The Mossbauer effect and ab initio investigations of an electric ¯eld gradient at 57Fe nuclei in Pt3Fe compound
are presented. It is shown that nonzero 57Fe electric ¯eld gradient exists in the cubic Pt3Fe. Ab initio study
of Pt3Fe in antiferromagnetic state con¯rms the presence of electric ¯eld gradient at 57Fe nuclei. Lattice, local
valence electron (3d, 4p) and weakly bound 3p core electron contributions to electric ¯eld gradient are separated
out and discussed in the context of the electronic structure changes upon the antiferromagnetic phase transition

Deniszczyk, Józef

Olszewski, W.

Parzych, G.

Rećko, K.

Satuła, D.

Szymański, K.

Waliszewski, J.

Acta Physica Polonica A

English

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Hyperfine interactions of 57Fe in Pt3Fe in Pt 3Fe - Ab initio and Mossbauer effect studies  Author: Józef Deniszczyk, D. Satuła, J. Waliszewski, K. Rećko, W. Olszewski, G. Parzych, K. Szymański  Citation style: Deniszczyk Józef, Satuła D., Waliszewski J., Rećko K., Olszewski W., Parzych G., Szymański K. (2009). Hyperfine interactions of 57Fe in Pt3Fe in Pt 3Fe - Ab initio and Mossbauer effect studies. "Acta Physica Polonica A" (Vol. 115, nr 1 (2009), s. 197-199).  Vol. 115 (2009) ACTA PHYSICA POLONICA A No. 1Proceedings of the European Conference “Physics of Magnetism” (PM’08), Poznan´ 2008Hyperfine Interactions of 57Fe in Pt3Fe — Ab Initio andMo¨ssbauer Effect StudiesJ. Deniszczyka, D. SatuÃlab, J. Waliszewskib, K. Rec´kob, W. Olszewskib, G. Parzychcand K. Szyman´skibaInstitute of Materials Science, University of SilesiaBankowa 12, 40-007 Katowice, PolandbFaculty of Physics, University of BiaÃlystok15-424 BiaÃlystok, PolandcKs. Anny 7/54, 18-404 ÃLomz˙a, PolandThe Mo¨ssbauer effect and ab initio investigations of an electric field gradient at 57Fe nuclei in Pt3Fe compoundare presented. It is shown that nonzero 57Fe electric field gradient exists in the cubic Pt3Fe. Ab initio studyof Pt3Fe in antiferromagnetic state confirms the presence of electric field gradient at57Fe nuclei. Lattice, localvalence electron (3d, 4p) and weakly bound 3p core electron contributions to electric field gradient are separatedout and discussed in the context of the electronic structure changes upon the antiferromagnetic phase transition.PACS numbers: 71.15.Ap, 71.15.Nc, 71.20.–b, 71.20.Be, 71.20.Lp, 75.50.Bb, 76.80.+y1. IntroductionThe ordered Pt3Fe alloy of cubic Cu3Au (L12) struc-ture shows an antiferromagnetic (AFM) phase transi-tion at TN = 150 K [1] displaying the magnetic orderof(12 ,12 , 0)-type (AFM2) at high and of(12 , 0, 0)-type(AFM1) at lower temperatures [2]. The non-collinearmagnetic structure in Pt3Fe was also reported from low--temperature neutron diffraction data [3]. The com-pound was measured by the Mo¨ssbauer effect method [4]but no information on the electric field gradient (EFG)tensor was reported. The electronic structure of Pt3Fewas calculated by ab initio methods [5] but the hyper-fine interaction parameters were not given. We present acomplete, Mo¨ssbauer effect and ab initio, study of Pt3Fecompound. The aim of band structure calculations wasto elucidate the physical mechanism responsible for theoccurrence of the EFG at the 57Fe nuclei in AFM Pt3Fe.With this aim the ab initio electronic structure calcula-tions for Pt3Fe were carried out for paramagnetic (NM),ferromagnetic (FM) and both AFM ground states. The57Fe hyperfine parameters were determined and com-pared with the experimental data.2. Investigation detailsThe samples were prepared by arc melting from plat-inum, natural iron and 57Fe isotope, with the ratio of57Fe to natural Fe equal to 0.22 for the first sample and0.99 for the second. The first one, after homogeniza-tion of the ingot (56 h at 1150 K), was powdered andthen annealed in the vacuum by heating to 1280 K andcooling gradually from 1180 K at the rate 0.35 K/h for236 h. The absorber of 19 mg/cm2 thick was prepared.The second sample, homogenized during 12 h at 1200 K,was made in the form of foil with average thickness of12.4 mg/cm2. Final annealing of the foil was similar asfor the powders. The Mo¨ssbauer effect measurementswere performed in constant acceleration mode and the57Co isotope in Cr matrix was used as a source of 57Feresonant radiation.The electronic structure calculations were performedwith the use of the WIEN2k code [6] employing the gen-eral potential linear augmented plane wave (FP-LAPW)method within the density functional theory (DFT) for-malism. The gradient corrected local spin density ap-proximation form of the exchange correlation potentialgiven in [7] was used. The core electron states were par-titioned into strongly bound true core states (Fe: 1s–2p,Pt: 1s–4d), which were treated atomic-like in the spher-ical all-electron