Controlled complete suppression of single-atom inelastic spin and orbital cotunnelling
B. Bryant, R. Toskovic, A. Ferrón, J. L. Lado, A. Spinelli, J. Fernández-Rossier, A. F. Otte
CControlled) complete) suppression) of) single2atom) inelastic) spin) and)orbital)cotunnelling) !B.!Bryant ,!R.!Toskovic ,!A.!Ferrón ,!J.!L.!Lado ,!A.!Spinelli ,!J.!FernándezARossier ,!and!A.!F.!Otte !! Department* of* Quantum* Nanoscience,* Kavli* Institute* of* Nanoscience,* Delft* University* of* Technology,*Lorentzweg*1,*2628*CJ*Delft,*The*Netherlands** International* Iberian* Nanotechnology* Laboratory* (INL),* Avenida* Mestre* José* Veiga,* 4715
F310* Braga,*Portugal** Instituto* de* Modelado* e* Innovación* Tecnológica* (CONICETFUNNE),* Avenida* Libertad* 5400,* W3404AAS,*Corrientes,*Argentina** * *[email protected]* ! The$ inelastic$ portion$ of$ the$ tunnel$ current$ through$ an$ individual$ magnetic$ atom$ grants$ unique$access$to$read$out$and$change$the$atom’s$spin$state ,$but$it$also$provides$a$path$for$spontaneous$relaxation$and$decoherence .$Controlled$closure$of$the$inelastic$channel$would$allow$for$the$latter$to$be$switched$off$at$will,$paving$the$way$to$coherent$spin$manipulation$in$single$atoms.$Here$we$demonstrate$complete$closure$of$the$inelastic$channels$for$both$spin$and$orbital$transitions$due$to$a$ controlled$ geometric$ modification$ of$ the$ atom’s$ environment,$ using$ scanning$ tunnelling$microscopy$ (STM).$ The$ observed$ suppression$ of$ the$ excitation$ signal,$ which$ occurs$ for$ Co$ atoms$assembled$into$chain$on$a$Cu N$substrate,$indicates$a$structural$transition$affecting$the$ d z2 $orbital,$effectively$cutting$off$the$STM$tip$from$the$spinEflip$cotunnelling$path.$$ Cotunnelling. is. a. two2step. process. that. may. happen. whenever. an. electron2confining. island. (e.g.. an.atom,.molecule.or.quantum.dot).is.weakly.coupled.to.two.electrodes:.an.electron.hops.from.the.first.electrode.to.the.island.and.another.electron.hops.from.the.island.to.the.second.electrode..If.the.final.state. has. a. different. energy. than. the. initial. state,. the. cotunnelling. process. is. inelastic. and. can. only.occur. if. sufficient. bias. voltage. is. applied.. This. effect. has. proven. highly. useful. in. probing. e.g..molecular.vibrations ,.excitations.of.quantum.dots .and.carbon.nanotubes ,.and.spin2flip.excitations.on.molecules .and.single.atoms ..Inelastic.processes.involving.a.spin2flip.can.only.occur.when.tunnelling.into.a.singly2occupied.level ...Atomic. assembly. of. magnetic. nanostructures. allows. for. fine. control. of. parameters. such. as. single2atom. magneto2crystalline. anisotropy . and. spin. coupling .. Here. we. show,. using. both. spin. and.orbital.inelastic.excitation.spectra,.that.strain.induced.by.neighbouring.atoms.can.lead.to.a.change.in.the. orbital. filling,. resulting. in. complete. closure. of. an. inelastic. cotunnelling. channel.. For. Co. atoms.assembled. into. chains. we. observe. a. complete. suppression. of. spin. excitations,. accompanied. by. a.partial.suppression.of.newly.observed.orbital.excitations.at.higher.energy..Fig..1.shows.an.STM.topographic.image.and.inelastic.tunnelling.spectroscopy.