Electronic signatures of successive itinerant, magnetic transitions in hexagonal La2Ni7

We use high-resolution angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations to study the electronic and magnetic properties of La2Ni7, an itinerant magnetic system with a series of three magnetic transition temperatures upon cooling, which end in a weak itinerant antiferromagnetic (wAFM) ground state. Our APRES data reveal several electron and hole pockets that have hexagonal symmetry near the $\Gamma$ point. We observe significant reconstruction of the band structure upon successive magnetic transitions at T1 = 61 K, T2 = 57 K and T3 = 42 K. The experimental data are in a reasonable agreement with DFT calculations, demonstrating their applicability to itinerant antiferromagnet systems. Our results detail the effects of magnetic ordering on the electronic structure in a Ni-based weak antiferromagnet.

Magnetic ordering in an intermetallic system can stem from two different contributions.
The the first contribution is from local magnetic moments resulting in Curie-Weiss susceptibility. The effect of local magnetic moments is well understood by the Heisenberg model in the mean-field approximation [20][21][22]. The other component is itinerant magnetism. In this regime, long range magnetic order arises due to spin fluctuations of itinerant electrons [23,24]. Current theories work reasonably well in the limits of these two scenarios, that is, when either local magnetic moments or itinerant fluctuations play a dominant role .
Whereas it is relatively easy to discover or identify examples of local moment intermetallics compounds (e. g. by simply incorporating trivalent, moment bearing rare earths) the design or discovery of examples of itinerant magnetic systems is much harder given that many transition metal based intermetallic compounds simply become non-moment bearing. Following the discovery of Fe-based superconductors [2,6,7], there has been a renewed push to design, discovery or identify itinerant, weak (or fragile) antiferromagnetic systems [18,19].
Angle resolved photo-electron spectroscopy has, recently, also been focusing on the diverse changes that magnetic ordering can have on the band structure, depending, in part on the size of the ordered moments as well as their degree of hybridization with the conduction electrons. On one end of this spectrum is recent work on magnetic topological systems [25,26] as well as rare-earth bearing semi-metals such as NdBi [27][28][29]; on the other end of this spectrum is work on Fe-based superconductors such as pure and doped BaFe 2 As 2 [6,30,31] as well as CaKFe 4 As 4 [32][33][34]. One of the questions that has emerged is how sensitive can ARPES be to very small moment ordering. The discovery and study of a wider range of wAFM systems will help clarify this question. * canfield@ameslab.gov † adamkam@ameslab.gov 2 La 2 Ni 7 is a rare example of a small moment (∼ 0.1 µ B /Ni), itinerant magnetic system that shows a cascade of three magnetic ordering temperatures: T 1 ∼ 61 K, T 2 ∼ 57 K and T 3 ∼ 42 K [35] corresponding to C, B and A phases, respectively. The low temperature state has long been thought to be associated with wAFM ordering [35][36][37][38][39][40][41] and recent band structure predictions [42] have proposed a wAFM associated with a long wavelength periodicity along the c-axis, which even more recently have been borne out by single crystal neutron diffraction measurements [43]. Recent single crystal growth and characterization of this system [35] has made it very attractive as a possible wAFM that could be amenable to ARPES measurements. Indeed the neutron scattering study [43] has identified the propagating wave vectors of these three wAFM phases as all along the c-axis. While the C and B phases have the same incommensurate wave vectors, the direction of the magnetic moments are different and can be tilt away from the c-axis. In contrast, the lowest-T wAFM A phase has a commensurate wave vector of (0 0 1), which corresponds to a block-wise AFM configuration, i.e., intra-block FM but inter-block AFM coupling with the magnetic moments pointing along the c-axis, confirming the earlier proposed configuration. Each block is half of the chemical unit cell in the A state with the block-wise AFM.
In this paper, we report direct measurements of the band structure using the ARPES and compare them to DFT calculations for both paramagnetic (PM) and the lowest temperature AFM state that has had it magnetic structure predicted by DFT and confirmed by neutron scattering measurements [43]. We find that magnetic transitions in La 2 Ni 7 are accompanied by observable changes in the band structure, both at E F and well below. We observe that the PM state of La 2 Ni 7 is characterized by several electron and hole pockets near the Γ and M points and zone boundaries, in a reasonable agreement with DFT calculations. In the magnetically ordered states, several band splitting occur around the Γ and M points. While our detailed analysis of ARPES data suggest that the successive band splittings are more pronounced in the K-Γ-K direction, these effects are also observed along M -Γ-M in the proximity of E F .

