spintronics is based on the property of electron spin

1. Spintronics
A new class of device based on the quantum of electron spin, rather than
on charge, may yield the next generation of microelectronics
Sankar Das Sarma
T he last half of the 20th century, it
has been argued with considerable
justification, could be called the micro-
carrying out processing and data stor-
age on the same chip), investigators
have been eager to exploit another
the flow of charge. In fact, the spin-
tronics dream is a seamless integration
of electronic, optoelectronic and mag-
electronics era. During that 50-year pe- property of the electron—a characteris- netoelectronic multifunctionality on a
riod, the world witnessed a revolution tic known as spin. Spin is a purely single device that can perform much
based on a digital logic of electrons. quantum phenomenon roughly akin to more than is possible with today’s mi-
From the earliest transistor to the re- the spinning of a child’s top or the di- croelectronic devices.
markably powerful microprocessor in rectional behavior of a compass needle.
your desktop computer, most electron- The top could spin in the clockwise or The Logic Of Spin
ic devices have employed circuits that counterclockwise direction; electrons Spin relaxation (how spins are created
express data as binary digits, or bits— have spin of a sort in which their com- and disappear) and spin transport
ones and zeroes represented by the ex- pass needles can point either “up” or (how spins move in metals and semi-
istence or absence of electric charge. “down” in relation to a magnetic field. conductors) are fundamentally impor-
Furthermore, the communication be- Spin therefore lends itself elegantly to a tant not only as basic physics questions
tween microelectronic devices occurs new kind of binary logic of ones and but also because of their demonstrated
by the binary flow of electric charges. zeros. The movement of spin, like the value as phenomena in electronic tech-
The technologies that emerged from flow of charge, can also carry informa- nology. One device already in use is the
this simple logic have created a multi- tion among devices. One advantage of giant magnetoresistive, or GMR, sand-
trillion dollar per year global industry spin over charge is that spin can be eas- wich structure, which consists of alter-
whose products are ubiquitous. In- ily manipulated by externally applied nating ferromagnetic (that is, perma-
deed, the relentless growth of micro- magnetic fields, a property already in nently magnetized) and nonmagnetic
electronics is often popularly summa- use in magnetic storage technology. metal layers. Depending on the relative
rized in Moore’s Law, which holds that Another more subtle (but potentially orientation of the magnetizations in the
microprocessors will double in power significant) property of spin is its long magnetic layers, the electrical resistance
every 18 months as electronic devices coherence, or relaxation, time—once through the layers changes from small
shrink and more logic is packed into created it tends to stay that way for a (parallel magnetizations) to large (an-
every chip. long time, unlike charge states, which tiparallel magnetizations). Investigators
Yet even Moore’s Law will run out are easily destroyed by scattering or discovered that they could use this
of momentum one day as the size of collision with defects, impurities or change in resistance (called magnetore-
individual bits approaches the dimen- other charges. sistance, and “giant” because of the
sion of atoms—this has been called the These characteristics open the possi- large magnitude of the effect in this
end of the silicon road map. For this bility of developing devices that could case) to construct exquisitely sensitive
reason and also to enhance the multi- be much smaller, consume less electric- detectors of changing magnetic fields,
functionality of devices (for example, ity and be more powerful for certain such as those marking the data on a
types of computations than is possible computer hard-disk platter. These disk
Sankar Das Sarma is Distinguished University with electron-charge-based systems. drive read/write heads have been
Professor at the University of Maryland, College Those of us in the spintronics (short for wildly successful, permitting the stor-
Park, where he has been on the physics faculty
spin electronics) community hope that age of tens of gigabytes of data on note-
since 1980. He received his Ph.D. from Brown
by understanding the behavior of elec- book computer hard drives, and have
University in 1979. He is a widely published and
highly cited theoretical condensed matter physicist tron spin in materials we can learn created a billion-dollar per year indus-
with broad research interests in electronic proper- something fundamentally new about try. Groups have also been working to
ties of materials and nonequilibrium statistical solid state physics that will lead to a develop nonvolatile memory elements
mechanics. Internet: dassarma@physics.umd.edu; new generation of electronic devices from these materials, possibly a route
http://www.physics.umd.edu/rgroups/spin/ based on the flow of spin in addition to to instant-on computers.
