Pressure dependence of the BaFe${}_2$As${}_2$ Fermi surface within the spin density wave state

Measuring surface conductivity we have observed the evolution of Shubnikov de Haas oscillations under quasihydrostatic pressure for the pnictide parent compound BaFe${}_2$As${}_2$. Prior results in the reconstructed state have observed small pockets which emerge from zone folding as a result of structural changes with cooling. For pressures below 20 kbar, both Fermi surface orbits grow in size. The effective masses increase with pressure suggesting enhanced correlation in the system, and a series of magnetic breakdown orbits are observed confirming that band structure calculations setting them in close proximity are correct.

Figure 1

(a) Quantum oscillations are observed in surface conductivity at fields as low as ∼3.5 T with $T\sim 30\mathrm{mK}$ and $B\parallel c\mathrm{axis}$. The background was subtracted from the data using a three term polynomial. (b) The TDO circuit frequency change from a field sweep ($T\sim 350\mathrm{mK}$) to 35 T (red/light) and the first derivative (black/dark) which clearly shows the quantum oscillations. (c) FFT spectrum for ambient pressure results. (d) Cooling and warming curve for 4-probe resistance showing evidence of twinning. The inset shows a more detailed view. The ∼0.5 K separation between cooling (2 K/min) and warming (0.5 K/min) curves reflects a lag in temperature response during cooling and is not intrinsic to the sample. (e) Contour plot of the frequencies from angular dependence taken from $\theta =0^{\circ }$ ($B\parallel c\mathrm{axis}$) to $\theta ={90}^{\circ }$ ($B\parallel ab\mathrm{plane}$). Dashed lines arefit to $F\left(\theta \right)\sim F_0/{\{{\cos }^2\left(\theta \right)+{\left[(1/\eta )\sin \left(\theta \right)\right]}^2\}}^{0.5}$, where η = (major/minor) axis for the ellipsoid. (f) Contour plot of the frequencies from angular dependence taken with field aligned in the $ab$ plane showing the four-fold symmetry created by twinning. The long dashed and dot-dashed lines are fits to the same form as (e). The solid and short dashed lines are fits to oblate ellipsoids where the ratio of major/minor axes is inverted.

Figure 2

(a) Linear pressure dependence of the α orbit. (b) The γ orbit grows with increasing applied pressure up to ∼16 kbar where a $P^2$ dependence of $\left(P\right)\sim 91+0.24P^2$ is found. Different pressure techniques and conditions are shown as symbols in the figure with red squares indicating the ambient pressure value. Pressure dependence of the ε orbit is also shown (see text for discussion). (c) Angular dependence of the FFTs taken at $P\sim 10\mathrm{kbar}$.

Figure 3

Pressure dependence of the effective masses for the (a) γ orbit and (b) α orbit at $\theta =0^{\circ }$. Upper inset: temperature dependence to 7.0 K for $P\sim 13.2\mathrm{kbar}$. The symbols follow the same convention as Fig. 2. Lower inset: Effective mass fit (dashed lines) to the temperature dependence. The sizes of the markers correspond to error size taken from the noise floor of the FFTs.

Figure 4

(a) Fourier spectrum of BaFe${}_2$As${}_2$ oscillations at ambient pressure and $\theta =0^{\circ }$ orientation shown on a log scale. An exponential decay is observed for the peak amplitudes except the first harmonic for the γ orbit.[33] Red dashed lines are a guide to the eye. (b) Fourier spectrum at ambient pressure tilted ∼28° away from the $c$ axis where odd harmonics have been reduced by spin zeros. The Fourier spectrum showing the fundamental, harmonics, and combination frequencies shifted by pressure are shown at (c) ambient pressure and (d) pressure ∼16.1 kbar. (c) and (d) have been expanded along the amplitude axis to show the harmonic and combination peaks more clearly. All measurements shown in (a) to (d) were taken at ∼440 mK.