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ABSTRACT We report the first case of the successful measurements of a localized spin antiferromagnetic transition in delafossite-type PdCrO2 by angle-resolved photoemission spectroscopy

(ARPES). This demonstrates how to circumvent the shortcomings of ARPES for investigation of magnetism involved with localized spins in limited size of two-dimensional crystals or multi-layer

thin films that neutron scattering can hardly study due to lack of bulk compared to surface. Also, our observations give direct evidence for the spin ordering pattern of Cr3+ ions in PdCrO2

suggested by neutron diffraction and quantum oscillation measurements and provide a strong constraint that has to be satisfied by a microscopic mechanism for the unconventional anomalous

Hall effect recently reported in this system. SIMILAR CONTENT BEING VIEWED BY OTHERS ANGLE-RESOLVED PHOTOEMISSION SPECTROSCOPY Article 14 July 2022 DIRECT OBSERVATION OF ALTERMAGNETIC BAND

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Article Open access 27 June 2022 INTRODUCTION Angle-resolved photoemission spectroscopy (ARPES) has been one of the most powerful tools to investigate the electronic structure of crystalline

solids. With the help of the third generation synchrotron facilities and the electron spectrometers with angle resolved mode, ARPES now can be utilized for the study of the magnetic

structure as well as the electronic one1. In particular, ARPES has revealed various kinds of magnetic fluctuations in high-temperature superconductors and magnetic thin films, providing key

information to understand the underlying physics2,3. However, there is the last piece of the puzzle left in ARPES for magnetic structure study: observing a long range ordering of localized

magnetic moments. Actually, Fermi surface (FS) folding induced by many kinds of order other than localized magnetic moments has been observed by ARPES. The most probable reason for this

exception is that the potential difference by localized moment ordering is so small that the band electrons can hardly feel the potential change, resulting in negligible or non-detectable

changes in the photoemission signals. Here, at long last, we report the first case of the successful ARPES measurements of a localized spin antiferromagnetic transition in delafossite-type

PdCrO2. Our observations give direct evidence for the spin ordering pattern of Cr3+ ions in PdCrO2 suggested by neutron diffraction4,5 and quantum oscillation measurements6 and provide a

strong constraint that has to be satisfied by a microscopic mechanism for the unconventional anomalous Hall effect (UHAE) recently reported in this system7. Also, this demonstrates a new

pathway for investigation of magnetism in limited size of two-dimensional crystals or multi-layer thin films that neutron scattering can hardly study due to lack of bulk compared to surface.

RESULTS Metallic delafossite-type oxides (Fig. 1a) ABO2 (A = Pd and Pt; B = Cr, Co and Rh) are famous for their good conductivity8. In particular, the PdCoO2 exhibits the best conductivity

in the normal state oxides. The conductivity is even better than that of Pd metal and so this case has been scrutinized at length by ARPES study9, x-ray absorption spectroscopy study10,

_ab-initio_ band structure calculations11,12 and thermo-transport study13. The large two-dimensional FS consisting of the fast conduction electrons with a long life time was confirmed to be

the origin of the anisotropic high conductivity in the previous studies. The interesting and noticeable features for PdCoO2 are two-fold; the metallic Pd layers with the large _sp_-like band

dispersions and the insulating triangular lattice CoO2 with the low-spin (S = 0, 3_d_6) configuration. When the Co3+ ion in the trigonally distorted octahedron MO6 (M = transition metal

ion) is replaced by Cr3+ ions in the same crystal structure, the only difference with respect to the electronic structure lies in the spin quantum number of the _t_2_g_ manifolds in the

transition-metal ions. It simply changes the quantum number from S = 0 (full filling) to S = 3/2 (half filling), i.e. from non-magnetic CoO2 to magnetic CrO2 triangular lattice. In this

case, since the Cr ions form a two-dimensional triangular lattice (2DTL) with the antiferromagnetically interacting local spins, the system becomes much more attractive. As is well known,

