Phase transitions in ferromagnetic monolayers: A playground to study fundamentals

Transcription

1 Phase transitions in ferromagnetic monolayers: A playground to study fundamentals Klaus Baberschke Institut für f r Experimentalphysik Freie Universität t Berlin Arnimallee 14 D D Berlin-Dahlem bab@physik.fu-berlin.de T crit, Phase Transitions Spin Reorientation Transition Magnetic Anisotropy Energy Manipulation of the SRT Summary, Take Home 1/24

2 Para- to ferromagnetic phase transition, Curie temperature, Bulk Fe, Co, Ni have only one T C, each (few % changes are possible). For ultrathin films T C can be manipulated from zero to T bulk C. New and Great! How do we measure T C? χ ac increases at T C ; dc-moke vanishes! 2/24

3 Ni(111)/W(11) Different T C for Ni(111) and Ni(1). How can this be explained? Ni(1)/Cu(1) T T T ( ) d ( ) C ( ) 1/ cd C K. B. Appl. Phys. A 62, 417 (1996) #171 C finite size scaling, If T C changes the reduced temperature T/T C = t is important. 3/24

4 Finite size scaling is a general phenomenon and not specific for FM. The difference lies in the different correlation lengths. (1 ) t 4/24

5 Close to T C fluctuations (Gaussian or critical) increase. This increases the linewidth in magnetic resonance spectroscopy. Fe 3+ -V O / SrTiO 3 Yi Li, K. B., PRL 68, 128 (1992) #126 Th.v. Waldkirch, K.A. Müller, W. Berlinger, PRB (1973) 5/24

6 Element specific UHV-XMCD measurements M (arb. units) ML Cu 4.8 ML Ni Cu(1) T C Ni = 275K 2.8 ML Co 2.8 ML Cu 4.8 ML Ni Cu(1) 37K T * Ni T (K) P. Poulopoulos, K. B., Lecture Notes in Physics 58, 283 (21) M (ka/m) ML Cu 2.8 ML Ni Cu (1) T* C,Ni T C,Ni T C,Ni 2. ML Co 3. ML Cu 2.8 ML Ni Cu (1) 38 K T (K) A. Scherz et al. PRB 65, (25) The large shift of T C Ni can NOT be explained by the static exchange field of Co. 6/24

7 Enhanced spin fluctuations in 2D (theory) P. Jensen et al. PRB 6, R14994 (1999) Ni T / T C J inter 1 K 3 K =3 K MF Co/Cu/Ni trilayer.9 Tyablikov (or RPA) decoupling d Ni (ML) + Spin-Spin correlation function S i S j t z + z S i S j Si S j S i Si S j S i Sj S i RPA z + Si S j, mean field ansatz (Stoner model) is insufficient to describe spin dynamics at interfaces of nanostructures J.H. Wu et al. J. Phys.: Condens. Matter 12 (2) 2847 E=E AFM E FM (ev/m L) - T ( o K) T= o K T=25 o K T 1/ max E FM 2 E NM E FM 1 E TOT FM coupled AFM coupled (a) (b) (c) d NM Single band Hubbard model: Simple Hartree-Fock ansatz is insufficient Higher order correlations are needed to explain T C -shift 1/ max (arbitrary unit) 7/24

8 Two phase transitions at T C Ni and T C Co? Norm. XMCD Difference (arb.units) L 3,2 Co -edges Ni -edges 45K L 3,2 x2 1.3ML Co 2.1ML Cu 2.1ML Cu 4ML Ni 4 ML Ni Cu(1) Cu(1) Photon Energy (ev) Magnetization M (Gauss) [11] M sat M sat 2 AFM M Ni Temper ature (K) [1] easy M Co [11] ext H, k easy M Ni Crossover of M Co (T) and M Ni (T) A further reduction in symmetry happens at T c low A. Scherz et al. J. Synchrotron Rad. 8, 472 (21) #248, 245 8/24

