Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides

The electronic structure and magnetic ordering in La₁₋xPrxCo₂P₂ (x=0, 0.25, and 1) phosphides have been studied theoretically using the fully relativistic spin-polarized Dirac linear muffin-tin orbital (LMTO) band-structure method. The X-ray absorption and X-ray magnetic circular dichroism spectra a...

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Datum:	2015
Hauptverfasser:	Bekenov, L.V., Moklyak, S.V., Antonov, V.N.
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Sprache:	English
Veröffentlicht:	Інститут фізики конденсованих систем НАН України 2015
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spelling	irk-123456789-1542042019-06-16T01:26:00Z Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides Bekenov, L.V. Moklyak, S.V. Antonov, V.N. The electronic structure and magnetic ordering in La₁₋xPrxCo₂P₂ (x=0, 0.25, and 1) phosphides have been studied theoretically using the fully relativistic spin-polarized Dirac linear muffin-tin orbital (LMTO) band-structure method. The X-ray absorption and X-ray magnetic circular dichroism spectra at the Co L₂,₃ and Pr M₄,₅ edges have been investigated theoretically within the framework of the LSDA+U method. The core-hole effect in the final state as well as the effects of the electric quadrupole E₂ and magnetic dipole M₁ transitions have been investigated. Good agreement with experimental measurements has been found. На основi зонних розрахункiв повнiстю релятивiстським спiн-поляризованим лiнiйним методом МТорбiталей (ЛМТО) теоретично вивченi електронна структура i магнiтне впорядкування у фосфiдах La₁₋xPrxCo₂P₂ (x = 0,0.25, та 1). В рамках методу LSDA+U теоретично дослiдженi рентгенiвськi спектри поглинання та спектри рентгенiвського циркулярного дихроїзму на краях поглинання CoL₂,₃ i PrM₄,₅. Вивчено вплив остовної дiрки в кiнцевому станi, а також електричних квадрупольних E₂ i магнiтних дипольних M₁ переходiв. Отримано добре узгодження з експериментальними результатами. 2015 Article Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides / L.V. Bekenov, S.V. Moklyak, V.N. Antonov // Condensed Matter Physics. — 2015. — Т. 18, № 3. — С. 33701: 1–11. — Бібліогр.: 58 назв. — англ. 1607-324X arXiv:1510.06542 DOI:10.5488/CMP.18.33701 PACS: 71.28.+d, 71.25.Pi, 75.30.Mb http://dspace.nbuv.gov.ua/handle/123456789/154204 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The electronic structure and magnetic ordering in La₁₋xPrxCo₂P₂ (x=0, 0.25, and 1) phosphides have been studied theoretically using the fully relativistic spin-polarized Dirac linear muffin-tin orbital (LMTO) band-structure method. The X-ray absorption and X-ray magnetic circular dichroism spectra at the Co L₂,₃ and Pr M₄,₅ edges have been investigated theoretically within the framework of the LSDA+U method. The core-hole effect in the final state as well as the effects of the electric quadrupole E₂ and magnetic dipole M₁ transitions have been investigated. Good agreement with experimental measurements has been found.
format	Article
author	Bekenov, L.V. Moklyak, S.V. Antonov, V.N.
spellingShingle	Bekenov, L.V. Moklyak, S.V. Antonov, V.N. Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides Condensed Matter Physics
author_facet	Bekenov, L.V. Moklyak, S.V. Antonov, V.N.
author_sort	Bekenov, L.V.
title	Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides
title_short	Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides
title_full	Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides
title_fullStr	Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides
title_full_unstemmed	Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides
title_sort	electronic structure, magnetic ordering and x-ray magnetic circular dichroism in la₁₋xprxco₂p₂ phosphides
publisher	Інститут фізики конденсованих систем НАН України
publishDate	2015
url	http://dspace.nbuv.gov.ua/handle/123456789/154204
citation_txt	Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides / L.V. Bekenov, S.V. Moklyak, V.N. Antonov // Condensed Matter Physics. — 2015. — Т. 18, № 3. — С. 33701: 1–11. — Бібліогр.: 58 назв. — англ.