this kind of spin geometry would produce the magnetic frustration and the possible quantum liquid ground state14,15. Further, this system has highly metallic layers and so it provides a rare

opportunity to investigate the interactions between the frustrated local magnetic moments in a 2DTL and the itinerant electrons in an adjacent layer. Indeed, recent transport studies have

reported that an unconventional anomalous Hall effect (UAHE) was observed in this system, revealing an exotic behavior of an antiferromagnetic 2DTL with metallic layers6,7. However, since

the UAHE reported in this system requires an incompatible spin ordering to the known antiferromagnetic ordering, more refined experimental and theoretical characterization is essential to

understand the underlying physics. Figure 1b shows a top view of an upper Cr (big yellow balls) layer, a Pd (red balls) layer and a lower Cr (small yellow balls) layer in the delafossite

structure. When the system is antiferromagnetic below T_N_ = 37.5 K, the neutron powder diffraction study suggested that the spin directions of the Cr ions are ordered into a non-collinear

120° structure. In this spin structure, the Cr ions are classified into three kinds (denoted as A, B and C in Fig. 1b) with respect to their spin directions. The intensity analysis of the

magnetic Bragg peaks suggested that the three spin vectors lie in a plane containing the c-axis4,5. The adjacent Cr layer has the same structure as denoted as A', B' and C' in

Fig. 1b, but the exact phase difference between the layers is not clear. The crystal structure and the suggested magnetic phase for our samples were checked by the X-ray diffraction (XRD)

and neutron diffraction (ND) measurements above and below T_N_ as shown in Figs. 1(c) and 1(d). The superstructure peaks around 26° in the low temperature (T = 20 K) ND pattern are not seen

at the paramagnetic phase (T = 60 K), indicating that the origin of the peaks is spin ordering. Meanwhile, there are neither superstructure peaks at the corresponding angles () nor

differences between the XRD patterns above and below T_N_ except for the normal peak position shifts due to thermal lattice expansion. This shows that the symmetry of the crystal structure

does not change across the magnetic transition. The S = 3/2 spin quantum number of the Cr3+ ions and the metallic behavior of the Pd layers are revealed in the Cr 2_p_ → 3_d_ x-ray

absorption spectra (XAS) and the Pd 3_d_ x-ray photoemission spectrum (XPS) as shown in Fig. 2. The XAS spectra drawn with red line (T = 60 K) and with blue line (T = 28 K) in Fig. 2a were

obtained with the photon polarization vector normal to the _ab_-plane of the single crystalline samples. The electron configuration and the spin state can be determined by comparing the XAS

spectrum with that of a reference system since a transition metal 2_p_ → 3_d_ absorption spectrum is a kind of fingerprint for the electronic energy structure of the transition metal ions16.

If we compare our XAS spectra with that of Cr2O3 and of CrO2, each of which represents a trivalent S = 3/2 Cr ion and a tetravalent S = 1 Cr ion, respectively17, the valence and the spin

state of the Cr ions in PdCrO2 are clearly determined to be trivalent and S = 3/2 irrespective of the magnetic phase. The metallic Pd layers can be checked by analyzing the Pd 3_d_ XPS

spectrum as shown in Fig. 2b. As is the case of iso-structural PdCoO2, the asymmetric line shape is prominent, indicating that the photoholes are well screened by the conduction electrons

through the creation of electron-hole pairs across the Fermi level9. The quantitative line shape analysis with the Doniach-Šunjić (DS) model18 gave the asymmetric parameter value of α =

0.26. This value is a little larger than that of Pd metal but equal to that of PdCoO2 and lies in a reasonable region9,19. These spectroscopic observations support the idea that PdCrO2 is an

ideal system to investigate the detailed balance between the itinerant electrons and the adjacent localized spins in the 2DTL. A phase transition involving the superstructure was directly

observed by our ARPES measurements as shown in Fig. 3a. At the temperature of 100 K (bottom), we observed only one large electron-like hexagonal FS in a Brillouin zone (BZ). Meanwhile, at

