Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Magnetic Sensitive Force Microscopy Alexander Schwarz
Institut für Angewandte Physik, Universität Hamburg, Jungiusstr. 11, 20355 Hamburg, Germany
• Magnetism Basics (Part I & II) • atomistic approach (origin of magnetism, magnetic exchange mechanisms) • phenomenological approach (hysteresis, domains, domain walls)
• Magnetic Force Microscopy (MFM; Part I)
• tip preparation and tip properties • separation of forces • examples (thin films, superconductors, …)
• Magnetic Exchange Force Microscopy (MExFM; Part II)
• tip preparation and tip properties • separation of forces • examples (imaging, spectroscopy, switching, dissipation …)
• CO molecule: contrast formation (role of electrostatic forces)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
MFM on Superconductors
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Imaging of Flux Lines with MFM
MFM-tip
1 µm
Abrikosov Flux Line Lattice Bi2Sr2CaCu2O8: λ ≈ 180 nm
λ ξ x
B
nC B
j
nC
MFM
MFM information depth ≈ λ
field cooling: B applied below Tc flux lines (vortices) remain, even if B → 0
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Bi2Sr2CaCu2O8
TC ≈ 85 K λ ≈ 180 nm ξ ≈ 1 nm
c = 3.08 nm
pancake vortex
flux line
VORTEX MATTER
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Straight vs. Curved Flux Lines
5.1 K
1 µm
5.1 K
1 µm
irradiated sample after field cooling ⇓ columnar defects • randomly distributed • strong pinning • Bose Glass
as grown sample after field cooling ⇓ intrinsic point defects • randomly distributed • weak pinning • Bragg Glass
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Flux Line Lattice Melting 5.1 K
1 µm
5.1 K
1 µm
5.1 K
1 µm
5.1 K
1 µm
5.1 K
1 µm
5.1 K
1 µm
5.1 K
1 µm
5.1 K
1 µm
5.1 K
1 µm
5.1 K
1 µm
23.2 K
1 µm
34.5 K
1 µmfield cooling: B = 3.2 mT scan area: 5.5 µm × 5.5 µm
A. Schwarz et al., NJP 12, 033022 (2010).
38.1 K
1 µm
49.7 K
1 µm
54.1 K
1 µm
5.1 K
1 µm
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Thermal Fluctuations and Disorder
1
2
4
5
3
0 50 6040302010T in K
400
360
320
280
240
200
160
FL
R i
n nm
RFL∝√T
E
E
2λ
D
k TB
rr0
∆r∆r thth
rp
E
E
2λ
D
k TB
rr0 rp
∆rth
depinning CuO2- planes
pancake vortex
flux line
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Vortices and Antivortices
dark (antivortex) Mtip ↑↓ flux line
2 µm bright (vortex)
Mtip ↑↑ flux line
2 µm
matching field: number of columnar defect = number of flux lines
field ramp: Mtip ↑↑ B
BSCCO field cooling: Mtip ↑↓ B
BSCCO
A. Schwarz et al., APL 88, 012507 (2006).
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Part II
Magnetic Exchange Force Microscopy
(MExFM)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Magnetic Exchange
Interaction
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Two Interacting Electrons with Spin
spin states χi χ1+= ↑ χ1-=↓
χ2+=↑ ↑↑ > ↑↓ >
χ2-=↓ ↓↑ > ↓↓ >
2 electron state χ(s,m) s m
0 0 singlett antismmetric
↑↑ > 1 +1 triplett
symmetric 1 0
↓↓ > 1 -1
Coulomb Interaction V(r) + Pauli Principle (Fermi-Dirac & Indistinguishability) ⇒ Alignment of Spins ⇒ Magnetic Order
no spin dependent term!
s = s1 - s2 , …, s1 + s2 = s1 ± s2 = 0,1 and m = -s, +s = -1,0,+1 (∆m = 1)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Two Interacting Atoms: The H2 Molecule
total wave function = spatial wave function × spin wave function electron = Fermion ⇒ antisymmetric total wave function if spatial wf antisymmetric ⇒ spin wf symmetric if spatial wf symmetric ⇒ spin wf antisymmetric
H = H0 + W ; H0: 2 non-interacting H atoms; W: interaction terms
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Coulomb-, Overlap- and Exchange-Integral
antiparallel spins; s = 0 (singlett) :
parallel spins; s = 1 (triplett) :
ground state energy of one H atom in the 1s state
overlap integral
Coulomb integral
exchange integral
ϕ0 = 1s wave function of the H atom
bonding state
antibonding state
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Connection to Heisenberg Model
antiparallel spins; s = 0 (singlett) :
parallel spins; s = 1 (triplett) :
in general: J ≠ A!