II. METHODS
Single crystals of La 2 Ni 7 were grown out of a La-rich (relative to La 2 Ni 7 ) binary, hightemperature melt. Elemental La (Ames Laboratory, 99.99+% pure) and Ni (Alpha, 99.9+% 3 pure) were weighed out in a La 33 Ni 67 atomic ratio and placed into a tantalum crucible which was sealed with solid caps on each end and a perforated cap in the middle to act as a filter for decanting. [18,44] The assembled Ta crucible was then itself sealed into an amorphous silica tube with silica wool above and below it to act as cushioning. This growth ampoule was then place in a resistive box furnace. The furnace was then heated to 1150 • C over 10 hours, held at 1150 • C for 10 hours, cooled to 1020 • C over 4 hours and then very slowly cooled to 820 • C over 300 hours at which point the growth ampoule was removed and decanted in a centrifuge to separate the La 2 Ni 7 single crystals from the residual liquid. [18] Crystals grew as well faceted plates with clear hexagonal morphology (see Fig. 1 (c) ). As shown in Ref. [35] the crystallographic c-axis is perpendicular to the hexagonal surface of the plates.
Previous studies indicated that La 2 Ni 7 crystallizes in two different structures (rhombohedral or hexagonal) based on stacking of the layers along the c direction. The single crystals grown using method described above were single phase with a hexagonal Ce 2 Ni 7 type structure.
The samples show magnetic ordering below T 1 = 61 K and underwent successive re-ordering at T 2 = 57 K and T 3 = 42 K.
The samples were cleaved in situ at base pressure lower than 5 × 10 −11 Torr, yielding shiny, flat, mirrorlike surfaces along the basal plane of the hexagonal structure. High photon energy (21.2 eV) ARPES data were acquired using a laboratory-based system consisting of a Scienta R8000 electron analyzer and a Gammadata helium UV lamp. The angular resolution was ∼ 0.1 • and 1 • along and perpendicular to the direction of the analyzer slits, respectively.
The energy resolution was set at 5 meV. Low photon energy data (6.7 eV) was acquired using tunable laser ARPES system that consists of picosecond Ti:Sapphire oscillator, a fourth harmonic generator [45] and Scienta DA30 analyzer. The angular resolution was ∼ 0.1 • and 1 • along and perpendicular to the direction of the analyzer slits, respectively. The energy resolution was set at 1 meV. In both cases the energy corresponding to the chemical potential was determined from the Fermi edge of a polycrystalline Cu reference in electrical contact with the sample.
Band structures have been calculated in density functional theory [46,47] (DFT) with PBE [48] exchange-correlation functional, a plane-wave basis set and projected augmented wave method [49] as implemented in VASP [50,51]. For bulk band structures of nonmagnetic and block-wise anti-ferromagnetic configurations of La 2 Ni 7 , the primitive hexagonal unit cell with experimental lattice parameters [52] have been used with a Monkhorst-

