К.. V. Lamonova, О.. V. Gornostaeva, S. M. Orel, Yu. G. Pashkevich

Transcription

1 Electronic structure and peculiarities of te single-ion magnetic anisotropy of rare-eart ions in te iron oxypnictides RFeAsO (R Ce, Pr, Nd, Sm, Gd) К.. V. Lamonova, О.. V. Gornostaeva, S. M. Orel, Yu. G. Paskevic O. O. Galkin Donetsk Institute for Pysics and Engineering, National Academy of Sciences of Ukraine, 8311, Donetsk, Ukraine

2 La Ce Pr Nd Sm Gd Tb Dy Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

3 Te first part of te question as been studied in te work of Maeter wit co-autors in Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

4 Magnetic interaction between Fe and R subsystems r r r r H... + J F F + J L L +... ( ) ( ) Fe R Fe R Fe R Fe R Fe R ex IR Fe R τ 1 L 3y 0 τ L 1y L 1z τ 3 L 3z L 3x ( ) ( ) Fe R Fe R Fe R Fe R Fe R an ex 3xz 3x 3z 3zx 3z 3x H... + I L L + I L L +... r r r r r r r r r r L m m m + m L m + m m m z z τ L 1z L 1y τ 5 0 L 3y τ 6 0 L 1x τ 7 L 3x L 3z τ 8 L 1x 0 x 1 3 I 3xz (CeFeAsO) ~ 65.3 T/μ B y x 1 3 y Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

5 Direction of te magnetic moments on te R site induced by te L 3x Fe order. CeFeAsO PrFeAsO Te sign of te coupling constant I 3xz Fe-R is different in te Ce and te Pr compounds resulting in orientation of te induced moments. It is known even in SC state te magnetic ordering of R-subsystem reserves! 5 Electronic Structure and Electron Spectroscopy, May 0-3, 013, Kyiv, Ukraine

6 Te second part of te problem te role of magnetic anisotropy of R-ions -as been studied in te work of Gornostaeva wit co-autors in Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

7 Objective of te work Energy levels of te R 3+ ions, g-factor values, temperature dependences of magnetic susceptibility components and fourt-order anisotropy constants ave been calculated using te modified crystal field teory (MCFT). Te iron-subsystem effect on te magnetic properties of R 3+ ions was teoretically studied for bot crystallograpic pases observed experimentally. * O. V. Gornostaeva et al., Low Temp. Pys.., 39, Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

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9 Single-ion magnetic anisotropy E SO λ (L S) E SO << E CF <L> 0 M g S μ B S E SO >>E CF J L+S M g J μ B J

10 Effective spin-hamiltonian for te 3d-ion r r H Γ, γ H + H Γ, γ μ H S eff SO Z B Crystal Field Teory Hee >> HCF >> HSO >> HZ FI { Z, q, ξ } const eff eff nl ( ) r r r r Γ, γ μ + λ Γ, γ B ( H L) ( L S) E E Γ, γ Γ, γ Γ, γ ( μ μν μ ν λ μν μ ν μ μν μ ν ) H g H S Λ S S Λ H H eff B B μν, М. Ргусе, 1950 g ( δ λλ ), μν μν μν μν, xyz,, Single-ion anisotropy Λ μν Γ, γ L Γ, γ Γ, γ L Γ, γ μ E E Γ, γ Γ, γ Γ, γ ν

11 Modified Crystal Field Approac (MCFA) Ψ H H0 + Vee + VCF + VSO + VH n e N n eq n r n k r r r r V + + ξ r l s + l + s H r r r R ( )(, ) (, ) i i i μb i i i> j k 1i 1 i 1 i 1 ij i k n V μν εδ μν 0, μ, ν 1,..., C + 1 ( ) ( ) V SLM M V SLM M μν Ψ γ S L Ψ γ S L ψ nlm ( SLJM J ) a μ Φ ( 1,, K, n) lms Rnl r α Ylm( ϑ ϕ) μ μ α ( ) (, ),, Z eff ( l+ 1)( s ) na B К. V. Lamonova et al., J. Pys. Cem. A. 115, (011). E. S. Zitlukina et al., J. Pys.: Condens. Matter. 19, (007). 11 Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

