Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite

The electronic and magnetic structures of Mn₃CuN are investigated theoretically from first principles using the fully relativistic Dirac LMTO band structure method. Mn₃CuN possesses a magnetic phase transition at TC = 143 K from a high temperature paramagnetic phase to a low temperature ferromagneti...

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Datum:	2014
Hauptverfasser:	Antonov, V.N., Bekenov, L.V.
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Veröffentlicht:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2014
Schriftenreihe:	Физика низких температур
Schlagworte:	Низкотемпеpатуpный магнетизм
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spelling	irk-123456789-1195392017-06-08T03:07:22Z Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite Antonov, V.N. Bekenov, L.V. Низкотемпеpатуpный магнетизм The electronic and magnetic structures of Mn₃CuN are investigated theoretically from first principles using the fully relativistic Dirac LMTO band structure method. Mn₃CuN possesses a magnetic phase transition at TC = 143 K from a high temperature paramagnetic phase to a low temperature ferromagnetic one with a noncollinear magnetic structure. The transition is accompanied by a structural change from the cubic to the tetragonal lattice. In low temperature phase two Cu moments and two Mn moments (Mn₂ and Mn₃) ferromagnetically align along the c axis while other four Mn1 magnetic moments are canted from the c axis to [111] direction by angle Q= ±76.2. The x-ray absorption spectra and x-ray magnetic circular dichroism (XMCD) spectra of Mn₃CuN are investigated theoretically from first principles. The origin of the XMCD spectra in the Mn₃CuN compound is examined. The calculated results are compared with the experimental data. 2014 Article Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite / V.N. Antonov, L.V. Bekenov // Физика низких температур. — 2014. — Т. 40, № 7. — С. 825-834. — Бібліогр.: 66 назв. — англ. 0132-6414 PACS 75.50.Cc, 71.20.Lp, 71.15.Rf http://dspace.nbuv.gov.ua/handle/123456789/119539 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Низкотемпеpатуpный магнетизм Низкотемпеpатуpный магнетизм
spellingShingle	Низкотемпеpатуpный магнетизм Низкотемпеpатуpный магнетизм Antonov, V.N. Bekenov, L.V. Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite Физика низких температур
description	The electronic and magnetic structures of Mn₃CuN are investigated theoretically from first principles using the fully relativistic Dirac LMTO band structure method. Mn₃CuN possesses a magnetic phase transition at TC = 143 K from a high temperature paramagnetic phase to a low temperature ferromagnetic one with a noncollinear magnetic structure. The transition is accompanied by a structural change from the cubic to the tetragonal lattice. In low temperature phase two Cu moments and two Mn moments (Mn₂ and Mn₃) ferromagnetically align along the c axis while other four Mn1 magnetic moments are canted from the c axis to [111] direction by angle Q= ±76.2. The x-ray absorption spectra and x-ray magnetic circular dichroism (XMCD) spectra of Mn₃CuN are investigated theoretically from first principles. The origin of the XMCD spectra in the Mn₃CuN compound is examined. The calculated results are compared with the experimental data.
format	Article
author	Antonov, V.N. Bekenov, L.V.
author_facet	Antonov, V.N. Bekenov, L.V.
author_sort	Antonov, V.N.