(IETS).measurements.of.a.dimer.of.Co.atoms,.constructed.using.atom.manipulation.on.a.Cu N.surface,.and.also.of.a.Co.trimer.and.tetramer.constructed.as.extensions.of.the.dimer..All.nanostructures.were.constructed.with.two.unit2cell. spacing. along. the. direction. of. the. neighbouring. N. atoms. ( x ,.but.can.be.fitted.with.simulated.spin.excitation.spectra .by.including.an.antiferromagnetic. exchange. coupling. of. 2. meV. (supplementary. Fig.. S1).. A. remarkable. effect. occurs.for. chains. of. 3. atoms. or. longer. (Fig.. 1. b. and. c):. the. end. atoms. of. the. chains. show. spin. excitation.teps. around. 8. and. 13. mV,. but. no. steps. are. seen. on. the. inner. atoms,. even. up. to. 75.meV. (see.supplementary.Fig..S2)..The.theoretical.maximum.energy.for.a.single. Δ S=1.spin.flip.transition.is. Δ max =. λΔ SL max .=.66.meV ,.between.orbital.states.split.by.the.spin2orbit.coupling. λ .=.22.meV.with.maximum.unquenched.orbital.momentum.L max .=3..Fig.. 2b. shows. IETS. spectra. of. a. Co. hexamer. on. Cu N,. again. without. steps. on. the. inner. atoms..Significant.changes.are.also.seen.in.spectroscopy.performed.at.higher.bias.voltage..In.spectra.taken.on. the. end. atoms. up. to. ±.1. V,. a. prominent. peak. at. +500. mV. is. observed. (Fig..2c);. single. Co. atoms.show. similar. spectra. (red. curve).. But. for. the. inner. atoms,. all. spectroscopic. features. at. positive.voltage,.including.the.peak.at.+500.mV,.disappear..Also,.spectral.features.at.negative.bias.are.more.pronounced. on. the. inner. atoms.. The. correspondence. between. suppression. of. steps. at. low. voltage.and.high.positive.voltage.is.found.for.all.Co.atoms.on.Cu N..The.spectral.feature.at.+500.mV.may.be.associated.with.an.inelastic.excitation.that.involves.a.change.in.orbital.filling,.as.observed.previously.in.quantum.dots ..A.schematic.of.spin.and.orbital.excitation.processes.is.shown.in.Fig..3..Spin.IETS.transitions.involve.a.single.spin.flip.and.thus.cost.the.Zeeman.and/or. magnetic. anisotropy. energy. of. a. few. meV:. electrons. tunnel. onto. and. off. the. same. orbital..Orbital. IETS. transitions. involve. tunnelling. on. and. off. different. orbitals,. creating. an. orbital. excited.state..The.energy.cost.of.these.transitions.will.be.the.crystal.field.splitting,.which.is.of.order.several.hundred.meV ...The.combined.suppression.of.both.spin.IETS.and.orbital.IETS.transitions.can.be.understood.in.terms.of.a.simple.qualitative.model..The. d z2 .orbital.of.the.magnetic.atom.dominates.transport.between.the.tip. and. the. atom:. the. other. d . orbitals. couple. only. to. the. substrate.. Therefore,. all. spin. and. orbital.cotunnelling.excitations.must.involve.the. d z2 .orbital ..In.case.the. d z2 .orbital.is.half2filled.(Fig..3a),.spin.and.orbital.excitations.are.allowed.for.both.voltage.polarities..This.is.the.case.for.single.Co.atoms.and.for.outer.atoms.of.chains..If.the. d z2 .orbital.is.either.fully.occupied.or.empty,.however,.spin.excitations.are.blocked.completely.and.orbital.excitations.can.occur.only.at.negative.sample.voltage.