Heisenberg modell :
J = J(r) distance dependent magnetic exchange coupling constant
J > 0 ⇒ ferromagnetic order J < 0 ⇒ antiferromagnetic order
skalar product: no magnetic interaction for perpendicular spins
exchange coupling constant
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Magnetic Coupling in Metals Direct versus Indirect Coupling
f-metals (Gd): no direct exchange, s-f coupling = spin carrying strongly localized f-electrons polarize conduct-tion band electrons (RKKY)
d-metals (Fe, Ni, Co): little direct exchange, mostly s-d coupling = spin carrying localized d-electrons polarize conduction band electrons
≈ half distance to nearest neigbor ≈ half distance to nearest neigbor
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Magnetic Exchange Force Microscopy
(MExFM) suggested 1991, realized 2007 on NiO(001)
U. Kaiser, A. Schwarz, and R. Wiesendanger, Nature 446, 522 (2007).
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Forces in Force Microscopy
Electromagnetic Forces
• electrostatic force • magnetostatic force
• van der Waals force
• chemical force • magnetic exchange force • repulsive forces
z
Fts
MFM (z > 10 nm)
AFM/MExFM
atomic resolution
steps (topography)
-1 nN
-0.3 nm
0 nN
magnitude of forces: magnetic exchange ≈ 0.1 N (d < 0.5 nm) magnetostatic 1 pN (d > 10 nm)
1 nm
10 nm
100 nm
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
electron mediated short-range magnetic exchange interaction & chemical interaction
Separation of Short-Ranged Forces
magnetic coating
Heisenberg model for spin-spin interaction:
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Tip Preparation Si-cantilever (f0 ≈ 190 kHz, cz ≈ 40 - 150 N/m; Si surface is oxidized) in-situ coating with magnetic material (Fe, Cr, …) by thermal evaporation antferromagnetic tips: no stray field ⇒ less influence on sample! total coverage (instead of just one side) or bulk tips are Ok, because only
foremost apex atom matters on the fly preparation: intended collisions between tip and surface to create
atomically sharp and magnetically sensitive nanotip trial and error procedure (no real control) with three options
• tip stays as it was: continue preparation • tip becomes worse: continue preparation • tip becomes good: start the real experiment
no magnetic contrast, although tip is magnetic: SNR < 1, spin of foremost tip atom perpendicular to surface spins (Heisenberg model!), fast switching (superparamagnetic) tip
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Z-Height & Dissipation Analysis
Δz < 0 : tip becomes longer (sharper) ΔED < 0: less dissipation due to adhesion hysteresis (more stable) possible transitions : + + + − − + − − wanted transition : − − (sharper and more stable) with magnetic c(2x2) contrast
p(1×1) p(1×1)
p(1×1) c(2×2)
p(1×1) p(1×1)
1. ML (afm) 1. ML (afm) 2. ML (fm) 2. ML (fm)
c(2×2)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Atomic Contrast on NiO(001)
NiO:
antiferromagnetic bulk insulator due to super-exchange between Ni atoms via O bridges
antiferromagnetic ordered Ni rows on (001) surface
*Ciraci, Baratoff, Batra, PRB 41 2763 (1990) **Teobaldi et al., PRL 106, 216102 (2011)
AFM on NiO(001)
chemical contrast * ⇒ maxima = oxygen
electrostatic contrast ** ⇒ maxima = oxygen
1 nm c(1×1)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Magnetic Contrast on NiO(001)
NiO:
antiferromagnetic bulk insulator due to super-exchange between Ni atoms via O bridges
antiferromagnetic ordered Ni rows on (001) surface
MExFM on NiO(001)
magnetic contrast on minima = Ni-sites * in **: contrast on maxima!
1 nm c(2×1)
*U. Kaiser et. al., Nature 446, 522 (2007). ** H. Hosoi et al., Nanotech. 15, 506 (2004).
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Raw Data Analysis and Distance Dependence left : chemical contrast only maxima = oxygen (cation) minima = nickel (anion)
4 peaks in Fourier image represent structural surface unit cell
right: recorded closer to surface additional row-wise contrast on nickel atoms
2 additional peaks in Fourier image represent magnetic surface unit cell
H. Hosoi, K. Sueoka, and K. Mukasa in Nanotechnology 15, 506 (2004): modulation on maxima (O-sites!) in unit cell averaged data, but no peaks in Fourier image shown!