title	Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite
title_short	Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite
title_full	Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite
title_fullStr	Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite
title_full_unstemmed	Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite
title_sort	electronic structure and x-ray magnetic circular dichroism in the mn₃cun perovskite
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2014
topic_facet	Низкотемпеpатуpный магнетизм
url	http://dspace.nbuv.gov.ua/handle/123456789/119539
citation_txt	Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite / V.N. Antonov, L.V. Bekenov // Физика низких температур. — 2014. — Т. 40, № 7. — С. 825-834. — Бібліогр.: 66 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT antonovvn electronicstructureandxraymagneticcirculardichroisminthemn3cunperovskite AT bekenovlv electronicstructureandxraymagneticcirculardichroisminthemn3cunperovskite
first_indexed	2025-07-08T16:08:06Z
last_indexed	2025-07-08T16:08:06Z
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fulltext	© V.N. Antonov and L.V. Bekenov 2014 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7, pp. 825–834 Electronic structure and x-ray magnetic circular dichroism in the Mn3CuN perovskite V.N. Antonov and L.V. Bekenov Institute for Metal Physics, 36 Vernadsky Str., Kiev 03142, Ukraine E-mail: antonov@imp.kiev.ua Received February 20, 2014, published online May 21, 2014 The electronic and magnetic structures of Mn3CuN are investigated theoretically from first principles using the fully relativistic Dirac LMTO band structure method. Mn3CuN possesses a magnetic phase transition at TC = 143 K from a high temperature paramagnetic phase to a low temperature ferromagnetic one with a noncollinear magnetic structure. The transition is accompanied by a structural change from the cubic to the tetragonal lattice. In low tem- perature phase two Cu moments and two Mn moments (Mn2 and Mn3) ferromagnetically align along the c axis while other four Mn1 magnetic moments are canted from the c axis to [111] direction by angle = 76.2. The x-ray absorption spectra and x-ray magnetic circular dichroism (XMCD) spectra of Mn3CuN are investigated theoretical- ly from first principles. The origin of the XMCD spectra in the Mn3CuN compound is examined. The calculated re- sults are compared with the experimental data. PACS: 75.50.Cc Other ferromagnetic metals and alloys; 71.20.Lp Intermetallic compounds; 71.15.Rf Relativistic effects. Keywords: electronic structure, ternary manganese compounds. 1. Introduction Ternary manganese compounds with a formula Mn3MX (M = Ga, Sn, Zn, Cu and X = C and N) and the cubic crystal structure of a perovskite type have attracted much interest due to the peculiar relationship between lattice and mag- netism which leads to a large variety of magnetic orderings and structural transformations [1–9]. The control of mag- netostructural correlations in a magnetic metal is extremely important in various advanced industrial applications. By tuning the magnetostructural correlations, various useful functions, such as ferromagnetic shape memory effect [10,11], negative thermal expansion [12], and magneto- caloric effects [13,14], have been developed. In particular, magnetostruction [15], one of the most important properties of a magnetic metal, has a high potential for practical appli- cations, such as in actuators and magnetic switching devices. One of the most attractive materials exhibiting magnetostructural correlations are antiperovskite manga- nese nitrides Mn3MN (M: transitional metal or semicon- ducting element) [8]. The antiperovskites possess so called magnetovolume effect (MVE), such as negative thermal expansion (NTE) [16–20]. A large volume expansion in antiperovskite manganese nitrides is triggered by magnetic transition from high-temperature (high-T) paramagnetic (PM) phase to low-temperature (low-T) antiferromagnetic (AF) or ferromagnetic (FM) ordered phases. Another type of the peculiar relationship between the lattice and mag- netism is the shape deformation by external magnetic field or magnetostriction. Magnetostriction often occurs without the volume change and it provides information comple- mentary to that obtained from the volume effect. From a technological viewpoint, shape control by external field is one of the most important functions of metallic ferro- magnets and has high potential in the design of actuating devices and sensors [15]. Shibayama and Takenaka [21] explored the magnetostriction in Mn3CuN. It is exception- ally ferromagnetic among antiperovskite manganese ni- trides Mn3MN (M: Zn, Ga, Ag, etc.) most of which are antiferromagnetic. They found that Mn3CuN exhibits large magnetostriction