MAGNETIC EFFECTS IN SIMULATIONS OF STRUCTURAL TRANSFORMATIONS BELOW AND ABOVE THE MAGNETIC TRANSITION TEMPERATURE:

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1 MAGNETIC EFFECTS IN SIMULATIONS OF STRUCTURAL TRANSFORMATIONS BELOW AND ABOVE THE MAGNETIC TRANSITION TEMPERATURE: Navigatig i space o atoms ad spis I. A. Abrikosov Departmet o Physics, Chemistry ad Biology IFM, Liköpig Uiversity, Swede

2 IN COLLABORATION WITH : M. Ekholm, B. Allig, T. Marte, P. Steeteg, Departmet o Physics, Chemistry, ad Biology IFM, Liköpig Uiversity, Swede A. V. Ruba, Applied Materials Physics, The Royal Istitute o Techology, Swede

3 Liköpig, Swede 60 Uppsala The Swedish Strategic Research Ceter i Materials Sciece or Naoscale Surace Lud Egieerig Lars Hultma Lars Hultma; 163 August 2007

4 Igor Abrikosov Bo Serelius Theoretical Physics Igor Abrikosov, Proessor Ab iitio electroic structure theory Materials simulatios Mesoscopic physics, semicoductor structures i the quatum regime, trasport ad chaos Uderstadig o udametal molecular iteractios Dyamical simulatios o metallic heterostructures Eergy localizatio i descrete systems No-liear dyamics o aharmoic lattices Karl-Fredrik Berggre Magus Johasso Sergei Simak Leoid Pourovskii Iria Yakimeko Ferec Tasadi Peter Müger

5 Studets ad Postdoctoral Fellows totally 46 PhDs rom Theoretical Physics: Has Lid Marcus Ekholm, SeRC Olga Vekilova Tobias Marte Postdoc Olle Hellma Peter Steeteg Pro. Eyvaz Isaev, ALVA lector Björ Allig Assistat Proessor Dr. Weie Olovsso, Bitr. Lektror&applicatioexpert

6 CONTENTS : Predictive simulatios: what is it? Coiguratioal thermodyamics o alloys: methodology overview: Koh-Sham descriptio Geeralized Isig descriptio Coiguratioal thermodyamics o magetic alloys Iluece o magetic state o chemical order-disorder trasitio temperature i Fe-Ni permalloy Coclusios

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8 Alloys G E + PV TS Accelerator o protos Coolig media Fuel Target

9 Gibbs ree eergy: G E + PV TS Equilibrium i alloys: Chemical potetial μ I G I T. P, J I Gibbs-Duhem relatio SdT VdP + I I dμ I 0

10 Kutsso et al. J. Appl. Phys. 108,

11 Ti x Cr y Al z N: decompositio patters T0K T1300 K

12 Ti 0.31 Al 0.62 Cr 0.07 coatig: DSC aalysis ad hardess H. Lid, R. Forse, B. Allig, N. Ghaoor, F. Tasadi, M. Johasso, IAA, M. Ode, submitted

13 Coiguratioal thermodyamics o alloys rom irst-priciples F k B T l Z Z s exp The characteristic time or the electroic degree o reedom i d-metals is give by itersite hoppig, related to the d-bad width, W d, as W d ~10-15 s. The magetic degree o reedom, related to the trasverse excitatios o magetic momet, has characteristic time proportioal to the iverse spi-wave requecy ~ s. For the lattice vibratios phoos the characteristic time is proportioal to the iverse o the Debye requecy, which is the order o ~ s. Thereore, we cosider F s as the costraied ree eergy o the alloy with a give atomic coiguratio s: F k T l exp[ E A. V. Ruba ad I. A. Abrikosov, Rep. Prog. Phys. 71, s B p,, F E kt m e s s p, m, e / k B T ]

14 LDA, GGA, etc. VASP, Wie2k,CASTEP, ABINIT, KKR, etc. 2 +V KS x 1,R 1,R 2,...,R N 2m I φ i x 1,R 1,R 2,...,R N e I ε i φ i x 1,R 1,R 2,...,R N I h2 Supercell, CPA, etc. P. E. A. Turchi, I. A. Abrikosov, et al., CALPHAD 31,

15 Ordered compouds

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17 Solutio phases: supercell method