(Fig..3b),.as.observed.for.inner.atoms...The. change. in. filling. of. the. d z2 . orbital. may. be. due. to. changes. in. the. crystal. environment. of. the. Co.atom..DFT.calculations.(Figs..3c.and.d).indicate.that.for.inner.atoms.of.Co.chains,.the.N2Co2N.angle.θ.is. almost. collinear. (175°),. whereas. for. a. single. Co. atom. θ. =. 150°.. This. drastic. change. in. structure.influences.the.atom’s.magneto2crystalline.anisotropy..This.can.be.verified.by.spin.IETS.spectra,.which.show.that.Co.atoms.assembled.into.chains.show.a.substantial.anisotropy.enhancement.compared.to.single. atoms.. Figs.. 4a. and. b. show. IETS. spectra. of. a. tetramer:. as. before,. on. the. inner. atoms. spin.excitations.are.suppressed,.as.well.as.positive2bias.orbital.excitations..Without.spin.IETS.steps.on.the.inner.atoms,.we.cannot.directly.measure.their.magnetic.anisotropy..However,.in.a.minority.of.cases . (4.out.of.20.structures). we.observed.Co.N2row.chains.in.which.spin.excitations.on.the.inner.atoms.were.not.suppressed.(Figs..4c,.and.supplementary.Fig..S3)..Significantly,.in.these.cases.all.atoms.also.show. the. prominent. orbital. IETS. peak. close. to. +500. mV. (Fig.. 4d),. reinforcing. the. correlation. of.suppression. of. spin. and. positive2bias. orbital. transitions.. We. believe. that. in. these. minority. cases. all.the.atoms.of.the.chain.have.a.partially.occupied. d z2 .orbital...We.can.fit.simulated.spin.IETS.spectra.to.all.the.atoms.of.the.“unsuppressed”.chain.(Fig..4c).and.the.end.atoms.of.the.“suppressed”.chain.(Fig..4a),.by.varying.only.the.component. Λ xx .of.the.anisotropy.tensor. Λ ,.corresponding.to.the.chain.axis.( x ).direction..The.anisotropy.of.the.inner.atoms.of.the.suppressed”.chain.may.be.estimated.by.its.effect.on.the.outer.atom.spectra..We.find.that.all.atoms.have. a. larger. Λ xx. than. a. single. Co. atom,. and. that. the. inner. atoms. of. both. chains. have. a. larger. Λ xx .than.the.outer.atoms..Moreover,.all.atoms.of.the.“suppressed”.chain.have.a.larger.anisotropy.than.those.of.the.“unsuppressed”.chain..This.effect.may.be.understood.in.terms.of.changes.in.the.crystal.field:. as. θ. approaches. 180°. the. crystal. field. approaches. the. high2symmetry. linear. case,. and. the.magnetic. anisotropy. increases. rapidly .. Since. the. inner. atoms. of. the. “suppressed”. chain. have. the.largest. Λ xx . we. can. infer. that. they. have. θ. closest. to. 180°.. End. atoms. of. chains. have. smaller. θ,. and.hence.smaller. Λ xx ,.than.the.inner.atoms...We.compared.DFT.simulations.of.the.magnetization.density.for.different.Co.structures.on.Cu N.(Figs..3e.and.f)..For.a.single.Co.atom.the.magnetization.profile.in.the. xz .plane.has.a. d xz .+. d z2 . character,.but.for.an.inner.atom.of.a.chain,.it.shows.the.perfect.fourfold.symmetry.of.the. d xz % orbital,.indicating.that.the. d z2 . orbital. is. no. longer. contributing. to. magnetism.. This. is. due. to. strong. hybridization. of. the. d z2 . orbital. with. the. N. orbitals,. which. occurs. since. the. N2Co2N. angle. θ. is. almost. 