up to 0.2% even in a polycrystalline. This magnetostriction can be reasonably explained in terms of the rearrangement of thermoelastic martensite variants by the magnetic field; that is, Mn3CuN can be classified as a FM shape memory alloy. Generally, magnetostriction orig- inates from anisotropy in the wave function of the elec- trons that induce a magnetic moment. The anisotropy of the electron cloud produces magnetocrystalline anisotropy, V.N. Antonov and L.V. Bekenov 826 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 that is, a tendency for a magnetic moment to align along a certain crystallographic direction, which is a dominant factor for magnetostriction in an FM shape memory alloy. In the case of Mn3CuN, however, large magnetocrystalline anisotropy is not expected because the 3d orbitals of Mn are almost half-filled, resulting in an almost isotropic elec- tron cloud, and because the crystallographic anisotropy of Mn3CuN is much smaller than that of typical FM shape memory alloys. Mn3CuN undergoes the first-order transition from a high-T PM to a low-T FM phase at the Curie temperature TC = 143 K [22]. At TC, the structural deformation simul- taneously occurs from a high-T cubic unit cell (Pm3m) to a low-T tetragonal one with shorter c axis, 1 ( / <1, 4/ ),T c a P mmm but the volume is conservative. The lattice parameters a and c are 3.9075 Å and 3.8502 Å at 100 K, respectively, and the tetragonality c/a is estimated to be 0.9853 [23]. In Mn3CuN the results of neutron diffraction show that the magnetic moments of Mn atoms are much smaller than the 4–5 B observed in other ordered manganese alloys [8]. This result indicates a strong itinerant character of 3d electrons of Mn atoms in Mn3CuN. The energy band structure of the Mn3MX (M=Ga, Sn, Zn, Cu and X=C and N) systems has been calculated by various methods [24–28]. In the present study, we focus our attention on the theoretical investigation of the x-ray magnetic circular dichroism (XMCD) in the low tempera- ture non-collinear phase of Mn3CuN. Takenaka et al. [29] explored the magnetic states of Mn and Cu in Mn3CuN using the x-ray magnetic circular dichroism. They evaluat- ed the spin and orbital magnetic moments, sm and ,lm respectively, not only for Mn but also for Cu. The theoreti- cal investigations of the origin of the XMCD spectra at the K edges of Mn in the ferromagnetic cubic phases of Mn3GaC and Mn3ZnC were carried out in Ref. 27 using the LSDA approximation. The electronic and magnetic structure as well as the XMCD spectra in the low tempera- ture noncollinear Mn3ZnC perovskite were studied in Ref 30. This paper is organized as follows. Section 2 presents a description of the perovskite Mn3CuN crystal and magnet- ic structures as well as the computational details. Section 3 is devoted to the electronic structure and XMCD spectra of the Mn3CuN compound calculated in the fully relativistic Dirac LMTO band structure method. The calculated results are compared with the available experimental data. Finally, the results are summarized in Sec. 4. 2. Crystal structure and computational details General properties of spin density waves. The magnetic configuration of an incommensurate spin spiral shows the magnetic moments of certain atomic planes varying in di- rection. The variation has a well-defined period determined by a wave vector q. When the magnetic moment is con- fined to the lattice sites the magnetization M varies as [31] cos ( )sin ( ) ( ) = sin ( )sin ( ) , cos ( ) n n n n n n n n n m qr M r qr (1) where the polar coordinates are used and nm is the mag- netic moment of atom n with a phase n at the position rn. Here we consider only planar spirals, that is, = /2n which also give the minimum of the total energy. The magnetization of Eq. (1) is not translationally invariant but transforms as ( )= ( ) ( ),DM r R qr M r (2) where R is a lattice translation and D is a rotation around the z axis. A spin spiral with a magnetization in a general point r in space can be defined as a magnetic configuration which transforms according to Eq. (2). Since the spin spiral describes a spatially rotating magnetization, it can be cor- related with a frozen magnon. Because the spin spiral breaks translational symmetry, the Bloch theorem is no longer valid. Computationally, one should use large super-cells to obtain total-energy of the spin spirals. However, when the spin-orbit interaction is neglected spins are decoupled from the lattice and only the relative orientation of the magnetic moments is important. Then, one can define generalized translations which con- tain translations in the real space and rotations in the spin space [32]. These generalized translations leave the mag- netic structure invariant and lead to a generalized Bloch theorem. Therefore the Bloch spinors