12 MCFA parameters for 3d- and f-elements Z Z σ CF FI CF eff eff ξ ξ ( Z ); q const nl nl eff eff Z ξ q 3d-elements СF eff ( Z ) 3d 3d eff eff const ξ const ξ nl α n 3 l Z β Z eff ( l + 1)( l + 1 ) Z ξ q CF eff f-elements f eff Z FI eff const const 1 Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

13 Experimental and calculated crystal levels of R 3+ -ions in [RO As ]-coordination complex Exp. * Calc. ** * S. Ci, et al, PRL 101, 170 (008). ** O. V. Gornostaeva et al FNT 013 Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

14 Calculation of g-factors and reconstruction of g- tensor components Δ 0 g ( αβγ,, ) ΔE μ ΔH B ( αβγ,, ) r ξ α β γ ( cos, cos, cos ) g ( αβγ ) r r μ H r μ H B r μ B gj ˆ r μ H B r H r gj ˆ r gˆ ξ T 1 Electronic Structure and Electron Spectroscopy, May 0-3, 013, Kyiv, Ukraine

15 g-factors and g-tensors calculated by MCFA and CFT MCFA g-tensors for te lowest doublet of Ce 3+ in two pases Cmma P/nmm CFT P/nmm g g J ψ ( I) J + ψ ( I),571; g g J ψ ( I) J z ψ ( I) 0, Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

16 Anisotropy of Kramers ion To determine te anisotropy of te Kramers ion we sould: 1.to measure (calculate) te g-factor values at least for 6 crystallograpic directions;.to reconstruct te g-tensor components and to diagonalize te g-tensor; 3.te largest component of te diagonalized g-tensor togeter wit te eigenvector of g-tensor indicate easy direction of te magnetic moment. Tis direction is determined by te site crystallograpic symmetry of paramagnetic ion. 16

17 Te temperature dependence of te Ce 3+ magnetic susceptibility μ k C( T T χ σρ Cσρ T g() i B ) N ε N () i σρ ε() i σρ ( ) σρ exp exp i 1 kt i 1 kt μ0 H ex 5 Т :, - χ x, Δ - χ y, - χ z Black symb. μ 0 H int 0 T Wite symb. - μ 0 H int 0 T 17 Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

18 Experimental and calculated dependences of magnetic susceptibility for CeFeAsO 18 μ0 H ex 1 Т (exp. ) μ0 H ex 5 Т (exp. ) * * * A. Jesce et al., New Journal of Pysics (009). μ0 H ex 1 Т (calc.) μ0 H ex 5 Т (calc.) Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

19 Fourt-order of anisotropy constant 19 ( ) 8 α γ K II ) ( 1 1 (0) ) ( z y x z y x z F F δ γ β α χ χ r... ) 6 ( 3 1 ) ( 1 ) ( ) ( y x y x z J K g F F χ χ r II ϕ x z y Magnetic moment direction in tetrapase coincides wit one in ortopase! Magnetic moment direction in tetrapase coincides wit one in ortopase! <110> <110> <110> <110> Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

20 Temperature dependence of R 3+ susceptibility components Ce 3+ : in te bot pases te easy direction is [110] axis Nd 3+ : in tetrapase te easy direction is [010] axis in ortpase te easy direction is [110] axis Sm 3+ : in te bot pases te easy direction is [100] axis

21 Conclusions We propose new approac - modified crystal field teory - to calculate te magnetic properties of rare-eart ions. Tis approac allows to calculate te energy levels of 3d- and f-ions in arbitrary crystal environment wit accounting of spin-orbit interaction. We sow tat te rare eart ions in te crystal-environment wit symmetry always remain in igly anisotropic magnetic state. If tis anisotropy is easy plane one tan te R magnetic fluctuations always induce te Fe magnetic fluctuations, wic are perpendicular to te plane One sould stress tat te iron magnetic subsystem as easy plane anisotropy. Accordingly, te easy plane Fe magnetic fluctuations will produce te rareeart magnetic fluctuations along ard axis. We conclude tat due to interplay between iron and rare eart subsystems in te R111 compounds te magnetic fluctuations of iron subsystems even in te doped nonmagnetic case never been isotropic. 1 Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine

22 . Structural and magnetic transitions in CeFeAsO T S 158 K T N (Fe) 10 K T N (Ce). K PM PM AFM AFM P/ nmm Cmma Cmma Cmma Electronic Structure and Electron Spectroscopies, May 0-3, 013, Kyiv, Ukraine