18 Cluster expasio o the total eergy Φ Φ Φ Φ Φ tot tot i i V E E V F F F F F. Tasadi, IAA, ad I. Katardjiev, Appl. Phys. Lett. 94, Special quasiradom structure method [A. Zuger et al., Phys. Rev. Lett. 65, ] Φ Φ V V B x Al 1-x N A. V. Ruba ad I. A. Abrikosov, Rep. Prog. Phys. 71,

19 Solutio phases: coheret potetial

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21 c + 1-c

22 Gree s uctios

23 [ ] -1 [mz-bk,z] 2

24 A B c 1 c A A B B B B B A B A A B A B B A B A A A B B A A Coheret Potetial Approximatio CPA 1 ge V r 1 [ me ~ r 3 Bk, E ] d k ~ UL BZ ULBZ ~ ge ; me ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ m ~ A g E 1+ ge ~ [ m 1 ge B E me ~ ] A B ~ A B g ~ E cg A B E + 1 c g E

25 Locally Sel-cosistet Gree s Fucto method LSGF I. A. Abrikosov et al., Phys. Rev. Lett. 76,

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27 g ii E ij g ~ ii E + g~ Em j LIZ [ ~ j j ] ji E m E g E

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30 g ll E lj g ~ ll E + g~ Em j LIZ [ ~ j j ] jl E m E g E

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35 Locally Sel-cosistet Gree s Fuctio method LSGF 1 r ge ~ UL V BZ ULBZ [ ] 1 me ~ 3 Sk d k r g i E ge ~ + [ ~ ] m i E g i E, i SC geme ~ g ii E 1 ge ~ g i E N SC i SC ij g~ ii E + g~ Em j LIZ I. A. Abrikosov et al., Phys. Rev. Lett. 76, [ ~ j j ] E m E g ji E, i SC

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39 Koh-Sham Hamiltoia occ r r V V V V r V r V H r r H i i Mad XC EXT H KS KS KS i i i KS φ φ φ ε φ *,...R R, R,,...R R, R, ] [ ] [ ] [ ],...R R, R, [ ],...R R, R, [ 2 1,...R R, R,,...R R, R, M 2 1 M 2 1 M 2 1 M M 2 1 M 2 1 [] ], [ E E ] r - r r r 2 1 r[ r r r r T E XC II E V d d V d EXT Φ r r r r r r r r r Geeralized Isig Hamiltoia tot i i E V Φ Φ A. V. Ruba ad I. A. Abrikosov, Rep. Prog. Phys. 71,

40 ..., s j i s tot V V V E mi 2... } { : L.S.M by oud are the I m V m E V N N str pot

41 Metal to isulator trasitio i Ti 1-x Al x N B. Allig, A. V. Ruba, A. Karimi, O.Peil, L. Hultma, ad I. A. Abrikosov, Phys. Rev. B 75,

42 B. Allig, A. V. Ruba, A. Karimi, L. Hultma, ad IAA, Phys. Rev. B 83,

43 B. Allig, A. V. Ruba, A. Karimi, L. Hultma, ad IAA, Phys. Rev. B 83,

44 The Mote Carlo method Calculatios o averages at temperature T: Z T k E A A s B s s exp Create the Marcov chai o coiguratios: T k E Z P B s s exp 1 Balace at the equilibrium state: T k E s s W T k E s s W B s B s ' exp ' 'exp E Δ 1 0 exp 0 0 > Δ > Δ Δ r r T k E E E B Atoms exchaged ΔE

45 i

46 Pd H J ij s i s j

47 Cluster expasio o the total eergy Φ Φ Φ Φ Φ tot tot i i J E E J F F F F B. Allig, T. Marte, ad IAA, Phys. Rev. B 82, Special quasiradom structure method or paramagetic systems Φ Φ J J PM CrN

48 Disordered Magetism Disordered Local Momet Model

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51 M. Ekholm,, IAA, Phys. Rev. Lett. 105,

52 M. Ekholm,, IAA, Phys. Rev. Lett. 105,

53 CONCLUSIONS : Eiciet methodologies have bee developed or the treatmet o coiguratioal disorder i solids Magetic state ilueces strogly iteratomic chemical iteractios Cosequetly, magetism has to be treated accurately upo simulatios o materials properties