9 Magnetic Anisotropy Energy (MAE) 1. Magnetic anisotropy energy = f(t) 2. Anisotropic magnetic moment f(t) M (G) [111] [1] Ni [111] [1] 1 2 B (G) L ~.1 G 3 MAE = M db ½ M B ½ 2 2 G 2 Characteristic energies of metallic ferromagnets binding energy 1-1 ev/atom exchange energy mev/atom cubic MAE (Ni).2 µev/atom uniaxial MAE (Co) 7 µev/atom K. B. Lecture Notes in Physics, Springer 58, 27 (21) MAE erg / cm 3.2 µev / atom 1µeV/atom is very small compared to 1 ev/atom total energy but all important 9/24

10 The origin of MAE There are only 2 origins for MAE: 1) dipol-dipol interaction (μ 1 r)(μ 2 r) and 2) spin-orbit coupling λ L S (intrinsic K or E band ) 1/24

11 Free energy density of MAE, K (intrinsic, after substraction of the shape anisotropy 2M 2 ) tetragonal [e.g. Ni, Co, Fe (1) / Cu (1) ]: E tetr = - K 2 z 2 E tetr - 1 / 2 K 4 z 4-1 / 2 K 4 ( x 4 + y 4 ) +... (B.Heinrich et al.) = - K 2 cos 2-1 / 2 K 4 cos 4-1 / 2 K 1 4 / 4 (3+cos4) sin (Bab et al.) = (K 2 + K 4 ) sin 2-1 / 2 ( K / 4 K 4 ) sin 4-1 / 8 K 4 cos4 sin = K 2 sin 2 + K 4 sin 4 + K 4 cos4 sin (traditional) hexagonal [e.g. Ni (111), Gd (1) / W (11) ]: E hex = k 2 sin / 2 k 2 cos2 sin 2 + k 4 sin 4 + k 6 sin 6 + k 6 cos6 sin K = k 2 Y 2 + k 4m Y 4 m +... Legendre polyn. (B. Coqblin) each K i has a volume and surface contribution K i = K i v + 2K i s /d M. Farle Rep. Prog. Phys. 61,755 (1998) K. B. Handb. Magn. Magn. Mat. 3, 1617 (27) # see web 11/24

12 Spin reorientation in bulk ferromagnets PR 132, 192 ( 63) SRT for hcp Co sin = (K 2 /2K 4 ) 1/2 Gd c AXIS c c 33 6 M M c M LB III, 19a, p.45 Gd ist not isotropic, it has K 2, K 4, K 6 At the extremal value of K 2 a reorientation and second maximum in appears T ( C) 12/24

13 SRT in ultrathin Ni films K /2 M 2 4 a) 1 (a) Ni(111)/rough W(11) Ni(1)/Cu(1) [1] K 2 /2 M 2 A. Berghaus, M. Farle, Yi Li, K. B. Second Intern. Workshop on the Magnetic Properties of Low-Dimensional Systems. Proc. in Physics 5, 61 (1989) #18 b) -1 2 [11] -2 (c) K /2M [1] 1 (b) (c) (b) (a) K /2M 2 2 [1] M. Farle et al., PRB 55, 378 (1997) #176 Only with K 4 a continues SRT is possible! sin = (K 2 /2K 4 ) 1/2 Do not use K eff = 2M 2 K i because f(t) and g(t) are different. Use the ratio K i / 2M 2 f(t) / g(t) What causes the SRT? There is only one reason, the K i (T,d)! 13/24

14 from B. COQBLIN p. Higher order MAE K i Gd bulk TC Ni is the only 3d ferromagnet for which T C (d) is measured over the full range of temperature and thickness 14/24

