Single Atom Magnets? 1. Magnetic Anisotropy 2. Magnetism of individual Co Adatoms 3. Single Atom Magnets? 4. Single Molecule Magnets at Surfaces
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1 Single Atom Magnets? 1. Magnetic Anisotropy 2. Magnetism of individual Co Adatoms 3. Single Atom Magnets? 4. Single Molecule Magnets at Surfaces
2 Basic properties of a permanent magnet Magnetization "the strength of the magnet" depends on the magnitude of the atomic magnetic moments. M H Magnetic Order "the essence of macroscopic magnetism" The individual atomic moments must be aligned to produce a net magnetization paramagnetic material M Magnetic Anisotropy "the stubborness of a magnet" is the tendency to maintain the magnet orientation along a fixed spatial direction. H ferromagnetic material
3 Magnetocrystalline anisotropy in the hardest 3d element Co hcp - easy axis: (0001) 1400 [0001] c [0001] Easy M [emu/cm (emu/cm 3 ] ) [1010] [1010] Hard H [Oe] H [Oe] K = 4.1 x 10 5 J/m 3 = 45 µev/atom S. Kaya, Sci. Rep. Tohoku Univ. 17, 639 (1928).
4 Magnetocrystalline anisotropy in bulk alloys K (ergs/cm 3 ) Ni NiO.Fe 2 O 3 Fe Cubic CoOFe 2 O 3 BaO.6Fe 2 O 3 Co MnAl CoPt FePt Fe 14 Nd 2 B YCo 5 SmCo 5 SmFe 11 Ti L/d= 1.1 L/d= 2.0 L/d=10.0 Hexagonal Tetragonal Other Shape (Fe) ,000 Ib/in 2 100,000 Ib/in 2 Stress ,000 Ib/in 2 K (mev/atom)
5 Pt(111) ML subsurface C Co/Pt(111) Single Adatoms ML 10 K Å Å 200 Å mean size atoms/cluster H. Brune, Surf. Sci. Rep. 31, 121 (1998).
6 X-ray Magnetic Dichroism (XMD) Combines chemical selectivity of X-ray Absorption Spectroscopy (XAS) with magnetic (dichroic) sensitivity Uniquely determines orbital m L and spin m S magnetic moments and their anisotropies K in element specific way orbit synchrotron storage ring variable energy, polarized X-rays photoemitted electrons L eft R ight 0 monochromator B I s
7 X-ray Magnetic Dichroism (XMD) Combines chemical selectivity of X-ray Absorption Spectroscopy (XAS) with magnetic (dichroic) sensitivity Uniquely determines orbital m L and spin m S magnetic moments and their anisotropies K in element specific way Absorption Spin down Spin up E F E (h ) 2p 3/2 2p 1/2 E (h )
8 X-ray Magnetic Dichroism (XMD) Combines chemical selectivity of X-ray Absorption Spectroscopy (XAS) with magnetic (dichroic) sensitivity Uniquely determines orbital m L and spin m S magnetic moments and their anisotropies K in element specific way L 3 : 2p 3/2 3d E Spin down Spin up L E F R E (h ) 2p 3/2 2p 1/2 E (h )
9 Sum Rules of XMCD 15 ML Co/Pt(997) m L = 4 3 h d A 3 + A 2 XAS 3&2 Intensity [a.u.] L 3 L 2 + M P - M P m S +7m T = h d A 3 4A 2 XAS 3&2 A m L m S +7m T = 2 3 A 3 + A 2 A 3 2A 2 A Photon energy [ev] with m T magnetic spin dipole moment
10 Co/Pt(111) Ensemble Measurements with XMCD M XMCD-intensity T =5.5K normal grazing (70 ) B (Tesla) fit: R ˆm ˆB+K( ˆm ê) ˆm ˆBe kt d m = m 0 R ˆm e ˆB+K( ˆm ê) 2 kt d m 0 saturation value of Co induced Pt moment ê, ˆm, and ˆB unit vectors of easy axis, magnetization, and field K uniaxial anisotropy 2 m L =1.1 ± 0.1 µ B,K =9.3 ± 1.6 mev
11 Origin Orbital Magnetism: K and m L (size) K (mev/atom) magnetic anisotropy energy orbital magnetic moment m L ( B /atom) n (atoms) 0.0 P. Gambardella et al. Science 300, 1130 (2003).