muffin-tin (MT) potential, and weaklybound semicore states (Fe: 3sp, Pt: 4f and 5sp) consid-ered as local orbitals (LO) [8] and treated as band-likestates in the full potential with no shape approximation.For the true core states, the fully relativistic DFT for-malism was employed, while the other states were solvedwithin the scalar-relativistic approximation neglectingthe spin–orbit interaction. For all studied phases the MTradii of 2.2 a.u. for Fe and 2.4 a.u. for Pt were chosen.The set of the k vectors and the values of RKmax factorwere chosen to gain the total energy precision of 10−6 Ry(197)198 J. Deniszczyk et al.and the EFG relative error less than 1%. All calculationswere performed for the experimental lattice parameters.The EFG tensor was calculated using the formula derivedby Weinert [9] for the shape model of periodic charge dis-tribution used in the FP-LAPW method. The formuladivides the EFG in contribution of electrons located in-side MT sphere (local EFG) and the part dependent onthe charge distributed outside the MT sphere, called lat-tice EFG [10]. In our calculations the contribution toEFG of true core states is omitted but, as argued in [10],it is negligible in metals.3. Results and discussionThe room temperature X-ray measurements revealthe single L12 phase for both samples and the latticeparameter was found as 0.3868(1) nm (powder) and0.3871(1) nm (foil), in agreement with the data presentedin [1, 2]. The diffraction pattern did not exhibit the c/adistortion with the accuracy of 10−5. The Mo¨ssbauerspectra were analyzed within the transmission integralapproach. Because the local atomic environment of Featom in Pt3Fe is of cubic symmetry firstly we have fit-ted a Zeeman sextet to the experimental spectra. Thefitted function is shown in Fig. 1a (solid line). The dif-ference between experimental spectrum and the fittedfunction clearly shows the shift of outer doublet withrespect to the inner quartet which indicates the presenceof the quadrupolar splitting (QS) of the Zeeman sextet.To exclude the drive nonlinearity as a possible reasonof the line shift we performed fits on calibration spec-trum of α-Fe treating QS in the same way as used inFig. 1. The fits of the same quality for QS = 0 andQS treated as free parameter were found. In both casesthe shift of lines was zero with the uncertainty one orderof magnitude smaller than the QS found in Pt3Fe whichexcludes drive nonlinearity as the possible reason of de-viations shown in Fig. 1a. With this in mind another fitfor Pt3Fe was performed with the QS taken into account.Assuming a nonzero EFG at Fe nucleus a good qualityfit was obtained (solid line in Fig. 1b) with the QS val-ues of −0.038(7)mms for the ground state, independent ofthe sample preparation. We obtained the magnitude ofmagnetic hyperfine field consistent with that reported in[2, 4].Our calculations give the ground state band structure(Fig. 2) and magnetic properties of Pt3Fe in NM, FMand AFM1 phases similar to that reported in [5]. Themagnetic moment of Fe (3.23 µB in FM state) enhancesslightly in AFM state (AFM1: 3.27 µB, AFM2: 3.24 µB).The magnetic moment of Pt (0.37 µB in FM state) dis-appears in the AFM2 state while in the AFM1 state thePt atoms located in the ferromagnetically ordered planeshave the magnetic moment of 0.15 µB parallel to planemagnetization. The Pt atoms surrounded by two pairsof Fe magnetic moments of opposite polarization are notpolarized. Calculations have shown that the transitionfrom FM state to either AFM state does not change theFig. 1. Mo¨ssbauer spectrum of ordered Pt3Fe mea-sured at T = 13 K and fitted function with only mag-netic dipolar (a) and both magnetic dipolar and electricquadrupolar interactions (b) taken into account. Solidlines show the fitted function.MT charges by more than ≈ 0.005 electrons. This effectand the fact that the crystal structure does not changeupon the FM → AFM phase transition means that thelattice source of EFG is not effective in AFM Pt3Fe andthe question emerges as to the source of the QS we ob-serve in the AFM Pt3Fe. We claim that the asymmetryof the valence electron charge distribution, which occursin AFM state, is the dominant source of the EFG in AFMPt3Fe.Fig. 2. The Pt3Fe total density of states per spin direc-tion with separated atomic contributions, calculated inparamagnetic (NM), ferromagnetic (FM) and two an-tiferromagnetic (AFM1, AFM2) phases. The Feu andFed denote Fe atoms with opposite spin moment orien-tation. The vertical dash-dot line indicates the Fermilevel.The band structure of Pt3Fe is dominated by the hy-bridizing Pt 5d and Fe 3d states (Fig. 2). In the NMstate the anti-bonding band of hybridized Fe 3d and Pt 5dHyperfine Interactions of 57Fe in Pt3Fe . . . 