180°,. leading. to. a.situation.which.is.equivalent.to.the.picture.shown.in.Fig..3,.in.which.the.Co. d z2 .orbital.is.fully.filled..Thus,.we.have.a.mechanism.whereby.a.transition.to.a.higher2symmetry.crystal.environment.leads.to.a.modification.of.the.orbital.filling,.and.an.effectively.fully2filled,.non2magnetic. d z2 .orbital..This.effect.is.not.observed.for.chains.of.Fe.on.Cu N :.these.show.a.smaller.θ.(supplementary.Fig..S4).and.hence.are.not.expected.to.show.strong.hybridization.effects..We.can.account.for.the.two.different.types.of.N2row.structures.shown.in.Fig..4.by.variation.in.local.strain.. Single. Co. atoms. on. Cu N. show. just. a. ± .and.chains.are.highly.sensitive.to.strain..Since.θ.is.already.close.to.180°,.a.small.change.in.strain.caused.by.subsurface.defects.can.drive.a.large.change.in.anisotropy,.and.can.also.reach.the.critical.value.of.θ.that.triggers.the.transition.to.a.hybridised. d z2 .orbital..In. summary,. we. have. demonstrated. how. modifications. in. the. crystal. environment. of. a. single. Co.atom.can.result.in.complete.closure.of.both.spin.and.orbital.cotunneling.paths..A.small.variation.in.an.external.parameter.(strain).can.effectively.turn.spin.excitations.on.and.off,.similar.to.the.role.of.a.gate. voltage. changing. the. occupancy. of. a. quantum. dot. from. odd. to. even .. In. the. present.experiment.we.can.controllably.modify.this.strain.by.adding.an.extra.atom.to.a.nanostructure.(Figs..1,. S3).. We. foresee. that. if. magnetic. nanostructures. were. assembled. on. a. piezoelectric. substrate,. it.would. be. possible. to. control. the. global. strain,. providing. a. method. to. tune. orbital. occupancy,. and.thereby.inelastic.channel.closure,.through.a.separate.voltage.signal... $Methods$ Measurements. were. carried. out. at. 330.mK. in. ultra2high. vacuum. (<.2×10 –10 .mbar),. in. a. commercial.STM. system. (Unisoku. USM21300S).. The. Cu N. substrate. was. prepared. in. situ. by. N . sputtering. of. a.Cu(100). crystal.. Co. atoms. were. evaporated. onto. the. precooled. Cu N. surface.. STM. tips. were.prepared. by. indenting. commercial. Pt2Ir. STM. tips. into. the. Cu. surface.. Co. nanostructures. were.assembled. on. the. Cu N. surface. using. vertical. atom. manipulation.. For. IETS. measurements,.differential. conductance. (d I /d V ). spectra. were. recorded. with. a. lock2in. amplifier,. using. an. oscillation.amplitude.of.50. µ V.rms,.at.a.typical.conductance.values.of.1. µ S.for.spectra.up.to.20.mV.and.2.nS.for.spectra.up.to.1.V. $ imulated.IETS.spectra.are.produced.by.diagonalization.of.a.spin.Hamiltonian.that.includes.nearest2neighbour. Heisenberg. exchange. interaction. as. well. as. magnetic. anisotropy. in. terms. of. a. second2order. perturbative. treatment. of. the. spin2orbit. coupling .. Resulting. lineshapes. are. generated. by.taking.interactions.with.the.substrate.electrons.into.account.up.to.third.order ..DFT. calculation. were. carried. out. using. Quantum. Espresso. (QE) . and. Elk .. Structural. relaxations.were.performed.using.QE.with.PAW.pseudopotentials.and.PBE.exchange.correlation.functional,.for.the.cells.with.3x3.and.3x2.with.4.layers.of.Cu(100).and.1.layer.of.N,.corresponding.to.the.monomer.and.the.chain..These.calculations.show.a.decrease.in.the.N2Co2N.angle.