Nanomagnetism Part III Atomic-scale properties Olivier Fruchart - PowerPoint PPT Presentation

Nanomagnetism – Part III Atomic-scale properties Olivier Fruchart Institut Néel (CNRS-UJF-INPG) Grenoble - France http://neel.cnrs.fr Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

SKETCH OF THE LECTURES Part I – Magnetization reversal Part II – Techniques Part III – Atomic-scale properties Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.2 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

MOTIVATING THE LECTURE – The need for nanomagnetism (reminder) Fundamental issues for nanomagnetism Magnetic grain media of current hard disks  Is a small grain (ferro)magnetic? Count number of surface atoms  Is a small grain stable against thermal fluctuations? − 21 J ≈ 25 meV k B T  300 K ≈ 4 × 10 100 k B T  300 K ≈ 2.5 eV Derive from macroscopic arguments  Decades-old (yet still modern) topic Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.3 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

TABLE OF CONTENTS 1. Ferromagnetic order in low dimensions  Structure and magnetic order  Magnetic moments (surfaces etc.)  Magnetic ordering (thermal effects) 2. Magnetic energy anisotropy 3. Interfacial effects Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.4 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

1. FERROMAGNETIC ORDER – Metastable phases (fcc Fe) Robustness of ferromagnetic orders Theory: phase diagram of fcc iron (Fe) Properties of bulk Fe (P,T) ambiant conditions Body-Centered Cubic (bcc) Ferromagnetic − 1 ≈ 2.2  B atom L ow S pin T C = 1043 K T>1185 K A nti- F erro N on- M agn. Face-Centered Cubic (fcc,  -Fe ) & L ow S pin H igh S pin No magnetic order V. L. Moruzzi et al. , PRB39, 6957 (1989) See also: O.K. Andersen, Physica B 86, 249 (1977) Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.5 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

1. FERROMAGNETIC ORDER – Metastable phases (fcc Fe) Effect of strain on the crystalline structure Magnetism of fcc Fe Fe/Cu(001) 300K growth with MBE: fcc>bcc 300K growth with PLD: fcc  High-spin and low-spin fcc phases? P. Ohresser et al., PRB59, 3696 (1999) Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.6 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

1. FERROMAGNETIC ORDER – Metastable phases (fcc Fe) Spin-density wave antiferromagnetism Fe/Cu(001) Ferro. See also: H. L. Meyerheim et al., SDW - AF Phys. Rev. Lett. 103, 267202 (2009) D. Qian et al., PRL87, 227204(2001) Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.7 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

1. FERROMAGNETIC ORDER – Surface magnetism – Naive views Probing surface magnetization Some results • Fe/W(110) : 0.14ml(+0.35µ B ) Surface techniques at OK • UHV/Fe(110); Ag/Fe(110): 0.26ml(+0.65µ B ) • Mossbauer with probe layers Plot m ( t ) at 0K: • Cu/Ni(111): -0.5ml • Magnetometry • Overlayers: Pd/Ni(111)/Re(0001) • XMCD (Too) simple picture: band narrowing at surfaces  Enhanced moment at surfaces E E d Bulk Surface s-p d s-p picture picture k k Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.8 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

1. FERROMAGNETIC ORDER – Surface magnetism – Towards single atoms Co/Pt(997) Co/Pt(111) A. Dallmeyer et al. , Phys.Rev.B 61(8), R5153 (2000) Conclusions • Bulk: m L =0.14 µ B /at. P. Gambardella et al., Science 300, 1130 (2003) • Surface: m L =0.31 µ B /at. Conclusions • Bi-atomic wire: m L =0.37 µ B /at. • From bulk to atoms: • Mono-atomic wire: m L =0.68 µ B /at. considerable increase of orbital moment • 2 atoms closer to wire than 1 atom • bi-atom: m L =0.78 µ B /at. • bi-atomic wire closer to surface than wire • atom: m L =1.13 µ B /at. P. Gambardella et al., Nature 416, 301 (2002) Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.9 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

1. FERROMAGNETIC ORDER – Surface magnetism – Polarizability and Stoner criterium Exchange polarization at interfaces Spontaneous polarization – Stoner criterieum Small Rh(4d) clusters studied in flight Pd( D )/Ni(111)/Re(0001) (Stern-Gerlach experiment) TOM U. Gradmann, Handbook… Fe/Pd multilayers XMCD A. J. Cox et al., PRL71, 923 (1993) A. J. Cox et al., PRB49, 12295 (1994) Handwavy explanation based on I   ,   F  1 J. Vogel et al., PRB55, 3663 (1997) Stoner criterium Conclusion: Pd sigifnicantly Conclusion: recuced bandwidth may polarized over several layers even drive ferromagnetism Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.10 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

1. FERROMAGNETIC ORDER – Magnetic ordering Elements of theory • Ising (1925). No magnetic order at T>0K in 1D Ising chain. • Bloch (1930). No magnetic order at T>OK in 2D Heisenberg. (spin-waves; isotropic Heisenberg) • → N. D. Mermin, H. Wagner, PRL17, 1133 (1966) • Onsager (1944) + Yang (1951). Magnetic anisotropy 2D Ising model: Tc>0K stabilizes ordering Experiments Ni(111)/Re(0001) R. Bergholz and U. Gradmann, JMMM45, 389 (1984) Tc interpreted with molecular field Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.11 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

1. FERROMAGNETIC ORDER – Magnetic ordering Naïve model Molecular field 2  B 2 J  J  1  T C = 0 z n W,1 ng J z s z b 3 k B N atomic layers 〈 z 〉= z b − 2  z b − z s  z neighbors -1 ∆ T ( t ) ~ t c N Less naïve… Experiments Thickness-dependant molecular field λ - ∆ T ( t ) ~ t c λ = 1 G.A.T. Allan, PRB1, 352 (1970) Conclusion : U. Gradmann, Handbook of Magn. Mater. Vol.7, ch.1 (1993) Naïve views are roughly correct Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.12 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

1. FERROMAGNETIC ORDER – Magnetic ordering Effect of lateral size H.J.Elmers et al. , Phys.Rev.Lett.73, 898(94) U. Gradmann, Handbook of Magn. Mater. 7 (1993) Conclusion Tc also depends on size of islands (lateral dimensions) Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.13 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

3. Magnetic anisotropy 1. Ferromagnetic order in low dimensions 2. Magnetic energy anisotropy  Microscopic origins of Magnetic Anisotropy Energy (MAE)  Surface versus magneto-elastic anisotropy  From surfaces (2D) to atoms (0D) 3. Interfacial effects Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.14 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

2. Magnetic anisotropy – Basics Dipolar energy Mutual energy of two magnetic dipoles : µ   3 0 = − E μ . μ ( μ . r ).( μ . r )   1,2 1 2 1 2 3 2 π   4 r r Let us assume two magnetic dipoles 2 with vertical direction, either ‘up’ or ‘down’ : θ [ ] µ 2 0 θ = µ µ − θ E ( ) 1 3 cos cos 2 θ = ( ) 1 / 3 1,2 1 2 3 C 1 π 4 r Parallel alignment is favored for θ < θ ≈ ° 54 . 74 C Antiparallel alignment is favored for θ > θ ≈ ° 54 . 74 C ‘Cone’ of alignment Conclusions • Nanostructures: long axis favored • Films: in-plane favored 1 e z 2 = µ M d 0 Z 2 Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.15 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/