Spin and Orbital Magnetism of Atoms on MgO

Spin and Orbital Magnetism of Atoms on MgO
Susanne Baumann, William Paul, Ileana G. Rau, Christopher P. Lutz, Andreas J. Heinrich IBM Almaden, San Jose, USA University of Basel, Switzerland Want to motivate the use of L Motivate to think beyond a simple spin Hamiltonian And I’m gonna do maybe a risky thing: this is a more theoretical talk where I will introduce a simple model to use based on DFT calculations that can be a helpful tool in STM work

? ? Data Storage S N 1956 today time magnet size (= bit size)
Data Storage e.g. in Hard drives is S N magnet size (= bit size)

Outline Introduction Magnetic Atoms on thin MgO Summary Magnets
Materials and Methods Probing the Spin States with STM XMCD Measurements Modelling the Magnetic States with Spin and Orbital Moment Summary 75nm x 75nm V = 100mV, I = 10pA

S N S N Magnets magnetic moment µ – strength of a magnet
magnetic anisotropy – preferred axis energy N S S N Properties such as magnetic moment and anisotropy are important when single domain magnets Anisotropy can be e.g. due to shape Magnetic anisotropy energy determines the thermal stability Long relaxation time (if speeking of small magnets) If we talk about such small magnets the relaxation doesn’t always occur over the barrier but it there can be quantum effects coming into play e.g. quantum tunneling of magnetization The quantum effects (tunneling) could significantly destabilize the states with opposite magnetic moment

What does magnetism depend on?
L on the atomic scale: magnetic moment: µ = µS + µL S magnetic anisotropy: - anisotropy in L: due to ligands d-orbitals and - spin-orbit coupling: locks S to L SOC lock the direction of L and S to be in the same direction

free atom has no preferred axis → no anisotropy magnetic moment µ can point in every spatial direction in terms of d-levels: → all levels are degenerate d-orbitals free atom degenerate d-orbitals ‹µZ› = 0

free atom has no preferred axis → no anisotropy magnetic moment µ can point in every spatial direction in terms of d-levels: → all levels are degenerate d-orbitals mL = +2 +1 -1 -2 Energy levels are filled according to Hunds rules: Maximze spin (Coulomb) Maximze L free atom d-orbitals of a free Co atom L = 3 S = 3/2 ‹µZ› = 0

in a molecule or on top of a surface ligands influence the energy levels d-orbitals on top of a surface or in a molecule d-orbitals of a free Co atom L = 3 S = 3/2

Quenching of the orbital moment
in a molecule or on top of a surface ligands influence the energy levels d-orbitals non-degenerate quenching of the orbital moment, µ consists of mostly spin d-orbitals in a solid or molecule 〈LZ 〉= 0 〈SZ 〉= 3/2 L = 3 S = 3/2 d-orbitals of a free Co atom Point out transition from 2 fold (as in Cu2N our prev. substrate) to MgO with 4fold symmetry on top of a surface or in a molecule µ 𝐿 𝑧 ≈ 0

Degenerate d-orbitals
degenerate d-orbitals (e.g. dxz, dyz) + orbital moment L can remain L = 3 S = 3/2 d-orbitals of a free Co atom Point out transition from 2 fold (as in Cu2N our prev. substrate) to MgO with 4fold symmetry on top of a surface or in a molecule with high symmetry µ 𝐿 𝑧 > 0 some d-orbitals degenerate 〈LZ 〉> 0 〈SZ 〉= 3/2

on top of a surface or in a molecule
Magnetic properties ligands give the system a preferred axis → anisotropy ligands influence the size the magnetic moment µ by influencing L Some configurations are preferred over others: this is the preferred axis, or the anisotropy If ligands manage to keep some degeneracy one can preserve an orbital moment on top of a surface or in a molecule with high symmetry

Co/Fe Atoms on MgO / Ag(001)
Co/Fe on top of O 50nm x 50nm V = 3V, I = 10pA Mg O Ag Co/Fe Growth at 10^-6 torr oxygen atomosphere,

