We present the ab initio investigations of the electronic and magnetic properties of magnetocaloric
Gd(Ni1xFex)3 alloys. To simulate fractional concentrations the supercell approach was implemented and di erent con gurations of iron atoms were considered. Energetical analysis of site preference and magnetic order was performed. The concentration dependence of the averaged total and local magnetic moments and of the valence band photoemission spectra are presented and discussed in reference to experimental data

Borgieł, Władysław

Deniszczyk, Józef

Woźniakowski, Andrzej

Acta Physica Polonica A

English

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Ab initio study of electronic structure and magnetic properties of Gd(Ni 1-xFex)3 alloys  Author: Józef Deniszczyk, Andrzej Woźniakowski, Władysław Borgieł  Citation style: Deniszczyk Józef, Woźniakowski Andrzej, Borgieł Władysław. (2012). Ab initio study of electronic structure and magnetic properties of Gd(Ni 1-xFex)3 alloys. "Acta Physica Polonica A" (Vol. 121, nr 5/6 (2012), s. 1156-1158).  Vol. 121 (2012) ACTA PHYSICA POLONICA A No. 56Proceedings of the European Conference Physics of Magnetism 2011 (PM'11), Pozna«, June 27July 1, 2011Ab Initio Study of Electronic Structure and MagneticProperties of Gd(Ni1 xFex)3 AlloysJ. Deniszczyk, A. Wo¹niakowskiInstitute of Materials Science, University of Silesia, Bankowa 12, 40-007 Katowice, Polandand W. BorgieªAugust Cheªkowski Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, PolandWe present the ab initio investigations of the electronic and magnetic properties of magnetocaloricGd(Ni1 xFex)3 alloys. To simulate fractional concentrations the supercell approach was implemented and dierentcongurations of iron atoms were considered. Energetical analysis of site preference and magnetic order wasperformed. The concentration dependence of the averaged total and local magnetic moments and of the valenceband photoemission spectra are presented and discussed in reference to experimental data.PACS: 71.20.Be, 79.60.Bm1. IntroductionMetallic gadolinium serves as a generic material fora magnetocaloric application but due to high costs andhigh chemical reactivity in a pure form cannot be used.A transition-metal (TM) alloys with gadolinium are ex-tensively studied in searching for a new magnetocaloricmaterials. Recently the electronic structure and mag-netic properties of crystalline Gd(Ni1 xFex)3 alloys weremeasured by means of dierent methods [1]. The mea-surements have shown that in the Ni-rich region thealloys display magnetocaloric properties but with rela-tively low Curie temperature. Increasing the Fe contentsyields a linear decrease of the saturation magnetizationwhile the Curie temperature reaches the maximum atx  0:5. The X-ray photoelectron spectroscopy (XPS)valence band measurements reveal the presence of cor-relation between the magnetic properties and electronicstructure near the Fermi level. In addition, the shift ofGd 4f band to lower binding energy (BE) and broad-ening with increasing iron contents was observed. Theaim of presented investigations was to determine the elec-tronic structure, structural and magnetic properties ofGd(Ni1 xFex)3 alloys by the ab initio methods and elu-cidate the microscopic origin of observed properties.2. Computational procedureThe electronic structure calculations were performedusing the WIEN2k code [2] based on the full-potential lin-earized augmented plane wave (FP-LAPW) method [3].The electronic states were partitioned into core states:([Kr]4d10 for Gd and [Ne] for Fe and Ni); local orbitals corresponding author; e-mail: jozef.deniszczyk@us.edu.pl[3] (5s, 5p for Gd and 3s, 3p for Fe and Ni) and va-lence states (4f , 5d, 6s for Gd and 3d, 4s for Ni and Fe).The core states were treated in a fully relativistic man-ner while for the local orbitals and valence states thescalar-relativistic approximation was applied. The GGAexchange-correlation (XC) potential was used in the formgiven in [4]. For the strongly correlated Gd 4f bandstates the XC potential was corrected by the Hubbardcorrelation interaction using the GGA+U method [5].The eective Ue = 0:55 Ry was established by xingthe majority spin Gd 4f band at their BE measuredin GdNi3 and was kept xed for all calculated compo-sitions. Atomic mun-tin spheres radii were taken as2.5 a.u. and 2.3 a.u. for Gd and Fe(Ni), respectively. Thek-mesh was generated such as to provide approximately200 k points in the irreducible wedge of the Brillouinzone. Other parameters inuencing the computationalprecision [2] were xed to assure the total energy pre-cision of 10 1 mRy. The XPS spectra were calculatedby convolution of partial densities of states (DOS) withLorentzians