can still be character- ized by a k vector in the Brillouin zone, and can be written as /2 /2 e ( ) ( ) = e . e ( ) i ki k i k u d qr kr qr r r r (3) The functions ( )ku r and ( )kd r are invariant with re- spect to lattice translations having the same role as for normal Bloch functions. Due to this generalized Bloch theorem the spin spirals can be studied within the chemical unit cell and no large super-cells are needed. Although the chemical unit cell can be used, the presence of the spin spiral lowers the symmetry of the system. Only the space- group operations that leave invariant the wave vector of the spiral remain. When considering the general spin space groups, i.e., taking the spin rotations into account, the space-group operations which reverse the spiral vector together with a spin rotation of around the x axis are symmetry operations [32]. Although the original formulation of the local-spin- density approximation of the density-functional theory allowed noncollinear magnetic order, first-principles cal- culations for this aspect have begun only recently (for a review, see Ref. 33). One application has been the study of noncollinear ground states, for example, in -Fe (Refs. 34–36) or in frustrated antiferromagnets [37,38]. In Electronic structure and x-ray magnetic circular dichroism in the Mn3CuN perovskite Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 827 addition, the noncollinear formulation enables studies of finite-temperature properties of magnetic materials. Since the dominant magnetic excitations at low temperatures are spin waves which are noncollinear by nature, it is possible to determine the magnon spectra and ultimately the Curie temperature from first principles [39–43]. Re- cently, the noncollinear magnetic configurations were investigated in the Heusler alloys Ni2MnGa, Ni2MnAl [31] and IrMnAl [44]. The total energies for different spin spirals were calculated and the ground-state magnet- ic structures were identified. Magnetocrystalline anisotropy. Magnetic anisotropy is an important parameter, since in many instances their use- fulness is determined by the magnetic anisotropy, i.e., by the extent to which the magnetization retains its orientation in response to magnetic field. As the most important mag- netic anisotropy, the magnetocrystalline anisotropy is re- lated to the crystal symmetry of a material. The mag- netocrystalline anisotropy energy (MAE) describes the tendency of the magnetization to align along specific spa- tial directions rather than to randomly fluctuate over time. The MAE determines the stability of the magnetization in bulk as well as nanoparticle systems. Extensive studies of ferromagnetic bulk materials and thin films have highlight- ed the MAE dependence on crystal symmetry and atomic composition. Whereas the exchange interaction among electron spins is purely isotropic, the orbital magnetization, via the spin-orbit interaction, connects the spin magnetiza- tion to the atomic structure of a magnetic material, hence giving rise to magnetic anisotropy [45]. The calculation of the magnetocrystalline anisotropy en- ergy has been a long-standing problem. A first theory of the MAE in Fe and Ni was formulated by Brooks [46] and Fletcher [47], who emphasized that an 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 pioneer- ing work the band structure was oversimplified to three em- pirical bands [46,47]. Recent investigations [48–52] elabo- rated 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 calculating the MAE from first principles poses a great computational challenge. The prime obstacle is the smallness of the MAE of only a few meV/atom, a value which ought to result as the difference of two total energies for different magnetization directions, which are both of the order of 4 10 4 eV/atom. Owing 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 [48]. Recent contributions aimed con- sequently at improving the numerical techniques [50,53], and the correct easy axis was obtained for hcp Co, but not for fcc Ni [50]. Halilov et al. [51] reported an ab initio in- vestigation of the magnetocrystalline anisotropy energy in bcc Fe and fcc Co and Ni. They introduce the spin-orbit scaling technique, which yields the correct easy axis for Fe and Co, but a vanishing MAE for Ni. The internal energy of ferromagnetic materials depends on the direction of spontaneous magnetization. We consid- er here one part of this energy, the MAE, which possesses the crystal symmetry of the material. For the material ex- hibiting uniaxial anisotropy, such as a hexagonal or tetrag- onal crystals, the MAE can be expressed as [48] 2 4 6 1 2 3( ) = sin sin sinE K K K 2 3sin cos[6( )] ...K (4) where iK is the anisotropy constant of the ith order, and are the polar angles of the Cartesian