Atomic-scale Engeered Spins at a Surface Chiung-Yuan Lin IBM Almaden Research Center

Nanomagnetism and Information Technology Magnetism is at the heart of data storage. Many novel computations schemes are based on manipulation of magnetic properties. Courtesy of Hitachi J.R. Petta et al. Science 309, 2180 (2005) A. Imre et al. Science 311, 205 (2006)

Nanomagnets Fabricated nanomagnets can recreate model spin systems such as spin ice. A small number of atomic spins can be coupled in metal clusters or molecular magnetic structures. R.F. Wang et al., Nature 439, 303 (2006) Fe8, courtesy ESF. M.B. Knickelbein Phys. Rev. B 70, 14424 (2004)

Assembly and Measurement of Nanomagnets Top-down Bottom-up Atomic-scale control O P Manipulate structures

STM Studies of Atomic-Scale Spin-Coupling Manipulation on thin insulators: build individual nanomagnets with an STM Spin Excitation Spectroscopy: collective spin excitations of individual nanostructures 10Mn chain Mn atom Magnetic Field Energy |5/2,+5/2> |ST,m> |5/2,+3/2> |5/2,+1/2> |5/2,-1/2> |5/2,-3/2> |5/2,-5/2> |0,0> Magnetic Field Energy |1,-1> |1,0> |1,+1> |ST,m> Science 312, 1021 (2006)

Keep it Simple: Free Mn Atom 3d Mn: S = 5/2, L = 0, J = 5/2 Half filled d-shell Weak spin-orbit interactions

Scanning Tunneling Spectroscopy: LDOS Ef eV tip sample dI/dV V Features in the local DOS are reflected in dI/dV.

Magnetic Atoms on Surfaces Atom’s spin is screened by conduction electrons (Kondo effect) A thin insulating layer may isolate the atomic spin Metal surface Thin insulating layer

Inelastic Electron Tunneling Spectroscopy |eV| < D Elastic Channel Open Inelastic Channel Closed Ef eV sample tip X D |eV| > D Elastic Channel Open Inelastic Channel Open Ef eV sample tip D Non-magnetic tip Thin insulator Magnetic atom dI/dV kBT < D σe+σie σe Non-magnetic sample eV -D D

Methods of Electronic-structure Calculation Plane wave Atomic spheres Atomic partial wave Atomic partial wave Interstitial region Full-potential Linearized Augmented Plane Wave basis Periodic-slab geometry (5-layer Cu + 8-layer vacuum) Density Functional Theory Generalized Gradiant Approximation (GGA) PBE96: Perdew et al., PRL 77, 3865 (1996) Structure Optimization

Methods of Electronic-structure Calculation vacuum vacuum vacuum FLAPW basis Periodic-slab geometry (5-layer Cu + 8-layer vacuum) Density Functional Theory Generalized Gradiant Approximation (GGA) PBE96: Perdew et al., PRL 77, 3865 (1996) Structure Optimization

Methods of Electronic-structure Calculation FLAPW basis Periodic-slab geometry (5-layer Cu + 8-layer vacuum) Density Functional Theory Generalized Gradiant Approximation (GGA) PBE96: Perdew et al., PRL 77, 3865 (1996) Structure Optimization

Thin Insulator: CuN Islands on Cu(100) 1nm N Cu a0=Ö2d0 d0 CuN Mn Mn Mn Mn Mn Mn Cu(100) CuN monolayer Atomic resolution on CuN Mn atoms bind to Cu and N sites Cu(100)

DFT Calculation of Electron Density in CuN 1.80Å 0.25Å Cu+0.5 Cu+0.5 Cu+0.5 Cu Cu N atoms are approximately coplanar with Cu atoms on CuN surface.