θ.from.175°.for.the.Co.chain.to.150 o .for.the.monomer...In.the.case.of.the.monomer,.relaxed.structures.overestimate.the.Co2Cu.coupling ,.thereby.reducing.the. spin.. To. demonstrate. the. correlation. between. θ. and. the. magnetization. profile,. we. therefore.show.in.Fig..3d.the.profile.for.a.monomer.with.reduced.N2Co2N.angle.θ.=.110°,.for.which.S=3/2,.in.agreement.with.experiment..The.magnetization.profiles.were.calculated.using.all2electron.LAPW.Elk.code,. with. LDA+U. in. the. fully. localized. limit. and. Yukawa. scheme . with. a. screening. length. of. 1.88.atomic.units... $Acknowledgements$ This.work.was.supported.by.the.Dutch.funding.organizations.FOM.and.NWO.(VIDI).and.by.the.Kavli.Foundation.. JFR. acknowledges. financial. support.by. MEC2Spain. (FIS20132473282C2222P).and.Generalitat.Valenciana.(ACOMP/2010/070.and.Prometeo)..This.work.has.been.financially.supported.in. part. by. FEDER. funds.. JLL. and. JFR. acknowledge. financial. support. by. Marie2Curie2ITN. 6079042SPINOGRAPH..AF. acknowledges. Marie. Curie. COFUND. (grant. number. 600375). and. CONICET.. The.authors.thank.Markus.Ternes.for.providing.the.software.to.simulate.IETS.spectra. $$ $igure$ 1:$ Suppression$ of$ spin$ inelastic$excitations$ in$ Co$ nanostructures.$
Structural.model,.STM.topograph.and.IETS.spectra.of.a.Co.dimer.built.by.atom.manipulation.on.Cu N. (a) , $ and.a.Co.trimer $(b)$ and $ tetramer. (c)$ built.as.extensions.of.the.dimer..The.spectra.of.the.dimer,.and.the.edge.atoms.of.the.trimer.and.tetramer. (shown. in. green). show. spin. IETS.steps.. Spectra. of. the. inner. atoms. of. the.trimer. and. tetramer. (blue). show. no. spin.excitations.... . igure$2:$Orbital$and$spin$excitations$in$a$Co$nanostructure$ (a)$ structure. of. a. Co. N2row.hexamer.on.Cu N $(b)$ spin $ IETS.spectra.of.a.Co.hexamer,. showing. suppression. of. IETS. steps.on. inner. atoms.. A. topographic. image. at.+20.mV. is. shown. (inset). (c)$ higher. bias.spectra. on. the. same. hexamer.. The. peak. at.+500. mV. sample. bias. seen. on. the. single. Co.(indicated). is. attributed. to. an. orbital.excitation:.the.same.peak.is.seen.on.the.end.atoms. of. the. hexamer,. though. slightly.shifted..In.the.inner.atoms.of.the.hexamer.all.positive. bias. spectral. features. are.suppressed..A.topographic.image.at.+500.mV.is.shown.(inset). $$$ $igure$ 3:$ Suppression$ of$ orbital$ and$ spin$ IETS$transitions.$ (a)$
Schematic. of. spin. and. orbital.inelastic. transitions.. The. d z2 . orbital $ (blue) $ couples.to.the.tip.and.the.substrate:.the.other.d.orbitals. (green). couple. only. to. the. substrate..Inelastic.spin.excitations.involve.a.spin.flip.of.an.electron. on. a. single. orbital:. inelastic. orbital.excitations. involve. a. transition. to. an. orbital.excited. state.. In $ the. case. of. a. magnetic. atom.with. a. half. filled. d z2 . orbital. (a)$ spin. IETS. and.orbital. IETS. transitions. are. allowed. for. both.tunnelling.directions.