Coexistence of localized and itinerant magnetism in intercalated iron-selenide (Li,Fe)OHFeSe

The electronic structure and magnetism of a new magnetic intercalation compound (Li0.8Fe0.2)OHFeSe are investigated theoretically. The electronic structure calculations predict that the Fe in the (Li,Fe)OH intercalated layer is in +2 valence state, i.e. there is electron doping to the FeSe layer, resulting in the shrinking of the Fermi surface (FS) pocket around Gamma and a strong suppression of dynamical spin susceptibility at M in comparison with the bulk FeSe compound. The ground state of the FeSe layer is a striped antiferromagnetic (SAFM) metal, while the (Li,Fe)OH layer displays a very weak localized magnetism, with an interlayer ferromagnetic (FM) coupling between the FeSe and intercalated (Li,Fe)OH layers. Moreover, the (Li,Fe)OH is more than a block layer; it is responsible for enhancing the antiferromagnetic (AFM) correlation in the FeSe layer through interlayer magnetic coupling. We propose that the magnetic spacer layer introduces a tuning mechanism for spin fluctuations associated with superconductivity in iron-based superconductors.


I. INTRODUCTION
Since the discovery of superconductivity in the layered iron-based compound LaO 1−x F x FeAs [1], more iron pnictide and selenide compounds, including the 1111 (ROFeAs, R = La, Sm, Nd, etc.), 111 (AFeAs, A = Li, Na, etc.), 122 (BaFe 2 As 2 and KFe 2 Se 2 , etc.) and 11 (FeSe and FeTe) systems [2][3][4][5][6][7], have been successfully synthesized. Of all these materials, FeSe and its intercalated compounds A x Fe 2−y Se 2 (A = alkali metal; K, Rb and Cs, etc.) have drawn extensive attention due to their interesting local interactions and Fermi surface (FS) topology which is distinct from other iron-pnictides [8][9][10][11][12][13]. Although the superconducting transition temperature T c is relatively low in bulk FeSe (8 K) [14], it is greatly increased by tuning the crystalline structures. For example, applying high pressure can enhance the T c up to 37 K in bulk FeSe [15], K intercalation can result in K 1−x Fe 2−y Se 2 compounds with a T c of 30 K [3], and more surprisingly, it has been found that a single layer FeSe grown on SrTiO 3 substrates can boost the T c [16]. All these findings indicate the key role of the two-dimensional (2D) FeSe planes. On the other hand, due to the proximity of antiferromagnetism (AFM) and superconductivity in these iron-based compounds, magnetism has become a central issue to resolve the mystery of superconductivity in these materials. The origin of magnetism has been hotly debated and has attracted great interest about whether it comes from a FS nesting mechanism of itinerant electrons or a frustrated superexchange one of localized electrons [4,[17][18][19][20][21][22]. The strong variation of T c with structural parameters in FeSe and its derived compounds provides a unique playground in which to investigate the nature of magnetism, the roles of localized and itinerant electrons and their connection with superconductivity in iron-based superconductors [23][24][25][26].
Recently, a novel iron-selenide compound (Li,Fe)OHFeSe has been found to exhibit a high superconducting transition temperature T c up to 40 K [27][28][29][30] be a very interesting model system to study how a spacer layer of magnetism interacts with the FeSe layers and how such an interaction can affect the superconductivity in FeSe layers.
In this paper, in order to uncover the roles of the two different kinds of Fe ions in (Li,Fe)OHFeSe, we performed first-principle calculations and disentangled the 3d-bands of Fe2 from other bands using Wannier functions. We find that the (Li 0.8 Fe 0.2 )OH layer con-