_T_ = 20 K (top), it is clearly seen that the extra FS features other than the original FS appear in our constant energy ARPES intensity map at the Fermi level (_E__F_). Since PdCrO2 is

known to have an antiferromagnetic phase below _T__N_ = 37.5 K, these new FSs are naturally attributed to the folded FS's arising from the reduced BZ of an antiferromagnetic phase. If

this is the case, it is a milestone in ARPES because no ARPES study has reported a successful observation on a long range ordering of localized spins in a magnetic system. However, to

justify this conclusion, the other possible reasons must be checked. First, a structural transition accompanied by the antiferromagnetic transition is suspected, but this possibility can be

excluded by our temperature-dependent ND/XRD as explained in Figs. 1(c) and 1(d). The temperature-dependent diffractions show only a normal thermal expansion behavior and no abrupt peak

shift around _T__N_. Second, charge ordering or charge density wave is a candidate, but this can be also ruled out by the temperature-dependent X-ray diffraction study that shows no

extra-peaks below _T__N_. Furthermore, we did not observe any signal indicating mixed valency of the cations or charge disproportionation in our temperature-dependent core-level XPS study,

as partly shown in Fig. 2. Last, a temperature-dependent surface reconstruction should be checked for a possible origin since ARPES is a surface-sensitive probe. As to this possibility,

however, a recent ARPES study on PdCrO2 has reported totally different and temperature-independent surface FSs from ours as well as almost identical bulk FSs to ours20. This clearly shows

that our temperature-dependent FS folding is not relevant to a surface reconstruction. Thus, the band folding in our ARPES data cannot but be relevant to the magnetic transition. The

electronic structure of PdCrO2 measured by ARPES in the paramagnetic phase is very similar to that of iso-structural non-magnetic PdCoO2 except for the absence of surface states9,12. Both

systems commonly have a two-dimensional FS with a rounded hexagonal cross section in a BZ. In Fig. 3b, we show the ARPES image cut along the vertical dotted line in Fig. 3a bottom and the

calculated band structure along the Γ-K line using the linearized augmented plane wave method with local orbitals (LAPW + LO) in the generalized gradient approximation (GGA). For simplicity,

the calculation was set in the rhombohedral unit cell assuming a ferromagnetic ordering, which produces the over-split Fermi points, P1 and P2. Except for the spin-split feature, the

calculated band structures are quite consistent with the ARPES results. The conduction band is very dispersive, indicating that its characters are mostly hybridized 4_d_-5_s_ orbitals of Pd,

as in the case of PdCoO2. The carrier velocity given by at point P0 estimated in the ARPES data is , while the velocities at point P1 and P2 in the calculation are 3.4 and , respectively.

The faster carrier velocity in the ARPES data than that in the band calculation probably originates from the underestimation of the Pd 5_s_-4_d_ orbital mixing in the density functional

theory by neglecting the correlation effect of Cr 3_d_ electrons. The inverse mean free path (1/_l__MFP_ ~ Δ_k_ = 0.021(1) Å−1) and the relaxation time (τ = 1/_v__k_Δ_k_ = 5.7(4) × 10−15 s)

are comparable to those of PdCoO2. The electronic structure of the antiferromagnetic phase does not look much different from that of the paramagnetic phase except for the folded bands. Also,

the folded bands are almost identical to the original ones at least near the Fermi level as can be compared in Fig. 3c, where they are displayed along the Γ′-Γ_AFM_ line in the

antiferromagnetic phase of Fig. 3a top in three different manners, namely the ARPES intensity image (bottom), its waterfall plot derived from the momentum distribution curves near the Fermi

level (middle) and the fitted curve at the Fermi level (top), respectively. For example, if we compare the velocity _v__x_ of the folded conduction band at Pfold in Fig. 3c to that of P_AFM_

and of P_PM_ in Fig. 3a, all values fall within . The change of the FS topology in the antiferromagnetic phase can be also readily checked in Fig. 3c. The dispersion of the folded

