From electronic structure to magnetism

Transcription

1 From electronic structure to magnetism Olle Eriksson, Department of Physics and Astronomy, Uppsala University And School of Science and Technology, Örebro University

2 Collaborators Abrikosov, Bergman, Bergqvist, Björkman, Bluegel, Brena, Burlamaqui, Cardias, Chico, Chimata, Delczeg-Czirjak, Delin, Di Marco, Etz, Grechnev, Grånäs, Hellsvik Iusan, Johansson, Katsnelson, Kimel, Kirilyuk, Klautau, Klintenberg, Kvashnin, Koumpouros, Lichtenstein, Locht, Luder, Mentink, Nordström, Panda, Pereiro, Rodrqigues, Rasing, Rodriques, Russ, Sanyal, Szilva, Szunyogh, Thonig, Thunström, Yudin, Wills 1

3 Density functional theory

4 Energy dispersion for Cu

5 Energy dispersion for Si

6 Spin-polarised energy dispersion for Fe

7 Β Spin moments of Fe-Co alloys Magnetic moment per atom (µ ) Expt 2 bcc fcc B 1 hcp Fe alloy Co PHYSICAL REVIEW B 59, 419 (1999)

8 Wunderkind Misha finished gymnasium at age 14, received PhD at age 23, and habilitation at age 28 professor age 33-34

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10 Heisenberg Model A picture of localised spins Magnetization is a classical vector, assigned to each site With

11 1 4 d" TrL i G"ij (") j ˆ = exp i ~'i ~ˆ /2 1U G#ji (") (25) (15) 2µB (23) 2 ˆ Exchange parameters(26) H ˆ iu ˆ =H ˆ 01 + H ˆ+ HGij= (z)u=h j ˆ0 ˆ Mapping procedure ˆ Z (z) ˆE z XH f ˆ H= d" TrL 2 ij 4 1 i G"ij (") j G#ji (") ~'i Expansion of the Hamiltonian in Exchange parameters from ab initio: " # " # s s (16) ~'j 2 and gives (i! (i!nn) ) G G Tr! i G (i!nn)) jj(i! (27) (17) n )n ) G n) n) i (i! ijij(i! ji (i! ji (i! Z 1 Ef Jij = d" TrL i G"ij (") j G#ji (") 4 1 X 1 #1 " # 1"2 ˆ " # ~ X ˆ ˆ H = Tr! i (i!n ) Gij (i!n ) j (i!n ) G(28) Hi + i (i!n ) 2 i (i! ) ji (i!n ) 'i n ) = Hi n 4 Tr! = T (18) ij 1 " Local exchange field Green s Ji!ijn= G#ji (i!nfunction ),n= Tr 1! i (i!n ) Gij (i!inter-site n ) j (i!n ) 4 1 ˆ ˆ" H ˆ# G (z) = i G(z) j = i j (29) i = Hi ij i ˆ z H " # 2 Local exchange field i (i!n ) Gij (i!n ) DOS(E) j (i!n ) Inter-site Greens function Gji (i!n ) ~'i m=n E " Nj = # ~'j Z Ef " (")d" 1 (25) ~'j 2 (19) i Z Ef (24) # (")d" 1 Lichtenstein et al JMMM (1987), Katsnelson et al67prb (2000), Lichtenstein et al JMMM 65 (1987) et ˆ ij =Kvashnin ˆ al H hinlm H jnprb l m 0 i (2015) (26)

12 Heisenberg spin Hamiltonian M vs T for bcc Fe

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14 Atomistic Landau-Lifshitz equation Separate fast variables (electrons) and slow (atomic spins) and the EOM together with Landau- Lifshitz damping term gives: Precession Damping The effective field B is given by

15 Spin wave dispersion spectrum 30 Gd 25 E [mev] Γ M K Γ A Γ

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17 Science and Philosophy Misha presented one of his 5 books on philosophy and religion to old-president Mikhail Gorbachev, 2000

18 Magnonics and the majority gate

19 Chiral excitations

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21 The Lion of Science

22 Dynamical mean field theory 1

23 Dynamical mean field theory U-matrix expressed in terms of Slater integrals The Hubbard model is mapped into an Anderson Impurity Model FICTITIOUS SYSTEM REPRODUCING THE DYNAMICS The mapping is made with the condition of preserving the local Green s function and is exact in the limit of infinite nearest neighbors