Co/Fe Atoms on MgO / Ag(001)
Co/Fe on top of O four-fold symmetry (4 Mg atoms) Mg O Ag Co

How we Measure Magnetic Atoms on MgO
scanning tunneling microscope (STM) x-ray magnetic circular dichroism (XMCD) In our case we use 2 techniques: STM and XMCD on single atoms resolves energy levels lifetime measurement total magnetic moment µ on ensemble of atoms ▪ element specific ▪ measures spin (µS) and orbital (µL) ▪ moments independently all measurements at K, 0-7 T, in UHV

How we Measure Magnetic Atoms on MgO
scanning tunneling microscope (STM) x-ray magnetic circular dichroism (XMCD) In our case we use 2 techniques: STM and XMCD density functional theory (DFT) multiplet simulations

Spectroscopy on Atoms with STM
lock-in V DC+AC STM tip magnetic atom insulating layer substrate tip substrate 18

dI/dV [pA/mV] Sample Voltage [mV] dI/dV tip substrate 19

IETS (inelastic electron tunneling spectroscopy): conductance steps at different excitation energies spin excitations magnetic atom dI/dV V0 -V0 E V0 eV0 E0 dI/dV [pA/mV] tip substrate Sample Voltage [mV] 20

IETS (inelastic electron tunneling spectroscopy): conductance steps at different excitation energies spin excitations dI/dV [pA/mV] Sample Voltage [mV] dI/dV V0 -V0 V0 10nm x 10nm V = 0.1V, I = 10pA Co 21

Spectroscopy on Co on MgO
IETS (inelastic electron tunneling spectroscopy): conductance steps at different excitation energies spin excitations V0 = ± 57.5mV (0T) dI/dV 14 12 10 8 V0 dI/dV [pA/mV] Bare MgO spectrum shows some wiggles too 10nm x 10nm V = 0.1V, I = 10pA -100 -50 50 100 sample voltage [mV] Co Co atom on MgO bare MgO Rau, I.G.*, Baumann, S.*, et al. Science 344, (2014) 22

Spectroscopy on Fe on MgO
smaller excitation energy: V0 = ±14.0mV -20 -10 10 20 19 21 22 23 dI/dV [pA/mV] Sample Voltage [mV] Fe on MgO dI/dV V0 10nm x 10nm V = 0.1V, I = 10pA Co Fe B = 0T Baumann, S., et al. arXiv: , (2015) 23

Spectroscopy on Fe on MgO
smaller excitation energy: V0 = ±14.0mV however, larger than on other surfaces -20 -10 10 20 19 21 22 23 dI/dV [pA/mV] Sample Voltage [mV] Fe on MgO dI/dV Hirjibehedin, C.F. et al. Science 317, (2007). V0 Fe on Cu2N Fe V0 = ± 0.2, 3.8 and 5.7mV (0T) B = 0T Baumann, S., et al. arXiv: , (2015) 24

X-ray Magnetic Circular Dichroism (XMCD)
770 780 790 photon energy [eV] absorption [a.u.] X-ray absorption and XMCD spectra circular polarized x-rays I sample photo-emitted electrons

X-ray absorption and XMCD spectra
X-ray Magnetic Circular Dichroism (XMCD) X-ray absorption and XMCD spectra energy EF m+ valence band m+ m- 3d absorption [a.u.] x-rays m+ m- - difference core levels 770 780 790 2p photon energy [eV] 〈𝜇〉 ≠ 0

X-ray absorption and XMCD spectra
X-ray Magnetic Circular Dichroism (XMCD) Fe 770 780 790 photon energy [eV] absorption [a.u.] m+ m- - difference X-ray absorption and XMCD spectra XMCD [a.u.] photon energy [eV] 770 780 790 800 1.0 0.5 0.0 -0.5 -1.0 T = 3.5K Co

