Ab-initio modeling of hyperfine parameters and its relation with local and macroscopic properties

Transcription

1 João Nuno Gonçalves Postdoctoral fellow (FCT) Departamento de Física and CICECO Universidade de Aveiro, Portugal Ab-initio modeling of hyperfine parameters and its relation with local and macroscopic properties

2 V. S. Amaral 1, A. S. Fenta 1, A. Baghizadeh 4 J. G. Correia 2 A. Stroppa 3, S. Picozzi 3 T. Butz 5 1. Departamento de Física and CICECO, Universidade de Aveiro, Portugal 2. Instituto Tecnológico e Nuclear, Instituto Superior Técnico, Universidade Técnica de Lisboa, Sacavém, Portugal 3. CNR-SPIN, L Aquila, Italy 4. Departamento de Engenharia de Materiais e Cerâmica and CICECO, , Universidade de Aveiro, Portugal 5. Universität Leipzig Institut für Experimentelle Physik II Nukleare Festkörperphysik, Germany Acknowledgments project CERN/FP/123585/2011 [Fundação para a Ciência e Tecnologia (FCT) and COMPETE/FEDER program] PEstC/CTM/LA0011/2011 and PEstC/CTM/LA0011/2013 FCT/CNR bi-lateral agreement 2013/ FCT grants SFRH/BPD/82059/2011 (J. N. Gonçalves) SFRH/BD/51140/2010 (A. Baghizadeh) SFRH/BD/84743/2012 (A. Fenta) 2

3 Outline Hyperfine interactions magnetic dipole, electric quadrupole Experimental motivation, theoretical methods AMnO 3 (A=Ba,Sr) hexagonal illustration of local environments and comparison with experiments Ferroelectrics EFGs and polarization Multiferroics YMnO 3 /YMn 2 O 5 changes with transitions Sr 0.5 Ba 0.5 MnO 3 Rhombohedral lone-pair multiferroics BiFeO 3 and PbNiO 3 3

4 Outline Hyperfine interactions magnetic dipole, electric quadrupole Experimental motivation, theoretical methods AMnO 3 (A=Ba,Sr) hexagonal illustration of local environments and comparisons with experiments Ferroelectrics EFGs and polarization Multiferroics YMnO 3 /YMn 2 O 5 changes with transitions Sr 0.5 Ba 0.5 MnO 3 Rhombohedral lone-pair multiferroics BiFeO 3 and PbNiO 3 4

5 Hyperfine interactions Nuclear moments interact with externals fields, which causes the splitting of the nuclear energy levels Magnetic dipole interaction between Nuclear magnetic dipole moment and Magnetic Hyperfine Field B hf (T) Electric quadrupole interaction between nuclear quadrupolemoment and Electric Field Gradient: EFG (10 21 Vm -2 ) MATERIAL SPECIFIC Local (angstrom or nanoscale) quantities and sensitive to short time scale dynamic phenomena (ns) 5

6 Magnetic dipole interaction - Hyperfine Field Related to local moments and induced moments at the different sites in the solid Due to different origins/components Fermi Contact Field - from the electron spin density penetrating the nucleus, from the s electrons (or relativistic p 1/2 electrons) Orbital field and Dipolar Field (for example, calculated at on-site atomic spheres with spinorbit coupling) = + + v S S Sensitive test of the theory: for exemple, theoretical core B FC usually underestimated by 5 to 15 T by Local Density Approximation of density functional theory 6

7 Electric Quadrupole interaction Electric Field Gradient (EFG) Symmetric Tensor of rank 2, second positional derivatives of Coulomb potential at the nucleus Convention for naming diagonal components, according to their magnitude: V zz V yy V xx Traceless: V xx + V yy + V zz = 0 Two parameters used: V zz and η= (V xx -V yy )/V zz 3 directions, for V zz,v yy, V xx, or three euler angles Non-spherical charge p, d and f charge densities - Also a sensitive test to calculations, and structural aspects. 7

8 Outline Hyperfine interactions magnetic dipole, electric quadrupole Experimental motivation, theoretical methods AMnO 3 (A=Ba,Sr) hexagonal illustration of local environments and comparisons with experiments Ferroelectrics EFGs and polarization Multiferroics YMnO 3 /YMn 2 O 5 changes with transitions Sr 0.5 Ba 0.5 MnO 3 Rhombohedral lone-pair multiferroics BiFeO 3 and PbNiO 3 8