516 American Scientist, Volume 89

2. Figure 1. Physicists and engineers are creating an entirely new generation of microelectronic devices that operate on a quantum mechanical
property of electrons called “spin” rather than on the electron’s electrical charge. These investigators are racing to use spin effects to create
transistors and other circuit elements, including quantum computers, in a field known as spintronics. Shown here is an artist’s depiction of a
proposal by Bruce Kane, now at the University of Maryland, for a quantum computer based on the nuclear spin of phosphorus atoms. The
quantum properties of superposition and entanglement may someday permit quantum computers to perform certain types of computations
much more quickly using less power than is possible with conventional charge-based devices. For an explanation of how a quantum com-
puter might work, see Figure 7.
Researchers and developers of spin- function as spin polarizers and spin applications, many basic questions per-
tronic devices currently take two differ- valves. This is crucial because, unlike taining to combining semiconductors
ent approaches. In the first, they seek to semiconductor transistors, existing met- with other materials to produce viable
perfect the existing GMR-based technol- al-based devices do not amplify signals spintronic technology remain unan-
ogy either by developing new materials (although they are successful switches or swered. For example, it is far from well
with larger populations of oriented spins valves). If spintronic devices could be understood whether or how placing a
(called spin polarization) or by making made from semiconductors, however, semiconductor in contact with another
improvements in existing devices to pro- then in principle they would provide material would impede spin transport
vide better spin filtering. The second ef- amplification and serve, in general, as across the interface. In the past, our
fort, which is more radical, focuses on multi-functional devices. Perhaps even strategy for understanding spin trans-
finding novel ways both to generate and more importantly, semiconductor-based port in hybrid semiconductor struc-
to utilize spin-polarized currents—that devices could much more easily be inte- tures was to borrow knowledge ob-
is, to actively control spin dynamics. The grated with traditional semiconductor tained from studies of more traditional
intent is to thoroughly investigate spin technology. magnetic materials. More recently,
transport in semiconductors and search Although semiconductors offer clear however, investigators have begun di-
for ways in which semiconductors can advantages for use in novel spintronic rect investigation of spin transport
2001 November–December 517

3. (similar, in effect, to the source and
drain, respectively, in a field effect tran-
sistor). The emitter emits electrons with
their spins oriented along the direction
of the electrode’s magnetization, while
the collector (with the same electrode
magnetization) acts as a spin filter and
accepts electrons with the same spin
only. In the absence of any changes to
the spins during transport, every emit-
ted electron enters the collector. In this
random spin spin alignment device, the gate electrode produces a
field that forces the electron spins to
precess, just like the precession of a
spinning top under the force of gravity.
The electron current is modulated by
the degree of precession in electron
spin introduced by the gate field: An
electron passes through the collector if
its spin is parallel, and does not if it is
antiparallel, to the magnetization. The
Datta-Das effect should be most visible
for narrow band-gap semiconductors
such as InGaAs, which have relatively
large spin-orbit interactions (that is, a
unmagnetized magnetized magnetic field introduced by the gate
current has a relatively large effect on
Figure 2. Spins can arrange themselves in a variety of ways that are important for spintronic
devices. They can be completely random, with their spins pointing in every possible direc- electron spin). Despite several years of
tion and located throughout a material in no particular order (upper left). Or these randomly effort, however, the effect has yet to be
located spins can all point in the same direction, called spin alignment (upper right). In solid convincingly demonstrated experi-
state materials, the spins might be located in an orderly fashion on a crystal lattice (lower mentally.