12 Magnetic Remanence in a Single Adatom? Co/Pt(111): Spin-relaxation time expected from K = 9.2 mev: T 1 = 1 s at 2 K! 0 E m 1 (T 1 ) -1 +1
13 Single Adatom Magnetization Curves taken by SP-STP di/dv (a.u.) m ( B ) T = 4.2 K fit T = 0.3 K fit fit: m z = cm with R 0 cos e E(,B)/kT d R, e E(,B)/kT d 0 E(,B)= m(b B t ) cos K cos 2 K =9.3meV m, B t, and c fit parameter B (T) B z m V t =0.3 V, I t =0.8 na, V mod = 20 mv F. Meier et al. Science 320, 82 (2008).
14 Co/g/ Pt(111), Ir(111), and Ru(0001) F. Donati, S. Rusponi et al.
15 Calculations Co/graphene Co 2 /benzene Adsorption-site 6-fold hollow H. Johll et al., PRB 79, (2009); O. V. Yasyev et al., PRB 82, (2010). Influence of e correlations 2.4 B 1.6 B 2.2 B 1.9 B E E2 E1 4s A1 U = 0 ev S = 1/2 Co 2 Bz E E2 E1 4s A1 U = 2 ev S = 1 MAE (SO) (mev) MAE (SO+OP) (mev) +51[+74] +334[+519] E E2 E1 4s A1 K =-8meV U = 4 ev S = 3/2 T. O. Wehling et al., PRB 81, (2010). R. Xiao et al., PRL 103, (2009); PRB 82, (2010). Co/graphene K = 5 40 mev
16 STM Spin-Excitation-Spectroscopy for Co/graphene di/dv (ns) Å T 4 T 8 T V t (mv) z = const. at V t = 15 mv & I t =0.25 na V mod,p-t-p =0.2mV, T=0.4 K 5 Å
17 Magnetic properties: Co-H 3 complex di/dv (ns) d 2 I/dV 2 (arbitrary units) T T 4 T 4 T 6 T T T T V t (mv) V t (mv) z = const. at V t = 20 mv & I t =0.1 na,v mod,p-t-p =0.2 mv,f mod = 611 Hz,T =0.4 K
18 Field-Splitting Spin and Anisotropy 9.5 m=-1 m=+1 Transition energy (mev) B=0T B=8T 8.1 mev 8.1 mev 9.2 mev 7.1 mev Magnetic field (T) Ĥ = gµ B B Ŝ + DŜ2 z Spin S = 1 m Z = 0 ground state m Z = ±1 Zeeman-split excited states Landé factor g =2.2 ± 0.4 e ective magnetic moment 2.2 ± 0.4 µ B magnetic anisotropy D = 8.1 ± 0.4 mev F. Donati et al. PRL 111, (2013).
19 XMCD (arb. units) XAS (arb. units) XAS (arb. units) Normal incidence (0 ) Gazing incidence (70 ) µ + + µ - (exp.) µ + + µ - (calc.) µ + - µ - (exp.) µ + - µ - (calc.) =0.01 ML,B =6.8 T,T=2.5 K µ + Co/g/Ru(0001) µ - µ Energy (ev) Energy (ev) µ - µ + + µ - µ + - µ - Energy (ev) e 2 e 1 a 1
20 Co/g/Ru(0001) Normal incidence (0 ) Grazing incidence (70 ) M /Msat (0 ) Magnetic Field (T) =0.01 ML,T =2.5 K
21 XMCD (arb. units) XAS (arb. units) XAS (arb. units) Normal incidence (0 ) µ + - µ - (exp.) µ + - µ - (calc.) =0.01 ML,B =6.8 T,T=2.5 K µ + Co/g/Ir(111) µ - µ + µ + + µ - (exp.) µ + + µ - (calc.) Gazing incidence (70 ) Energy (ev) Energy (ev) µ - µ + + µ - µ + - µ - Energy (ev) e 1 a 1 e 2
22 Co/g substrate dependence g/ru(0001) (23 23) z min = 2.1 Å K =8.4 ± 2.9 mev out-of-plane g/ir(111) (9.32 ± ± 0.3) z min = 3.4 Å weak in-plane g/pt(111) (4 4) K = z min = 3.3 Å 8.1 ± 0.4 mev in-plane For z min M. Batzill, Surf. Sci. Rep. 67, 83 (2012). F. Donati et al. PRL (2014).