(bias.polarities)..In $ the.case.of. a. fully. filled. (or. empty). d z2 . orbital. (b)$ spin.excitations. are. blocked,. and. orbital. excitations.are. only. possible. for. tunnelling. from. substrate.to. tip,. i.e.. negative. sample. bias. $ (c)$ DFT.calculated $ relaxed. structure. for. Co. monomer.and. (d) .infinite.double2spaced.Co.chain.on.Cu N..Calculated. magnetization. density. is. shown. for. (e)$ a.Co.monomer.and. (f) .infinite.chain. $ $igure$ 4:$ Magnetic$ anisotropy$ of$ Co$nanostructures$(a) .IETS.spectra.of.each.atom.of.a.Co.tetramer.built.on.Cu N..IETS.steps.on.the.inner.atoms.are.suppressed,.in.the.same.way. as. in. Fig.. 1e.. Solid. lines. are. simulated.spectra. allowing. the. anisotropy. parameter. Λ xx .to.vary.as.indicated.between.the.end.and.inner. atoms.. Λ zz . =. 6.0.eV . and. Λ yy . =. 0. in. all.cases,. the. antiferromagnetic. spin. coupling. is.2.5.meV.. For. comparison,. single. Co. may. be.fitted. with. Λ xx . =. 6.2. eV .. Simulated. spectra.are.not.shown.for.inner.atoms.since.in.these,.the. spin. IETS. transitions. are. suppressed.. (b) .Higher.bias.spectra.on.the.same.tetramer.as.(a).. Note. suppression. of. the. positive. bias.spectral.features.in.the.inner.atoms.. (c) .IETS.spectra.of.each.atom.of.another.Co.tetramer.built. on. Cu N,. in. which. spin. excitations. are.not.suppressed..This.is.thought.to.be.due.to.local. lattice. strain.. Simulated. spectra. are.shown.as.for.(a)..The.antiferromagnetic.spin.coupling.is.2.meV. $(d) .Higher.bias.spectra.on.the.same.tetramer.as. (c) ..The.spectra.are.all.observed. to. be. similar. to. that. of. a. single. Co.atom.... $ ... . Science . .466–9.(2004)..2.. Loth,.S.,.Baumann,.S.,.Lutz,.C..P.,.Eigler,.D..M..&.Heinrich,.A..J..Bistability.in.atomic2scale.antiferromagnets.. Science . .196–9.(2012)..3.. Spinelli,.A.,.Bryant,.B.,.Delgado,.F.,.Fernández2Rossier,.J..&.Otte,.A..F..Imaging.of.spin.waves.in.atomically.designed.nanomagnets.. Nat.%Mater. . ,.782–5.(2014)..4.. Jaklevic,.R..&.Lambe,.J..Molecular.Vibration.Spectra.by.Electron.Tunneling.. Phys.%Rev.%Lett. . .1139–1140.(1966)..5.. Stipe,.B..C..Single2Molecule.Vibrational.Spectroscopy.and.Microscopy.. Science% .1732–1735.(1998)..6.. De.Franceschi,.S.. et%al. .Electron.Cotunneling.in.a.Semiconductor.Quantum.Dot..
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F310* Braga,*Portugal** Instituto* de* Modelado* e* Innovación* Tecnológica* (CONICETFUNNE),* Avenida* Libertad* 5400,* W3404AAS,*Corrientes,*Argentina* ! !Figure!S1!Comparison!of!single!Co!and!Co!dimer!spectra!(a)! dI/dV!spectrum!of!a!single!Co!atom!on!Cu N!(dots).!The!solid!line!is!a!simulated!spin!IETS!spectrum!using!S!=!3/2,! Λ xx !=! Λ zz! =!6.2!eV E1 ,! Λ yy! =!0,!equivalent!to!D!=!2.7!meV,!E!=!0.!Interactions!with!substrate!electrons!are!taken!into!account!up!to!3 rd !order,!using!an!antiferromagnetic!KondoEexchange!coupling!J K ρ s =! − (b)! dI/dV!spectra!of!each!atom!of!a!Co!dimer!on!Cu N!(dots).!This!is!the!same!dimer!as!shown!in!Fig.!1.!Solid!lines!are!simulated!spin!IETS!spectra!including!an!antiferromagnetic!spin!coupling!of! − Λ xx !