Introduction

High-transition temperature (Tc) superconductivity in iron-pnictides/chalcogenides1 emerges from the multi-band electronic structure near the Fermi level (EF) composed of the five Fe 3d orbitals. Most of the parent compounds exhibit an antiferromagnetic (AF) order at TN and tetragonal-to-orthorhombic structural transitions just at or slightly above TN (Ts). In addition, the lifting of degeneracy in Fe 3d xz /3d yz (xz/yz) orbitals, the so-called orbital anisotropy2,3,4 was observed by angle-resolved photoemission spectroscopy (ARPES), for various materials, such as the BaFe2As2 family5,6,7, NaFeAs8,9, and FeSe10,11. The orbital anisotropy is a possible explanation for the origin of the electronic nematicity8,10,11,12,13 which has been intensively studied in terms of magnetic origin14,15. It is theoretically suggested that the orbital fluctuation evolves near the orbital-ordered state16,17. This results in a sign-preserved s++-wave superconductivity, whereas a sign-changing s±-wave superconductivity is induced by the spin fluctuation18,19. The nature of the orbital order, in particular, the extent of the persistence of the orbital anisotropy against the ion-substitution, can help understand the mechanism of high-Tc superconducting (SC) transition in iron-based materials.

The persistence of the orbital-anisotropic state, however, has only been investigated for some shallow-doped Ba(Fe1-xCo x )2As2 materials6,20. For an accurate tracking of the intrinsic orbital anisotropy beyond the SC dome, both materials and methods need to be selected carefully. The application of ARPES on strain-free crystals enables the avoidance of an extrinsic anisotropy which increases the onset T of the orbital anisotropy (To)21. In addition, the isovalent-ion substituted system is the most suitable for the thorough investigation of the degeneracy lifting in the xz/yz orbitals, without the influence of the chemical potential shift induced by carrier doping. Thus, we used ARPES on strain-free BaFe2(As1−xP x )2 (AsP122) crystals with 0.00 ≤ x ≤ 0.87 for the study of the x–T region showing an orbital-anisotropic electronic structure.

Results

The x-dependence of the E-k images around the X/Y point

The electronic structure of BaFe2As2 is highly two-dimensional as indicated by the calculated Fermi surfaces (FSs) in Fig. 1a. Figure 1b shows the FS image for x = 0.61 from the ARPES with hν = 40.8 eV. The energy–momentum (E–k) image along (0,0) and (π,π) and the image of its second E derivative are shown in Fig. 1c and d, respectively. They exhibit two hole bands at the Brillouin zone (BZ) center (α and β bands), and an electron band and a hole band at the BZ corner (γ and δ bands). According to the band calculation, the δ band reaching the γ band at 50 meV below EF is composed of xz/yz orbital characters. Previous ARPES on BaFe2As2 demonstrated that degeneracy lifting in the xz/yz orbitals appears in the δ band in the orthorhombic AF state6.

Figure 1
figure 1

(a) First-principles band calculations of FSs for x = 0.00. (b) FS mapping at x = 0.61 by hν = 40.8 eV. aT represents the inplane lattice parameter of the tetragonal structure. (c,d) E-k image and its second E derivative image for x = 0.61 along (0,0) – (π,π) direction. Two electron bands crossing EF around (π,π) is not separately detected in this experimental condition. (e1–k1) E-k images at the BZ corner on twinned crystals of 0.00 ≤ x ≤ 0.74. (e2–k2) The second E derivative E-k images of 0.00 ≤ x ≤ 0.74. (e3–k3) Schematic band dispersions obtained from (e2) to (k2). Blue and red curves correspond to the band dispersions of yz and xz orbitals, respectively. Broken curve in (e3) shows the degenerate xz/yz band at higher T.

Full size image

Here, we focus on the δ band at the BZ corner at low T, for the strain-free (twinned) crystals, to determine the orbital anisotropy Φo = E yz  − E xz . Figures 1e1–k1 and e2–k2 show the E–k images and their second E derivative around the BZ corner for 0.00 ≤ x ≤ 0.74, respectively. For x = 0.00, we observed a pair of hole bands with similar dispersions as indicated by the red and blue curves in Fig. 1e3. Previous ARPES on de-twinned BaFe2As2 crystals confirmed the upward shift of the yz hole band and the downward shift of the xz hole band, appearing at different BZ corners6 (X and Y points). In the case of twinned crystals, the δ bands composed of yz and xz orbitals at the X and Y points overlap in the E–k image at the BZ corner. Thus, the observation of the pair of hole bands in the orthorhombic AF state can be interpreted as degeneracy lifting in the xz/yz orbitals, i.e. in-plane orbital anisotropy.

