Lecture 2: Magnetic Anisotropy Energy (MAE)

Transcription

1 Lecture : Magnetic Anisotropy Energy (MAE) 1. Magnetic anisotropy energy = f(t). Anisotropic magnetic moment f(t) [111] T=3 K Characteristic energies of metallic ferromagnets M (G) 5 3 [1] 1 binding energy 1-1 ev/atom [111] exchange energy 1-13 mev/atom µl ~~.1 G cubic MAE (Ni). µev/atom [1] uniaxial MAE (Co) 7 µev/atom Ni 1 B (G) 3 1µeV/atom is very small compared to 1 ev/atom total energy but all important K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 1

2 There are only origins for MAE: 1) dipol-dipol interaction (µ 1 r)(µ r) and ) spin-orbit coupling? L S (intrinsic K or E band ) O. Hjortstam, K. B. et al. PRB 55, 156 ( 97) R. Wu et al. JMMM 17, 13 ( 97) Structural changes by.5 Å increase MAE by -3 orders of magnitude (~. 1µeV/atom) K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5

3 K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 3

4 Free energy density of MAE, K (intrinsic, after substraction of πm ) tetragonal [e.g. Ni, Co, Fe (1) / Cu (1) ]: E tetr = - K a z - 1 / K 4^ a 4 z / K 4 (a x + a 4 y ) +... (B.Heinrich et al.) = - K cos q - 1 / K 4^ cos 4 q - 1 / K 1 4 / 4 (3+cos4j) sin 4 q +... (Bab et al.) = (K + K 4^) sin q - 1 / ( K 4^ + 3 / 4 K 4 ) sin 4 q - 1 / 8 K 4 cos4j sin 4 q +... = K sin q + K 4^sin 4 q + K 4 cos4j sin 4 q +... (traditional) hexagonal [e.g. Ni (111), Gd (1) / W (11) ]: E hex = k sin q + 1 / k cosϕ sin θ + k 4 sin 4 q + k 6^ sin 6 q + k 6 cos6j sin 6 q +... K = k Y + k 4m Y m Legendre polyn. (B. Coqblin) each K i has a volume and surface contribution K i = K i v + K i s /d K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 4

5 Spin reorientation in bulk Gd from B. COQBLIN p. PR 13, 19 (63) TC Gd c AXIS c c 33 6 M M c M Gd ist not isotropic, it has K, K 4, K 6 Note also finite MAE above T C K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 5

6 Spin reorientation in bulk Ni und Co Ni fcc SRT for hcp Co sinθ = (K /K 4 ) 1/ T/T~.8 C~ LB III, 19a, p.45 At the extremal value of K a reorientation and second maximum in χ appears K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 6

7 Ferromagnetic resonance on Fe n /V m (1) superlattices K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 1 MAE (µev/ atom) Fe b). MAE=E [1] -E [11] a=3.5 Å (+.8%) a=.83 Å (-1.3%) [1]Fe/V [11] MgO MgO T/T C a) K K,K 4 (µev/atom) K 4 K 4II Fe V T (K) K4II (µev/atom) XMCD Integral (arb. units) 1-1 prop. µ S prop. µ L L 3 L XMCD V x5 Fe µ S µ L µ S µ L g< g> Photon Energy (ev) A.N. Anisimov et al. J. Phys. C 9, 1581 (1997) and PRL 8, 39 (1999) and Europhys. Lett. 49, 658 () g.64.9 g µ / µ L S XMCD: µ L / µ S(Fe) FMR: µ L / µ S (Fe+V) µ L / µ S(V) 4nm Fe Fe Fe4/V 4 Fe /V 5 µ/µ L S µ(µ ) /V bcc (1) Fe/V superlattice 5 µ(µ ) L B S B.15 bcc Fe-bulk.1 FMR bulk Fe XMCD MAE µev/atom

8 K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct For thin films the Curie temperature can be manipulated vacuum K S1 K V ε = -3.% K S substrate ε 1 = +.5% (a p Ni bulk =.49Å) (a p Cu bulk =.55Å) t=t/t C (d) P. Poulopoulos and K. B. J. Phys.: Condens. Matter 11, 9495 (1999)

9 Free energy density of MAE, K K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 1 (intrinsic, after substraction of πm ) tetragonal [e.g. Ni, Co, Fe (1) / Cu (1) ]: E tetr = - K a z - 1 / K 4^ a 4 z / K 4 (a x + a 4 y ) +... (B.Heinrich et al.) = - K cos q - 1 / K 4^ cos 4 q - 1 / K 1 4 / 4 (3+cos4j) sin 4 q +... (Bab et al.) = (K + K 4^) sin q - 1 / ( K 4^ + 3 / 4 K 4 ) sin 4 q - 1 / 8 K 4 cos4j sin 4 q +... = K sin q + K 4^sin 4 q + K 4 cos4j sin 4 q +... (traditional) hexagonal [e.g. Ni (111), Gd (1) / W (11) ]: E hex = k sin q + 1 / k cosϕ sin θ + k 4 sin 4 q + k 6^ sin 6 q + k 6 cos6j sin 6 q +... K = k Y + k 4m Y m Legendre polyn. (B. Coqblin) each K i has a volume and surface contribution K i = K i v + K i s /d