left) forming a nonmagnetic material. Or the spins may be on a lattice and be aligned as in a Another interesting concept is the
magnetic material (lower right). all-metal spin transistor developed by
Mark Johnson at the Naval Research
across interfaces in all-semiconductor spin devices may be well suited to Laboratory. Its trilayer structure con-
devices. In such a scenario a combina- such tasks, since spin is an intrinsically sists of a nonmagnetic metallic layer
tion of optical manipulation (for exam- quantum property. sandwiched between two ferromag-
ple, shining circularly polarized light nets. The all-metal transistor has the
on a material to create net spin polar- Spintronic Devices same design philosophy as do giant
ization) and material inhomogeneities The first scheme for a spintronic device magnetoresistive devices: The current
(by suitable doping as in a recently dis- based on the metal-oxide-semiconduc- flowing through the structure is modi-
covered class of gallium-manganese- tor technology familiar to microelec- fied by the relative orientation of the
arsenide ferromagnetic materials) can tronics designers was the field effect magnetic layers, which in turn can be
be employed to tailor spin transport spin transistor proposed in 1989 by controlled by an applied magnetic
properties. Supriyo Datta and Biswajit Das of Pur- field. In this scheme, a battery is con-
In addition to the near-term studies due University. In a conventional field nected to the control circuit (emitter-
of various spin transistors and spin effect transistor, electric charge is intro- base), while the direction of the current
transport properties of semiconduc- duced via a source electrode and col- in the working circuit (base-collector)
tors, a long-term and ambitious sub- lected at a drain electrode. A third elec- is effectively switched by changing the
field of spintronics is the application of trode, the gate, generates an electric magnetization of the collector. The cur-
electron and nuclear spins to quantum field that changes the size of the chan- rent is drained from the base in order
information processing and quantum nel through which the source-drain to allow for the working current to
computation. The late Richard Feyn- current can flow, akin to stepping on a flow under the “reverse” base-collec-
man and others have pointed out that garden hose. This results in a very tor bias (antiparallel magnetizations).
quantum mechanics may provide great small electric field being able to control Neither current nor voltage is ampli-
advantages over classical physics in large currents. fied, but the device acts as a switch or
computation. However, the real boom In the Datta-Das device, a structure spin valve to sense changes in an exter-
started after Peter Shor of Bell Labs de- made from indium-aluminum-ar- nal magnetic field. A potentially signif-
vised a quantum algorithm that would senide and indium-gallium-arsenide icant feature of the Johnson transistor
factor very large numbers into primes, provides a channel for two-dimension- is that, being all metallic, it can in prin-
an immensely difficult task for conven- al electron transport between two fer- ciple be made extremely small using
tional computers and the basis for romagnetic electrodes. One electrode nanolithographic techniques (perhaps
modern encryption. It turns out that acts as an emitter, the other a collector as small as tens of nanometers). An im-
518 American Scientist, Volume 89

4. portant disadvantage of Johnson’s
transistor is that, being all-metallic, it
will be difficult to integrate this spin gate V
transistor device into existing semicon-
ductor microelectronic circuitry. ferromagnetic emitter ferromagnetic collector
As noted previously, a critical disad-
vantage of metal-based spintronic de- InAlAs
vices is that they do not amplify sig-
nals. There is no obvious metallic InGaAs
analog of the traditional semiconductor
transistor in which draining one elec-
tron from the base allows tens of elec-
trons to pass from the emitter into the
collector (by reducing the electrostatic
barrier generated by electrons trapped
in the base). Motivated by the possibili- ferromagnetic ferromagnetic
ty of having both spin polarization and emitter collector
amplification, my group has recently
studied a prototype device, the spin-
polarized p-n junction. (In the p, or pos- InAlAs
itive, region the electrons are the mi-
nority carriers, holes the majority; in the
n, or negative, region the roles are re-
versed.) In our scheme we illuminate
the surface of the p-type region of a gal-
lium arsenide p-n junction with circu- InGaAs
larly polarized light to optically orient
the minority electrons. By performing
a realistic device-modeling calculation
we have discovered that the spin can
be effectively transferred from the p
side into the n side, via what we call
spin pumping through the minority ferromagnetic ferromagnetic
channel. In effect, the spin gets ampli- emitter collector
fied going from the p to the n region
through the depletion layer. InAlAs
One possible application of our pro-
posed spin-polarized p-n junction is
something we call the spin-polarized
solar cell. As in ordinary solar cells,
light illuminates the depletion layer of
a semiconductor (such as gallium ar- InGaAs
senide), generating electron-hole pairs.