The x-dependence of the second E derivative of the energy distribution curves

The schematics of the band dispersions around X/Y points shown in Fig. 1e3–1k3 were obtained from the spectral dips of the second E derivative of the energy distribution curves (EDCs), which represents the energy levels of the δ band at each k. Figure 2a–i show the second E derivative of the EDCs near the X/Y point in an interval of 0.025 Å−1 at 30 K for x = 0.00 and 0.07, at 20 K for x = 0.52, 0.74, 0.87, and at 10 K for x = 0.30, 0.45, and 0.61, respectively. The systematic parallel shift of the double dip feature as a function of k suggests a clear degeneracy lifting in the xz/yz orbitals in the δ bands for 0.0 ≤ x ≤ 0.30. For higher x values, the orbital anisotropy becomes unclear and, eventually, a single δ band was observed for x = 0.74 and 0.87 down to 20 K. These observations indicate that an orbital anisotropy persists in the optimally doped regime and possibly higher doping level where static orthorhombicity and antiferromagnetism no longer exist.

Figure 2
figure 2

(a–i) x dependence of second E derivative EDCs in an interval of 0.025 Å−1 near X/Y point at 30 K for x = 0.00 and 0.07, 20 K for x = 0.52, 0.74 and 0.87, 10 K for x = 0.24, 0.30, 0.45 and 0.61, respectively. Black open circles represent dip positions in the spectra corresponding to the energy position of the δ hole bands.

Full size image

E-k images around X and Y points of the detwinned single crystals for x = 0.3

It is worth mentioning that the signature of orbital anisotropy was found even in the tetragonal SC state (Fig. 1h3 and i3). To investigate the degeneracy lifting in the xz/yz orbitals in the SC state, we performed ARPES on the de-twinned crystals at x = 0.30. As schematically shown in Fig. 3a and b, a uniaxial pressure was applied to the single crystals along the [1 1 0] direction in the tetragonal notation. This direction is denoted by the y-axis, corresponding to the shorter b-axis in the orthorhombic notation. The x-axis corresponds to the a-axis in the orthorhombic notation. In the ARPES experiments, the crystals were rotated around [0 0 1] in situ by 90°, for the separate detection of the δ bands along the k x - and k y -directions (Fig. 3c).

Figure 3
figure 3

(a,b) Geometry 1 and 2 for the ARPES on de-twinned crystals, respectively. (c) Momentum cut corresponding to the Geometry 1 (2) as indicated by a red (blue) line. Photons of hν = 40.8 eV probe the BZ center near the Γ plane and the BZ corner near the Z plane, respectively. (d1,d2) ARPES images of de-twinned BaFe2(As0.7P0.3)2 at 12 K (T < Tc) by around X along k y and Y along k x , respectively. The peak positions from EDCs and MDCs of ARPES images are superimposed by red (xz) and blue (yz) markers, respectively. (d3) Differences between APRES images around X(||k y ) and Y(||k x ) at 12 K. Red and blue intensities represent δ bands of xz and yz orbitals, respectively. (e1–e3) Similar to (d1-d3) recorded at 30 K (T ∼ Tc). (f1–f3) Similar to (d1–d3) recorded at 150 K (T ≫ Tc).

Full size image

Figure 3d1 and d2 show the band dispersions symmetrised with respect to the X and Y points, respectively, obtained for the SC state at x = 0.30. The peak positions of the EDCs and momentum distribution curves (MDCs), plotted in Fig. 3d1 and d2, indicate that the δ band attains higher energy at Y (||k x ), thus confirming the existence of orbital anisotropy in the SC state. The first-principles band calculation for BaFe2As2 indicates that the δ band at X (||k y ) [Y (||k x )] is composed of xz (yz) orbital; these orbitals are marked with red (blue) in Fig. 3d1 and d2. The orbital anisotropy, Φo = E yz −E xz , is determined to be ~30 meV at a momentum cut of ~0.3 Å−1 away from the X/Y point, which is comparable to that of the twinned crystals [Fig. 1h3]. These results indicate that the lifting of the xz/yz orbital degeneracy in the SC state is not quantitatively affected by the de-twinning procedure. A similar ARPES measurement at 30 K (T ≈ Tc) demonstrates a comparable magnitude of orbital non-equivalency, suggesting that the superconductivity onset has negligible effect on it (Fig. 3e1 and e2). At 150 K (T ≫ Tc), the δ bands composed of xz and yz orbitals become equivalent (Fig. 3f1 and f2), thus recovering the C4 symmetry of the tetragonal lattice in the high T region. To emphasise the separation between the xz and yz orbital bands, we present images showing the difference of intensities between the E–k image at X (||k y ) and that at Y (||k x ), recorded at 12 K (Fig. 3d3), 30 K (Fig. 3e3), and 150 K (Fig. 3f3).

