Fermi surface of ${\mathrm{IrTe}}_2$ in the valence-bond state as determined by quantum oscillations

We report the observation of the de Haas–van Alphen effect in ${\mathrm{IrTe}}_2$ measured using torque magnetometry at low temperatures down to 0.4 K and in high magnetic fields up to 33 T. ${\mathrm{IrTe}}_2$ undergoes a major structural transition around $\sim 283\left(1\right)\mathrm{K}$ due to the formation of planes of Ir and Te dimers that cut diagonally through the lattice planes, with its electronic structure predicted to change significantly from a layered system with predominantly three-dimensional character to a tilted quasi-two-dimensional Fermi surface. Quantum oscillations provide direct confirmation of this unusual tilted Fermi surface and also reveal very light quasiparticle masses (less than $1m_e$), with no significant enhancement due to electronic correlations. We find good agreement between the angular dependence of the observed and calculated de Haas–van Alphen frequencies, taking into account the contribution of different structural domains that form while cooling ${\mathrm{IrTe}}_2$.

Figure 1

The effect of the structural transition in ${\mathrm{IrTe}}_2$. (a) The HT and LT reciprocal vectors, $c_{\text{HT}}^{*}$ and $c_{\text{LT}}^{*}$, are indicated together with a representation of a tilted Q2D Fermi surface in the VBS state. (b) Single crystal x-ray diffraction taken above and below $T_s\sim 283.5$ K. Below $T_s$ a superstructure forms with vectors ${\mathbf{q}}_0^{\prime }=(0,1/5,1/5)$ and ${\mathbf{q}}_0=(1/5,0,1/5)$ within the $0kl$ and $h0l$ planes for sample S1 (with two domains) and only ${\mathbf{q}}_0^{\prime }$ for sample S2 (one domain), all indexed in the HT hexagonal unit cell. (c) Angular dependence of torque for sample S1 at constant magnetic field (10 T) and temperatures. The shaded region shows the shift in angle while cooling through $T_s$. (d) The temperature dependence of the torque signal, ${\tau }_0$, and the shift in the phase, ${\varphi }_0$ (as defined in the text), showing strong anomalies at $T_s$. The rotation in the ($ac$) plane is always defined in the HT rhombohedral structure ($P\overline{3}m1$ symmetry).

Figure 2

Quantum oscillations in ${\mathrm{IrTe}}_2$. (a) Field dependence of torque for sample S2 measured at $0.4$ K for different orientations in magnetic field. (b) The corresponding FFT spectra (with amplitudes scaled as $A^{3/4})$ using a large field window $5–33$ T to separate lower frequencies below 2 kT and $20–33$ T to detect higher frequencies. (c) Temperature dependence of quantum oscillations for sample S1 at $\theta ={54}^{\circ }$. The inset shows the temperature dependence of the scaled FFT amplitudes for individual frequencies fitted to the Lifshitz-Kosevich formula (8–18 T) to extract the effective masses, $m^{*}$ [29].

Figure 3

Comparison between the measured and calculated angular dependence of the dHvA frequencies of ${\mathrm{IrTe}}_2$ for (a) sample S1 (top panels) and (b) S2 (bottom panel). The experimental data are compared with calculations (solid lines in different color corresponding to the five different quasi-two-dimensional bands shown at the right) for domains D1 and D3 for sample S1 and domain D1 for sample S2, with the local dHvA frequency minima for each domain indicated by the dashed lines. In the color maps, the FFT amplitudes are scaled as $A^{3/4}$ collected every $4.5^{\circ }$. The frequency branches not compared to simulations correspond to the second harmonics of the most intense frequencies. The calculated angular dependence of the predicted dHvA frequencies and the Fermi surfaces corresponding to the (c) HT structure and (d) LT dimerized structure for the six possible domains D1–D6. The Brillouin zones of both structures are indicated by the solid lines.