conduction bands (the red dots and the yellow inverse triangles in each panel) along the Γ′-Γ_AFM_ line produces one hole-like hexagonal FS and two electron-like triangular FSs in a BZ, as

shown in Fig. 4. The detailed analysis on the cross-sectional FS areas in the antiferromagnetic phase is represented in Fig. 4. Based on the ARPES-measured FS image, we determined the size

of a rounded hexagonal FS δ of paramagnetic phase and translated it by the reciprocal lattice vectors to reproduce the folded FSs. The diagonal length and the height in Fig. 4 are 1.94(5)

and 1.76(4) Å−1, respectively, which are ~5% reduced in comparison with those of PdCoO2. The cross-sectional area of each FS branch is α = 0.083(9), β = 0.35(2), = 1.05(4) and δ = 2.66(6) 

Å−2, respectively. These are remarkably consistent with the recent quantum oscillation measurements, where the frequency for each FS branch is α ~ 0.8, β ~ 3.3, ~ 10.5 and δ ~ 27.5 kT,

respectively6. DISCUSSION Now that the observed FS folding clearly originates from the localized spin antiferromagnetic ordering, it is important to understand why and how this observation

was realized in our ARPES measurements. We think that the key factor is a considerable hybridization between the localized Cr 3_d_ orbitals and the itinerant Pd 4_d_ orbitals through the

oxygen anions. This feature has been also revealed in the recent quantum oscillation study6. In the antiferromagnetic phase, in addition to the normal hopping between Pd ions, the conduction

electron in the O-Pd-O dumbbells has spin-dependent hopping paths through three kinds of Cr ions A(A'), B(B') and C(C') in the adjacent upper(lower) layer, as shown in Fig.

1b. Taking into account both the normal hopping and the magnetic hopping, each strength of which is parameterized by _t_0 and _t_1 for the magnetic super-cell, we considered a single layer

model crystal to set up the tight-binding Hamiltonian described in detail below. Figure 5 shows the band structure of our model crystal. When the magnetic hopping is absent (_t_0 = 1, _t_1 =

0), the model crystal has one rounded hexagonal FS that resembles the ARPES-measured FS in the paramagnetic phase as shown in Fig. 5a. When turning on the magnetic hopping, the folded bands

get their intensities and the antiferromagnetic order of the Cr layers is reflected in the FS map of Fig. 5b and c. The optimal resemblance is obtained at _t_1 ~0.4 in this model. Here, we

point out that the absolute value of _t_1 can be different from the true value to some degree because of the simplification of our TB model, but it shows a trend consistent with the

essential features observed in the ARPES measurements. The success of this model strongly implies that the hybridization between the conduction electrons and the localized spins plays a key

role in observing the ordering of the localized spins in ARPES. Actually, this also explains why the surface states observed by Sobota _et al._ do not appear in our ARPES data20. The surface

states appear in the ARPES data obtained with photons, but are absent in our ARPES data. The photoionization cross section ratio of Cr 3_d_ to Pd 4_d_ is for 55 eV photons and for 120 eV

photons, respectively21. Thus, the surface states with mostly Pd 4_d_ characters appear much intensely in the 55 eV ARPES data. By the same argument, the folded bands in the

antiferromagnetic phase are strongly hybridized with the Cr 3_d_ orbitals, so they appear only in our 120 eV ARPES data. The FS folding due to the antiferromagnetic superstructure observed

in ARPES provides a strong constraint on the microscopic origin of the UAHE recently reported in this system. Until now, two studies have reported the UAHE, but the details are quite diverse

yet6,7. Takatsu _et al._ found an unusual nonlinear field dependence of the Hall resistivity curve, ρ_xy_(_H_), with a hump under a magnetic field of 1–3 T at temperatures below _T_* ~ 20 K

and interpreted it as an UAHE. In order to explain the nonlinearity of ρ_xy_(_H_) in the frame of the scalar spin chirality mechanism22,23, they proposed another magnetic structure with a