Gambardella, P. et al. PRL, 88 (2002)
X-ray Magnetic Circular Dichroism (XMCD) Fe single atoms XMCD [a.u.] photon energy [eV] 770 780 790 800 1.0 0.5 0.0 -0.5 -1.0 Co on Potassium Co Gambardella, P. et al. PRL, 88 (2002) Co on K

Fe single atoms large orbital moment energy core levels XMCD [a.u.] photon energy [eV] 770 780 790 800 1.0 0.5 0.0 -0.5 -1.0 half filled orbitals valence band - Point out how difficult to measure this - Extreme case of L=3 meaning a half filled band at Ef Co

Fe single atoms large orbital moment normal large anisotropy grazing XMCD [a.u.] photon energy [eV] 770 780 790 800 1.0 0.5 0.0 -0.5 -1.0 multiplet calculation simulation also gives information about the ground state of the magnetic atom Point out how difficult to measure this Co

multiplet calculation Fe

Calculations L S influence of surrounding atoms – ligand filed
spin-orbit coupling starting point: free atom ground state Mg O Co/Fe L S In this model we will study the influence of ligand field and SOC Starting from the free-atom states – 25 degenerate states for Fe Co atom d7 Fe atom d6 L = 2, S = 2 L = 3, S = 3/2

Calculations density functional theory (DFT) calculations - determine atom positions point charge model to calculate the ligand field parameters Fe Co Almost same height above the oxygen Oxygen more pulled up for Fe than for Co spin-density shows more four-fold influence for Fe than for Co

Stevens, K.W.., Proc. Phys. Soc. A, (1952)
Calculations density functional theory (DFT) calculations - determine atom positions point charge model to calculate the ligand field parameters Stevens operator equivalents to calculate the ligand field Fe Co Almost same height above the oxygen Oxygen more pulled up for Fe than for Co spin-density shows more four-fold influence for Fe than for Co 𝑶 𝟐 𝟎 = 𝟑 𝑳 𝒛 𝟐 −𝑳(𝑳+𝟏) 𝑶 𝟒 𝟎 = 𝟑𝟓 𝑳 𝒛 𝟒 − 𝟑𝟎𝑳 𝑳+𝟏 −𝟐𝟓 𝑳 𝒛 𝟐 +𝟑 𝑳 𝟐 𝑳+𝟏 𝟐 −𝟔𝑳(𝑳+𝟏) 𝑶 𝟒 𝟒 = 𝟏 𝟐 ( 𝑳 + 𝟒 + 𝑳 − 𝟒 ) Stevens, K.W.., Proc. Phys. Soc. A, (1952)

Calculations – Ligand Field in Detail
axial distortion due to O and Mg atoms 25 degenerate states Fe atom d6 L = 2, S = 2 Fe |𝑴 𝑳 , 𝑴 𝑺 LZ = ±2

Stevens operator equivalents axial distortion due to O and Mg atoms ML = ±2 states lowest in energy 𝑯 𝒂𝒙𝒊𝒂𝒍 = 𝑩 𝟐 𝟎 𝑶 𝟐 𝟎 + 𝑩 𝟒 𝟎 𝑶 𝟒 𝟎 |𝟎, 𝑴 𝑺 |±𝟏, 𝑴 𝑺 Fe LZ = ±2 𝑩 𝟐 𝟎 =−𝟏𝟓𝟎𝒎𝑽 𝑩 𝟒 𝟎 =−𝟏.𝟓𝒎𝑽 |±𝟐, 𝑴 𝑺 10 degenerate states

Stevens operator equivalents cubic distortion due to 4 Mg atoms splits/mixes the ML = ±2 states lowest energy level non-degenerate in ML 𝑯 𝒄𝒖𝒃𝒊𝒄 = 𝑩 𝟒 𝟒 𝑶 𝟒 𝟒 Fe LZ = ±2 |+𝟐, 𝑴 𝑺 + |−𝟐, 𝑴 𝑺 𝑩 𝟐 𝟎 =−𝟏𝟓𝟎𝒎𝑽 𝑩 𝟒 𝟎 =−𝟏.𝟓𝒎𝑽 𝑩 𝟒 𝟒 =𝟏𝒎𝑽 |+𝟐, 𝑴 𝑺 − |−𝟐, 𝑴 𝑺