9 Mössbauer effect Experimental Methods Nuclear Magnetic Resonance Nuclear Quadrupole Resonance Time-differential Perturbed angular correlations (TD-PAC) spectroscopy... System of 6 detectors with 90/180 relative orientations 9

10 TD-PAC R(t) Coincidince count rate (exponential decay + perturbed angular correlation) FT Hyperfine Magnetic Field (HMF) = Electric Field Gradient (EFG) = Asymmetry parameter (ƞ) = Some isotopes available: 111m Cd 111 Cd, 111 In 111 Cd, 77 Br 77 Se 17

11 Theoretical Methods First-principles Density Functional Theory Kohn-Sham WIEN2k: All electron, full-potential (linearized) augmented plane-wave + local orbitals (lo) method. - benchmark of DFT. VASP: The interactions between the electrons and ions are described using the projector-augmented-wave method. LDA/GGA-PBE (+U) approximations 11

12 Outline Hyperfine interactions magnetic dipole, electric quadrupole Experimental motivation, theoretical methods AMnO 3 (A=Ba,Sr) hexagonal illustration of local environments and comparisons with experiments Ferroelectrics EFGs and polarization Multiferroics YMnO 3 /YMn 2 O 5 changes with transitions Sr 0.5 Ba 0.5 MnO 3 Rhombohedral lone-pair multiferroics BiFeO 3 and PbNiO 3 12

13 CaMnO 3 orthorhombic (almost cubic) structure EFG how local is it? BaMnO 3 /SrMnO 3 polymorphs (Ba/Sr)MnO 3 higher ionic radii, means higher tolerance factor =, usually found with hexagonal structures 2H 4H Structural Chameleons (Ravindran et al. Phys. Rev. B), since several different polymorphs can be formed, depending on the synthesis conditions. One-dimensional strings of face-sharing MnO 6 octahedra are periodically broken. Adkin and Hayward, Chem. Mater. 19, 755 (2007) 6H 15R 13

14 BaMnO 3 6H BaMnO 3 15H BaMnO 3 4H Adkin and Hayward, Chem. Mater. 19, 755 (2007) Ba(hhh) always corresponds to the higher V zz. Are there other general rules? BaMnO 3 2H 14

15 EFG how local is it? Ba sites Osites Adkin and Hayward, Chem. Mater. 19, 755 (2007) Corner-sharing octahedra Mn sites Non-corner-sharing octahedra These rules, based only on the local environments (nearest layers along z), are general for all the four polymorphs studied (2H, 4H, 6H, 15R), provinding an illustration of the locality of the EFG(a few Angstrom). 15

16 PAC Measurements and calculations SrMnO 3-4H ab-initio supercell calculations of SrMnO 3-4H with Cd probes Sr 1-x Cd x MnO 3 V zz atcd 111 Cd is one of the most common nuclear excited states used for measuring hyperfine interactions with TDPAC. In many materials of interest, it is implanted as an impurity. V zz converges to the highly diluted limit of impurities for large supercells, when the interactions between the impurity and its periodic images vanish. Since the EFG is quite local, the supercells don t have to be very large 16

17 Measurements and calculations BaMnO 3-6H With 111m Cd, one site environment associanted to Cd subsitutional at Ba site, other site incompatible with Ba sites. With 111 In, one more environment occupied, with values higher than calculated for Cd substitution. 17

18 Hyperfine parameters These parameters provide atomic scale information. However, their interpretation is complicated, since they depend on the details of the electron density near the nucleus. However, they can sometimes be related to macroscopic quantities. For example, the magnetic hyperfine fields at the nuclei usually follow closely the temperature dependence of the corresponding magnetizations (sometimes with deviations). The EFG can also be related to other quantities, such as the electric polarization in polar materials. 18

19 Outline Hyperfine interactions magnetic dipole, electric quadrupole Experimental motivation, theoretical methods AMnO 3 (A=Ba,Sr) hexagonal illustration of local environments and comparisons with experiments Ferroelectrics EFGs and polarization Multiferroics YMnO 3 /YMn 2 O 5 changes with transitions Sr 0.5 Ba 0.5 MnO 3 Rhombohedral lone-pair multiferroics BiFeO 3 and PbNiO 3 19