series	Condensed Matter Physics
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first_indexed	2025-07-14T05:52:33Z
last_indexed	2025-07-14T05:52:33Z
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fulltext	Condensed Matter Physics, 2015, Vol. 18, No 3, 33701: 1–11 DOI: 10.5488/CMP.18.33701 http://www.icmp.lviv.ua/journal Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La1−xPrxCo2P2 phosphides L.V. Bekenov, S.V. Moklyak, V.N. Antonov Institute of Metal Physics of the National Academy of Sciences of Ukraine, 36 Vernadsky Blvd., 03142 Kyiv, Ukraine Received January 31, 2015 The electronic structure and magnetic ordering in La1−x Prx Co2P2 (x = 0,0.25, and 1) phosphides have been studied theoretically using the fully relativistic spin-polarized Dirac linear muffin-tin orbital (LMTO) band-structure method. The X-ray absorption and X-ray magnetic circular dichroism spectra at the CoL2,3 and PrM4,5 edges have been investigated theoretically within the framework of the LSDA+U method. The core-hole effect in the final state as well as the effects of the electric quadrupole E2 and magnetic dipole M1 transitions have been investigated. Good agreement with experimental measurements has been found. Key words: strongly correlated systems, band structure, magnetic moments, X-ray magnetic circular dichroism PACS: 71.28.+d, 71.25.Pi, 75.30.Mb 1. Introduction Ternary intermetallics AT2X2, where A − alkali, alkali-earth, rare-earth, or actinide metal, T − transi- tion metal, and X − nonmetal, often demonstrate intrinsically complex magnetic structures and a wide variety of physical properties. They belong to the ThCr2Si2 structure type and can be conveniently rep- resented as materials built by stacking covalently bonded transition metal-metalloid T2X2 layers, made of edge-sharing TX4 tetrahedra, with ionic A atoms. This body-centered tetragonal structure is rather simple with only one crystallographic site for each atomic species and only one variable positional pa- rameter, the z value of the X site. Due to the great variety of possible elements in this structure, over 1000 different compounds of this type are known already [1]. Some of these compounds exhibit fascinat- ing physical properties such as superconductivity, valence fluctuations, local and itinerant magnetism. Interest to these materials has been reinvigorated recently due to the discovery of non-Fermi-liquid be- havior in YbRh2Si2 [2] and high-temperature superconductivity in K-doped BaFe2As2 [3, 4]. In addition, materials with layered arrangements of magnetic moments are also of great interest because they tend to exhibit a highly anisotropic magnetic behavior. The magnetic properties of the silicides and germanides possessing this structure were studied by many groups [5–11]. Besides superconductivity, AT2X2 phases exhibit a plethora of other phase transition phenomena. Thus, SmMn2Ge2 becomes ferromagnetic below 348 K and then undergoes a transition to an antiferromagnetic state at 196 K, followed by a re-entrant ferromagnetic transition at 64 K [7]. This peculiar magnetic behavior stems from the layered structure and the presence of two magnetic sublattices in these materials and was later observed for a number of rare-earth manganese germanides and silicides [8–11]. Such sequential magnetic transitions have not been observed in isostructural phosphides which might explain why their magnetic properties have re- ceived somewhat less attention than the tetrelides. The isotypic phosphides were prepared much later [12] and the investigations of their magnetic properties have started only recently. In the compounds RT2P2 (R = lanthanides, T = Fe, Co, Ni) with the trivalent rare earth elements, mag- netic moments at the transition metal sites were observed only for the cobalt containing compounds © L.V. Bekenov, S.V. Moklyak, V.N. Antonov, 2015 33701-1 http://dx.doi.org/10.5488/CMP.18.33701 http://www.icmp.lviv.ua/journal L.V. Bekenov, S.V. Moklyak, V.N. Antonov [13–15]. Reehuis et al. carried out a comprehensive study of the structural and magnetic properties of ternary RCo2P2 materials [15–17]. Recently, Kovnir et al. [18–20] and other groups [21, 22] have demon- strated that the magnetic properties of the ThCr2Si2 type phosphides can be as rich and diverse as those of the aforementioned silicides and germanides, provided that proper iso- and aliovalent substitutions are made to modify the crystal and electronic structures of the materials. Ternary cobalt phosphides RCo2P2 appear to be on the verge of magnetic instability [20]. Indeed, LaCo2P2 is characterized by ferro- magnetic ordering of Co magnetic moments at 132 K [14, 18], while other representatives of this family (R = Ce, Pr, Nd, Sm) order