10 K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 13

11 K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct b ab initio calculations anisotropic µ L MAE O. Hjortstam, K. B. et al. PRB 55, 156 ( 97) MAE x LS µ L 4µB

12 SP-KKR calculation for rigit fcc and relaxed fct structures layer resolved E b =ΣK i at T= C. Uiberacker et al., PRL 8, 189 (1999) R. Hammerling et al., PRB 68, 946 (3) The surface and interface MAE are certainly large (L. Néel, 1954) but count only for one layer each. The inner part (volume) of a nanostructure will overcome this, because they count for n- layers. K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 15

13 K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct K / π M 4 a) 1 (a) Ni(111)/rough W(11) Ni(1)/Cu(1) [1] 1 ^ K / π M (b) A. Berghaus, M. Farle, Yi Li, K. Baberschke Absolute determ. of the mag. anisotropy of ultrathin Gd and Ni/W(11). Second Intern. Workshop on the Magnetic Properties of Low-Dimensional Systems. San Luis Potosi, Mexico, Proc. in Physics 5, 61 (1989) M. Farle et al., PRB 55, 378 (1997) -1 (c) b) [11] - K 4 / π M [1] 1 (b) (c) (a) K / π M [1] ^ Only with K 4 a continues SRT is possible! Do not use K eff = πm K i because f(t) and f (T) are different. Use the ratio K i / πm f(t) / f (T)

14 K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct Oxygen surfactant assisted growth: a new procedure to prepare ferromagnetic ultrathin films oxygen acts as surfactant for Fe, Co and Ni films on Cu(1) change of magnetic anisotropy by surfactant induced magnetic moment of surfactant

15 Improved growth by oxygen surfactant C. Sorg et al., Surf. Sci. 565, (4) M. Farle, Surf. Sci. Perspectives 575, 1- (5) K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 18

16 O( )R45 /Cu(1) missing row reconstruction c( )O/Ni/Cu(1) 47 ev evaporate 5.5 ML Ni nm nm nm 4 nm [1] [1] nm U =.11 V I =.65 na U =.11 V I = 1.55 na 4 nm [1] [1] oxygen top layer middle layer bottom layer [1] [1] from AES oxygen floats on top of Ni film oxygen top layer bottom layer R. Nünthel et al., Surf. Sci. 531, (3) K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 19

17 Local structure: Surface EXAFS Ni on O/Cu(1) oxygen K-edge SEXAFS 3 K hν R nn = (1.85±.3) Å h =.41 Å Comparison to theory (T.S. Rahman): R nn = 1.87 Å h =.44 Å R. Nünthel et al., Surf. Sci. 531, (3) K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5

18 K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 1 Electronic structure from X-ray absorption spectroscopy Ni L,3 -edge O K-edge p z 3d p xy 4sp NEXAFS no bulklike NiO is formed

19 Interface K S ( µ ev/atom) d C (ML) F V K film K (µev/atom) V Kbulk ( πm K ) cos θ ~ d(ml) πm t=.75 Experiment Ni/Cu(1) Ni vacuum K = K Ni + Cu cap Ni + O surfactant V + K S 1 + K d S Ni/vacuum Ni/Cu Ni/CO (van Dijken et al.) Ni/H (van Dijken et al.) Ni/O (surfactant) Theory /d (1/ML) Jisang Hong et al., Phys. Rev. Lett. 9, (4) K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5

20 Results of ab initio calculations K. Baberschke FU Berlin Jisang Hong Lectures et al., on magnetism Phys. Rev. #, Lett. Fudan 9, Univ Shanghai, Oct. (4) 5 3 Density of states MAE along ΓX axis O/Ni DOS (states/ev atom spin) surfactant grown Ni film clean Ni film E (ev) Γ clean Ni DOS shows that topmost Ni moment is basically unchanged O-induced surface state seen in the vicinity of X-point is responsible for change in MAE theory reveals induced moment in surfactant oxygen X

21 Induced magnetism in oxygen: Ni on O/Cu(1) oxygen K-edge XMCD orbital moment µ L BESSY: UE56/-PGM p xy 4sp theory: Ruqian Wu (UC Irvine): XAS (arb. units) - p z 3d 15 ML Ni on O/Cu(1) 3K Experiment Theory.. -. XMCD (arb. units) induced moments in oxygen: µ S =.53 µ B µ L =.1 µ B Photon Energy (ev) K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 4

22 Induced magnetism in oxygen: Co and Fe films Co on O/Cu(1) norm. Norm. XAS (arb. units) 1 Fe on O/Cu(1) norm. XAS (arb. units) 1 p z 3d p xy 4sp grazing normal 4 ML Co on O/Cu(1) 3K Photon Energy (ev) grazing normal 3 ML Fe on O/Cu(1) 3K K. Baberschke FU Berlin photon energy (ev) Lectures on magnetism #, photon Fudan energy Univ. (ev) Shanghai, Oct. 5 norm. XMCD (arb. units) norm. XMCD (arb. units) BESSY: UE56/-PGM hν hν M photon energy (ev) M 5

23 K. Baberschke FU Berlin Lectures on magnetism #, Fudan Univ. Shanghai, Oct. 5 6 Conclusion spin reorientation transition changes dramatically with surfactant surface anisotropy is strongly reduced in magnitude Fe, Co and Ni induce magnetic moment in surfactant fair agreement with ab initio calculations