Nobel Laureates 2007 Physics: Chemistry: Prof. Peter Grünberg, Prof. Gerhard Ertl, FZ Jülich Fritz Haber Institut der and MPG, Berlin Prof. Albert Fert, Paris
Giant Magneto Resistance: GMR Electrical resistance of stacked magnetic layers FAST transition discovery ) application Nobelprize 2007 Grünberg and Fert Co Magnetization Cu resistance current A. Fert, �� ���������� Paris ��������� ������������������� ���� ����������� ���� �!�"���#�$������%����� Magnetic field ��#�&'� ���""�$� ���"���"
Magnetic Anisotropy and How it can be controlled Dirk Sander Max"Planck"Institut für Mikrostrukturphysik, Halle, Germany www.mpi"halle.de Ni / Cu(100) Co / Cu(111) Stress and magnetism: Magnetic anisotropy 40x40 nm² Surface stress, Spin"STM Film stress, Magnetic switching Spin"polarization magnetoelastic stress
Acknowledgment Max Planck Institute of Microstructure Physics Jürgen Halle, Germany Kirschner Hirofumi Guillemin Zhen Sebastian Nicole Oka Rodary Tian Wedekind Kurowsky
Magnetism is everywhere! Magnetic anisotropy decisive for applications, and demanding for theory: Easy magnetization direction Remanent magnetization in view of temperature and stray fields
What will be covered? Experimental evidence for magnetic anisotropy and why do we worry… Typical energy scales involved Contributions to the magnetic anisotropy dipolar interactions spin)orbit)coupling How to quantify magnetic anisotropy Hard)axis magnetization loops Magnetoelastic coupling Magnetic switching and thermal stability (?) How to control the magnetic anisotropy crystalline order film thickness, lattice strain adsorbate coverage, temperature
Ferromagnetic nanostructures • L sample ~ L exch ~ L domain wall monodomain (Stoner)Wohlfarth switching ?) Bonet et al., PRL 83, 4188 (1999) we study: Co / Cu(111) • Temperature could overcome anisotropy kT ~ KV superparmagnetism Bean et al., JAP 30, 120S (1959) Néel, Ann. Geophys. 5, 99 (1949) •Atoms with low coordination K surface and / or M could be very high Gambardella et al., 50 nm Science 300, 1130 (2003) •Quantum effects (discrete states, collective tunneling) Bernand)Mantel et al., APL 89, 062502 (2006) Wernsdorfer et al. ,PRL 79, 4014 (1997)
Reminder about units: magnetic moment, magnetization, magnetic field Current loop and its magnetic moment m : A I m = I A [A m 2 ] e e � � = = = microscopic view: electron orbit with orbital moment m � B 2 m 2 m e e = × − 24 2 9 . 27 10 A m Natural unit of m : Bohr magneton � B Note: [A m 2 ] = [J T )1 ] Magnetization M : total magnetic moment per volume M: [A m )1 ] = [ J m )3 T )1 ] � I 1 = B 0 = Magnetic field B of induced by current I through wire: H B [ A/m ] π � 2 r 0 Custom: x)scale of hysteresis loop: � 0 H [T] m − = π 7 � 4 10 [ T ] ∫ 0 Note: energy density A 3 d � H M : [ J / m ] 0 1 T = 7.96 x 10 5 A / m
Contributions to the magnetic anisotropy energy dipolar origin: spin"orbit interaction: magnetocrystalline anisotropy magnetostriction [001] � l M M Ni contraction upon magnetization [001] Cu epitaxial lattice contraction [001]: polar magnetization 1 K1 = 0.4 <eV / atom B1= 650 <eV / atom 2 demag = f I M 0 2 11 <eV / atom lattice strain: decisive for anisotropy
Physical origin of magnetic anisotropy spin)orbit interaction Exchange energy refers only to the angle between spins, but NOT to the absolute orientation H ~ J s s exchange ij i j Relativistic quantum mechanics: ξ ⋅ H ~ s � SOC Spin)orbit constant: ξ (3d: 50 – 100 meV) spin)orbit interaction: electron spin s interacts with the magnetic moment of its own orbital motion l the orbital motion interacts with the crystal structure by electrostatic fields However, the orbital angular momentum is largely quenched in cubic crystals Electrons: hybrids of wavefunction of opposite m l Small magnetic anisotropy: cubic systems (IeV / atom), large anisotroy: reduced symmetry, e.g. hexagonal or strained systems (meV / atom) Dipolar crystalline anisotropy: (NOT shape anisotropy) hcp and strained cubic: neglible, as compared to SOC