antiferromagnetically at around room temperature [15] (with the exception of the Ce-containing compound, which shows an antiferromagnetic transition at 440 K purportedly due to the mixed valence of Ce). A substantial difference is also observed in the crystal structures of these compounds [23]. In LaCo2P2, the [Co2P2] layers are far from each other, with the interlayer P–P distance of 3.16 Å indicating essentially no bonding between the phosphorus atoms. By contrast, other RCo2P2 structures show a weakly covalent P–P interaction at relatively small interplanar P–P distances (2.57 Å in PrCo2P2 [18]). Thus, a drastic change in the magnetic behavior is accompanied by the formation of the P–P bonding pathway between the [Co2P2] layers. Kovnir et al. [18] embarked on the study of structural, magnetic, and electronic properties of qua- ternary compositions La1−xPrxCo2P2 (0 É x É 1). The choice of Pr was based on the fact that it does not exhibit a mixed valence like Ce, and, therefore, is the closest rare-earth neighbor of La in both the size and the formal ionic charge. They focused on the drastically different magnetic properties of LaCo2P2 and PrCo2P2, which exhibit ferromagnetic (TC = 132 K) and antiferromagnetic (TN = 305 K) ordering in the Co sublattice, respectively [18]. In both cases, a ferromagnetic arrangement of magnetic moments within the square plane of Co atoms is observed. In LaCo2P2, the Comoments are aligned in-plane and parallel to the moments in the other layers, leading to the ferromagnetic ground state [17]. In PrCo2P2, they are aligned perpendicular to the plane (along the c axis), but the antiparallel magnetic coupling between the neigh- boring planes results in antiferromagnetism [16]. In [24], magnetic behavior of La0.75Pr0.25Co2P2 was investigated by a combination of magnetic measurements, magneto-optical imaging, neutron diffraction, and X-ray absorption spectroscopy, including X-ray magnetic circular dichroism. The aim of this paper is a theoretical study, from the first principles, of the electronic structure, mag- netic ordering and X-ray magnetic circular dichroism in La1−xPrxCo2P2 (x = 0,0.25, and 1) compounds. The energy band structure of La1−xPrxCo2P2 (x = 0,0.25, and 1) compounds is calculated within the ab initio approach taking into account strong electron correlations by applying the local spin-density approx- imation (LSDA) to the density functional theory supplemented by a Hubbard U term (LSDA+U ) [25]. The paper is organized as follows. The computational details are presented in section 2. Section 3 presents the electronic structure, XAS and XMCD spectra of La1−xPrxCo2P2 (x = 0,0.25, and 1) compounds calculated in the LSDA+U approximation. The theoretical results are compared to experimental measurements. Fi- nally, the results are summarized in section 4. 2. Computational details X-ray magnetic circular dichroism. The absorption coefficient µλ j (ω) for incident X-ray of polarization λ and photon energy ħω can be determined as the probability of electronic transitions from initial core states with the total angular momentum j to final unoccupied Bloch states: µ j λ (ω) = ∑ m j ∑ nk ∣ ∣ ∣ 〈 Ψnk\|Πλ\|Ψ j m j 〉 ∣ ∣ ∣ 2 δ(Enk −E j m j −ħω)θ(Enk −EF) , (2.1) where Ψ j m j and E j m j are the wave function and the energy of a core state with the projection of the total angular momentum m j ;Ψnk and Enk are the wave function and the energy of a valence state in the n-th band with the wave vector k; EF is the Fermi energy. Πλ is the electron-photon interaction operator in the dipole approximation Πλ =−eαaλ , (2.2) where α are the Dirac matrices, aλ is the λ polarization unit vector of the photon vector potential, with a± = 1/ p 2(1,±i ,0), a∥ = (0,0,1). Here,+ and− denotes, respectively, left and right circular photon polar- izations with respect to the magnetization direction in the solid. The X-ray magnetic circular and linear 33701-2 La1−x Prx Co2P2 phosphides dichroism are given by µ+ −µ− and µ∥ − (µ+ +µ−)/2, respectively. Detailed expressions of the matrix elements in the electric dipole approximation may be found in [26–29]. The matrix elements due to the magnetic dipole and electric quadrupole corrections are presented in [29]. Magnetocrystalline anisotropy energy. The internal energy of a ferromagnetic material depends on the direction of spontaneous magnetization. The magnetocrystalline anisotropy energy (MAE), which pos- sesses the crystal symmetry of a material, is a part of this energy. The MAE is an important property that describes the tendency of the magnetization to align along specific spatial directions rather than to ran- domly fluctuate over time. TheMAE determines the stability of magnetization in bulk as well as