23 Reaching the Magnetic Anisotropy Limit of a 3d Metal Atom Co/MgO(100) S. Rusponi, F. Donati, L. Gragnaniello, EPFL I. G. Rau, S. Baumann, C. P. Lutz, A. J. Heinrich, IBM experiment S. Gangopadhyay, O. R. Albertini, R. Macfarlane, B. A. Jones, IBM DFT J. Dreiser, C. Piamonteze, F. Nolting, EPFL-PSI Endstation XTreme P. Gambardella and S. Stepanow, ETHZ multiplet calculations
24 Bonding configuration DFT structure and valence charge density in atomic units Side view STM tip X-ray MgO Ag Co/1 ML MgO/Ag(100) T = 1.2 K, I = 10 pa, V = 50 mv 7.5 nm x 7.5 nm Top view free Co atom Co on MgO Orbital occupancy xz z 2 L z = 0 yz L z = 1 Co spin density x 2 -y 2 xy L z = 2 L = 3 S = 3/2 L z = 3 S z = 3/2
25 Highest reported STM Spin Excitation Energies di/dv (pa/mv) T = 0.6 K Co MgO V bias (mv) di/dv (a.u.) B = 0 T V 13 V 02 B = 6 T V bias (mv) V bias (mv) mv 0.9 mv state 3 state 2 V 13 V 02 state 1 B state B (T)
26 XMCD and Multiplet Calculations XAS (a.u.) d-shell occupancy 7.44 electrons 2 1 normal grazing Experiment Simulation Photon energy (ev) XMCD (a.u.) Experiment Simulation normal grazing Photon energy (ev) L z S z L z S z L z S z ±1.25 ± ±0.42 ± Energy (ev) ±3 ±1.25 ±0.42 ±1.28 ±2.86 ± ± ± ±0.93 ± SOC for Co = 22 mev = L = 66 mev axial cubic SOC Ds, (Dt/Ds=const) mev Dq mev 0-66 mev V 13 V 02 magnetic field 0-7 T
27 XMCD Magnetization Curve & STM Spin-Relaxation Time 3.0 K L z +2S z =6µB, T = 3.5 K T 1 = 232 ± 17 µs Magnetization (a.u.) K Magnetic field (T) N (electrons/ probe pulse) A t (ms) T =3.5 K, after sat. at T, at -6.8 T T = 0.6 K, V pump = 90 mv, V probe = 20 mv I. Rau et al. Science 344, 988 (2014).
28 Magnetocrystalline anisotropy in bulk alloys K (ergs/cm 3 ) Ni NiO.Fe 2 O 3 Fe Cubic CoOFe 2 O 3 BaO.6Fe 2 O 3 Co MnAl CoPt FePt Fe 14 Nd 2 B YCo 5 SmCo 5 SmFe 11 Ti L/d= 1.1 L/d= 2.0 L/d=10.0 Hexagonal Tetragonal Other Shape (Fe) Co/Pt Co/MgO ,000 Ib/in 2 100,000 Ib/in 2 Stress ,000 Ib/in 2 K (mev/atom)
29 Ho/Pt(111) F. Donati, S. Rusponi et al.
30 Magnetic bi-stability for Ho/Pt(111)? free atom E J J +1 +J 1 +J C 3v crystal field E Ψ 0 J 0 +J J z uniaxial anisotropy E a ±6 Ψ h.c.p. C 3v f.c.c. C 3v s ±6 Ψ J +1 +J 1 Ψ 7 Ψ +7 J +J Ψ 8 Ψ +8 J 0 +J J z J z T. Miyamachi et al., Nature 242, 503 (2013).
31 Magnetic bi-stability for Ho/Pt(111) - STM di/dv (arbitrary units) di/dv (arbitrary units) B = 0 T B = 0.05 T B = 0.10 T B = 0.14 T Time (s) T = 0.7 K T = 4.4 K Time (s) 5 nm T = 0.7 K, V t = 5 mv, I t = 50 na B =0T,V t = 5 mv, I t = 50 na T. Miyamachi et al., Nature 242, 503 (2013).
32 Magnetic bi-stability for Ho/Pt(111) - XMCD XAS XMCD XAS (arb. u.) 3 2 Experiment (0 ) 1 Experiment (55 ) 0-1 Calc. J z = ± 6 (0 ) -2 Calc. J z = ± 6 (55 ) -3-4 Calc. J z = ± 8 (0 ) -5 Calc. J z = ± 8 (55 ) Energy (ev) XMCD (arb. u.) 0-1 Experiment (0 ) Experiment (55 ) Calc. J z = ± 6 (0 ) Calc. J z = ± 6 (55 ) Calc. J z = ± 8 (0 ) Calc. J z = ± 8 (55 ) Energy (ev)
33 Magnetic bi-stability for Ho/Pt(111) - XMCD M(H) E(J z ) 1 Normal 40 XAS (arb. u.) Grazing J z = ± 6 J z = ± 8 Energy (mev) Field (T) J z J z = ± 4 and 6 mixing F. Donati et al., PRL 113, (2014).
