Electronic structure of the metallic antiferromagnet PdCrO${}_2$ measured by angle-resolved photoemission spectroscopy

PdCrO${}_2$ is material which has attracted interest due to the coexistence of metallic conductivity associated with itinerant Pd $4d$ electrons and antiferromagnetic order arising from localized Cr spins. A central issue is determining to what extent the magnetic order couples to the conduction electrons. Here we perform angle-resolved photoemission spectroscopy (ARPES) to experimentally characterize the electronic structure. We find that the Fermi surface has contributions from both bulk and surface states, which can be experimentally distinguished and theoretically verified by slab band structure calculations. The bulk Fermi surface shows no signature of electronic reconstruction in the antiferromagnetic state. This observation suggests that there is negligible interaction between the localized Cr spin structure and the itinerant Pd electrons measured by ARPES.

Figure 1

(a) Constant-energy map of ARPES intensity at $E_{\mathrm{F}}$, showing three FS pockets. The data is symmetrized about $k_x=0$. The BZ boundaries and high-symmetry points are indicated. The contours labeled (c)–(f) represent the cuts shown in the subsequent panels. (b) Constant-energy map at a binding energy of 0.2 eV. Hole bands centered at the M point are observed. (c)–(f) Energy-momentum cuts at the momenta specified in panel (a). The four bands discussed in the text are labeled b${}_1$ through b${}_4$.

Figure 2

Constant-energy maps during the temperature cycling process. (a), (b), and (c) are taken at $E_{\mathrm{F}}$ at 10, 50, and 10 K, sequentially, on the same sample. (d)–(f) The corresponding maps at $E_{\mathrm{F}}-0.2$ eV. Note the disappearance of bands b${}_2$, b${}_3$, and b${}_4$ during the cycling process.

Figure 3

(a) Cartoon of the FS reconstruction expected in the AFM state. (b) ARPES cut at $k_y=0$ at $T=10$ K. The red dashed line represents the AFM BZ boundary. (c) Second derivative of the cut along $k_x$, helping to remove background and emphasize weak spectral features. No folded bands are observed. (d) The corresponding momentum distribution curves. (e)–(g) The same information for the cut along $k_y=-0.2$ Å.

Figure 4

The different spin configurations considered for the band structure calculations in this work: (a) AFM order. The Cr spins exhibit 120${}^{\circ }$ structure with $\sqrt{3}\times \sqrt{3}$ periodicity. The $c$-axis coupling between Cr layers is antiparallel. (b) Same, but with parallel $c$-axis coupling. (c) FM order. The FM unit cell is identical to the NM unit cell.

Figure 5

FS of PdCrO${}_2$ from band structure calculations. (a) Bulk calculation with AFM spin configuration and parallel interlayer coupling. The outer black hexagon represents the NM BZ boundary, while the red dashed lines mark the AFM BZ boundary. The structure can be understood as a single hexagonal FS in the NM BZ which is folded into the AFM BZ. (b) Bulk calculation with FM spin configuration. No folding is observed due to the equivalence of the FM and NM BZs. The resulting FS agrees well with experiment, except for a small splitting due to the FM order (red/blue colors represent up/down spins). (c) Slab calculation with O-terminated surface. (d) Slab calculation with Pd-terminated surface. The Pd-terminated slab calculation shows good agreement with experiment.