Physics Today Atomic spins on surfacesAndreas Heinrich Citation: Physics Today 68(3), 42 (2015); doi: 10.1063/PT.3.2720 View online: http://dx.doi.org/10.1063/PT.3.2720 View Table of Contents: http://scitation.aip.org/content/aip/magazine/physicstoday/68/3?ver=pdfcov Published by the AIP Publishing

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42 March 2015 Physics Today www.physicstoday.org

Atomic and solid-state physics have mostlyled separate lives. Atomic physics wasborn in the 1920s out of a desire to un-derstand the optical and magnetic prop-erties of atoms in the gas phase; it was

in that playground that quantum mechanicsemerged. In contrast, solid-state physics maturedthrough the purification of materials; that purifica-tion was, among other aspects, crucial to under-standing the influence of chemical doping on con-ductivity in semiconductors and led to the plethoraof electronic devices we enjoy today. Not surprisingly,the experimental and theoretical concepts used inthe two fields are often quite different. For example,the magnetic properties of isolated gas atoms aredescribed by quantum spin states, whereas the mag-netic properties of solids are obscured by the forma-tion of a band structure.

Half of all atoms in the periodic table are mag-netic in the gas phase by virtue of their odd numberof electrons, but magnetic solids are much rarer. Tofind them, one usually turns to transition metals andrare-earth solids, whose atomic spin properties arepreserved in their partially filled d and f electronshells. To explore magnetism in more exotic materi-als, researchers in the 1950s and 1960s intensivelystudied the electron spin resonance of nonmagneticinsulators after doping them with transition-metaland rare-earth atoms.1 The dopant atoms, thoughembedded in the solid, retain their quantum spinstates, as if still in the gas phase. Spin resonance hasundergone a major revival in recent years throughinvestigations of individual defects in insulators.Perhaps the most prominent subject is the so-callednitrogen–vacancy defect in diamond, thanks to itspotential applications in quantum computing andsensing (see the article by Lilian Childress, Ronald

Walsworth, and Mikhail Lukin, PHYSICS TODAY, October 2014, page 38).

Atom-like magnetic defects in solids interactwith conduction electrons and thus influence the be-havior of electronic devices. Putting magnetic atomsin the gap between the two electrodes of a micron-scale planar tunnel junction offered a conceptuallyeasy way to probe those interactions as currentpassed through the atoms. The electrical transportproperties observed at low voltages deviated wildlyfrom the naively expected linear Ohm’s law behav-ior—a deviation often called the “zero-bias anom-aly.”2 In retrospect, it’s clear that understanding thetransport anomaly was all but impossible. The un-controlled placement of the magnetic atoms in tun-nel junctions and the atoms’ strongly varying inter-actions with their local environments presented toocomplicated a system.

In this article I describe experiments developedover the past decade that overcome the randomplacement and probe junctions one spin at a time.

Looking for single spinsThe most important ingredient for researching indi-vidual magnetic atoms in tunnel junctions is a scan-ning tunneling microscope (STM), which can local-ize an electric current through a single atom. It wasinvented in 1981 by Gerd Binnig and Heinrich Rohrer(figure 1a), who received the 1986 Nobel Prize inPhysics for the achievement. In an STM, an atomicallysharp tip is brought to within a few atomic diame-ters of a clean surface, and a bias voltage is appliedbetween them to establish a tunneling current.

In one mode of operation, the bias voltage isfixed and the tip height is adjusted to keep the current constant while the tip scans across the sur-face; the height modulation maps the topography.Shortly after the STM’s invention, Binnig andRohrer used that technique to settle a long-standingdebate about the atomic structure of a particular for-

Andreas Heinrich leads a research team at the IBM AlmadenResearch Center in San Jose, California.

Andreas Heinrich

ATOMICSPINSon surfaces

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mation on the surface of silicon, a significant feat forthe new tool.

Half a decade after the STM’s discovery, DonaldEigler, shown in figure 1b, successfully wed the ex-perimental techniques of low-temperature physicsto the ultrahigh-vacuum environment common insurface-science experiments and created the firstSTM that could be brought to bear on surfaces at liq-uid-helium temperature. Low-temperature systemsinvariably cause vibrations—for example, from thebubbling of cryogenic liquids or the mechanicallydriven circulation of helium gas. Engineering a plat-form that would isolate the STM tip, which must beheld stable to within one hundredth of an atomic di-ameter, from such vibrations was impressive.