nanopar- ticle systems. Extensive studies on ferromagnetic bulk materials and thin films have highlighted the MAE dependence on crystal symmetry and atomic composition. While the exchange interaction among elec- tron spins is purely isotropic, the orbital magnetization connects the spin magnetization to the atomic structure of a magnetic material via the spin-orbit interaction, giving rise to the magnetic anisotropy [30]. The calculation of the magnetocrystalline anisotropy energy has been a long-standing problem. A first theory of the MAE in Fe and Ni was formulated by Brooks [31] and Fletcher [32], who emphasized that the energy band picture in which the effect of spin-orbit (SO) coupling is taken into account in a perturbative way could provide a coupling of the magnetization orientation to the crystallographic axes of approximately the right order of magnitude. In this pioneering work, the band structure was oversim- plified to three empirical bands [31, 32]. Recent investigations [33–37] elaborated the MAE problem using ab initio calculated energy bands obtained within the local-spin density approximation to the density functional theory. Although it is beyond doubt that LSDA energy bands are superior to empirical bands, it turned out that the calculation of the MAE from first principles poses a great computational challenge. The prime obstacle is the smallness of the MAE, which is of only a few meV/atom, a value that ought to result from the difference of two total energies for different magnetization directions, which are both of the order of 104 eV/atom. Due to this numerical problem, it remained at first unclear if the LSDA could at all describe the MAE correctly, since the wrong easy axis was obtained for hcp Co and fcc Ni [33]. Recent contributions aimed consequently at improving the numerical techniques [35, 38], with the result that the correct easy axis was obtained for hcp Co, but not for fcc Ni [35]. Halilov et al. [36] reported an ab initio investigation of the magnetocrystalline anisotropy energy in bcc Fe and fcc Co and Ni. They introduced a spin-orbit scaling technique that yielded the correct easy axis for Fe and Co, but a vanishing MAE for Ni. For thematerial exhibiting uniaxial anisotropy, such as a hexagonal crystal, the MAE can be expressed as [39] E (θ) = K1 sin 2 θ+K2 sin 4θ+K ′ 3 sin 6θ+K3 sin 2θcos [ 6(φ+ψ) ] +·· · , (2.3) where Ki is the anisotropy constant of the i th order, θ and φ are the polar angles of the Cartesian coordi- nate system where the c axis coincides with the z axis (the Cartesian coordinate system is chosen so that the x axis is rotated through 90◦ from the a hexagonal axis) and ψ is a phase angle. Both themagnetic dipole interaction and the SO coupling give rise to theMAE, the former contributing only to the first-order constant K1. Here, we deal with the MAE caused only by the SO interaction. Both themagneto-optical effects and theMAE have a common origin in the SO coupling and exchange splitting. Thus, a close connection between the two phenomena seems plausible. In this paper, the MAE is defined as the difference between two self-consistently calculated fully rela- tivistic total energies for two different magnetic field directions, E (θ)–E〈001〉. Crystal structure. LaCo2P2 and PrCo2P2 belong to the ThCr2Si2 body-centered tetragonal structure type (figure 1). The space group is I4/mmm (No. 139) with Pr (La) at the 2a positions (0, 0, 0), Co at the 4a positions (0, 1 2 , 1 4 ) and P at the 4e positions (0, 0, z); z = 0.3697 and 0.3568 in PrCo2P2 and LaCo2P2, re- spectively [16, 17]. In this structure, the transition metal atoms (Co) form planar square nets, and the nonmetal atoms (P) cap the centers of the squares above and below the planes in a chessboard-like fash- ion. The resulting [Co2P2] layers are separated by layers of rare-earth metal cations (Pr or La). The Pr atom in PrCo2P2 has 8 P nearest neighbors at the distance of 3.0329 Å and 8 Co atoms at the 3.1094 Å distance, the shortest P–P distance is equal to 2.5247 Å. In LaCo2P2, the La atom has 8 P nearest neighbors 33701-3 L.V. Bekenov, S.V. Moklyak, V.N. Antonov x y z Pr Co P Pr La Co P Figure 1. (Color online) Schematic representation of the PrCo2P2 structure. Figure 2. (Color online) Schematic representation of the La1−xPrxCo2P2 (x = 0.25) structure. at the distance of 3.1265 Å and 8 Co atoms at the 3.3551 Å distance, the P–P distance in LaCo2P2 is much larger and is equal to 3.1621 Å. The calculations of the energy band structure of La1−xPrxCo2P2 (x = 0,0.25, and 1) compounds were performed for a×a×2c supercells of the tetragonal structure with space group of P4/mmm (No. 123). The structure refinement parameters of La1−xPrxCo2P2 compounds are presented in [18]. The crystal struc- ture of La0.75Pr0.25Co2P2 is presented in figure 2. The Pr atom in this compound has 8 P nearest neighbors at the distance of 3.0329 Å and 8 Co atoms at the 3.1094 Å distance. The Co atoms are surrounded by 4 P atoms at the distance of 2.2688 Å and 4 Co atoms at the distance of 2.7577 Å, 4 La atoms are at the 3.1094 Å distance from Co. Calculation details. The calculations presented in this work were performed using the spin-polarized fully relativistic linear muffin-tin orbital (SPR LMTO) method [40–42] for the experimentally observed lattice constants: a = 3.6 Å, c = 9.688 Å for PrCo2P2 [16], a = 3.8145 Å, c = 11.041 Å for LaCo2P2 [17], and a = 3.8260 Å, c = 10.9031 Å for La1−xPrxCo2P2 (x = 0.25) [24]. The basis consisted of the Pr (La) s, p , d , and f ; Co s, p , and d ; P s, p , and d LMTO’s. The k-space integrations were performed with the improved tetra- hedron method [43], and the self-consistent charge density was obtained with 1063 irreducible k-points. To attain good convergence in total energy, a large number of k points should be used in calculations. To resolve the difference in total energies and to investigate the magnetocrystalline anisotropy, we used 13824 k points in the irreducible part of the Brillouin zone, which corresponds to 82944 tetrahedra in the full zone. The X-ray absorption and dichroism spectra were calculated taking into account the exchange split- ting of core levels. We also take into account the core-hole effect in the final state using the supercell approximation. The similar approximation has been used by several authors [44, 45]. The finite lifetime of a core hole was accounted for by folding the spectra with a Lorentzian. The widths of core level spec- tra ΓL2 = 1.13 eV and ΓL3 = 0.47 eV for Co, and ΓM4,5 = 0.75 eV for Pr were taken from [46]. The finite apparative resolution of a spectrometer was accounted for by a Gaussian with the width of 0.6 eV. It is well known that the LSDA fails to describe the electronic structure and properties of the systems in which the interaction among the electrons is strong. In recent years, more advanced methods of elec- tronic structure determination such as the LSDA plus self-interaction corrections (SIC–LSDA) [29, 47], the 33701-4 La1−x Prx Co2P2 phosphides LSDA+U [25] method, the GW approximation [48] and the dynamical mean-field theory (DMFT) [49–51] have sought to remedy this problem and have met considerable success. The LSDA+U method is the sim- plest among them and most frequently used in the literature. We used the “relativistic” generalization of the LSDA+U method which takes into account the spin-orbit coupling so that the occupation matrix of localized electrons becomes non-diagonal in spin indexes. This method is described in detail in our pre- vious paper [52] including the procedure to calculate the screened Coulomb U and exchange J integrals, as well as the Slater integrals F 2, F 4, and F 6. The screened Coulomb U and exchange J integrals enter the LSDA+U energy functional as external parameters and should be determined independently. The value of U can be estimated from the photo- emission spectroscopy (PES) and X-ray Bremsstrahlung Isochromat Spectroscopy (BIS) experiments. Be- cause of the difficulties with unambiguous determination of U , it can be considered as a parameter of the model. Then, its value can be adjusted to achieve the best agreement of the results of LSDA+U calcu- lations with PES or optical spectra [53]. While the use of an adjustable parameter is generally considered an anathema among first principles practitioners, the LSDA+U approach does offer a plausible and prac- tical method to treat approximately strongly correlated orbitals in solids. The Hubbard U and exchange parameter J can be determined from supercell LSDA calculations using the Slater’s transition state tech- nique [54, 55] or from constrained LSDA calculations [55–57]. Cococcioni and Gironcoli [58] have also provided an internally consistent, basis-set independent method based on the linear response approach for the calculation of the effective interaction parameters in the LSDA+U method. The constrained LSDA calculations produce U = 6.17 eV, J = 0.87 eV for Pr and U = 4.1 eV, J = 0.81 eV for Co in PrCo2P2, as well as U = 6.08 eV, J = 0.83 eV for La and U = 4.0 eV, J = 0.8 eV for Co in LaCo2P2. These values of U and J were used in our calculations presented below. P ar tia l de ns ity of st at es [s ta te s/ (a to m eV )] P3p LaCo2P2 -1.0 -0.5 0.0 0.5 1.0 PrCo2P2 -1.0 -0.5 0.0 0.5 1.0 Co3d LaCo2P2 -4 -2 0 2 PrCo2P2 -4 -2 0 2 -1 0 1 -2 0 2 La4f -5 0 5 Energy (eV) -20 -10 0 10 20 Pr4f -5 0 5 Energy (eV) -20 -10 0 10 20 Figure 3. (Color online) Partial density of states of LaCo2P2 and PrCo2P2. The insert in themiddle panel shows the energy distribution of the x y orbitals. 