broken periodicity below _T_*. Meanwhile, Ok _et al._ measured the Hall resistivity up to _H_ = 32 T and found nonlinearity both at _H_ ~ 2 T, and near the Néel temperature _T__N_. The

latter was interpreted as an UAHE possibly originating from the finite scalar spin chirality induced by an external high magnetic field at the temperature region with antiferromagnetic

spin-fluctuations, but the former as a magnetic breakdown effect. Our ARPES measurements directly evidenced that the periodicity is sustained at least down to _T_ = 20 K. Here, it is worth

addressing that the ARPES data was obtained over the whole momentum space, so that the confidence on the new ordering pattern is incomparable to that from other data measured at single

momentum point such as diffraction patterns. Combined our ARPES result with the absence of any abrupt behavior in the magnetization curve _M_(_H_) as a function of applied magnetic field for

PdCrO27, the UAHE at the high magnetic field region near _T__N_ is more consistent. The successful observation of the local spin order by ARPES also suggests a novel method for magnetic

structure study of a small two-dimensional crystal such as AgNiO2, Ag2MO2 (M = Cr, Mn, Ni), Fe1.3Sb or an epitaxial thin film with localized magnetic moments for which neutron scattering is

usually not applicable due to the low efficiency. Our experimental results demonstrate that ARPES can be more suitable for these cases if a few metallic layers are covered on the surface

with balanced hybridization to the local magnetic moments. METHODS The single crystals of PdCrO2 were grown by the NaCl flux method using powder samples described in the literature24. The

powder samples were synthesized by the following metathetical reaction: Pd + PdCl2 + 2LiCrO2 → 2PdCrO2 + 2LiCl. In this step, the precursor LiCrO2 was prepared by the solid state reaction

method, starting from the stoichiometric mixture of Li2CO3 and Cr2O3 at 850°C for 24 hours. The obtained crystals are silvery hexagonal plates and the typical size is 1.5 × 1.5 × 0.1 mm3.

The XRD/ND experiments were performed on the powder samples to check the crystallographic/magnetic phases. The XRD patterns were obtained at the 3A beamline of the Pohang Light Source (PLS)

with . The ND patterns were obtained at the high-resolution powder-diffraction neutron beamline of HANARO research reactor, Korea. The neutron beam was monochromatized to 1.833 Å by using

single-crystal Ge (331) plane. The XAS measurements were performed at the 2A beamline of the PLS. The chamber pressure, resolving power of the photon beam and the sample temperature were

kept at ~10−9 Torr, 2500 and below 20 K, respectively. After the single crystalline samples were cleaved _in situ_, the absorption spectra were recorded in the total electron yield mode and

were normalized by the photon flux. The photoemission experiments were performed at the 4A1 beamline of the PLS with a Scienta SES-2002 electron spectrometer25. Linearly polarized light was

incident on the samples with polarization vector parallel to the k_x_-direction in the ARPES data. The photon energy was set to for ARPES and to for XPS. The total energy resolution is ~60 

meV and the momentum resolution was set to be ~0.01 Å−1. The crystals were cleaved _in situ_ by the top post method at the temperature of 100 K under the pressure of ~7.0 × 10−11 Torr. Due

to the quasi two-dimensional structure of the crystals, the cleaved surface was shiny and well oriented. After cleaving the samples, we collected the ARPES data in the paramagnetic phase at

100 K and then lowered the sample temperature to 20 K for the antiferromagnetic measurements. After collecting the low temperature ARPES data in a full range of _k_-space, we raised the

sample temperature to 100 K again to check the disappearance of the folded band in a partial range of _k_-space. Unlike the PdCoO2 case9, we did not apply the thermal cycling process to