28 degenerate states Co atom d7 L = 3, S = 3/2 Co

𝑯 𝑳𝑭 = 𝑩 𝟐 𝟎 𝑶 𝟐 𝟎 + 𝑩 𝟒 𝟎 𝑶 𝟒 𝟎 + 𝑩 𝟒 𝟒 𝑶 𝟒 𝟒 ML = ±3 states lowest in energy not split due to cubic Hamiltonian lowest energy level degenerate Co |±𝟑, 𝑴 𝑺 LZ = ±2 𝑩 𝟐 𝟎 =−𝟐𝟔𝒎𝑽 𝑩 𝟒 𝟎 =𝟎.𝟑𝒎𝑽 𝑩 𝟒 𝟒 =−𝟎.𝟐𝒎𝑽

Fe Co 𝑩 𝟐 𝟎 =−𝟏𝟓𝟎𝒎𝑽 𝑩 𝟐 𝟎 =−𝟏𝟓𝟎𝒎𝑽 𝑩 𝟒 𝟎 =−𝟏.𝟓𝒎𝑽 𝑩 𝟒 𝟒 =𝟏𝒎𝑽 𝑩 𝟐 𝟎 =−𝟐𝟔𝒎𝑽 𝑩 𝟒 𝟎 =𝟎.𝟑𝒎𝑽 𝑩 𝟒 𝟒 =−𝟎.𝟐𝒎𝑽 lowest energy non-degenerate = quenched orbital moment lowest energy degenerate

Fe Co λ = -12.4 λ = -21.3 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =𝟎 |±𝟑, 𝑴 𝑺 〈 𝑳 𝒛 =±𝟑 |+𝟐, 𝑴 𝑺 + |−𝟐, 𝑴 𝑺 |+𝟐, 𝑴 𝑺 − |−𝟐, 𝑴 𝑺 〈 𝑳 𝒛 =±𝟐 2x5 degenerate states 8 degenerate states lowest energy non-degenerate = quenched orbital moment lowest energy degenerate

Fe Co λ = -12.4 very sensitive to four-fold symmetry not influenced by the four-fold symmetry λ = -21.3 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =𝟎 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =±𝟐 lowest energy non-degenerate = quenched orbital moment lowest energy degenerate

Calculations – Spin-Orbit Coupling
Fe Co λ = -12.4 λ = -21.3 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =𝟎 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =±𝟐 ~ doublet doublet 𝑯 𝑺𝑶𝑪 =𝝀 𝑳 𝑺 states split roughly with λ2 states split linear with λ

Fe Co λ = -12.4 λ = -21.3 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =𝟎 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =±𝟐 Spin gets polarized due to the SOC 〈 𝑳 𝒛 =±𝟑, 𝑺 𝒛 = ±𝟏.𝟓 〈 𝑳 𝒛 =±𝟏.𝟗𝟓, 𝑺 𝒛 = ±𝟐 𝑯 𝑺𝑶𝑪 =𝝀 𝑳 𝑺 states split roughly with λ2 states split linear with λ

Fe Co λ = -12.4 λ = -21.3 ~ maximal possible splitting 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =𝟎 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =±𝟐 55 meV 23 meV 𝑯 𝑺𝑶𝑪 =𝝀 𝑳 𝑺 states split roughly with λ2 states split linear with λ