3. Results 3.1. Electronic structures of LaCo2P2 and PrCo2P2 Figure 3 presents the partial density of states (PDOS) for LaCo2P2 and PrCo2P2. The P 3s states are locatedmostly between−13.6 eV and−10.0 eV below the Fermi level (not shown), while the 3p states of P are found between −6.8 eV and 6.1 eV in LaCo2P2 and between −7.5 eV and 5.8 eV in PrCo2P2. The spin splitting of the P 3p states is quite small. The Co 3d states occupy the energy in- terval between −6.9 eV and 5.5 eV and hybridize strongly with the P 3p states. The La 4 f empty states occupy the 3.2 − 4.5 eV energy interval in LaCo2P2. The Pr 4 f empty states are from 1.5 eV to 4.8 eV above the Fermi level. Two Pr 4 f spin-up electrons occupy a small energy interval around −3 eV. The crystal field at the Co site (D2d point sym- metry) in both compounds causes the splitting of Co 3d orbitals into three singlets a1 (d3z2−1), b1 (dx y ), b2 (dx2−y2 ) and a doublet e (dy z and dxz ). A two peak structure of the minority- and majority- spin Co d states is found in the close vicinity of the Fermi energy. We found that the two peaks (occu- pied in the majority-spin channel at −0.5 eV and 33701-5 L.V. Bekenov, S.V. Moklyak, V.N. Antonov empty in the minority-spin channel at 0.3 eV) are of the x y character. These peaks are rather broad in LaCo2P2 and very narrow and intensive in PrCo2P2. Such a difference can be explained by differ- ent nearest-neighbors interatomic Co−Co and Co−P distances. The Co−Co distance is equal to 2.697 Å and 2.757 Å in LaCo2P2 and PrCo2P2, respectively. Also, the Co−P distance is larger in LaCo2P2 than in PrCo2P2 by 0.027 Å. Pr Co P La (a) (b) Figure 4. (Color online) Schematic representation of themagnetic ordering in PrCo2P2 (left-hand column) and LaCo2P2 (right-hand column). Our self-consistent calculations reveal a ferromagnetic arrangement ofmagnetic moments in PrCo2P2. The spin magnetic moments at the Pr and Co sites are aligned along the c axis with the antiparallel mag- netic coupling between the neighboring planes resulting in antiferromagnetism (left-hand column of fig- ure 4). The similar magnetic arrangement was observed experimentally by Reehuis et al. [16]. The theo- retical calculations give a ferromagnetic arrangement of magnetic moments in LaCo2P2, the Co moments are aligned in-plane and parallel to the moments in the other layers (right-hand column of figure 4). Fig- ure 5 (upper panel) shows the MAE as a function of the polar angle θ. The minimum of the total energy corresponds to the magnetic configuration with the Co moments aligned in-plane in agreement with the experimental observation [17]. The theory produces quite a small value of MAE of around 0.28 meV per formula unit in LaCo2P2. The lower panel of figure 5 shows the anisotropy of spin magnetic moments at the Co site in LaCo2P2 as a function of the polar angle θ. The spin ms and orbital ml magnetic moments at the Co site in PrCo2P2 are larger than in LaCo2P2. Our band structure calculations yield the magnetic moments for the Co atoms ms = 0.825 µB, ml = 0.120 µB in PrCo2P2 and ms = 0.665 µB, ml = 0.066 µB in LaCo2P2. The induced spin magnetic moments at the P site are of 0.011 µB and 0.016 µB for the PrCo2P2 and LaCo2P2, respectively. The orbital moments at the P sites are small in both compounds (mP l = 0.005 µB). The orbital magnetic moment at the La site is extremely small mLa l = −0.002 µB, however, we found quite a large orbital moment at the Pr site in PrCo2P2 (mPr l = 0.509 µB). 33701-6 La1−x Prx Co2P2 phosphides 3.2. Electronic structure, X-ray absorption and XMCD spectra in La1−x Prx Co2P2 com- pounds Figure 6 presents the partial density of states in La1−xPrxCo2P2 for x = 0.25. The energy position and shape of PDOS slightly differ from the corresponding PDOS of LaCo2P2 and PrCo2P2. The P 3p PDOS has more pronounced peaks near the Fermi level due to the larger P 3p − Co 3d hybridization. The positions of the empty La and Pr 4 f states are shifted closer to the Fermi level in comparison with the reference compounds. Also, the shape of the energy distribution of Pr 4 f states slightly differ from the corresponding 4 f PDOS in PrCo2P2 and LaCo2P2. Such differences might be explained by different lattice constants and different numbers and distances of the nearest neighbors. -0.3 -0.2 -0.1 0.0 E (θ ) - E (0 ) [m eV /f. u. ] 0 30 60 90 120 150 180 θ (deg) 0.0 0.1 0.2 0.3 m s( θ) -- m s( 0) [µ B ]x 10 -2 L3 L2 theory exper. 