Pack [53] (5 5 3) k-point mesh including the Γ point and a kinetic energy cutoff of 270 eV.
Tight-binding models based on maximally localized Wannier functions [54][55][56] have been constructed to reproduce closely the bulk band structures in the range of E F ±1 eV with La sdf and Ni sd orbitals. Then the spectral functions and Fermi surface of a semi-infinite La 2 Ni 7 (001) surface were calculated with the surface Green's function methods [57][58][59][60] as implemented in WannierTools [61].
Among them, Ni5 (2a) acts as the boundary separating the cell into two blocks along the c-axis with each occupying one of the two prisms in the half-cell blocks. Using the A state with block-wise AFM configuration identified by neutron study [43], we have calculated the moment on Ni sites as 0.11 µ B on Ni1 (12k), 0.27 µ B on Ni2 (6h), 0.17 µ B on Ni3 (4f), 0.19 µ B on Ni4 (4e) and 0.00 µ B on Ni5 (2a), which are in a good agreement with the earlier DFT calculation [42].  [35], as well as the recent determination of the ordering wave vectors (and their temperature dependencies) for the zero field, A, B, and C phases, we performed the ARPES studies to understand the effects of the magnetic transitions on the electronic structure.
The crystal structure of La 2 Ni 7 is shown in Fig. 1(a). Grey spheres represent Ni atoms and green ones are La atoms. The unit cell consists of two [La 2 Ni 4 +2LaNi 5 ] blocks as can be seen in Fig. 1(b) and is highly anisotropic with large values of lattice constant c = 24.71Å compared to the in plane lattice constant a = 5.058Å. In the lowest temperature, wAFM state ( A state in the H-T phase diagram shown in Fig. 1 (d)), each [La 2 Ni 4 +2LaNi 5 ] cluster can be considered as a ferromagnetic (FM) block. Each FM block includes two LaNi 5 layers and these blocks are separated by the non-magnetic La 2 Ni 4 layer [42,43]. The La 2 Ni 4 layer at the center of the unit cell provides the inversion center of the nearest neighbors Ni atoms.
The top and bottom blocks have opposite orientations of magnetic moments. As a result, the unit cell consists of two opposing FM blocks with non-magnetic layer in between which result 5 in weakly coupled AFM structure [42]. Fig. 1(c) shows picture of single crystal of La 2 Ni 7 and Fig. 1(d) shows the Brillouin zone (BZ) along with the labels of the high symmetry points. Fig. 1(e) shows H-T phase diagram of La 2 Ni 7 .
Motivated by the clear delineation of multiple magnetic phases in the H-T phase diagram (based on features in magnetization, specific heat and electrical resistivity data) [35] and results of recent neutron scattering [43], we performed ARPES studies to understand the effects of the magnetic transitions on the electronic structure.
In Fig. 2, we focus on Fermi surface (FS) and band dispersion in the PM state. Fig. 2(a) shows the ARPES intensity integrated within 10 meV about the chemical potential. Areas  We investigated the temperature dependence of the band dispersion. High resolution, temperature dependent data are presented in Fig. 3 and Fig. 4. Since long-range magnetic ordering introduces gap opening or band splitting at high symmetry points, we investigated the band structure along different high symmetry lines. First, The FS and band dispersion 6 along the K-Γ-K direction are shown in Fig. 3. Fig. 3(a) shows the ARPES intensity integrated within 10 meV about the chemical potential, which reveals the FS at 70 K (PM state) near the Γ point. Fig. 3(b) shows the measured FS for T=22K, i.e. in the T < T 3 , or A, magnetically ordered state. Fig. 3(c) shows calculated FS in the PM state near the Γ point and Fig. 3(d) Fig. 3(h). Upon transition to A phase additional splitting of the hole band at Γ occurs. To understand the details of the band splitting, we plot EDCs at the Γ point across the successive magnetic transitions. The result is shown in Fig. 3(i). The red curve (PM state) shows the highest intensity point at ∼ 50 meV with the shoulder peak at ∼ 100 meV below the E F . On the other hand, the yellow curve (C state) exhibits the highest intensity peak at ∼ 110 meV and the shoulder peak at ∼ 50 meV below the E F . The green curve (B state) shows clearly two separated peaks located at 50meV and 110 meV below the E F . In addition, the blue curve (A state) shows the emergence of two extra peaks near the E F . Consequently, our detailed analysis of the ARPES data suggests that each of the different magnetically ordered states significantly modifies the band dispersion.
We can use calculations to model the band structure for the two states, the paramagnetic state (with no long range magnetic order) and the lowest temperature wAFM state (where we use the magnetic order suggested in Ref [42,43]) with results shown in Figs. 3(j) and (k). Fig. 3(j) shows calculated band dispersion along the K-Γ-K direction in the PM state.
Indicating presence of a flat band and hole pockets near the E F . Overall, hole-like band dispersion observed by ARPES measurement in the PM state are described by the calculation reasonably well. The calculation result in the AFM state is shown in Fig. 3(k) In order to further study the difference in the dispersion between the PM and wAFM state, given that long range magnetic ordering may induce the band splitting along different high symmetry directions, we investigated band dispersion along different high symmetry direction. In Fig. 4, we focus on the band dispersion along the (M -Γ-M ) direction. The band structure in the PM state consists of several hole pockets near the Γ point ( Fig. 4(a)).  Fig. 4(c) shows band dispersion in the A state. In addition to the band splitting observed at the K-Γ-K direction, our ARPES data along the M -Γ-M direction exhibit additional band splitting near the E F (k ∼ ±0.13Å −1 ). Since 3d orbital from Ni lies close to the E F , the splitting may be connected to spin fluctuation from the 3d electrons, but the exact mechanism of the splitting should be scrutinized in future studies. To understand the details of the magnetic states, we plot MDCs at the E F in Fig. 4(e). 8 The red curve shows the MDC in the PM state. The green arrow marks the location of the peak position at 80 K. The blue curve represents the MDC in the A state. In both cases, there are clear peaks at ∼ ±0.7Å −1 . Black arrows mark two split peak positions in the A state. Although our calculation model suggests that magnetic ordering emerges along the out of plane direction, the comparison of the MDCs suggests that there is a band splitting along the in-plane direction near the E F in the A state. This may suggest that their is extra magnetic ordering along the in-plane direction. The EDC measured at the Γ confirms that the splitting also occurs along energy axis (Fig. 4(f)). Peak positions are marked by black bars. In the A state, we observed band splitting and an extra peak at the E F as compared to the K-Γ-K direction, even though the band splitting is more pronounced in the K-Γ-K direction.
As shown in Fig.3

IV. CONCLUSIONS
In summary, we studied the electronic structure of wAFM La 2 Ni 7 by means of ARPES and DFT calculations. Our data reveal complex array of band splittings and shifts caused by successive magnetic transitions. While there is some overall agreement in the shape of the FS between calculation and ARPES data in PM state, there are more significant differences in details of the band dispersion. The experiment does not detect the flat band located near E F that was predicted by DFT, possibly because the calculated value of E F is higher than one measured in experiments and this band being it is cut-off by the Fermi function in experimental data. Upon transition to AFM ground state, the flat band is absent in the calculations, in better agreement with data, however the predicted significant changes in the 9 FS are not confirmed by the experiment. The evolution of pattern of band splittings that is observed in experiment upon successive magnetic transitions is not completely reproduced by the calculations. We therefore demonstrate that the series of magnetic transitions in this material leads to significant and rather complex changes in the band structure that is a reasonable agreement with calculations for A state. Since the structural models for remaining states B and C are not yet known, we are not able to perform proper DFT calculations for these. It appears that La 2 Ni 7 is a good test system that can be used for improving our understanding of relation between magnetic ordering and band structure and computational modeling.