Manipulation of Mn on Cu(100) / CuN Move tip in Apply 2.0V Pull tip back Pick up Atom

Manipulation of Mn on Cu(100) / CuN Move tip in Apply -0.5V Pull tip back Pick up Atom Drop off

Spectroscopy of Mn Dimers Cu N Mn Large step at ~6mV splits into three distinct steps at high fields

Coupled Spins 5 4 … 1 S=5/2 Ä S=5/2  ST = S=5/2 Ä S=5/2  ST = For ST=0 (singlet) the first excited state is ST=1 (triplet) Three excitations around constant energy shift |0,0> B E |1,-1> |1,0> |1,+1> |ST,m>

Chains of Mn Atoms 2 3 4 5 6 7 8 9 1nm 1nm 1Mn 10Mn CuN Cu(100) N Cu IBM Almaden STM Lab has built chains of up to 10 Mn atoms on Cu binding sites Mn Mn Mn

Spectroscopy of Mn Chains 2 3 4 5 6 7 8 9 1nm 10 Spectra change dramatically with each additional Mn atom.

Heisenberg Model of Spin Coupling J S Phenomenological Exchange Coupling J = Coupling strength Si = spin of ith atom Assumptions All spins are the same Nearest-neighbor coupling All J are the same J > 0 (antiferromagnetic coupling)

Heisenberg Dimer Spectrum SG=0 and SE=1 Atomic spin affects numbers of levels but not spacing First excited state at J J S

Determination of Spin Coupling Strength From the dimer spectrum J=6.2meV Variations in J of ±5% for different dimers at various locations J=6.2meV

Determination of Atomic Spin Using J = 6.2meV, we find S=5/2 STM determines both J and S! S=3 S=5/2 S=2 J=6.2meV

Heisenberg Model for Longer Chains Use J = 6.2meV and S=5/2 Odd chains ground state spin = 5/2 excited state spin = 3/2 Even chains ground state spin = 0 excited state spin = 1

Unit Cells Used in Calculating Mn on CuN Single Mn, smallest unit cell Mn dimer, smallest unit cell Single Mn, larger unit cell N Cu Mn Mn 10.80Å 7.20Å 7.20Å

Electron Density with an Adsorbed Mn Atom Cu+0.5 Cu+0.5 Cu Cu Cu N atoms move farther out of surface Cu layer towards Mn atom. Cu atom being pushed into the surface. This “isolates” the free spin of Mn atom.

Mn Spin from DFT majority () minority () Free Mn atom 3d 5 S=5/2

A new kind of atomic-scale magnet Mn N Mn N N Cu Cu Cu Cu Cu Surface N atoms isolate and bridge Mn atoms. This is a “surface” assembled magnet.

Control of Spin Coupling Strength J=6.2meV J=2.7meV STM can switch J by a factor of 2 by selecting the binding site

GGA+U GGA+U (strong Coulomb repulsion on Mn 3d) Calculating U by constraint GGA Calculating U Lock d-orbital into the atomic sphere Do GGA for Mn d3 d2.5 and d3 d1.5 U =Δεd of the above two

Calculating Exchange Coupling H=J S1·S2 Cu N |±|S=5/2, Sz=±5/2 DFT total energies 2S2J= ++|H|++  +- |H| +- = E  E

Calculating Exchange Coupling (in meV) Mn on Cu site Mn on N site GGA (U=0) 18.5 -1.8 (ferromagnetic!) GGA + U(calculated) 6.50 ±0.05 2.5 GGA + U(calculated+1ev) 5.4 5.1 STM 6.2±0.3 2.7

Summary of theoretical work The nontrivial structure of the engineered spins requires DFT to determine. Calculated structure shows a new kind of molecular magnets. GGA+U produces correct S and very accurate J; very helpful for searching a system of desired S and J.

What’s Next Can we understand IETS processes? matrix elements, selection rules, transition strengths What is the origin of the exchange coupling? superexchange, delocalized electrons Are other interactions possible? vary distances, shapes, types of atoms Can we control anisotropy effects? Find a way to store and transfer spin information: bits and circuits based on atomic spins

Thanks to Barbara Jones Cyrus Hirjibehedin Chris Lutz Andreas Heinrich