0 2 4 6 X A S (a rb .u ni ts ) 770 780 790 800 Energy (eV) -2 -1 0 1 X M C D (a rb .u ni ts ) Figure 5. (Color online) MAE (upper panel) and anisotropy of spinmagnetic moments at the Co site (lower panel) in LaCo2P2 as functions of the polar angle θ. Figure 6. (Color online) Partial density of states in La1−xPrxCo2P2 for x = 0.25. The spin magnetic moments at the Pr and Co sites (1.955 µB and 0.815 µB, respectively) are aligned along the c axis in La0.75Pr0.25Co2P2 with antiparallel magnetic moments at the La sites (ms =−0.002 µB and −0.007 µB for two nonequivalent La sites). The orbital magnetic moments are equal to 0.054 µB, 0.109 µB, and 0.020 µB for Pr, Co, and La sites, respectively. The orbital moments at the P sites are small (mP l = 0.001 µB). Figure 7 (upper panel) shows the X-ray absorption spectra at the Co L2,3 edges in La0.75Pr0.25Co2P2 measured at 5 K [24] with a 1 T magnetic field applied along the c axis compared with the theoretically calculated ones in the LSDA+U approximation. The Co L3 X-ray absorption spectrum possesses four ma- jor fine structures: a major peak at 779 eV and three high energy shoulders at 780.5 eV, 782.5 eV and 787.5 eV. The theory describes reasonably well the energy position and relative intensity of all the fine structures except the shoulder at 780.5 eV. Due to the electric dipole selection rules (∆l =±1; ∆ j = 0, ±1), the major contribution to the absorption at the L3 edge stems from the transitions 2p3/2 → 5d5/2, with a weaker contribution from the 2p3/2 → 5d3/2 transitions. For the latter case, the corresponding 2p3/2 → 5d3/2 radial matrix elements are only slightly smaller than for the 2p3/2 → 5d5/2 transitions. The angular matrix elements, however, strongly suppress the 2p3/2 → 5d3/2 contribution. Therefore, the contribution to the XAS spectrum at the L3 edge from the transitions with ∆ j = 0 is one order of magnitude smaller than the transitions with ∆ j = 1 [28]. 33701-7 L.V. Bekenov, S.V. Moklyak, V.N. Antonov The lower panel of figure 7 presents the XMCD experimental spectra of La0.75Pr0.25Co2P2 at the Co L2,3 edges and the theoretically calculated ones. The LSDA+U calculations describe reasonably well all the features of the experimental XMCD spectra. A study of the 4 f electron shell in rare earth compounds is usually performed by tuning the energy of X-ray close to the M4,5 edges of rare-earth where the electronic transitions between 3d3/2,5/2 and 4 f5/2,7/2 states are involved. Figure 8 shows the XAS and XMCD spectra at the Pr M4,5 edges in La0.75Pr0.25Co2P2 measured at 5 K [24] with a 1 T magnetic field applied along the c axis compared with the theoretically calculated ones in the LSDA+U approximation. The Dirac-Hartree-Fock-Slater single-particle approxima- tion used in this work to calculate the core states is not capable of producing a correct energy position of the spectra (because the self-interaction correction, different kinds of relaxation processes and other many-particle effects were not taken into account). Therefore, we used the experimentally measured po- sitions of the spectra. The theoretically calculated XAS spectra have a rather simple line shape composed of two white line peaks at the M5 and M4 edges. The theory reproduces the shape of the M5 XAS spectrum very well. However, the experimentally measured M4 spectrum has a well pronounced fine structure at the low energy part that is not reproduced by the theory. We should mention here that a major shortcom- ing in the band structure approximation is that the multiplet structure is not included. For the Co L2,3 edges, this is not the major problem. However, for the Pr M4,5 edges, the core-valence electrostatic inter- actions can significantly effect the line shape of the XAS and XMCD spectra. The fine structure on the low energy side of Pr M4 XASs is believed to be due to the multiplet structure, which is not included in our calculations. A theoretical method that consistently includes both the band structure and the atomic-like multiplet structure of rare earth metals and compounds is highly desired. However, we should mention that it is still not clear why the multiplet structure is pronounced only at the Pr M4 edge and is not seen at the M5 edge. L3 L2 theory exper. 0 2 4 6 X A S (a rb .u ni ts ) 770 780 790 800 Energy (eV) -2 -1 0 1 X M C D (a rb .u ni ts ) M5 M4 theory exper. 