Eigler’s achievement enabled two great break-throughs: first, and most famous, the ability to moveatoms one at a time to build structures with atomic-scale precision; second, and possibly as important,the ability to measure the conductance through in-dividual atoms with the high energy resolution af-forded by the low temperature. (See PHYSICS TODAY,November 1993, page 17.)

Most of the magnetic field of an ordinary per-manent magnet comes directly from the unpairedelectron spins it contains. The energy of a quantumspin, such as the electron spin of a gas atom, is de-generate in the absence of a magnetic field. But when

a field is applied, the spin splits into differing en-ergy states. For atoms in free space, that Zeemansplitting is governed by the interplay of orbital andspin magnetic moments. When the atoms are em-bedded in a solid or collectively form a molecule,however, the splitting is altered by the local envi-ronment in ways that reveal valuable informationabout that environment.1

Magnetic measurementsCan an STM measure the Zeeman splitting one atomat a time? A back-of-the-envelope calculation quickly

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b

a

Figure 1. Pioneers of scanning tunneling microscopy.(a) Gerd Binnig and Heinrich Rohrer, shown here with one oftheir original instruments, invented the scanning tunneling microscope (STM) about 35 years ago. They overcame theconceptual and engineering challenge of placing a macroscopicobject—a sharp tip—an atomic-scale distance from a surfaceand demonstrated atomic-resolution imaging. (b) Donald Eiglerstands in front of the liquid-helium-temperature, ultrahigh-vacuumSTM he developed at IBM. (Photographs courtesy of IBM.)

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When adapted to cryogenic temperatures and high magneticfields, a scanning tunneling microscope can assemble andprobe spin chains, logic gates, and other configurations ofmagnetic atoms.

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suggests that in readily achievable magnetic fieldsof a few tesla, a temperature below 1 K is needed toreach the necessary energy resolution. But addi-tional modifications had to be added to the low-temperature STM to maintain its stability in highmagnetic fields. In November 1998, I joined Eigler’sgroup at the IBM Almaden Research Center, where,as a postdoc, I took on that challenge. At extremelylow temperatures and high fields, most materialsbecome at least partially magnetic, so a large part ofthe work was to replace many of the materials thatmake up the STM housing and components withless magnetic versions to prevent them from cou-pling to the surrounding superconducting magnet.

Five years later, my colleagues and I used thenewly developed 0.5-K, 7-T STM to measure theZeeman splitting of the spin states of individual mag-netic atoms on a surface. In our first experiment, weplaced manganese atoms on a thin, insulating filmof alumina to prevent their magnetic moments frommixing with the underlying copper’s large numberof conduction electrons.3 Box 1 describes the mech-anism underlying the spin excitation spectroscopy(SES) used in that work. Because the entire tunnelcurrent flowed through individual, widely spacedMn atoms, the magnetic signal turned out to be sur-prisingly large, with the inelastic tunneling cur-rent—that which flips the atom’s spin state—reach-ing about 25% of the total current.

An alternative approach to magnetic measure-ments using an STM is to outfit its tip with magneticatoms and measure the differential conductance inan applied magnetic field. At the heart of that ap-proach, known as spin-polarized scanning tunnel-ing microscopy and described in box 2, is the factthat a tunnel junction’s electrical conductancechanges with the relative magnetic orientation oftwo magnetic materials on opposite sides of the

junction—an effect called tunneling magnetoresis-tance. In the 1990s Roland Wiesendanger and hisgroup at the University of Hamburg in Germanyfirst applied that approach, studying bulk magneticsamples and thin-film magnetic materials. Later,around the same time my group introduced single-spin spin-excitation spectroscopy in 2002, researchersin Wiesendanger’s lab began measuring the magne-toresistance of tunnel junctions, each consisting ofan STM tip atop a single paramagnetic atom on ametal surface.4

What did researchers learn from those single-spin tunneling experiments? For one, we learnedthat no zero-bias anomaly exists in such controlledtunnel junctions, although some magnetic atoms onmetal surfaces show complex conductance variationsdue to correlations with substrate electrons (seePHYSICS TODAY, January 1998, page 17, and May 2002,page 21). Similarly, when magnetic atoms are placedon a thin, insulating layer, strong inelastic conduc-tance features arise from spin excitations in theatoms. In the case of spin-polarized tunneling, thosespectroscopic signatures are sensitive to the degreeof spin polarization of the tip and sample and maydiffer dramatically from spin-averaged measure-ments. The zero-bias anomaly in planar tunnel junc-tions may have stemmed from the spatial averagingover all those varying spectroscopic channels thatare present in macroscopic tunnel junctions.