II. METHOD
In our calculations, we adopt the full potential linearized augmented-plane-wave scheme based on density functional theory in the WIEN2K code [32]. Exchange and correlation effects are taken into account in the generalized gradient approximation (GGA) by Perdew, Burk, and Ernzerhof (PBE) [33]. In order to calculate the magnetic structure, a 1 × 1 × k points is adopted. In the disentanglement procedure, the maximally localized Wannier functions (MLWF) scheme, implemented with WANNIER90 [34] and WIEN2WANNIER [35], is performed.
In order to compare our numerical results with the experimental data, we adopt the structural data of (Li,Fe)OHFeSe given by neutron powder diffraction [28]. (Li,Fe)OHFeSe has a tetragonal space group P 4/nmm (No. 129) with lattice parameters a = 3.78Å (a = 3.76 and 3.82Å for the bulk FeSe [14] and FeSe/SrTiO 3 [36], respectively), and c = 9.16Å (c = 5.52Å for bulk FeSe), as shown in Fig. 1 We first study the NM phase of an ideal LiOHFeSe compound [37], which can serve as a reference for the (Li with six electrons occupied, which is consistent with the recent Mössbauer experiment [38], indicating that the FeSe layer is electron doped by the (Li 0.8 Fe 0.2 )OH layer.
The unique FS topologies in LiOHFeSe and its k z = 0 2D cut plot, as shown in Fig. 4(a) and (b), are very different from other iron-based superconductors [13,39,40], consisting of a small hole cylinder and two inner hole cylinders centered at Γ and two electron cylinders at M arising from Fe2 3d bands. As mentioned above, (Li 0.8 Fe 0.2 )OHFeSe can be regarded  Fig. 4(c). It is clearly found that the hole cylinders at Γ shrink, while the nearly degenerate electron cylinders at M enlarge. The (Li,Fe)OH layer therefore leads to a sharp change in the FS topology of the FeSe layer, which is very different from that of the bulk FeSe compound.
Considering the fact that the two inequivalent Fe ions in the doped LiOHFeSe system lead to a folded electronic structure, we also unfold it to one Fe scenario based on the band unfolding technique [42]. The unfolded orbital-resolved FS and band structure corresponding to one-Fe Brillouin zone (BZ) are shown in Fig. 5 and Fig. 6, respectively. The FS topology of (Li 0.8 Fe 0.2 )OHFeSe, as shown in Fig. 5(b), is greatly consistent with the result observed by the ARPES experiment [41]. The small hole FS mainly contributes from the xy orbital, while the large hole FS contributes from the xz and yz orbitals, and the two degenerate electron FSs from both the xy and xz, yz orbitals.
As seen in Fig. 6, the unfolded band structures are very similar to those of the FeSe compound [5]; in addition, a Fermi level shifts upwards by 0.1 eV. This indicates that the (Li 0.8 Fe 0.2 )OH spacer layer only provides electron doping and chemical pressure (strain) with respective to the FeSe system. The unfolded band structure displays an almost one-Fe (fiveorbital) picture, which is also observed by ARPES experiments in the iron-based compounds CsFe 2 As 2 and RbFe 2 As 2 [43].

B. Magnetic instability
In order to explore whether there is a FS nesting in (Li,Fe)OHFeSe and its associated magnetic instability, we calculate the bare spin susceptibility given by [40,44] Considering the moderate electronic correlation in iron-based systems, the multi-orbital random phase approximation (RPA) spin susceptibility χ RP A s is written as where χ 0 is the bare susceptibility defined in Eq. coupling, as shown in Fig. 1(b). The calculated magnetic moments are 3. respectively. We note that the magnetic state with the same spin configurations both for Fe1 In order to describe the magnetic interactions between spins in this system, a J 1 -J 2 -J 3 - -J c Heisenberg model is constructed as follows, According to Table I coupling plays a key role in the superconductivity of iron-based superconductors [19]. Thus the strong magnetic fluctuation induced by the (Li 0.8 Fe 0.2 )OH layer is possibly responsible for the high superconducting transition temperature T c in (Li,Fe)OHFeSe. Therefore our results demonstrate that the interplay between the different magnetic layers is a tuning factor for spin fluctuations associated with superconductivity in iron-based superconductors.
In fact, the enhancement of magnetism is also observed experimentally in other iron-based materials, which is usually ascribed to the influence of the interstitial Fe [46,47].
It is worth noting that there are many sensitive factors which may seriously affect the magnetism in (Li 0.8 Fe 0.2 )OHFeSe. One is the possible stoichiometric problem extensively existing in iron-based superconductors; for instance, excess Fe in the experiments may lead to contradictory results between theory and experiment, i .e. theoretically-predicted magnetic order was not observed experimentally for FeSe [8,48,49] and LiFeAs [50,51]. Another issue is the cation-disorder of Li and Fe ions in the (Li,Fe)OH layer of the (Li 0.8 Fe 0.2 )OHFeSe compound. Thus further neutron scattering and nuclear magnetic resonance experiments are needed to investigate the magnetism in (Li,Fe)OHFeSe.

IV. CONCLUSIONS
In summary, we have performed first-principle calculations and theoretical analysis to the electronic structures and magnetic properties of (Li,Fe)OHFeSe compounds. We find that the low energy physics of this novel iron-selenide superconductor (Li,Fe)OHFeSe is dominated by the FeSe layer, while the (Li,Fe)OH layer is not only a Mott insulating block layer, but is also responsible for the enhancement of the N.N.N. AFM correlations in the FeSe layer. We find that the ground state is SAFM configurations in both the FeSe and (Li,Fe)OH layers with weak FM interlayer coupling and, furthermore, the magnetic coupling strengths of Fe spins are evaluated. The coexistence of the localized and itinerant magnetism in (Li,Fe)OHFeSe provides a good example for investigating the interplay of localized and itinerant electrons, and the interplay of the magnetism and superconductivity.