Dependence of the orbital anisotropy on x and T

To determine the orbital-anisotropic region in the phase diagram, we performed ARPES on an AsP122 system for a wide range of x and T. Twinned crystals were used as the de-twinning procedure may extrinsically increase To21. Figures 4a1–a3 show E–k images around the X/Y point for x = 0.24 obtained at 130 K, 70 K, and 10 K, respectively. While a single δ band was observed at 130 K, it split into two at 70 K and 10 K, as indicated by the green curves. To see the T-dependence in detail, Fig. 4b shows the second E derivative of the EDCs at the momentum indicated by the dotted white lines in Fig. 4a1–a3, plotted for several T values. As can be seen in Fig. 4b, a single dip gradually splits into two with the decrease of T, indicating the evolution of the orbital anisotropy. The T value where the two-dip structure appears, corresponding to T o , was determined to be ∼110 K for x = 0.24. Similarly, To was determined to be ∼90 K for x = 0.30, ∼70 K for x = 0.45, and ∼50 K for x = 0.61, respectively (Fig. 4d,f, and h). It should be noted that the error bars of To are particularly large for 0.45 ≤ x ≤ 0.61 as the noise level is in the range of the intrinsic signal. At x = 0.74 and 0.87, down to 20 K the double-dip feature can no longer be observed, as shown in Fig. 4j and l. These findings are summarised in Fig. 5a and b. (In this work, we find that the relation of Ts < To holds in both as-grown and annealed crystals: The annealed crystals are considered to be of high purity and more homogeneous than the as-grown samples. The present result confirms that the inhomogeneity and/or fluctuations in the sample quality have no serious effect on the determination of To in the present ARPES).

Figure 4
figure 4

(a1-a3) Second E derivative of the E-k images for x = 0.24 taken at 130 K, 70 K and 10 K, respectively. Green curves are the guides to the eyes. (b) T dependence of the second E derivative EDCs of twinned samples of x = 0.24 taken at the momentum indicated by the broken lines in (a1-a3). Black open circles represent the spectral dips corresponding to the energy position of δ hole bands. (c1-c3) The same as (a1-a3) but for x = 0.30. (d) The same as (b) but for x = 0.30. (e1–e3) The same as (a1–a3) but for x = 0.45. (f) The same as (b) but for x = 0.45. (g1–g3) The same as (a1-a3) but for x = 0.61. (h), The same as (b) but for x = 0.61. (i1-i3) The same as (a1-a3) but for x = 0.74. (j) The same as (b) but for x = 0.74. (k1–k3) The same as (a1-a3) but for x = 0.87. (l) The same as (b) but for x = 0.87.

Full size image
Figure 5
figure 5

(a) Summary of x and T dependence of the orbital anisotropic parameter Φo = E yz − E xz estimated from the second E derivative EDCs. (b) Contour plot of Φo in the x-T phase diagram of AsP122 system. The measurement points were indicated by black dots.

Full size image

Discussion

As can be seen in Fig. 5b, To and Φo of the orbital anisotropy are monotonically suppressed toward the high-x region. Considering that both orthorhombic and AF phases show a similar sudden drop immediately below x ≈ 0.30, the orbital anisotropy seems to be decoupled from these two orders. Nevertheless, the x–T area where the orbital anisotropy appears is nearly equivalent to the electronic nematic region above Ts and TN, determined by the torque magnetometry and X-ray diffraction (XRD) measurements22. This coincidence suggests that the loss of rotational symmetry in the lattice and magnetism cooperatively evolve with the orbital anisotropy from the high-T region. Theoretical studies13 suggest that the imbalance of the xz/yz orbitals in the order of 10 meV resolves the magnetic frustration between (π, π) and (π, −π), resulting in the enhancement of spin fluctuations. Nuclear magnetic resonance studies23 on AsP122 reported the spin fluctuations evolving around To in a wide range of x, which possibly supports the above scenario.