Second, we researchers learned that the transi-tion from the magnetic behavior in solids, charac-terized by their spin-polarized band structure, tothe atomic character of quantum spins can be sur-prisingly complex and rich. Even today, many spinproperties in tunnel junctions with single or smallclusters of magnetic atoms are not fully understood.Nonetheless, the simplification of tunnel junctionsto well-controlled individual magnetic atoms and

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Atomic spins

A quantum spin can be described with discrete spinstates, the energy eigenstates that depend on thequantum state of the spin. The simplest example is aspin-1⁄2 atom in a magnetic field B. The field gives rise tothe Zeeman energy EZ, which lifts the degeneracy ofthe two spin states, usually called up and down. To putthe Zeeman energy scale into perspective, note that the energyto flip an atom’s spin at a magnetic field B of 1 T is four orders ofmagnitude smaller than that of a typical molecular bond. Butprovided one has access to a stable enough scanning tunnelingmicroscope (STM), spin excitation spectroscopy (SES) can exploitthe eigenstates’ discrete nature.

In SES, an STM’s nonmagnetic tip is placed in tunnelingrange of a spin on a surface, as shown here. Often that spin isplaced atop a thin insulator (green) to slightly decouple it fromthe underlying conduction electrons in the substrate (brown).The conductance—or more precisely, the differential conduc-tance dI/dV, where I is the tunnel current—of the tunnel junc-tion is then measured as a function of bias voltage V along withexternal parameters such as magnetic field. As the applied volt-age is increased, the conductance remains constant until thetunneling electrons deliver enough energy to excite the spinfrom the ground to an excited state. At that voltage, a character-

istic change in differential conductance occurs. Below the exci-tation voltage threshold, the electrons can only tunnel via anelastic channel, but above the threshold, an inelastic channelopens as well. The conductance of the tunnel junction is gener-ally greater when both channels are open, and dI/dV increases ina stepwise fashion.

The voltage at which the step in SES occurs is a direct mea -sure of the energy required to flip the spin or, equivalently, thestrength of the Zeeman interaction. Besides the magnetic field,the local environment of the binding site also strongly modifiesthe magnetic behavior of atoms on surfaces. In many cases aspin prefers to point along a particular spatial direction, and theenergy cost, known as magnetic anisotropy and often referredto as the zero-field splitting, can be directly measured with SES.In addition, SES can be used to measure the coupling strengthbetween spins, as, for example, in the spin chains discussed inthe main text.

Box 1. Spin excitation spectroscopyV

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Zeeman splitting Spin excitation spectra

dIdV/

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Ez

eV

B

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nanostructures has dramatically eased the task ofunderstanding their electron-transport propertiesfor experimentalists and theorists alike.

Spin chainsCombining single-atom STM spectroscopy withprecise atom manipulation allows the study of arti-ficial structures5 such as one-dimensional spinchains, logic gates, and spin storage devices. Tradi-tionally, access to spin-chain physics was achievedusing bulk materials whose strongly anisotropicstructure renders their magnetic properties effec-tively one dimensional (see the article by YoshinoriTokura in PHYSICS TODAY, July 2003, page 50). But aspin chain consisting of atoms on a surface allowsprecise control: Every spin can be prepared andflipped on cue, and their exchange energy—the spins’coupling strength—can be directly measured. TheSTM does each of those tasks (see PHYSICS TODAY,July 2006, page 13).

Figure 2a shows an example of an STM-assembled chain of iron atoms on a thin, insulatingsubstrate.6 When scanned with a nonmagnetic tip,each Fe atom appears identical, as a small bump in

the chain. When scanned with a spin-polarized tip,as shown in figure 2b, by contrast, four Fe atoms ap-pear short and the other four appear tall, a manifes-tation of the change in tunneling current that occursas the tip encounters opposite spin alignments in Feas it moves along the chain.

Box 2 explains the mechanism for such spincontrast. In an antiferromagnetic chain, one of thetwo states shown in figure 2b can emerge: In one,the leftmost atom appears in the spin-up state (tall),its neighbor appears spin down (short), and atomsin the rest of the chain follow suit with alternatingspins. In the other state, the atoms have the oppositespin orientations, with the leftmost atom spin down.The two states, mirror images of each other, areoften called Néel states. In the sense that each atomin the chain points either up or down, one can callthe spin chain classical. At any instant, a classicalchain resides in either of its two degenerate spinconfigurations.