The huge built-in electric field in the
layer (typically 104 volts per centime-
ter) swiftly sweeps electrons into the n Figure 3. Datta-Das spin transistor was the first spintronic device to be proposed for fabrica-
region and holes into the p region. If a tion in a metal-oxide-semiconductor geometry familiar in conventional microelectronics. An
wire connects the edges of the junction, electrode made of a ferromagnetic material (purple) emits spin-aligned electrons (red
spheres), which pass through a narrow channel (blue) controlled by the gate electrode (gold)
a current flows. If the light is circularly
and are collected by another ferromagnetic electrode (top). With the gate voltage off, the
polarized (from filtered solar photons, aligned spins pass through the channel and are collected at the other side (middle). With the
for instance), the generated electrons are gate voltage on, the field produces magnetic interaction that causes the spins to precess, like
spin polarized. (Holes in III-V semicon- spinning tops in a gravity field. If the spins are not aligned with the direction of magnetiza-
ductors—for example, gallium arsenide, tion of the collector, no current can pass. In this way, the emitter-collector current is modulat-
indium arsenide and others—which are ed by the gate electrode. As yet, no convincingly successful application of this proposal has
most useful for opto-spin-electronic been demonstrated.
purposes, lose their spin very quickly,
so that their polarization can be ne- ˇ
Most recently, Igor Zutic , Jaroslav
´ junction around the electrodes. If the
glected.) As the spin-polarized elec- Fabian and I have proposed a new kind depletion layer is wider than the elec-
trons created in the depletion layer of magnetic field effect transistor. Elec- trodes, no (or very small) electric cur-
pump the spin into the n region, the re- trodes of an external circuit are placed rent flows. As the width decreases,
sulting current is spin polarized. perpendicular to the p-n junction. The more and more electrons come into
Hence, photons of light are converted current is determined by the amount of contact with the electrodes and the cur-
into oriented spins. available electrons in the region of the rent rapidly increases. Traditionally,
2001 November–December 519

5. is spin-polarized. Today, the range of
materials we can study has significant-
ly increased, including novel ferro-
magnetic semiconductors, high-tem-
base perature superconductors and carbon
nanotubes. But several questions—
such as the role of the interface sepa-
rating different materials and how to
create and measure spin polarization—
collector emitter
still remain open and are of fundamen-
tal importance to novel spintronic ap-
plications.