0 20 40 X A S (a rb .u ni ts ) 920 930 940 950 960 Energy (eV) -4 0 4 X M C D (a rb .u ni ts ) Figure 7. (Color online) Experimental and the- oretically calculated X-ray absorption (upper panel) and XMCD (lower panel) spectra of La0.75Pr0.25Co2P2 at the Co L2,3 edges. Figure 8. (Color online) Experimental and the- oretically calculated X-ray absorption (upper panel) and XMCD (lower panel) spectra of La0.75Pr0.25Co2P2 at the Pr M4,5 edges. Figure 8 (lower panel) shows the calculated Pr M4,5 XMCD spectra in the LSDA+U approximation for La0.75Pr0.25Co2P2 together with the corresponding experimental data [24]. The experimentally measured dichroism is rather large. The XMCD spectra at the M5 and M4 edges have a two-peak structure. The dichroism is positive at a lower energy and negative at a higher energy at the Pr M5 edge, while the Pr M4 XMCD spectrum has a negative minimum at a lower energy and a positive maximum at a higher 33701-8 La1−x Prx Co2P2 phosphides energy. The LSDA+U calculations quite well describe all the features of the experimental XMCD spectra at the M4,5 edges. The theory also correctly reproduces the relative intensities of the XAS and XMCD spectra at the M5 and M4 edges, namely, the XAS is larger at the M5 edge than at the M4 edge, while the XMCD spectra show the opposite behavior with larger dichroism at the M4 edge in comparison with the M5 edge. When a 3d core-electron is photo-excited to an unoccupied 4 f state, the distribution of the charge changes to account for the created hole. We investigated this core-hole effect in the final state using the supercell approximation. We found that the final-state interaction has little effect on the shape of the XAS and XMCD spectra at the Pr M4,5 edges. We also investigated the effect of the electric quadrupole E2 and magnetic dipole M1 transitions. We found that the M1 transitions are extremely small in comparison with the E2 transitions and can be neglected. The E2 transitions are much weaker than the electric dipole transitions E1. They are almost invisible in the XAS and have a very small effect on the XMCD spectra at the Pr M4,5 edges. 4. Summary The electronic structure andmagnetic ordering in La1−xPrxCo2P2 (x = 0,0.25, and 1) phosphides have been studied theoretically using the fully relativistic spin-polarized Dirac LMTO band-structure method. The self-consistent calculations reveal a ferromagnetic arrangement of magnetic moments in PrCo2P2. The spin magnetic moments at the Pr and Co sites are aligned along the c axis with the antiparallel magnetic coupling between the neighboring planes resulting in antiferromagnetism. LaCo2P2 possesses a ferromagnetic arrangement of magnetic moments where the Co moments are aligned in-plane and parallel to the moments in the other layers. The theory gives quite a small value of MAE in LaCo2P2 (around 0.28 meV per formula unit). We have studied the X-ray magnetic circular dichroism at the Co L2,3 and Pr M4,5 edges in La0.75Pr0.25Co2P2. The calculations show good agreement with the experimental measurements. The core-hole effect was found to be very small on the shape of the XAS and XMCD spectra at the Pr M4,5 edges. We found that the magnetic dipole M1 transitions are extremely small in comparison with the electric quadrupole E2 transitions and can be neglected. The E2 transitions were found to be weaker than the electric dipole transitions E1. 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Solovyev I.V., Dederichs P.H., Anisimov V.I., Phys. Rev. B, 1994, 50, 16861; doi:10.1103/PhysRevB.50.16861. 56. Dederichs P.H., Blügel S., Zeller R., Akai H., Phys. Rev. Lett., 1984, 53, 2512; doi:10.1103/PhysRevLett.53.2512. 57. Pickett W.E., Erwin S.C., Ethridge E.C., Phys. Rev. B, 1998, 58, 1201; doi:. 58. Cococcioni M., de Gironcoli S., Phys. Rev. B, 2005, 71, 035105; doi:10.1103/PhysRevB.71.035105. Електронна структура, магнiтне впорядкування та рентгенiвський магнiтний циркулярний дихроїзм у фосфiдах La1−xPrxCo2P2 Л.В. Бекеньов, С.В. Мокляк, В.М. Антонов Iнститут металофiзики iм. Г.В.Курдюмова НАН України, бульв. Вернадського 36, 03142, Київ На основi зонних розрахункiв повнiстю релятивiстським спiн-поляризованим лiнiйним методом МТ- орбiталей (ЛМТО) теоретично вивченi електронна структура i магнiтне впорядкування у фосфiдах La1−xPrx Co2P2 (x = 0,0.25, та 1). В рамках методу LSDA+U теоретично дослiдженi рентгенiвськi спектри поглинання та спектри рентгенiвського циркулярного дихроїзму на краях поглинання CoL2,3 i PrM4,5 . Вивчено вплив остовної дiрки в кiнцевому станi, а також електричних квадрупольних E2 i магнiтних ди- польних M1 переходiв. Отримано добре узгодження з експериментальними результатами. Ключовi слова: сильно скорельованi системи, зонна структура, магнiтнi моменти, рентгенiвський магнiтний циркулярний дихроїзм 33701-11 http://dx.doi.org/10.1103/PhysRevB.50.16861 http://dx.doi.org/10.1103/PhysRevLett.53.2512 http://dx.doi.org/10.1103/PhysRevB.71.035105 Introduction Computational details Results Electronic structures of LaCo2P2 and PrCo2P2 Electronic structure, X-ray absorption and XMCD spectra in La1-xPrxCo2P2 compounds Summary

Electronic structure, magnetic ordering and X-ray magnetic circular dichroism in La₁₋xPrxCo₂P₂ phosphides

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