coordinate system where the c axis coincides with the z axis (the Cartesian coordinate system was chosen such that the x axis is rotated through 90 from the hexagonal axis) and is a phase angle. Both the dipolar interaction and the spin-orbit coupling give rise to the MAE, the former contributing only to the first-order constant K1. Hear, we deal with the MAE caused only by the spin-orbit interaction. Both magneto- optical effects and MAE have a common origin in the spin- orbit coupling and exchange splitting. Thus, a close con- nection between the two phenomena seems plausible. The MAE is, in this paper, defined as the difference be- tween two self-consistently calculated fully relativistic total energies for two different crystallographic directions, <001>( )E E . To attain good convergence in the total energy a large number of k points has to be used in the calculations. In the present work the total energy has been calculated with an accuracy high enough to be able to re- solve the difference in total energies for different spin di- rections. X-ray magnetic circular dichroism. Using straightfor- ward symmetry considerations it can be shown that all magneto-optical phenomena (XMCD, MO Kerr and Fara- day effects) are caused by the symmetry reduction, in comparison to the paramagnetic state, caused by magnetic ordering [54]. This symmetry lowering has consequences only when spin-orbit coupling is considered in addition. Therefore, in order to calculate the XMCD properties one has to account for both magnetism and SO coupling at the same time when dealing with the electronic structure of the material considered. Within the one-particle approximation, the absorption coefficient for incident x rays is determined by the probability of electron transitions from an initial core state (with wave function j and energy )jE to a final unoc- cupied states (with wave functions nk and energies )nE k as V.N. Antonov and L.V. Bekenov 828 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 2( ) = \| \| \| \| ( ) ( ),j n j n j n F n E E E Ek k k k (5) where is the photon energy, its polarization and = eαa being the dipole electron–photon interaction operator, where α are Dirac matrices, a is the polari- zation unit vector of the photon vector potential [ =1/ 2(1, ,0), = (0,0,1)].za i a (Here / denotes, respectively, left and right circular photon polarizations with respect to the magnetization direction in the solid). Concurrent with the x-ray magnetic circular dichroism experimental developments, some important magneto- optical sum rules have been derived in recent years [55–58]. For the 2,3L edges the zl sum rule can be written as [59] 3 2 3 2 4 ( ) = 3 ( ) L L z h L L d l n d (6) where hn is the number of holes in the d band =10h dn n , zl is the average of the magnetic quantum number of the orbital angular momentum. The integration is taken over the whole 2p absorption region. The zs sum rule is written as 3 3 3 2 ( ) 2 ( ) 7 2 ( ) L L z z h L L d d s t n d (7) where zt is the z component of the magnetic dipole oper- ator 2= 3 ( )/ \| \|t s r r s r which accounts for the asphe- ricity of the spin moment. The integration 23 ( ) L L is tak- en only over the 3/2 1/22 (2 )p p absorption region. Crystal structure. Mn3CuN at room temperature crys- tallizes in the cubic perovskite-type structure with 3Pm m space group (No. 221). Mn atoms being at the face centers, Cu atoms at the corners, and N atoms at the body center (see Fig. 1). The Mn atoms have two N nearest neighbors at the 1.948 Å distance. The second coordination consists of 8 Mn atoms and 4 Cu atoms at the 2.755 Å. The paramagnetic to ferromagnetic phase transition in Mn3CuN at TC= 143 K is accompanied by a structural change from the cubic to the tetragonal lattice. The Mn moments in the low temperature ferromagnetic phase 4/P mmm space group, No. 123) constitute a noncollinear magnetic structure: Mn1 canting from the c axis to [111] direction, the Mn2 and Mn3 ferromagnetically align to the c axis (Fig. 2). In the low temperature tetragonal structure Mn–N interatomic distances are slightly increased in com- parison with the high temperature cubic phase up to the 1.954 Å. Mn1 atoms are surrounded by two Mn2 and two Mn3 atoms at the 2.743 Å distance and four Mn1 atoms at the 2.763 Å distance. The details of the computational method are described in Refs. 59,60, and here we only mention several aspects. The calculations were performed for the experimentally observed lattice constants (a = 3.896 Å for the cubic perovskite-type structure and a =3.9075 Å c/a =0.9853 for the low temperature tetragonal phase) using the spin- polarized linear-muffin-tin-orbital (LMTO) method [60,61] with the combined correction term taken into account. We used the von Barth–Hedin parametrization [62] for the