24 Exact Diagonalization Solver The finite size problem can be solved exactly with a direct construction of all the accessible many-body states. N=5 electrons in K=10 orbitals: M corresponds to K N Too large for standard computational resources! Block diagonalization up to 30 bath states! Local correlation effects in the electronic structure Igor Di of Mn Marco doped GaAs with LDA+DMFT Igor Di Marco

25 Exact Diagonalization Solver The finite size problem can be solved exactly with a direct construction of all the accessible many-body states. N=5 electrons in K=10 orbitals: Once the many-body states have been determined, the one-particle Green s function can be obtained through the Lehmann representation Local correlation effects in the electronic structure Igor Di of Mn Marco doped GaAs with LDA+DMFT Igor Di Marco

26 Paramagnetic NiO DOS Ni-3d O-2p Experiment Theory (DMFT) P. Thunström et al. PRL (2012)

27 Experimental scenario: STM image Constant-current topograph (10 mv, 0.5 na) Cross section of the unfiltered topograph N Cu Fe Experimental system: a single atomic layer of CuN to decouple the spin of the Fe atom from the underlying Cu (100) surface. Cross section- Fe atom has large apparent height of 2.6 Å. Science 317, 1199 (2007)

28 Spin excitation spectra for B=0 X4> X3> X2> X1> X0> E1 E2 E3 E4 Spin Hamiltonian H = D S z 2 + E(S x2 -S y2 ) = D S z 2 + E/2(S S -2 ) When S = 2, m s = -2, -1, 0, +1, +2 For experimental D = -1.55, E = 0.31 The eigen states are X0> = > > > X1> = > > X2> = > > X3> = > > X4> = > > > 4D 0 6E D 0 3E 0 6E E 0 3E 0 D E 0 4D E1 E1 E2 E2 E3 E3 E4 E4 Exp Exp LSDA LSDA LSDA+U LSDA+U HIA (FLL) ED

29 Magneto calorics 1

30 Hot area, temp=t 2 Magnetocaloric material that heats the environment Magnetocaloric material that cools the environment Cool area, temp=t 1

31 What is MCE? Temperature change ( T) induced in a magnetic material applying an external magnetic field H f H m dh T H M T H T S 0 0, ), ( C S T T m ad [P.Egolf] ),, ( ),, ( ),, ( ),, ( x T H S x T H S x T H S x T H S e l m

32 How to select materials?

33 Fe 2 P + B, Si, As

34 Fe 2 P + B, Si, As Fixed spin moment calculation E(M=m 1 +m 2 ) κ = a 1 c 1 /b 1 2 when 0.19 < κ< 0.45 metamagnetism

35 Fe 2 P + B, Si Fe I a1 > 0, b1 < 0, c1 > 0 Fe II a2 < 0, b2 > 0

36 FeMnP 0.75 Si theory --effect of chemical and magnetic disorder on phase stability --2 energy minimum in the FM phase

37 New permanent magnets 1

38 Permanent magnets

39 Conduction spectra B N (z-axes) B Hollow (x-axes) B out-of-plane (y-axes) The changes in the excitation energies are markedly different when the magnetic field is applied in the three different directions- evidence of strong magnetic anisotropy. Spin Hamiltonian: H = gµ B B.S + D S z 2 + E(S x2 -S y2 ) Zeeman Axial Transverse magnetic anisotropy Using the spin of a free Fe atom (S = 2), a best fit of all of the excitations give g = 2.11, D = 1.55 mev, and E = 0.31 mev. Primary anisotropy axis: along the N direction-indication of the importance of local molecular bonding for magneto crystalline anisotropy. Science 317, 1199 (2007)

40 Fe 2 P + B Constrained DLM model

41 Fe 2 P + B, Si, As J ij s are calculated in FM configuration as a function of c/a ratio, V, and chemical composition WE HAVE LEARNED Structural effects (manly the c/a ratio change) are important c/a ratio change affects crucially the Fe1-Fe2 inter sublattice interactions the calculated T C is highly overestimated