For an optimally doped sample at x = 0.3, we observed the orbital anisotropy appearing below ∼90 K, which is not suppressed by the onset of superconductivity (Fig. 3). While the orthorhombic structural phase has not been reported from XRD measurements24 at any T for x = 0.30, the present ARPES study may suggest the existence of some form of orthorhombicity, e.g. the local variation or fluctuation of the orthorhombicity, as detected for BaFe2As2 by neutron powder diffraction25. Nevertheless, recent polarized ultrafast optical measurements26 revealed a two-fold symmetric optical response occurring approximately at 40–60 K for an optimally doped AsP122 (x = 0.31), which can be explained by the orbital anisotropy in the present ARPES study. Scanning Laue microdiffraction measurements26 further suggested that such electronic anisotropy was decoupled from the strain anisotropy on the crystal surface. These results imply that the orbital anisotropy in the present ARPESstudy may not necessarily correspond to the presence of the lattice distortion.

The orbital anisotropy observed by the ARPES can also be interpreted as a dynamical ferro-orbital order, when the photoexcitation process is much faster than the time scale of the dynamical fluctuations. In the case of FeSe11 and NaFeAs8, the orbital anisotropy rapidly increases below T s , which suggests an instantaneous evolution of the ferro-orbital order at the orthorhombic structural transition. Regarding AsP122, there is a possibility that the anomalous normal state is characterised by the dynamical ferro-orbital order fluctuation extended in a wide range of the phase diagram. Another possibility is that the orbital anisotropy observed in the present ARPES study indicates the presence of an antiferro-type orbital order13. A recent ARPES study27 on Ba,KFe2As2 (BaK122) suggested that an antiferroic electronic structure is realised in a large portion of the non-magnetic state including the SC phase. The antiferroic electronic instability in BaK122 does not compete with the onset of superconductivity similarly to that observed for the orbital anisotropy in AsP122 (Fig. 3). It should be noted that the x–T region where the orbital anisotropy appears overlaps with the pseudo-gap (PG) region reported by an ARPES experiment7 and optical measurements28. Theoretical studies29,30 predict that spin-nematicity induces the PG in the density of states significantly above Ts. While the origin of the electronic nematicity in AsP122 needs to be further investigated, these results suggest that superconductivity in AsP122 emerges at the PG state where the C4 rotational symmetry is broken in lattice, magnetism, and orbital degrees of freedom. The different x- and T-dependences of the orbital anisotropy might be the key components for the systematic understanding of the diverse phase diagrams and SC gap symmetries in the iron-pnictide/chalcogenide superconductors.

In conclusion, we investigated the orbital anisotropy in the AsP122 system by using ARPES. We found that orbital anisotropy widely exists in the non-magnetic state, including the SC phase. It is monotonically suppressed toward the optimally doped regime and not observed around the over-doped regime. The orbital anisotropy, which possibly accompanies the anisotropic lattice and magnetism, is probably a crucial phenomenon to understand the anomalous normal state with PG and spin fluctuations, as realised in AsP122.

Methods

Sample growth and characterisation

Single crystals of AsP122 with x = 0.00 (TN,s = 136 K), x = 0.07 (TN,s = 114 K), x = 0.24 (TN,s = 55 K, Tc = 16 K), x = 0.30 (Tc = 30 K), x = 0.45 (Tc = 22 K), x = 0.52 (Tc = 15 K), x = 0.61 (Tc = 9 K), x = 0.74, and x = 0.87 were grown by a self-flux method as described in refs31 and32. Resistivity measurements32 suggest the high quality of the crystals with a residual resistivity ratio of ≤30.

Photoemission measurements

The ARPES measurements were performed using a VG Scienta R4000 WAL electron analyzer and a helium discharge lamp of hν = 40.8 eV. The energy resolution was set to 10 meV. The single crystals were cleaved at 200 K in ultrahigh vacuum of 5 × 10−11 Torr. The magnitude of the unidirectional strain applied by the detwinning device was in the order of 10 MPa33. The spectra were reproducible over 24-h measurement cycles. The E F of the samples was referenced to that of a gold film evaporated onto the sample holder.