PdCrO2 since the surface states reported in Ref. 20 were not observed in our ARPES measurements with photon energy. TIGHT-BINDING MODEL HAMILTONIAN As in the case of the PdCoO2 band

structure, the bands near Fermi level mainly consist of non-magnetic Pd and Pd 5 _s_ hybridized orbitals10,12. The Cr moments order as 120° super cell making six Cr spin-dependent hopping

paths (see Fig. 1b), but the total moments of Cr around a given O-Pd-O dumbell sum up to zero. Therefore, the magnetic moment of the Pd layer is constraint to zero by symmetry. Here, we

ignored all the higher order hopping to make the situation simple and only consider non-magnetic hopping term t0 (>0) and magnetic hopping term t1 (>0) in our tight-binding

Hamiltonian, where is the annihilation(creation) operator for a conduction electron and _i_, _j_, σ, σ′ are the indices for lattice sites and spin directions, respectively. The magnetic

hopping matrix is determined by the direction of Cr moments (overlap of electronic states) in the hopping path, as in the super-exchange. In this calculation, has been used, where _S__k_ is

the Cr moment in the hopping path _k_. To extract information of band unfolding spectral intensities, we use the following formalism26: where _K_(_k_) and _J_(_n_) denote the super-cell

(normal cell) crystal momentum and the band index, respectively. The effect of super-cell potential can be projected to the original BZ, giving spectral intensities. In the tight binding

form, the evaluation of |〈_kn_|_K J_〉|2 is trivial, i.e. they are just delta functions which can be determined by spatial relations. To set the Fermi surface, we integrate the states over BZ

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Article  ADS  Google Scholar  Download references ACKNOWLEDGEMENTS This work was supported by the National Research Foundation (NRF) of Korea Grant funded by the Korean Government (MEST)

(Nos. 2010-0010771 and 2012M2B2A4029607). K.K. and B.I.M. acknowledge the support of NRF (Nos. 2009-0079947 and 2011-0025237) and KISTI (No. KSC-2012-C2-27). H.D.K. was supported by NRF

funded by MEST (No. 2009-0090561). AUTHOR INFORMATION Author notes * Hyeong-Do Kim Present address: Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul, 151-747,

Korea AUTHORS AND AFFILIATIONS * Department of Physics, Chonnam National University, Gwangju, 500-757, Korea Han-Jin Noh, Jinwon Jeong, Bin Chang, Dahee Jeong, Hyun Sook Moon & En-Jin

Cho * Department of Physics, Pohang University of Science and Technology, Pohang, 790-784, Korea Jong Mok Ok, Jun Sung Kim, Kyoo Kim & B. I. Min * Pohang Accelerator Laboratory, Pohang

University of Science and Technology, Pohang, 790-784, Korea Han-Koo Lee, Jae-Young Kim, Byeong-Gyu Park & Hyeong-Do Kim * Korea Atomic Energy Research Institute, Daejeon, 305-353, Korea

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CONTRIBUTIONS The whole research was planned by H.J.N. PdCrO2 crystals were grown by J.J. ARPES measurements were performed by H.J.N., J.J., D.J., H.S.M., E.J.C., B.G.P. and H.D.K. Transport

measurements were performed by J.J. and J.S.K. XAS measurements were performed by H.J.N., J.J., H.K.L. and J.Y.K. ND/XRD experiments were performed by J.J., B.C., S.L., J.M.O. and B.G.P. TB

calculations were done by K.K. and B.I.M. J.Y.K. and H.K.L. maintained the XAS endstation. H.D.K. and B.G.P. maintained the ARPES endstation. H.J.N. wrote the paper with suggestions and

comments by J.S.K., K.K., B.I.M. and H.D.K. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. RIGHTS AND PERMISSIONS This work is licensed under a

Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ Reprints and permissions

ABOUT THIS ARTICLE CITE THIS ARTICLE Noh, HJ., Jeong, J., Chang, B. _et al._ Direct Observation of Localized Spin Antiferromagnetic Transition in PdCrO2 by Angle-Resolved Photoemission

Spectroscopy. _Sci Rep_ 4, 3680 (2014). https://doi.org/10.1038/srep03680 Download citation * Received: 29 August 2013 * Accepted: 17 December 2013 * Published: 14 January 2014 * DOI:

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