de Haas–van Alphen Oscillations in the Underdoped High-Temperature Superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$

The de Haas–van Alphen effect was observed in the underdoped cuprate ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$ via a torque technique in pulsed magnetic fields up to 59 T. Above a field of $\sim 30\mathrm{T}$ the magnetization exhibits clear quantum oscillations with a single frequency of 540 T and a cyclotron mass of 1.76 times the free electron mass, in excellent agreement with previously observed Shubnikov–de Haas oscillations. The oscillations obey the standard Lifshitz-Kosevich formula of Fermi-liquid theory. This thermodynamic observation of quantum oscillations confirms the existence of a well-defined, closed, and coherent, Fermi surface in the pseudogap phase of cuprates.

Figure 1

Torque versus magnetic field at different temperatures. Both up (50 ms) and down (250 ms) field sweeps are shown, as indicated by the arrows. Lower inset: Schematic of the cantilever. Upper inset: Magnetic field dependence of the torque ($\theta \simeq 5°$) at $T=1.4\mathrm{K}$ and of the Hall resistance ($\theta =0°$) measured in the same sample at $T=1.5\mathrm{K}$.

Figure 2

Main panel: Temperature dependence of the oscillation amplitude $A$ (where $A$ is determined from discrete Fourier analysis with a Blackmann window) plotted as $\ln (A/T)$ versus $T$ for various mean magnetic field values. Solid lines are fits to Eq. (1) with $m^{*}=1.76m_0$. Lower inset: Same data plotted as $A$ versus temperature. Upper inset: Fourier transform of the oscillatory part of the torque at $T=0.4\mathrm{K}$ and $T=0.8\mathrm{K}$ between 35 and 58 T, revealing a single frequency $F=540\mathrm{T}$.

Figure 3

(a) Field dependence of the oscillatory part of the torque for the various temperatures explored and (b) corresponding Dingle plots. Solid lines are best fits to Eq. (1) with $m^{*}=1.76m_0$ and $T_D=6.2\mathrm{K}$.

Figure 4

(a) Oscillatory part of the Hall resistance versus magnetic field at different angles at $T=3\mathrm{K}$. (b) Angular dependence of the deduced Shubnikov–de Haas frequency. Solid line is a fit to $F(\theta =0)/\cos (\theta )$.