exchange-correlation potential. Brillouin zone (BZ) inte- grations were performed using the improved tetrahedron method [63] and the charge self-consistency was obtained with 405 irreducible k-points. To improve the potential we include additional empty spheres both in the cubic Fig. 1. (Color online) Cubic perovskite-type crystal structure of Mn3CuN at room temperature. Fig. 2. (Color online) Low temperature magnetic structure of Mn3CuN. Electronic structure and x-ray magnetic circular dichroism in the Mn3CuN perovskite Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 829 perovskite-type structure and the low temperature tetrago- nal phase. The basis consisted of Mn and Cu s, p, d and f; N s, p, d and empty spheres s, and p LMTO's. The intrinsic broadening mechanisms have been ac- counted for by folding the XMCD spectra with a Lorentzian. For the finite lifetime of the core hole a con- stant width ,c in general from Ref. 64, has been used. The finite apparative resolution of the spectrometer has been accounted for by a Gaussian of 0.6 eV. 3. Results and discussion 3.1. Energy band structure The total and partial density of states (DOS) of cubic hy- pothetical ferromagnetic Mn3CuN are presented in Fig. 3. The occupied part of the valence band can be subdivided into several regions. N 2s states appear between –17.6 and –15.9 eV. Cu 3d states are fully occupied and cross the N 2p bands in a very narrow energy interval from –4.6 to –1.5 eV. N 2p states extend from –8.6 eV up to 9 eV. The states in the energy range –4.5 to 5.5 eV are formed by Mn d states. The crystal field at the Mn site 4( hD point sym- metry) causes the splitting of d orbitals into three singlets 1ga and 1gb 2(3 1z and 2 2),x y 2 ( )gb xz and a dou- blet ( , ).ge xy yz The 1 1g ga b and 2g gb e splittings are negligible in comparison with its width in LSDA calcula- tions. One should mention that there is quite a small N 2p – Mn d hybridization in the valence bands below the Fermi level. Mn3CuN in the cubic perovskite type crystal structure has a local magnetic moments of 2.283 B on Mn, 0.230 B on Cu and –0.115 B on N. The orbital moments are equal to 0.013 B, 0.003 B and 0.0002 B on the Mn, Cu and N sites, respectively. The interaction between the tran- sition metals is ferromagnetic, leading to a total calculated moment of 6.963 B. Mn3CuN partial DOS's for the low temperature tetrag- onal structure are presented in Fig. 4. For this crystal structure the spin magnetic moments are of 2.625 B on the noncollinear Mn1 atom sites, 2.390 B on the colline- ar Mn2,3 ones, 0.144 B on Cu and –0.068 B on N sites. The orbital moments are equal to –0.037 B, –0.003 B, –0.019 B and 0.002 B on the Mn1, Mn2,3, Cu and N sites, respectively. Figure 5 presents the variation of Mn 3d spin (upper panel) and orbital (middle panel) magnetic moments at the Mn1 and Mn2,3 sites with the canting Mn1 angle. The Mn1 3d orbital moments are negative for all the angle interval and reach its maximum absolute value at around 40 . The Mn2,3 3d orbital moments increase when the Mn1 canting angle changes from 0 to 35 , and then decrease with fur- ther increasing of the canting angle, cross the zero at 60 and oscillate around zero up to 90 . The 3d spin moments are also show different angle behavior for the Mn1 and Mn2,3 sites (Fig. 5(a)). The Mn1 3d spin magnetic mo- ments are larger for all the angle interval with the largest difference between the Mn1 and Mn2,3 spin moments when both the moments align along the c axis. The lower panel (c) shows the magnetocrystalline ani- sotropy energy with the canting Mn1 angle. We found that the ground state for the low-T phase of Mn3CuN is two Cu moments and two Mn (Mn2 and Mn3) moments ferromagnetically aligned to the c axis while four Mn1 magnetic moments are canted by 76.2 from the c axis to [111] direction (Fig. 2). It is important to note that this ground state with the canted Mn1 magnetic moments is very stable. Quite a large energy of 5.5 meV/unit cell is needed to transit from the ground state with the canted Mn1 magnetic moments to the state with all the magnetic Fig. 3. (Color online)The total (in states/(cell eV)) and partial (in states/(atom eV)) ferromagnetic density of states of Mn3CuN in the cubic perovskite-type structure. The Fermi energy is at zero. V.N. Antonov and L.V. Bekenov 830 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 moments oriented along the c axes. This fact helps to ex- plain the magnetization experiments carried out by Takenaka et al. Ref. 29. They investigated the element- selective magnetization defined as peak-height difference between the positive 2L peak and the negative 3L peak. They found that the magnetic-field dependence for Cu is different from that for Mn. The H dependence of the peak-height difference is