34 Endofullerenes Collaboration with T. Greber and J. Westerström, U Zürich
35 (a) Dy n Sc 3 n N@C80 (n = 1, 2, 3) bulk N 3- (b) (a) j 31 j 23 m/m sat 0.0 tunneling m/m (c) Energy Energy (d) Magnetization/molecule (µ n ) U µ 0 H (T) (e) (b) Energy C U R 3+ TUNNELING, REMANENCE, AND FRUSTRATION IN... m/m sat (a) Deviation (%) j FIG. 2. (Color online) -2.0(a) Hysteresis µ 0 H (T) curves 1.0 for recorded using SQUID magnetometry at 2 K with a field The µ data of 1 are reproduced from Ref. [22]. (b) Hilbert space topology of the 2 n 0 H (T) µ 0 H (T) µ 0 H (T) pseudospin states (n, ± d) in 1 3 n = 2 R. Westerström single-tunneling et al. JACS events 134, 9840 of one (2012); magnetic n = moment 1, 2, 3 R. between Westerström two states et al. at PRB the89, same energy. (2014). Red dashed lines involve (b) due to exchange and dipolar coupling m/m sat µ 0 H (T) 21 m/m sat -0.5 PHYSICAL REVIEW FM 0.0 coupl RAPID COMMUNICATIONS TUNNELING, REMANENCE, AND FRUSTRATION IN... PHYSICAL REVIEW B 89, (R) (2014) (a) m/m sat m/m sat µ 0 H (T) µ 0 H (T) µ 0 H (T) m/m sat frustra7on
36 Dy 2 ScN@C80/Rh(111) Sc 3+ N 3- I + + I Dy M 5 Dy M 5 0 I x 6- C 80 Dy 3+ Intensity (arb. u) Intensity (arb. u) I z I x 45 [111] 60 L photon 70 I z Magnetic field Photon energy (ev) Photon energy (ev) T, 4.0 K 3d 9 4f 10 multiplets in N 3 RE 3+ 2 ligand field
37 XMCD Magnetization Curves = 60, 2 T/min, 4.0 K multilayer -0.5 T 1 = 120 s µ 0 H(T) sub-ml Endohedral unit is aligned: Dy 2 ScN plane parallel to surface -0.5 T 1 = 30 s µ 0 H(T) R. Westerström et al. PRL 114, (2015).
38 Phthalocyanine double-decker Pc 2 Tb C. Wäckerlin, J. Dreiser, S. Rusponi et al.
39 Pc 2 Tb bulk AC χ (T): T b = 40 K (1 khz, 3.5 G), other SMMs T b 7 K SQUID, T = 1.7 K powder sample of 2 % [Pc 2 Tb] - TBA + in 98 % [Pc 2 Y] - TBA + gure 8. Energy diagram of the substates of the ground multiplets DC χ (T) and 1 H NMR: J z = ±6 E = 440 cm - 1 to J z = ± 5 N. Ishikawa et al. JACS 125, 8694 (2003); N. Ishikawa et al. JPCB 108, (2004).
40 Pc 2 Tb/MgO/Ag(100) STM 4 K, XMCD 3 K at XTreme beamline at SLS
41 Pc 2 Tb/MgO/Ag(100) photon flux and intrinsic lifetime τ - 1 = τ i τ ph - 1 τ i = 14 ± 4 min saturate at 4 T record M(t) at 0.5 T Φ 0 = photons nm - 1 s - 1, T = 3 K C. Wäckerlin et al. subm. Nat. Mater. Sep 04
42 Candidates for Single Atom Magnets Integer J in a C 4v symmetry: - For doublets with even J z, the conjugated states have Δm = 4n - They can be connected through transverse O 44 terms - If the ground state doublet has even J z, quantum tunneling of the magnetization - For doublets with odd J z, the conjugated states have Δm = 4n They cannot be connected through transverse O 44 terms - First order spin excitations (Δm = 0, ±1) are also forbidden among conjugated states for all values of a perpendicular magnetic field - If the ground state doublet has odd J z, long spin lifetime is possible
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