In the quantum world, though, a spin can re-side in two states at the same time, pointing up anddown simultaneously. Figure 3 shows an example:a linear chain of 10 Mn atoms that, unlike the Fe chain,

www.physicstoday.org March 2015 Physics Today 45

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Figure 3. A quantum antiferromagnetic spin chaincomposed of 10 manganese atoms (adjacent to onestanding apart) on a bed of insulating copper nitrideover conducting copper. (a) A scanning tunneling microscope assembled the chain one Mn at a time andthen imaged it with a nonmagnetic tip. The indistinctstructure suggests the presence of delocalized electronsshared among the atoms. (b) As the tip hovers aboveone of three different locations on the chain, an appliedvoltage injects current into the surface. The differentialconductance spectra depend little on the tip location,and in all three cases, a large step in electrical conduc-tance occurs around ±1 mV due to spin-flipping excita-tions. Further excitations, at ±2 mV and ±12 mV, take thechain into higher-energy states. (c) If an external mag-netic field is added, the degeneracy of the excitations is broken into three distinct states ∣ST, ms⟩. (d) In thisspectra of a much shorter chain—two coupled Mnatoms—the subtle triplet excitations at 6 mV are fullydiscernable only when the magnetic field reaches 7 T.(Adapted from ref. 5.)

Nonmagnetic tip

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Magnetic tip

Figure 2. A classical antiferromagnetic spin chaincomposed of eight iron atoms assembled on a coppernitride substrate appears as identical bumps (a) whenimaged using a nonmagnetic tip of a scanning tunnel-ing microscope (STM). But when the nonmagnetic tip isswapped out for a magnetic one (b), adjacent iron atomsalternate between appearing short and appearing tall.The contrast is the result of atomic-scale magnetoresis-tance, an effect in which each atom’s spin orientation,parallel or antiparallel to the tip’s field, influences howmuch current flows through the STM. The spin chain appears to be in a classical magnetic state, called a Néelstate, in which spins alternate between definite orienta-tions, either up or down. Both Néel states are equallylikely to occur in the antiferromagnetic chain, and thechain can be switched between them by temperature,quantum fluctuations, or controlled voltage pulses.(Adapted from ref. 6.)

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resides in a quantum-coherent ground state. In thatstate, the total spin ST and magnetization ms of thechain are both zero, which implies that the chain isnonmagnetic. The spectroscopic data confirm thatpicture of a quantum-coherent ground state. Whenthe chain is excited into one of its triplet states, thespins of the atoms don’t quite cancel, and the chainas a whole has a net spin ST of 1. The energy of thatexcitation changes as a function of chain length andsplits into three distinct excitation energies at finitemagnetic fields.

What distinguishes the two spin chains is thatan Fe atom’s spin has a strongly preferred spatialaxis, a so-called easy magnetic axis, whereas Mn isnearly isotropic. The Mn chain thus closely follows

the Heisenberg spin-interaction model, in which thetotal spin quantum number ST characterizes thestate of the chain. The Fe chain, on the other hand,follows the Ising model, in which spins always pointeither up or down along a certain spatial direction.Even an Fe chain shows more quantum mechanicalcharacter, however, as its length is reduced. Remov-ing two Fe atoms from an eight-member chain6 in-creases the quantum tunneling between the two Néelstates by a factor of about 1000.

Theoretical modeling of such spin chains, in-cluding their interaction with the local environ-ment, is an active field. For example, even thoughboth Fe and Mn spin chains are usually placed on an insulating monolayer, the conduction elec-

46 March 2015 Physics Today www.physicstoday.org

Atomic spins

Figure 4. Magnetic logic at the atomic scale.(a) This device consists of two ferromagnetic islands,α and β, that serve as inputs and two spin leads madeof iron atoms that serve as wires connecting them.The two spin leads meet in a central spot, where another atom (the output gate) is located, and alogical OR operation is performed. The gate’s spin isthen read by a scanning tunneling microscope (STM).(b) Externally applied magnetic fields set the islands’input states to either up or down, which appear darkblue or green in the STM images. The spin chainseach reside in an antiferromagnetic Néel state, so themagnetic state of the atom closest to an island, andtherefore the rest of them in the chain, are determinedby the island’s input state. As seen in the right STMimage, the spins of a six-atom chain flip when input βis flipped, while a four-atom chain remains unaffected.The logic table gives the state of an output gateatom as a function of both islands’ input states.(Adapted from ref. 7.)

Spintronics is an established field of solid-state elec-tronics in which the electron’s spin can be used, eitherwith or independently of its charge, to carry informa-tion in a circuit (see the article by Gary Prinz, PHYSICSTODAY, April 1995, page 58).8 At its core lies the fact thatelectrical current in magnetic materials depends on therelative alignment of the electron spin and the mate-rial’s magnetization. The technology can be appliedusing a scanning tunneling microscope (STM) by re-placing the normal tip—typically a metal such as tungsten—with a magnetic one such as chromium, as shown here. The in-strument, whose tunneling current depends on the relativealignment of the tip’s magnetization with the magnetization ofthe surface, can nowadays image magnetic materials down tothe atomic scale, including single magnetic atoms on surfaces.