characterized by a sharp increase at the low-field region for both Mn and Cu. However, the peak-height difference for Cu saturates at 2 kOe, whereas that for Mn shows only a kink at 2 kOe and continues to increase without saturation up to 19 kOe. Authors conclude that the two Cu and two ferromagnetically aligned Mn2,3 moments are considered to saturate at a magnetic field of 2 kOe. However, the four counting Mn1 magnetic mo- ments Mn1 considered to induce relatively weak magneti- zation under a magnetic field, resulting in the absence of saturation in the bulk magnetization up to 19 kOe. To reach the magnetic saturation, in other words to align all the magnetic moments along the c direction, one needs the energy much larger than provided by the magnetic field of 19 kOe. On the other hand, the magnetocrystalline anisotropy energy which has been estimated by the difference of total energies between the states with spin orientation along and perpendicular to the c axes was found to be rather small in Mn3CuN reaching 0.5 meV/unit cell in agreement with the suggestion of Takenaka et al. Ref. 29. 3.2. XMCD spectra At the core level edge XMCD is not only element- specific but also orbital specific. For 3d transition metals, the electronic states can be probed by the K, 2,3L and M2,3 Fig. 4. (Color online) Partial density of states (in states/(atom eV)) of Mn3CuN in the low temperature non-collinear tetragonal structure. The Fermi energy is at zero. Fig. 5. (Color online) Variation of Mn 3d spin (a) and orbital (b) magnetic moments at the Mn1 and Mn2,3 sites with the canting Mn1 angle. The lower panel shows the magnetocrystalline anisot- ropy energy with the canting Mn1 angle. Electronic structure and x-ray magnetic circular dichroism in the Mn3CuN perovskite Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 831 x-ray absorption and emission spectra. According to the dipole selection rules only the transitions with = 1, = 0, 1l j are allowed [59]. Therefore only elec- tronic states with an appropriate symmetry contribute to the absorption and emission spectra under consideration. Figure 6 shows the theoretically calculated Mn L2,3 x-ray absorption spectra (XAS) as well as XMCD spectra in Mn3CuN in comparison with the corresponding experi- mental data obtained by Takenaka et al. [29]. In order to compare the relative amplitudes of the L2,3 XMCD spectra we first normalize the theoretically calculated x-ray absorp- tion spectra to the experimental ones taking into account the background scattering intensity [65]. The LSDA describes reasonably well the shapes of the XAS spectra at the Mn L2,3 edge (Fig. 6(a)). Because of the electric dipole selection rules the major contribution to the absorption at the 3L edge stems from the transitions 3/2 5/22 5 ,p d with a weaker contribution from 3/2 3/22 5p d transitions. For the latter case the corresponding 3/2 3/22 5p d radial matrix ele- ments are only slightly smaller than for the 3/2 5/22 5p d transitions. The angular matrix elements, however, strongly suppress the 3/2 3/22 5p d contribution. Therefore the contribution to the XMCD spectrum at the 3L edge from the transitions with = 0j is one order of magnitude smaller than the transitions with = 1j [59]. The experi- mental x-ray absorption L3 spectrum have three peaks around 640.5, 642 and 645 eV, which are well repro- duced by the theoretical calculations. The intensity of the second fine structure at 642 eV is slightly underestimates by the theoretical calculations. Figure 6 (b) shows the experimental XMCD spectrum [29] measured at 20 K and the theoretically calculated one using the LSDA approximation for the low-T tetragonal phase. The theory is in good agreement with the experi- mental measurements, although the calculated magnetic dichroism is somewhat too small at 645 eV in comparison with the experimental measurements. The XMCD spectra at the L2,3-edges are mostly determined by the strength of the SO coupling of the initial 2p-core states and spin- polarization of the final empty 3/2,5/23d states while the exchange splitting of the 2p-core states as well as the SO coupling of the 3d-valence states are of minor importance for the XMCD at the L2,3 edge of 3d transition metals [59]. Although the number of Mn1 atoms which are canted 72.2 from the c axis to [111] direction is two times larg- er than the number of ferromagnetically aligned Mn2 and Mn3 atoms (Fig. 2) the main contribution to the L2,3 XMCD spectra comes from the Mn2,3 atoms (Fig. 6(b)). Takenaka et al. [29] apply sum rules [Eqs. (6),(7)] to es- timate the spin and orbital moments at the Mn and Cu sites. They found extremely small spin magnetic moment at the Mn site Mn 0.27s Bm which is almost one order of mag- nitude smaller than obtained in our band structure calcula- tions. The