of 0.25 eV width and multiplication by cor-responding cross-sections [6].3. Results and discussionIn the whole concentration range Gd(Ni1 xFex)3 al-loys crystallize in the rhombohedral crystal structure ofPuNi3-type (space group No. 166). The primitive cellconsists of three formula units. Gd atoms occupy single3a (0, 0, 0) and double 6c (0, 0, z1) positions. The TM(Ni, Fe) atoms locate at single-3b (0, 0, 1/2), double-6c(0, 0, z2) and sixfold-18h (x;   x; z3) sites. We haveoptimized the structure of parent GdNi3 compound withrespect to volume and c=a ratio and then internal atomiccoordinates were relaxed. The optimized volume and lat-tice parameters of GdNi3 dier from the experimental(1156)Ab Initio Study of Electronic Structure and Magnetic Properties . . . 1157values by less than 0.5%. Relaxation of atomic positionsfor GdNi3 gave z1 = 0:1393, z2 = 0:3329, z3 = 0:0813 andx = 0:5005. Calculations were performed for the wholeiron concentration range with the step xFe = 19 . Thelattice parameters were taken from the interpolation ofexperimental data [1]. The relaxed internal coordinatesobtained for GdNi3 were applied for all studied composi-tions. In simulations of fractional concentration, for eachconcentration several congurations of iron atoms wouldhave to be considered. Due to symmetry the number ofpossible iron congurations can be reduced signicantly,e.g. for nFe = 1 (xFe = 0:11) only three nonequivalentcongurations exist: Fe in 3b, Fe in 6c and Fe in 18h site.For concentration xFe = 0:11 we have performed detailedenergy analysis of site-preference and magnetic order, as-suming parallel (FM) and antiparallel (AF) alignment ofiron magnetic moments with respect to that of gadolin-ium.The results are collected in Table where the lowest to-tal energy of the AF solution with single iron at 18hwas taken as the reference energy. We have found thepreference of iron atoms to locate at 6c or 18h sites.For all congurations the AF magnetic order is ener-getically preferable, but the energy distance betweenAF and FM solutions for Gd(Ni0:89Fe0:11)3 is of only 20 meV/atom ( 230 K) which compares with kBTCfor this alloy [1]. The dierence between the FM and AFsolution calculated for GdFe3 was found few times larger( 90 meV/atom) and for GdNi3 compound only singleferrimagnetic ground state solution has been found.TABLERelative energies for site preference of iron atomsand magnetic order in Gd(Ni0:89Fe0:11)3. The totalenergy of AF solution for Fe 18h conguration isused as the reference energy.Magnetic order E [meV/atom]Fe3b Fe6c Fe18hFM 46 17 19AF 24 1 0Local atomic and total magnetic moments calculatedfor the AF magnetic order are presented in Fig. 1.For a given concentration the total magnetic momentfor dierent congurations vary only slightly (Fig. 1a).The experimental dependence of the saturation magne-tization on iron concentration in Gd(Ni1 xFex)3 is re-produced perfectly. We have found linear correlationMtot(nFe)   1:9nFe. The averaged atomic momentsvary only minutely with iron concentration (Fig. 1b).The Gd moment increases linearly from Gd = 7:12 Bin GdNi3 to Gd = 7:30 B in GdFe3. Magnetic momentsof TM ions polarize oppositely to Gd. Magnitude of Niincreases from 0.23 B at x = 0:00 to 0.59 B at x = 0:89while that of Fe decreases from 2.52 B at x = 0:11 to2.35 B at x = 1:00. The dependence of the averaged TMatomic moments on concentration xFe can be describedby linear relation: TM   2:1xFe 0:32. The calculatedmagnitudes of TM exceed those estimated on the basisof saturation magnetization measurements [1].Fig. 1. Dependence of the calculated total (a) andaveraged atomic (b) magnetic moments on iron con-centration compared with experimental saturation mo-ment [1]. Open symbols in (a) represent Mtot for dif-ferent congurations of Fe atoms and dashed line showsthe linear t to the concentration dependence of av-erage Mtot. Atomic magnetic moments, shown in (b)were obtained by averaging over congurations and overnonequivalent atomic positions.Fig. 2. Spin resolved total DOS with separated par-tial atomic contributions calculated for GdNi3 (a) andGdFe3 (b) compounds. Simulated XPS spectra forGd(Ni1 xFex)3 alloys  (c) and (d).Figure 2 shows the essential results for electronic struc-ture of Gd(Ni1 xFex)3 alloys. For clarity, we separatedsimulated valence band spectra into two energy windows.The dependence of the BE of Gd 4f states on iron concen-tration reproduces quantitatively experimental data [1].Upon complete replacement of nickel by iron the BE ofGd 4f states decreases by BE  0:51 eV (for compari-son exp :BE = 0:6 eV). Similarly as in experimental spec-1158 J. Deniszczyk, A. Wo¹niakowski, W. Borgieªtra, the calculated 4f line begins to shift