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Artefact or Signal? Scan Rotation
additional pair of peaks in FT behaves like signal peaks
→ we can exclude an in phase oscillatory noise source
dissipation
topography
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Magnetic Double Tip: Contrast Transfer
magnetic contrast found on Ni- and O-atoms
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Growth of Fe on W(001)
layer-by-layer growth: ML Fe wetting layer
DL step flow growth
DL island
ML : antiferromagnetic with out-of-plane anisotropy DL : ferromagnetic with in-plane anisotropy A. Kubetzka et al., PRL 94, 087204 (2005) K. v. Bergmann et al., PRB 70, 174455 (2004)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
MExFM on Fe Monolayer on W(001) chemical contrast magnetic contrast
10 p
m
0.25 nm [100]
10 p
m
0.25 nm [100]
Fe/W(001): Fe thin film on high Z substrate ⇓ hybridization and strong spin-orbit coupling
R. Schmidt et al., Nano Lett. 9, 200 (2009)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Magnetic Exchange Force Spectroscopy
(MExFS) R. Schmidt, C. Lazo, U. Kaiser, A. Schwarz, S. Heinze, and R. Wiesendanger Phys. Rev. Lett. 106, 257202 (2011).
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
3D Magnetic Exchange Force Spectroscopy
3D data set: topography + Δf (z) with atomic resolution
x
z
y
c(2×2) magnetic contrast and distance dependence of the tip-surface interaction
∆f is color coded
3D-FFS: ∆f(x,y,z) ⇒ E (x,y,z), F (x,y,z) Hölscher et al., APL 81, 4428 (2002)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Distance Dependence of the Magnetic Exchange Interaction
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Distance Dependence of the Magnetic Exchange Interaction
magnetic exchange interaction is short-ranged, strongly distance dependent and can be large (about 100 meV)
DFT ⇒ ap-configuration (↑↓) preferred (maxima in topography)
calculated from exp. Δf(z) data
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Spin Dependent Adhesion Hysteresis
E. Y. Vedmedenko, Q. Zhu, U. Kaiser, A. Schwarz, and R. Wiesendanger, Phys. Rev. 85, 174410 (2012).
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Spin-Dependent Dissipation: Spectroscopy
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Magnetization Switching Induced by
Magnetic Exchange Interaction
R. Schmidt, A. Schwarz, and R. Wiesendanger, Phys. Rev. B 86, 174402 (2012).
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Summary and Outlook: MExFM • sensitive to short range magnetic exchange interactions • separation from chemical force
• antiferromagnetic surfaces • non-collinear spin structures (has not been done yet) • field-dependent experiments (has not been done yet)
• spin-dependent dissipation • spin-dependent adhesion hysteresis • spin-excitations (has not been done yet)
• magnetic exchange force spectroscopy (MExFS) • magnetic switching utilizing the magnetic exchange interaction • MExFM on single atoms and molecules (has not been done yet)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Publications on MExFM Vacuum tunneling of spin-polarized electrons detected by scanning tunnelling microscopy R. Wiesendanger, et al., J. Vac. Sci. Technol. B 9, 519 (1990). first discussion on the feasibility of MExFM
Investigations on the topographical asymmetry of non-contact atomic force microscopy images of NiO(001) surface observed with a ferromagnetic tip. Hosoi, H., Sueoka, K. & Mukasa, K. Nanotechnology 15, 506–509 (2004). first claim of a successful MExFM experiment (see also 1st NCAFM book!), but not generally accepted, because of a dubious data evaluation
Magnetic exchange force microscopy with atomic resolution U. Kaiser, A. Schwarz, and R. Wiesendanger, Nature 446, 522 (2007). first MExFM experiment performed on the afm bulk insulator NiO(001)
Probing the Magnetic Exchange Forces of Iron on the Atomic Scale R. Schmidt, C. Lazo, H. Hölscher, U. H. Pi, V. Caciuc, A. Schwarz, R. Wiesendanger, and S. Heinze, Nano Lett. 9,200 (2009). MExFM experiment on afm Fe monolayer on W(001): much better SNR; itinerant metallic system
Quantitative Measurement of the Magnetic Exchange Interaction across a Vacuum Gap R. Schmidt, C. Lazo, U. Kaiser, A. Schwarz, S. Heinze, and R. Wiesendanger, Phys. Rev. Lett. 106, 257202 (2011). first magnetic exchange force spectroscopy data (MExFS)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Publications on MExFM Evaluating local properties of magnetic tips utilizing an antiferromagnetic surface U. Kaiser, A. Schwarz, and R. Wiesendanger, Phys. Rev. 78, 104418 (2008) magnetic double tips in MExFM data
Atomic-scale magnetic dissipation from spin-dependent adhesion hysteresis E. Y. Vedmedenko, Q. Zhu, U. Kaiser, A. Schwarz, and R. Wiesendanger, Phys. Rev. 85, 174410 (2012). first data on spin dependent dissipation
Magnetization switching utilizing the magnetic exchange interaction R. Schmidt, A. Schwarz, and R. Wiesendanger, Phys. Rev. 86, 174402 (2012). utilizing magnetic exchange interaction (instead of external magnetic field) for magnetic switching
Spin Resolution on NiO(100) by Force Microscopy utilizing Bulk Ferromagnetic Tips F. Pielmeier and F. J. Giessibl, Phys. Rev. Lett. 110, 266101 (2013). second true MExFM paper on NiO; first MExFM paper not from Hamburg Theory:
Foster & Shluger (NiO, very simple tip): Surf. Sci. 490, 211 (2001). Momida & Oguchi (NiO, one atom Fe tip): Surf. Sci. 590, 42 (2005). Lazo & Heinze (Fe/W; realistic multi-atom tips with relaxation): Phys. Rev B 84, 144428 (2011).