20 NaNO 2 EFG in Ferroelectrics Previous experiments and models Linear P 2 Rochelle salts BaTiO 3 and quadratic variation of V zz with polarization V. Bhide, M. Multani., Phys. Rev. 1966;149(1): D. Dening, Journal of Magnetic Resonance (1969). 1980;38(2): Y. Yeshurun, S. Havlin and Y. Schlesinger, Solid State communications (1978) 27: Dominant without inversion symmetry Dominant with inversion symmetry.

21 Energy and polarization -BaTiO 3 λ distortion (polar mode) Calculated P: 28.6 μc.cm -2 Experimental P:27 μc.cm -2 Polarization linear with distortion 21

22 EFG vs distortion/polarization BaTiO 3 EFG is quadratic with distortion Black lines calculations with other code (WIEN2k) and functionals. For the A, B, O1 atoms in the tetragonal perovskite, η=0. If η=0, V xx =V yy =-1/2V zz and a xx =a yy =-1/2a zz EFG is quadratic with polarization For the cases where η 0 (O2), this relation is not followed. 22

23 EFG vs polarization KNbO 3 EFGs also have the same quadratic variation with polarization The coefficients are different, obviously. But their sign is the same. a O2 is positive while for the other atoms it is negative. PbTiO 3 For the EFG at Pb and O2, a quartic term is also needed for a correct fit. V zz (P 2 ) at all atoms EFG at the O2 site (P 2 ) (V xx, V yy, V zz ) 23

24 Other components of the EFG tensor? V xx V yy V zz EFG at O2 vs P2 EFG at O2 vs distortion BaTiO3 PbTiO3 At the EFGO2 tensor of BaTiO 3, PbTiO 3 and CaTiO 3 there are interchanges of the tensor components due to the convention Ignoring this convention the variation is still usually quadratic for each component but there is not a simple proportionality with the undistorted V zz, as in the η=0 case.

25 BaTiO 3 - Orthorhombic Phase Similar quadratic variations are found in the orthorhombic phase for all atoms, all EFG components Vxx Vyy Vzz Ba Ti O1 O2

26 Correlation between EFG tensor components At the A, B, or O1 sites η= 0 and the correlation is trivial (V zz =-1/2V xx =- 1/2V yy ) What about at the O2 sites, where ηis not zero and changes with the distortion? A plot of one component against the other is needed. V zz (V xx ): when the EFG passes by η= 1 (V zz changes sign) the trajectory is not connected. A better plot is the Czjzek plot. Straight trajectories = Linear correlation

27 Comparison of different materials, with V zz at the A site. Element at A site Coefficient a approximately proportional to atomic number Z A 2

28 Conclusions -Ferroelectrics EFG as a local probe of polarization in ferroelectrics Mostly quadratic variation in different compounds/phases EFG components linearly correlated Coefficient Z 2 trend 28

29 Outline Hyperfine interactions magnetic dipole, electric quadrupole Experimental motivation, theoretical methods AMnO 3 (A=Ba,Sr) hexagonal illustration of local environments and comparisons with experiments Ferroelectrics EFGs and polarization Multiferroics YMnO 3 /YMn 2 O 5 changes with transitions Sr 0.5 Ba 0.5 MnO 3 Rhombohedral lone-pair multiferroics BiFeO 3 and PbNiO 3 29

30 30

31 YMnO 3 hexagonal multiferroic manganite Ferroelectric structure Buckling of Y planes + rotation of MnO-octahedra Collinear approximation to frustrated magnetism [following Medvedeva et al., J. Phys Condens. Matt. 12, 4947 (2000)] Arrows represent the spins. geometric ferroelectric, due to the negligible hybridization changes in the ferroelectric transition, in distiction to the more usual ferroelectrics. [B. B. van Aken et al., Nat. Mater. 3, 1476 (2004)] 31

32 YMnO 3 hexagonal multiferroic manganite from paraelectric-antiferromagnetic to ferroelectric-ferromagnetic How do the hyperfine parameters change EFG(V zz ) B hf EFG changes significantly only at the Y atoms EFG value for Mn changes sensitively with U (LDA: -4.9 LDA+U: -1.5) MHF changes at Mn and some O atoms. With paraelectric ferromagnetic calculation instead, EFGs would remain the 32 same but MHF at other sites would not be negligible.