Fe Co V02 V13 dI/dV [a.u.] sample voltage [mV] 52 54 56 60 62 58 λ = -12.4 λ = -21.3 14 meV 58 meV ~ maximal possible splitting 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =𝟎 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =±𝟐 55 meV 23 meV Keep in mind this is a calculation that has no fitting parameter, it only takes the values from the DFT calculations and still the result is fairly close to the experimental result. And the order of states is qualitatively reproduced as compared to the multiplet calculations as a fit to the XMCD results 𝑯 𝑺𝑶𝑪 =𝝀 𝑳 𝑺 states split roughly with λ2 states split linear with λ

Calculations – Zeeman Fe Co 𝑯 𝒁 = 𝝁 𝑩 𝑳 +𝟐 𝑺 𝑩 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =𝟎
λ = -12.4 λ = -21.3 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =𝟎 〈 𝑳 𝒛 =±𝟑 〈 𝑳 𝒛 =±𝟐 𝑯 𝒁 = 𝝁 𝑩 𝑳 +𝟐 𝑺 𝑩

Calculations Fe Co energy in a magnetic field |1〉 |2〉 |0〉 |3〉 𝜇 𝑧 |4〉 energy in a magnetic field |1〉 |2〉 |0〉 |3〉 𝜇 𝒛 〈 𝑳 𝒛 =±𝟏.𝟐 𝑺 𝒛 = ±𝟐 〈 𝑳 𝒛 =±𝟐.𝟗 𝑺 𝒛 = ±𝟏.𝟒 - Matches well with STM and XMCD results - good insight into understanding magnetism on the atomic scale - easy to predict what happens on other surfaces (as long as it preserves the atoms' configurations) =>〈 𝝁 𝒛 =±𝟓.𝟐 𝝁 𝑩 =>〈 𝝁 𝒛 =±𝟓.𝟓 𝝁 𝑩 𝑯= 𝑩 𝟐 𝟎 𝑶 𝟐 𝟎 + 𝑩 𝟒 𝟎 𝑶 𝟒 𝟎 + 𝑩 𝟒 𝟒 𝑶 𝟒 𝟒 + 𝝀 𝑳 𝑺 + 𝝁 𝑩 𝑳 +𝟐 𝑺 𝑩

Summary model of magnetic states based on DFT determined atom position
using point charge model and Stevens operator equivalents Almost same height above the oxygen Oxygen more pulled up for Fe than for Co spin-density shows more four-fold influence for Fe than for Co 𝑶 𝟐 𝟎 = 𝟑 𝑳 𝒛 𝟐 −𝑳(𝑳+𝟏) 𝑶 𝟒 𝟎 = 𝟑𝟓 𝑳 𝒛 𝟒 − 𝟑𝟎𝑳 𝑳+𝟏 −𝟐𝟓 𝑳 𝒛 𝟐 +𝟑 𝑳 𝟐 𝑳+𝟏 𝟐 −𝟔𝑳(𝑳+𝟏) 𝑶 𝟒 𝟒 = 𝟏 𝟐 ( 𝑳 + 𝟒 + 𝑳 − 𝟒 )

scanning tunneling microscopy (STM) x-ray absorption (XMCD)
multiplet simulations Andreas Heinrich (IBM) William Paul Ileana Rau Christopher Lutz Roger Macfarlane Bruce Melior Harald Brune (EPFL) Stefano Rusponi Fabio Donati Luca Graganiello Giulia Pacchioni Marina Pievetta Pietro Gambardella (ETH) Sebastian Stepanow Jan Dreiser (PSI) Cinthia Piamonteze Frithjof Nolting In our case we use 2 techniques: STM and XMCD density functional theory (DFT) Shruba Gangopadhay (IBM) Oliver Albertini Barbara Jones

IBM Almaden, San Jose, USA University of Basel, Switzerland

Spin and Orbital Magnetism of Atoms on MgO

Similar presentations

Presentation on theme: "Spin and Orbital Magnetism of Atoms on MgO"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Spin and Orbital Magnetism of Atoms on MgO

Similar presentations

Presentation on theme: "Spin and Orbital Magnetism of Atoms on MgO"— Presentation transcript:

Similar presentations

About project

Feedback