Because the tip’s magnetization can be fixed, it can be usedto measure the spin orientation of surface atoms. Most often, in-dividual magnetic atoms have no fixed magnetic orientation atzero field; instead, their spins become oriented with increasingfield. The blue curve in the figure here is the trace of the spin-polarized differential conductance dI/dV, for fixed tip height andvoltage, plotted as a function of applied magnetic field B. Atlarge enough positive and negative fields, the differential con-

ductance becomes constant, which indicates that the magneticmoment of the atom on the surface has reached its peak value.The orange traces indicate the hysteretic behavior of a magneticsurface atom or nanostructure whose magnetic state is bistable.

Such single-atom magnetization curves reveal details aboutthe interaction of the atom with its environment. Routinely usedto characterize magnetic materials, the curves allow, for instance,a comparison of single-atom measurements to the ensembleaverages given by bulk measurements.9 They can also be com-plicated by surface step-edge effects and material inhomo-geneities. Thus measurements of the simplest magnetic con-stituents can be revealing. Even weak interactions with othermagnetic atoms or extended magnetic nanostructures such asislands can be directly observed.

Box 2. Spin-polarized tunnelingCr

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trons in the underlying metal appear to help breakthe coherence; how that works in detail remains unresolved.

Devices and directionsIn a beautiful piece of recent work,7 Alexander Kha-jetoorians, Jens Wiebe, Bruno Chilian, and Wiesen-danger demonstrated logic operations with spinchains on the atomic scale. Figure 4 illustrates thebasic idea. Two magnetic islands serve as inputs;their magnetic states can be switched up or downusing applied magnetic field pulses. The islands’states are then transferred to two adjacent spinchains, each residing in an antiferromagnetic Néelstate. In figure 4b, the magnetic state of the right is-land is switched, which in turn switches the Néelstate of its adjacent spin chain. Where the two chainsmeet, the spin state depends on the states of bothchains; its output is read by a spin-polarized STM.

Classical spin chains such as the ones imagedin figure 2, and arrays such as the one on pages 42–43and the cover of this issue, can potentially be usedfor magnetic data storage.6 As discussed earlier,such chains reside in one of two ground states thatare equally stable; call one of the states 0 and theother 1. Given short voltage pulses, an STM canswitch the chain between those logic states to recordone bit of data. In data-storage applications, suchantiferromagnetic bits might actually offer some ad-vantages over ferromagnets whose longer-rangemagnetic fields can inadvertently flip adjacent bits.That advantage may allow denser packing in devices.

On the downside, however, the absence of long-range magnetic fields prohibits the use of readheads that sense the stray field and are now com-monplace among today’s computer hard drives.

Laboratory implementations of data storageand computation on the atomic scale reveal both thepromise and pitfalls of miniaturizing real-world de-vices. Many researchers are striving to harness theemergent quantum effects for computing purposes.Much more work is needed to assess whether thevarious scaling approaches are feasible, but there’sno doubt that controlling matter on an atomic scalewill continue to provide insights into the workingsof nature. And the richness of solids, such as the com-plex systems found in spin ices (see the article byRoderich Moessner and Art Ramirez, PHYSICS TODAY,February 2006, page 24), correlated-electron materi-als (see the article by Gabriel Kotliar and Dieter Voll-hardt, PHYSICS TODAY, March 2004, page 53), andother systems will also, no doubt, continue to inspirenovel devices.

References1. A. Abragam, B. Bleaney, Electron Paramagnetic Reso-

nance of Transition Ions, Oxford U. Press (2012).2. L. Y. L. Shen, J. M. Rowell, Phys. Rev. 165, 566 (1968).3. A. J. Heinrich et al., Science 306, 466 (2004).4. R. Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009).5. C. F. Hirjibehedin, C. P. Lutz, A. J. Heinrich, Science 312,

1021 (2006). 6. S. Loth et al., Science 335, 196 (2012).7. A. A. Khajetoorians et al., Science 332, 1062 (2011).8. See, for example, S. A. Wolf et al., Science 294, 1488 (2001).9. F. Meier et al., Science 320, 82 (2008). ■

ELECTRON GUN SYSTEMSFlood Beams, Small SpotsHigh BrightnessLaB6

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