Energy scales in magnetism and magnetic anisotropy Magnetic anisotropy energy scales are very small (IeV) as compared to bond energies, elastic energies = α 2 α 2 + α 2 α 2 + α 2 α 2 + α 2 α 2 α 2 + f K ( ) K ( ) � cubic 1 1 2 2 3 1 3 2 1 2 3 = θ + θ + 2 4 f K sin K sin � hex 1 2 α : Direction cosine i with respect to cubic axes θ : Angle M, c)axis D. Sander JPCM 16 (2004)R603
Dipole"dipole interactions Shape anisotropy and demagnetizing field Phanomenological picture: magnetic surface charges, outside : sources of stray field Inside: H dem oriented antiparallel to M demagnetizing field + + + + + + + + + + + + + H dem M ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) H dem : constant only for ellipsoids = − � H N M 0 dem D. Sander N : demagnetizing tensor, here N =1 JPCM 16 (2004) R603 Ms 1 ∫ 2 = − = f � H d M � M shape 0 dem 0 S 2 0
Stress: from films to surfaces 900 nm Cr / glass 5 atomic layers Fe / W(100) Au(111) 200 nm 80 nm 1.2 mm W. Wulfhekel et al., Hu et al., Crommie et al., EPL 49(2000)651 Acta Metall. 36 (1988)1301 PRL 80 (1998) 1469 nano"patterning of delamination surface stress magnetic anisotropy ������ ������� ������ ����������� ���������� ����� ����� ����������
Specific experimental equipment at the MPI Halle In)stitu preparation and magnetic measurements (separate: spin)STM) Auger electron spectroscopy Low energy electron diffraction Ion gun Evaporators Magneto)optical Kerr)effect Crystal curvatre stress measurements
Stress measurements magneto)elastic stress: film growth: magnetization reversal ( �� � ����� � ������ $�!������!��!���%� ����������&'�� ���������� ���������� ������ ��!�� � ����� � ������ � � � � � � ����������� � �������������������� ≈ ������� � ��������� typical stress: MPa �����!��#�!���������!"������!) �������������������������������������������� factor 1000 ������������������������������������������������� ������������������������������������� ����!"�#��������� 2 Y t 1 ( ) Rep. Prog. Phys. 62 (1999) 809 S S � τ = � τ = � t ( ) S F F − ν J. Phys.: Cond. Matter 16 (2004) R603 6 ( 1 ) R S Appl. Phys. A 87 (2007) 419 typical stress: GPa Sensors 8 (2008) 4466 J. Phys. : Cond. Matter 21 (2009) 134015
Magnetostriction
Simultaneous “magnetostriction” and MOKE 2 B λ = − 1 100 3 c 11
Experimental evidence of magnetic anisotropy Hard"axis magnetization loops (1) Alternative description: Anisotropy field H anis 1 = K � H anis M eff 0 S 2 I 0 H Here: Quantitative analysis of K eff possible K eff = 0.26 MJ / m 3 I 0 H anis = 0.3 T M ∫ = = S f K � H dM anis eff 0 0 Compare bulk Fe: 0.048 MJ / m 3 (3.5 IeV / atom) D. Sander Change of K: Fe thickness, temperature JPCM 16 (2004)R603
Quantitative analysis: hard"axis magnetization loops (2) Trick: small constant field (2 mT) along easy direction (e.g. sample length) small magnetizing field along sample width Weber et al., APL 70 (1997) 520. „hard)axis loop“ can be obtained Here: 2 mT along sample length Hysteresis loops with H along sample width � M = s Slope: � � H 0 anis = � H M s S 0 1 2 = = 3 K � M s 58 kJ/m eff 0 S 2 D. Sander JPCM 16 (2004)R603
Experimental determination of magnetic anisotropy (1) Fe / W(001): a combined MOKE and stress study Total energy density: Stress and magnetoelastic coupling: From in)plane measurements with small field For info Enders, Sander, Kirschner, JAP 85 (1999) 5279.
Fairly complete extraction of magnetic anisotropy (2) Enders, Sander, Kirschner JAP 85 (1999) 5279 Lattice strain in thicker films: deviation of K 4 from bulk Magnetoelastic coupling changes with strain
Stranski"Krastanov layers of Fe: in"plane SRT N width =0.12 N length =0.004 Rep Prog Phys 62 (1999) 809
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