2nd NCAFM Book: chapter on experimental data and a separate chapter on theory
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Carbon Monoxide and Metallic Tips Contrast Formation and Role of
Electrostatic Interactions
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
CO on Cu(111), NiO(001) and Mn/W(001)
CO on Cu(111) CO on Mn/W(001) CO on NiO(001) x in nm
closer by 0.2 nm
A. Schwarz et al., Appl. Phys. Lett. 105, 011606 (2014)
10 nm
Co on Mn/W
constant ∆f overview image: CO on Cu(111) imaging with metal coated Si tips: f0 ≈ 190 kHz, cz ≈ 150 N/m, A ≈ 1 nm
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Point Dipole Model for Metallic Tips
• 3 layer pyramidal tip: 5 D
• electrostatic potential can be represented by 3 D point dipole at foremost tip atom
Smoluchowski effect ⇒ tip apex exhibits electric dipole moment with its positive pole pointing towards surface: Teobaldi et al., PRL 106, 216102 (2011).
D. Gao et al., ACS Nano 8, 5339 (2014).
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Electric Dipole Moment of Carbon Monoxide
• gas phase: dative bond overcompensates electronegativity effect
⇒ small permanent dipole (0.12 D)
•CO adsorbs upright via C on top, bridge and hollow sites
⇒ charge redistribution •CO donates electrons from 5σ state into metallic d-state
•metal d-state back donates into 2π* antibonding state
⇒ dipole remains, but can possess different orientation and magnitude
G. Blyholder, J. Phys. Chem. 68, 2772 (1964).
CO on Cu(111): 0.2 D, same orientation B. N. J. Perrsson & M. Persson, Solid State Comm. 36, 175 (1989).
CO on NiO(001): 0.4 D, same orientation D. Gao et al., ACS Nano 8, 5339 (2014).
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Simulation: Constant Height Mode
Vdipole
Vsr-vdW
constant height mode
h = constant r2 = x2 + h2
tan(θ ) = x/h
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Irregular Contrast Patterns
2 nm 2 nm
Cr-tip; CO/Cu(111): closer by 0.2 nm
Cr-tip on CO/NiO(001)
experimental AFM image
vAFM simulation (two point dipole tip)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
Electrostatic Double Tip ⇔ Subatomic Features
2 nm 2 nm
CO/Cu(111) with Cr tip: closer by 0.2 nm
J. Welker & F. Giessibl, Science 336, 444 (2012): CO/Cu(111) with W-tip
electrostatic dipole double tip
subatomic resolution stemming from electronic fine structure of W-tip apex atom, but:
• poking of W tip into Cu substrate ⇒ Cu tip • a single atom tip exhibits a spherical charge density in
the vacuum region • tip induced translation prevent too small tip-sample
separartions ⇒ non-spherical electronic fine structure cannot be easily detected
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
MFM: Marcus Liebmann Ung Hwan Pi Uwe Kaiser MExFM: Uwe Kaiser Rene Schmidt Ung Hwan Pi Cesar Lazo (Stefan Heinze, CAU) CO: Josef Grenz Arne Köhler David Gao (Alex Shluger, UCL)
Fachbereich Physik
Institut für Angewandte Physik
Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]
THE END