Nesting of electron and hole Fermi surfaces in nonsuperconducting BaFe${}_2$P${}_2$

We report detailed measurements of the de Haas–van Alphen (dHvA) effect in BaFe${}_2$P${}_2$, which is the end member of the superconducting series, BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$. Using high-purity samples, we are able to observe dHvA oscillations from all the sheets of the Fermi surface and hence build up a detailed picture of its structure. The results show the existence of a highly warped section of hole surface, which may be the origin of the nodal superconducting gap structure in this series. Importantly, we find that even for this nonsuperconducting end member, one of the hole surfaces almost exactly nests with the inner electron surface. This suggests that improved geometric nesting does not drive the increase in pairing strength with decreasing $x$ in this system.

Figure 1

(a) An example torque vs field trace with background subtracted. (b) Fast Fourier transforms of the $\tau (H)$ data (from 6–18 T) at various angles, showing the distinct dHvA peaks. Harmonics are identified with the prefix 2. All data was taken at base temperature $T\simeq 0.35$ K. Note the peaks below 0.5 kT are due to noise, and features in the background cantilever magnetoresistance.

Figure 2

dHvA frequencies multiplied by cosine of the rotation angle vs angle. Panel (a) shows the calculations for the unshifted bands rotating from [001] toward [100]. In (b), the symbols show experimental data for rotations from [001] to both [100] and [110], whereas the solid lines show the calculations for the energy-shifted bands as described in the text (note that the predicted orbit ${\delta }_1$, which has $F\simeq 100$ T at $\theta =0^{°}$, is not shown).[5] Panel (c) shows the origin of the orbits on the calculated electron (e) and hole (h) FS sheets at an angle of $\theta ={20}^{°}$ (toward [110]).

Figure 3

Cross sections of the determined Fermi surface of BaFe${}_2$P${}_2$ in (a) the $\mathit{ab}$ plane at three different $k_z$ values (quoted in units of $c^{*}=4\pi /c$) and (b) a $c$-axis cut along the [110] direction and through the $\Gamma$ point. The largest band character element at each $\mathit{k}$ point is indicated.[19]