Mn 3L and the 2L spectra in Mn3CuN are strongly overlapped therefore the decomposition of a corre- sponding experimental 2,3L spectrum into its 3L and 2L parts is quite difficult and can lead to a significant error in the estimation of the magnetic moments using the sum rules. Besides, the experimentally measured Mn 2,3L x-ray ab- sorption spectra have background scattering intensity and the integration of the corresponding XASs may lead to an additional error in the estimation of the magnetic moments using the sum rules. Besides, XMCD sum rules are derived within an ionic model using a number of approximations [59,66]. It is interesting to compare the spin moments ob- tained from the theoretically calculated XAS and XMCD spectra through sum rule [Eq. (7)] with directly calculated LSDA values in order to avoid additional experimental problems. We obtain Mn1 sm = 1.84 B, Mn2,3 sm = 1.17 B from sum rules. These values are significantly smaller than the corresponding magnetic moments derived from the band structure calculations (2.63 B and 2.39 B for Mn1 and Mn2,3, respectively). However, they are still much larger than the experimental value Mn sm = 0.27 B [29]. One of the possible reasons of such small experimental magnetic moment might be a disorder effect. This question still needs an additional experimental investigation. Fig. 6. (Color online) The theoretically calculated isotropic ab- sorption spectra of Mn3CuN at the Mn L2,3 edges for the low temperature tetragonal structure (full blue line) in comparison with the experimental spectrum [29] (circles) measured at 20 K in the external magnetic field H = 19 kOe. The dotted line shows the theoretically calculated background spectrum (a); the experi- mental XMCD spectrum [29] measured at 20 K in the external magnetic field H = 19 kOe (circles) and theoretically calculated XMCD spectra for the low temperature tetragonal structure (b). V.N. Antonov and L.V. Bekenov 832 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 Figure 7 shows the theoretically calculated Cu L2,3 edge x-ray absorption spectra as well as XMCD spectra in Mn3CuN in comparison with the corresponding experi- mental data [29]. The experimentally measured Cu L2,3 XAS spectra possess rather large background intensity (Fig. 7(a)). Both the 3L and 2L XAS spectra contain in- tensive narrow low energy peaks and wide high energy shoulders which reflect the energy distribution of Cu 3d empty states (see Fig. 4). Figure 7(b) shows the theoretical- ly calculated XMCD spectra at the Cu 2,3L edges in com- parison with the experimentally measured ones [29]. The theory shows a very good agreement with the experiment for the x-ray absorption as well as for the XMCD. 4. Summary In Mn3CuN a magnetic phase transition occurs at TC =143 K, which has been classified as a first-order tran- sition from a paramagnetic phase to a ferromagnetic one with a noncollinear magnetic structure. The transition is accompanied by a structural change from the cubic to the tetragonal lattice. We have studied the electronic structure in the high-T ferromagnetic cubic phase and low temperature non- collinear phase of Mn3CuN perovskite compound in the LSDA approximation by means of an ab initio fully- relativistic spin-polarized Dirac linear muffin-tin orbital method. The magnetic unit cell of low-T ferromagnetic Mn3CuN contains two magnetic moments due to Cu and six magnetic moments due to Mn; two Cu moments and two Mn moments (Mn2 and Mn3) are ferromagnetically aligned along the c axis while other four Mn1 magnetic moments are canted from the c axis to [111] direction. We found that the ground state corresponds to the canting an- gle = 76.2 . We investigated the influence of the Mn1 canting angle on the total energy and 3d spin and orbital magnetic moments at Mn sites. We found that the Mn1 3d orbital moments are negative for all the angle interval and reach its maximum absolute value at around 40 . The Mn2,3 3d orbital moments increase when the Mn1 canting angle changes from 0 to 35 , and then decrease with fur- ther increasing of the canting angle, cross the zero value at 60 and oscillate around zero up to 90 . The 3d spin mo- ments also show different angle behavior for the Mn1 and Mn2,3 sites. The Mn1 3d spin magnetic moments are larger for all the angle interval with the largest difference be- tween the Mn1 and Mn2,3 spin moments when both the moments align along the c axis. We have studied theoretically the x-ray absorption and x-ray magnetic circular dichroism spectra at the Mn and Cu 2,3L edges in the low temperature noncollinear phase of Mn3CuN. 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Electronic structure and x-ray magnetic circular dichroism in the Mn₃CuN perovskite

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