against the magnetic field $B$. (c) The carrier density $n_H$ derived from ${\rho }_{\mathrm{co}}$ has a strong magnetic field dependence and is fitted by exponential function with $0.3B$ as a fitting parameter (shown as a dashed line).