to lower BEat xFe = 0:22 and with increasing iron content the shiftgrows monotonically. Detailed analysis of partial densityof states (DOS) has shown that BE of the Gd 4f or-bitals strongly depends on the position occupied by Gd(3a or 6c) and on the chemical composition of the nearestneighbour (NN) sites. Gadolinium atoms at 3a (Gd(3a))and 6c (Gd(6c)) sites dier in their local atomic environ-ment. The Gd(3a) atom neighbors with six TM (Ni, Fe)atoms located at 6c sites (dNN = 2:88 Å). The Gd(6c) hassix TM neighbors at 18h sites (dNN = 2:86 Å) and threeTM atoms at NNN 3b sites (dNNN = 2:96 Å). Calcula-tions have shown that in GdNi3 and GdFe3 compoundsthe Gd(3a)4f and Gd(6c)4f are split by  0:05 eV and 0:43 eV, respectively. For a given concentration of Featoms in Gd(Ni1 xFex)3 alloys the shift of the Gd 4fdepends also on the distribution of Fe atoms among the3a, 6b and 18h sites.For concentrations xFe = 0:11, 0.22 and 0.33 wehave tested dierent congurations of iron atoms. ForxFe = 0:11 the Gd3a and Gd6c the BE of 4f stateschanges only slightly with respect to that in GdNi3. ForxFe = 0:22 the Gd3a4f states either do not move or shiftslightly to higher BE while 4f states of Gd6c with fouriron atoms at NN sites shift to lower BE by  0:11 eV.For xFe = 0:33 the iron atoms at 18h sites do not changethe BE of Gd3a4f states, while when iron atoms oc-cupy completely the 3b and 6c sites they yield the shiftof Gd3a4f states to higher BE by  0:16 eV. For theGd6c atoms we have found that when up to two ironatoms locate at NN sites the BE of 4f states changesonly minutely while the presence of four and six ironatoms at NN sites of Gd6c atom gives the shift of BE by 0:12 eV and  0:53 eV, respectively. It is worth tonote that the Gd 4f states of majority and minority spinshift rigidly, leaving the exchange splitting constant. Forhigher iron concentration the Gd3a4f states graduallyshift to lower BE while the reduction of BE of Gd6c4fstates is more signicant. Because the shift to lower BEof 4f states in Gd3a and Gd6c atoms is dierent, thesplitting of the both group of states grows with increas-ing iron content. This calculated property explains thebroadening of 4f line with increasing iron concentrationobserved on measured XPS spectra [1]. We tried to anal-yse the shift of 4f states in terms of the chemical shiftmodel, relating the changes of BE of outer atomic or-bitals to the changes in the screaning of ionic potentialcaused by electronic transfer between atoms in unit cell.We did not nd correlation between the shift of 4f BEand interatomic electronic transfer. Calculated changesof the charge density inside Gd-nucleus, which might in-dicate intraatomic electronic charge redistribution, alsodo not correlate with shifts of Gd 4f states.In the Gd(Ni1 xFex)3 alloys with AF magnetic order,the minority spin 3d bands of TM atoms do not changequalitatively upon alloying (Fig. 2a, b). They are almostcompletely occupied, and keep below the Fermi level.The majority spin Fe 3d states locate around the Fermilevel, far above the Ni 3d states. With increasing ironcontent the DOS around the Fermi level enhances at theexpense of the DOS at BE > 2 eV. This redistributionof majority spin 3d-states aects the valence band pho-toemission spectra visible in Fig. 2d. In this respect thecalculated XPS agrees qualitatively with the results ofmeasurements [1].4. SummaryThe electronic structure calculations forGd(Ni1 xFex)3 series have shown the energeticalpreference for antiparallel mutual alignment of Gd andTM local magnetic moments. The calculated depen-dences of saturation magnetization and valence bandphotoemission spectra on iron concentration reproducequantitatively the measured ones.AcknowledgmentsThe work by J.D. was supported by the Ministry ofScience and Higher Education in Poland within grant no.N N202 200039.References[1] A. Bajorek, A. Chrobak, G. Cheªkowska,M. Kwiecie«, J. Alloys Comp. 485, 6 (2009).[2] Electronic structure calculations of solids using theWIEN2k package for material science, K. Schwarz,P. Blaha, G.K.H. Madsen, Comp. Phys. Commun.147, 71 (2002).[3] D. Singh, Plane Waves, Pseudopotentials and theLAPW Method, Kluwer Academic, Boston 1994.[4] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett.77, 3865 (1996).[5] V.I. Anisimov, F. Aryasetiawan, A.I. Lichtenstein,J. Phys., Condens. Matter 9, 767 (1997).[6] J.J. Yeh, I. Lindau, At. Data Nucl. Data Tables 32,1 (1985).

Ab initio study of electronic structure and magnetic properties of Gd(Ni 1-xFex)3 alloys

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Ab initio study of electronic structure and magnetic properties of Gd(Ni 1-xFex)3 alloys

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