=!8.0!eV E1 ,! Λ zz! =!6.2!eV E1 ,! Λ yy! =!0,!J K ρ s! =! − x )!axis!is!changed!from!the!single!atom!case.!! !! ! igure! S2! Spectra! of! a! Co! tetramer! up! to! 75! mV.! dI/dV! spectra! (dots)! of! a! Co! tetramer! similar! to!Fig.!1c!and!Fig.!4a,!at!up!to!75!mV.!On!the!inner!atoms,!no!spin!excitation!steps!are!seen.!The!solid!lines! are! simulated! spin! excitation! spectra.! Although! no! spin! excitations! are! observed! on! the! inner!atoms,!it!is!necessary!that!the!inner!atom!xEaxis!anisotropy! Λ xx !>!25!eV E1! to!reproduce!the!end!atom!spectra.!For!the!model!shown,!for!all!atoms!S!=!3/2,!J K ρ s! =! − Λ zz! =!6.2!eV E1 ,! Λ yy! =!0!and!the!antiferromagnetic! spin! coupling! is! − Λ xx !=! 13! eV E1 ,! for! the! inner! atoms! Λ xx !=!30!eV E1 .!The!model!reproduces!the!end!atom!spectra!accurately:!for!the!inner!atoms!it!predicts!a!step!at!30!meV!which!is!not!observed,!since!spin!excitations!on!these!atoms!are!suppressed!due!to!the!strongly!hybridised! d z2 !orbital.! ! ! igure!S3!Co!nanostructures!with!suppressed!and!unsuppressed!spin!excitations.! In!most!cases,!Co!chains! longer! than! two! atoms! built! on! Cu N! showed! supressed! spin! excitations! on! the! inner! atoms!(Fig.!1).!In!a!minority!of!cases!(4!out!of!20!structures),!Co!chains!up!to!four!atoms!long!were!observed!to!have!unsuppressed!spin!excitations.!This!effect!was!specific!to!certain!locations!on!the!substrate,!and!is!presumably!due!to!variations!in!local!strain!induced!by!subsurface!defects.! (a) !dI/dV!spectra!of!a! Co! trimer! and! (b) ! a! Co! tetramer,! as! shown! in! Fig.!4c,! constructed! as! an! extension! of! the! trimer,!both! of! which! show! unsuppressed! spin! excitations.! Simulated! Spin! IETS! spectra! are! shown! (solid!lines),!for!all!atoms!S!=!3/2,! Λ zz! =!6.2!eV E1 ,! Λ yy! =!0.!The!trimer!may!be!fitted!with! Λ xx =!7.0!eV E1 !for!all!atoms:! for! the! tetramer! Λ xx! =! 7.5! eV E1 ! for! the! end! atoms! and! 13! eV E1 ! for! the! inner! atoms.! For! both!structures!the!antiferromagnetic!spin!coupling!is! − K ρ s! =! − − (c) !dI/dV!spectra!of!a!Co!pentamer!constructed!as!an!extension!of!(b).!In!this!case!no!spin!IETS!steps!are!seen!on!the!inner!atoms:!suppression!of!spin!excitations!was!observed!on! all !structures!longer!than!four!atoms.!We!may!conclude!that!the!strain!induced!by!adding!a!Co!atom!to! the! structure! overcomes! the! local! lattice! strain,! pushing! all! inner! atoms! of! the! structure! beyond!the!critical!NECoEN!angle!that!leads!to!suppression!of!spin!excitations.!The!end!atom!spectra!may!be!simulated!using!a!similar!model!to!Fig.!S2:!for!all!atoms!S!=!3/2,!J K ρ s! =! − Λ zz! =!6.2!eV E1 ,! Λ yy! =!0,!the!antiferromagnetic!spin!coupling!is! − Λ xx !=!7.5!and!8.5!eV E1 ,!for!the!inner!atoms! Λ xx !=!20!eV E1 .!Note!that!the!anisotropy!values!are!smaller!than!in!Fig.!S2,!illustrating!the!effect!of!the!local!strain.! ! ! Figure!S4!Comparison!of!Co!chains!and!Fe!chains!on!Cu N!(a)! section!through!DFTEcomputed!relaxed!structure!of!an!infinite!chain!of!Co!atoms!on!Cu N,!as!shown!in!Fig.!3d .! The!NECoEN!angle! θ is!175°,!leading! to! strong! hybridization! of! the! d z2 ! orbital! and! suppression! of! spin! excitations.! (b)! Relaxed!structure!of!an!infinite!chain!of!Fe!atoms!on!Cu N.!The!NECoEN!angle! θ is!much!smaller!at!133°,!so!in!this!case!the! d z2z2