15 K V d (ML) K (1 6 erg/cm 3 ) To analyze SRT in thin films is difficult and tedious because there is a T and 1/d dependence: T/ T C (d) and K(T)=K V (T)+2K S (T)/d 4 2 II 2M 2 (t=.56) 2M 2 (t=.74) T 2M 2 (t=.79) II t =.56 t =.74 Ni/Cu(1) K v /d (1/ML) Gd(1)/W(11).79 G. André et al., Surface Science 326, 275 (1995) K. B. and M. Farle, J. Appl. Phys. 81, 538 (1997) K (ev/atom) Why does Ni undergo a SRT and Co not? => #33 K ( 2 ev/atom) T = 3 K d (ML) Co/Cu(111) U. Gradmann et al. (1993) F.J.A. den Broeder et al. (1991) this data M 2 bulk K V /d (1/ML) M. Farle et al., Surf. Sci. 439, 146 (1999) In a proper analysis, taking T/T C (d) in consideration, we always find a linear K=K V +2K S /d dependence. A departure from this Néel argument indicates changes in the x-tal structure. K 2 ( ev/atom) 4 2 bulk hcp Co T/T C = /24

16 Experimental FMR evidence for a continuous rotation FMR - H r (kg) a) b) 7.5 ML Ni/Cu (1) eq M T=9 K T/T c =.2 eq T=15 K T/T c = c) d) eq eq M T=332 K T/T c = H T=3 K T/T c =.7 Farle et al. PRB 56, 51 (1997) #185 SRT is caused by the temperature dependence of K i (T). 16/24

17 Hypothetical structure in theory 2 = -3.2% Growth of artificial nanostructures bcc, fcc tetragonal, trigonal 1 = +2.5% Tetragonal Ni(1) (a p Ni bulk =2.49Å) fcc Cu(1) substrate (a p =2.55Å) c + 2 Structural changes by.5 Å increase MAE by 2-3 orders of magnitude (~.21µeV/atom) O. Hjortstam, K. B. et al. PRB 55, 1526 ( 97) R. Wu et al. JMMM 17, 13 ( 97) a + 1 Bain path 17/24

18 Manipulation of SRT Magnetic moments at surface/interface UHV-SQUID measurements Theory: Hjortstam et al., PRB 53, 924 (1996) Pentcheva et al., PRB 61, 2211 (2) A. Ney et al. Europhys. Lett. 54, 82 (21) 18/24

19 Ni/Cu(1) Interface K S ( ev/atom) d C (ML) Ni/vacuum Ni/Cu Ni/CO (van Dijken et al.) F V K film K 2 (µev/atom) V Kbulk M K cos ~ d(ml) M 2 t=.75 K Experiment Ni/Cu(1) Ni vacuum Ni + Cu cap Ni + O surfactant K V K S 1 d K S 2 Ni/H 2 Ni/O (van Dijken et al.) (surfactant) Theory /d (1/ML).15.2 Jisang Hong et al., Phys. Rev. Lett. 92, (24) 19/24

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21 Results of ab initio calculations for O/Ni/Cu(1) Density of states MAE along X axis O/Ni DOS (states/evatomspin) surfactant grown Ni film clean Ni film E (ev) 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 Jisang Hong et al., Phys. Rev. Lett. 92, (24) 21/24

22 SP-KKR calculation for rigit fcc and relaxed fct structures layer resolved E b =K i at T= C. Uiberacker et al., PRL 82, 1289 (1999) R. Hammerling et al., PRB 68, 9246 (23) 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-2 layers. 22/24

23 Summary A whole variety of experiments on nanoscale magnets are available nowadays. Unfortunately many of the data are analyzed using theoretical static mean field (MF) model, also textbook for Untrathin Magnetic Structures use the bulk magnetism approach. Such a mean field ansatz is insufficient for nanoscale magnetism, we demonstrate the importance of higher order spin-spin correlations in low dimensional magnets. The spin is not a good quantum number, it ignores the orbital magnetism. The orbital magnetic moment creates the MAE. And the MAE manipulates the SRT. Conclusion: The magnetism of FM monolayers is a very reach playground and a fruitful collaboration between theory and experiment. 23/24

24 Take Home Cartoon (#xyz see publ.list) 24/24

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