Correlation Between Magnetism and Structure in Fe alloys: the case of Fe-Cr and Fe-Pt

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1 Correlation Between Magnetism and Structure in Fe alloys: the case of Fe-Cr and Fe-Pt Cyrille Barreteau (SPCSI) Chu Chun Fun (SRMP) Romain Soulairol (SRMP) Daniel Spanjaard (LPS) FePt Cr-SDW Service de Physique et Chimie des Surfaces et Interfaces (SPSCI) Service de Recherche sur la Métallurgie Physique (SRMP) Laboratoire de Physique des Solides (LPS) 1

2 Why Fe-Cr Material for nuclear industry FeCr alloy: resistance to corrosion, and irradiation. Decrease of swelling Structure material for future nuclear reactors (fission, fusion). GMR in FeCr multilayers 2

3 Why Fe-Cr Complex magnetic order Spin spiral in Fe fcc SDW in Cr bcc How magnetic order modifies the energetic of defects and vice versa.. Mixing energy Influence of magnetism on alloy properties 3

4 Methods Simulated time 1h 1ns DFT (SIESTA, PWSCF) Tight-Binding (TB) Kinetic Monte Carlo 0 Molecular dynamics with semi-empirical potentials Size of the system 100 at at. 10nm 1µm Code DFT - PWscf DFT - SIESTA TB-Stoner E XC GGA GGA - Pseudopot. NC, US, PAW NC - Basis Plane waves Localized Localized (spd) Efficiency/precision Very precise Precise and efficient Very efficient Size of the system < 500 at < 1000 at > 1000 at 4

5 Testing the methods Functional Effect: LDA vs GGA (PWscf PAW) E(d) M(d) 5

6 Testing the methods Pseudopotential Effect NC, US, PAW DE(eV) M(m B ) 6

7 Testing the methods Basis Effect NC (PWscf)~NC(Siesta) if the localized basis is well optimized Basis 1: DZ(2s), SZ(3p) SZ(5d)= 10 orbitals Basis 2: DZ(2s), SZ(3p) SDZP(10d)= 15 orbitals Minimimal Basis seems accurate enough! 7

8 Ground state of Cr: SDW!! Cr Experimental observation by neutron scattering (Corliss, 1959) : direction (001) et q 0,953. SDW µ = µ 0.cos(q.R) DE(q) SDW is never stabilized M(z) 8

9 Vacancy formation energy in Cr SDW 3a 0 3a 0 N 360 atoms 20a 0 f ( n 1) EV ( Cr) E ( n 1) Cr, V E( ncr) n Position V AF NM SDWnœud SDW- site inter. SDWsite max. Exp.* E f V (ev) * Landolt-Börnstein, PAS experiments (1985) SIESTA Vacancy formation is easier in a SDW node 9

10 Vacancy migration energy in Cr SDW Cr AF NM SDWsite µ max SDWnœud E mig Vac (ev) Migration energy lower in SDW : E mig Vac(SDW) < E mig Vac(AF, NM) Anisotropy of migration energy in SDW: E mig Vac(SDW node) < E mig Vac(SDW µ max ) Soulairol, Fu and Barreteau, PRB 83, (2011) 10

11 Solution energy of Fe in Cr SDW Strongly magnetic impurity: Fe Position AF NM SDWnœud SDW- site inter. SDWsite max E sol Fe (ev) SIESTA The solution energies are lower in the SDW. But ΔE(AF-SDW) is rather low for Fe ( < ΔE(AF-SDW) for Cu) Magnetic frustration of Fe in Cr : 2 possible spin states, µ Fe = 0 ou 2 µ B. Multiples metastable solution when %Fe. SDW experimentally stable for %Fe < 1.6% understanding the destruction mechanism of the SDW 11

12 FeCr Interfaces Interface energies Fe Interface E f interface (J/ m²) AF Cr NM Cr NCol. Cr (100) SDW Fe/Cr (100) Cr Interface 15 or 29 layers (for (110) or (100)) Fe/Cr (110) Fe/Cr (111) SIESTA Fe/Cr (100) interface is stabilized by magnetic effect contrary to the (110) interface Magnetic frustration Fe-Fe Fe-Cr Cr-Cr Two possible ways of relaxing the magnetic frustration: SDW with NM nodes near the interface ( exp. : Bödeker et al. PRL, 81, 914) Non collinear configurations (exp. : Fritzsche et al. PRB, 65, ) 12

13 SIESTA FeCr Interfaces Interface magnetic configurations Non collinear Collinear E f (NCol.) < E f (Col.) J/m² J/m² Non collinearity lowers interface energy in Fe/Cr (110). Perpendicular magnetic coupling between Fe and Cr 13

14 Cr clusters in Fe matrix Fe X Cr Y Fe 123 Cr 5 Fe 121 Cr 7 Fe 115 Cr 13 ΔE(Col - NCol) (mev/cr ou Fe) SIESTA Collinear configurations for small Cr clusters in an Fe matrix (N Cr = 5 and 7) Possible non collinear configurations of slightly lower energies for clusters of intermediate sizes (N Cr =13) [Longo et al. PRB 77, (2008) and Robles et al. PRB 74, (2006)] Possible non collinear configurations of slightly lower energies for clusters with (110) facets Cr Fe X X X z N Cr = 5 N Cr = 7 N Cr = 13 14