33 Sr 0.5 Ba 0.5 MnO 3 Cubic perovskite. Becomes tetragonal in the ferroelectric (multiferroic, ) phase. recently synthesized [Sakai et al. PRL 107, 13 (2012)] Very small displacements ~0.1 Å. in spite of a large negative magnetoelectriccoupling [Giovanetti et al. PRL109, (2012)] P~10 uc cm -2 The abinitioresults show that V zz changes very little with structural changes, in spite of the significant polarization, probably because the anisotropy in the electron density is located far from the nuclei (and EFG α 1/r 3 ). Maybe an interesting prospect for experiments aiming to measure dynamical effects, since the EFG is otherwise constant. 33

34 BiFeO 3, PbNiO 3 BiFeO 3 arguably the most studied multiferroic (high T C, T N ; thin films; high polarization...) P ~ 100 µc. cm -2 PbNiO 3 same structure, recently synthesized [J. Am. Chem. Soc. 133, (2011)], Approx. same Polarization [PRB 86, (2012)] Ferroelectric structure R3c Obtained from the cubic perovskiteby antiferrodistortiverotations of the oxygen octahedraaround the [111] axis and polar displacements of Bi(Pb) and Fe(Ni) in the [111] direction 34

35 BiFeO 3 EFG as a function of distortion amplitude. Very different sensitivities for the different atoms, as a function of polarization (ferroelectric displacements) 209 Bi NQR/NMR? Difficulties: limited to low temperatures Quadrupole interaction is a perturbation of the magnetic interaction, due to the local fields transferred from the Fe local environment Interpretation of the spectrum is difficult, and no value for the EFG is given. [A. A. Bush et al., JETP Lett. 78, 389 (2003)] 35

36 BiFeO 3 Almost quadratic dependence, with additional terms for large polarization variations necessary for a good fit Large variations at Bi show that electron density variations are located close to Bi, consistent with the lone-pair type mechanism. 36

37 PbNiO 3 16 V Pb V Ni V O 10 Ni - non-monotonic behavior O Tensor components correlated 37

38 PbNiO 3 Pb 6s-O 2p hybridization drives the ferroelectric distortion similar to BiFeO 3 or other Bi/Pb compounds 204m Pb PAC 38

39 Variation of EFG with P BiFeO 3 /PbNiO 3 Preliminary conclusions Variation generally more complex than in ferroelectrics Large EFGs at A sites, due to lone-pair mechanism and large p-states anisotropy. 39

40 YMn 2 O 5 multiferroicmanganite Ferromagnetic-paraelectric antiferromagnetic-ferroelectric Hyperfine parameters changes from FM to AFM Oxygen (3a) is identified with larger changes in hyperfine parameters. Locally quantify the change of electron density, spin density difference and difference density at the O3 atoms. Spin-dependent hybridization, produces electronic polarization Partzsch et al., Phys. Rev. Letters 107, (2011) 40

41 YMn 2 O 5 multiferroic manganite Local (O3a and O3b) Densities of states FM AFM 41

42 Summary EFGs and MHFs can discriminate different atomic sites, with different changes depending, for example, of different ferroelectric transitions. Its calculation was applied in diferent types of ferroics. Ferroelectric materials have a regular (mostly quadratic) variation of EFGs with the polar distortion andpolarization. YMnO 3 -large variations at Y, negligible changes at the other atoms, consistent with geometric ferroelectricity YMn 2 O 5 -small variations, except with one or two atoms more involved in the magnetic transition. Sr 0.5 Ba 0.5 MnO 3 -negligible variations of EFGs with ferroelectric distortions BiFeO 3 /PbNiO 3 -lone-pair type mechanism induces a very large variation of the EFG with polarization at the Bi/Pb site Other (recent) work: Heusler compounds, magnetovolume effects and graphene, calculation of hyperfine parameters in adatom probes as preparation of future UHV PAC measurements with some results in wet conditions 42

43 The end Thank you 43