199states forms at the Fermi level (εF). Upon the phase tran-sition to the FM state the exchange interaction results inthe shift of the majority spin Fe 3d band far below εFwith simultaneous reconstruction of 3d orbital energy lo-cation. As an effect almost complete occupation of thesebands is reached. The minority spin anti-bonding states(3d and 5d) shift above the εF leaving the bottom edgeof the band crossing the Fermi level. The crystal-fieldsplitting of Fe 3d states has effect in the different magni-tude of minority spin density of states D(εF) with 3d–egand 3d–t2g symmetry. The transition to the AFM statedoes not change the width and exchange splitting of thevalence band, but some important changes in the Fe 3dband structure can be observed. The majority spin statesaccumulate in the bonding energy region (≈ −4 eV) andhybridize strongly with the 5d states of Pt. The anti--bonding band of minority spin 3d states narrows andshifts above the εF. The lowering of the site symmetryof Fe position in AFM state (4/mmm) lifts partially thedegeneracy of 3d–t2g and 3d–eg states. Interband chargetransfer between the split 3d states of Fe results in theasymmetry in partial state population. The effect is sig-nificant mainly for minority spin states where approxi-mately 0.24 electrons change their orbital character fromt2g to the eg-type which leads to the enhancement of thepopulation of 3dz2 orbital and consequently of electroniccharge distribution along the z axis. The change of thecharacter of the 3d–5d majority spin band hybridizationand changes in the population of the minority spin Fe 3dorbitals generate the EFG at Fe nuclei in AFM Pt3Fe.TABLEMagnetic hyperfine field (Bhf) and main component ofelectric field gradient (ϑzz) with separated partial con-tributions. The ϑexp.zz was estimated for 14.41 keV57Fenuclear excitation, assuming the asymmetry parameterequal to zero and nuclear quadrupole moment of 57Feequal to 0.17 10−28 m2 [11].Bhf Lattice ϑzz [1021 V m−2][T] 3p-cor. 4p-val. 3d-val. TotalFM 25.6 – – – – –AFM1 16.2 −0.001 −0.29 0.03 2.12 1.85AFM2 18.7 0.003 0.13 −0.02 −0.62 −0.5Experimental ϑzz: −0.21× 1021 V m−2 at T = 13 K.The calculated hyperfine parameters in Pt3Fe are col-lected in Table and compared with the experimentaldata. The analytic formula of Weinert for the main com-ponent (ϑzz) of the diagonal EFG allows analysis of sepa-rate contributions of states located at different regions ofenergy scale and for different electronic orbital quantumnumbers. In agreement with calculations for metals re-ported in [10] we found that the lattice (ϑzz) is minutelysmall. The dominant contribution to ϑzz at Fe nucleicomes from the 3d-type valence electrons cancelled par-tially by weakly bound 3p core electrons due to shieldingeffect. The contribution of valence Fe 4p states is negli-gible. For both AFM phases the calculated asymmetryparameter is equal to zero.4. ConclusionsOur ab initio study shows that the AFM transitionin Pt3Fe forces the local valence and weakly bound coreelectron charge density reordering which lowers the localcharge density symmetry and is responsible for the oc-currence of the electric field gradient at Fe nuclei in theAFM Pt3Fe. The ϑzz is dominated by the 3d electroncontribution, the lattice part is negligible. Some shield-ing effect of Fe 3p states is observed. The ϑzz calculatedfor AFM2 phase is close to the experimental one at lowtemperature, which disagrees with experimentally basedconclusion that the AFM1-type of order realizes in theground state of Pt3Fe. The disagreement can originatefrom the noncollinear magnetic order and spin–orbit in-teraction, neglected both in our calculations.AcknowledgmentsThe work was partially supported as a research projectby the funds allocated for scientific research in years2008–2011.References[1] J. Crangle, J. Phys. (France) 20, 435 (1959).[2] G.E. Bacon, J. Crangle, Proc. R. Soc. A 272, 387(1963).[3] S. Yano, Y. Tsunoda, J. Magn. Magn. Mater. 319,1841 (2007).[4] P. Steinbach, R.A. Brand, W. Keune, J. Magn.Magn. Mater. 70, 102 (1987).[5] M. Podgo´rny, Phys. Rev. B 43, 11300 (1991).[6] K. Schwarz, P. Blaha, G.K.H. Madsen, Comp.Phys. Commun. 147, 71 (2002).[7] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett.77, 3865 (1996).[8] D. Singh, Plane Waves, Pseudopotentials and theLAPW Method, Kluwer Academic, Boston 1994.[9] M. Weinert, J. Math. Phys. 22, 2433 (1981).[10] P. Blaha, K. Schwarz, P.B. Dederichs, Phys. Rev. B37, 2792 (1988).[11] U.D. Wdowik, K. Ruebenbauer, Phys. Rev. 76,155118 (2007).

Hyperfine interactions of 57Fe in Pt3Fe in Pt 3Fe - Ab initio and Mossbauer effect studies

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Hyperfine interactions of 57Fe in Pt3Fe in Pt 3Fe - Ab initio and Mossbauer effect studies

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