15 Fe clusters in Cr matrix + attraction - répulsion Fe-Fe interaction energy SIESTA Environnement Cr AF AF NCol. SDW- node E b Fe-Fe (ev) µ Fe1 (µ B ) µ Fe2 (µ B ) Multiple magnetic states for Fe dimer in Cr. Precipitation of Fe is favored in Cr SDW. Configurations non colinéaires de faible énergie pour les clusters avec facettes (110). [001] X X X AF AF NCol. SDW node 15

16 FeX alloys DFT M. Levesque PhD. Mixing energy calculated at P=0 (Cr exp. [Mirebeau et al., PRL 53, 687 (1984)] ) Some trends in the periodic table FeV FeCr FeMn ΔE sol - - puis + + N d Fe-N d X Δµ = µ sol - µ bulk (µ B ) 1, ,85 16

17 FeX alloys E E ( n 1) Fe, Cr ( n 1) E( Fe) E( Cr ) V, Cr, Mn 1.85% at sol FeMn FeV FeCr PWscf Effet of d band filling on the solubility of V, Cr et Mn in Fe AF interaction between Fe and Cr, Mn or V favors AF solutions FeCr: intermédiate case : magnétisme is the driving force µ Cr < - 0.8µ B mixing µ Cr > - 0.8µ B demixing 17

18 Partial Conclusion Fe-Cr is a particularly complex system where magnetism plays a crucial role In the energetics. Questions and Comments Can we stabilize the SDW (Fermi Surface Nesting?) How could we introduce (spin and ion) temperature effects? Need for simpler models? 18

19 FePt phase diagram FePt L10 c a L10 structure cexp 3.72A cexp 1.36 aexp Vexp 27.7 A very high magnetic uniaxial anisotropy MAE=1.4meV/atom (exp.) a exp A 2 3 Good control of nanocrystal growth 19

20 Magnetic TB model H H0 Hmag HLCN HSOC H 0 : spd Tight-Binding (non magnetic)hamiltonian H mag : Stoner Hamiltonian H mag 1 2 i I mi. H LCN : local charge neutrality constraint H U ( n n ) i i U ( n n ) i i 0 0 LCN LCN i i d i, d i, d i id H SOC : Spin Orbit Coupling i H ( r R ) Li. S SOC i i i 2 2 d, i Rd, i () 0 r r dr 20

21 Determination of parameters H0 i i H jm jm ijm i=atom λ=orbital s px py pz dxy dxz d 2 2 xz d d x y 3z 2 r 2 Hopping integral Onsite term m ij i H jm i i H i ( R) R 21

22 Determination of parameters H 0 : Hopping integrals and onsite elements obtained from simultaneous fit of abinitio band structure and total energy curves of bulk non magnetic Fe and Pt Total energy Band structure 22

23 Determination of parameters H mag : Stoner parameter I adjusted to reproduce ab-initio M(d) of bulk Fe and Pt IFe H mag 1 2 i I mi. 0.88,0.95 ev IPt 0.60eV i Bcc Fe Fcc Pt 23

24 Determination of parameters H SOC : Spin Orbit Coupling adjusted to reproduce ab-initio band structure 2 2 SOC i i d, i Rd, i () i 0 H ( r R ) Li. S r r dr Fe 0.06eV Pt 0.57eV 24

25 Determination of parameters H LCN : local charge neutrality H U ( n n ) i i U ( n n ) i i 0 0 LCN LCN i i d i, d i, d i id Charge neutrality d orbital filling U U 20eV d 0 nid, adjusted to reproduce electronic and magnetic properties of FePt L10 n, Fe d n, Pt d M 3m M 0.35 Fe B Pt m B 25

26 Magnetic and Structural properties of FePtL10 FM vs AF Functionnal effect Structural effect 26

27 Magnetic and Structural properties of FePtL10 Magnetic Anisotropy Energy J.Phys.: Condens. Matter 17 (2005) 4157 Tight-Binding Remark: MAE too large! LSDA+U+SOC Disorder? 27

28 FePt L10 clusters R Clusters of increasing size Pt Fe R N N 43 N 55 cuboctahedron N N 135 N 141 N 147 cuboctahedron Not a spherical shell 28

29 Magnetic properties of FePt L10 clusters Repartition of spin magnetic moment in the cluster FM // z N 135 Ab-initio= Comput. Matt. Sci. 35 (2006)

30 Magnetic properties of FePt L10 clusters Repartition of spin magnetic moment in the cluster AF // x -0.4m B -3m B 0m B 3m B 0m B -3m B -0.4m B 30

31 AF vs FM order in FePt clusters Pt termination favors AF Fe termination favors FM Large Stoner parameter favors FM Large c/a favors FM FM FM FM AF FM AF N 43 N 55 N 79 N N N

32 MAE in FePt clusters Easy axis along z Except for N=135,147 (AF ordering) 32

33 Partial Conclusion Efficient and quantitative TB method for electronic and magnetic properties of metals and their alloys. Complex magnetic behavior of FePt clusters: FM vs AF, oscillating MAE etc.. influence of surface termination influence of c/a Questions and Comments Why is there no experimental evidence of AF order? LSDA+U Disorder? Strain effect? 33

34 THANK YOU FOR YOUR ATTENTION 34