As devices decrease in size, the scat-
Figure 4. In the spin transistor invented by Mark Johnson, two ferromagnetic electrodes— tering from interfaces plays a domi-
the emitter and collector—sandwich a nonmagnetic layer—the base. When the ferromagnets nant role. In these hybrid structures the
are aligned, current flows from emitter to collector (left). But when the ferromagnets have presence of magnetically active inter-
different directions of magnetization, the current flows out of the base to emitter and collec- faces can lead to spin-dependent trans-
tor (right). Although it can act as a spin valve, this structure shares the disadvantage of all- mission (spin filtering) and strongly in-
metal spintronic devices in that it cannot be an amplifier. fluence operation of spintronic devices
by modifying the degree of spin polar-
field effect transistors operate with an device could find use in magnetic sen- ization. One way to test these ideas is
applied electric field (voltage) along the sor technology such as magnetic read by directly injecting spins from a fer-
junction, as the width of the depletion heads or magnetic memory cells. romagnet, where the spins start out in
layer is sensitive to the voltage. We pro- Go with the Flow alignment, into a nonmagnetic semi-
pose to use instead a magnetic field. If If spintronic devices are ever to be conductor. Understanding this kind of
the n or p region (or both) is doped practical, we need to understand how spin injection is also required for hy-
with magnetic impurities, an external spins move through materials and how brid semiconductor devices, such as
magnetic field produces a physical ef- to create large quantities of aligned the Datta-Das spin transistor discussed
fect equivalent to applying an external spins. Thirty years ago, pioneering ex- in the previous section. But this situa-
voltage and could effectively tailor the periments on spin transport were per- tion is very complicated, and a com-
width of the junction. (At the same formed by Paul Tedrow and Robert plete picture of transport across the fer-
time, this affects spin-up and spin- Meservy of MIT on ferromagnet/su- romagnetic-semiconductor interface is
down electrons differently: A spin-po- perconductor sandwiches to demon- not yet available. In its absence, re-
larized current results as well). Such a strate that current across the interface searches have been studying a simpler
case of normal metal - semiconductor
contacts.
circularly polarized light Unfortunately, experiments on spin
injection into a semiconductor indicate
that the obtained spin polarization is
substantially smaller than in the ferro-
magnetic spin injector, spelling trouble
for spintronic devices. In this case,
holes where spins diffuse across the inter-
face, there is a large mismatch in con-
ductivities, and this presents a basic
p n obstacle to achieving higher semicon-
ductor spin polarization with injection.
An interesting solution has been pro-
IIIV posed to circumvent this limitation. By
semiconductor inserting tunnel contacts—a special
kind of express lane for carriers—in-
vestigators found that they could elim-
inate the conductivity mismatch. More-
over, to reduce significant material
differences between ferromagnets and
Figure 5. Spintronic solar cells have been proposed by the author and his colleagues. semiconductors, one can use a magnet-
Sunlight passes through a filter to produce circularly polarized light, which is absorbed in ic semiconductor as the injector. While
the region between p-type and n-type semiconductors. This creates spin polarized electron it was shown that this approach could
hole pairs in this so-called “depletion” layer, but if a semiconductor of the III-V variety is
lead to a high degree of spin polariza-
used (gallium arsenide, for example), the polarization is only retained by the electrons. The
inherent electric field at the layer boundaries sweeps the holes to the p side and the electrons
tion in a nonmagnetic semiconductor,
to the n side. Just as with a conventional solar cell, a wire connected from the p electrode to it only worked at low temperature. For
the n electrode will now have a current flowing in it, but in this case the current is spin successful spintronic applications, fu-
polarized. ture efforts will have to concentrate on
520 American Scientist, Volume 89

6. fabricating ferromagnetic semiconduc-
tors in which ferromagnetism will per-
sist at higher temperatures.
The issues involving spin injection
in semiconductors, as well as efforts to
fabricate hybrid structures, point to-
ward a need to develop methods to
study fundamental aspects of spin-po-
larized transport in semiconductors. magnetic p n magnetic
We recently suggested studying hybrid field field
semiconductor-superconductor struc- depletion
tures for understanding spin transmis- layer
sion properties, where the presence of
the superconducting region can serve
as a tool to investigate interfacial trans-
parency and spin-polarization. In ad-
dition to charge transport, which can
be used to infer the degree of spin-po-
larization, one could also consider pure
ˇ ´
spin transport. Igor Zutic and I have
Figure 6. In the magnetic field effect transistor proposed by the author and his colleagues, an
been able to calculate this in a hybrid external current flows vertically through the structure shown. Normally, semiconductors are
semiconductor structure with our “doped” with impurity atoms to create the p-type and n-type materials, but if these impuri-
model of the interface. We choose a ties are magnetic atoms, then a magnetic field applied in the direction shown can alter the
geometry where semi-infinite semicon- thickness of the middle depletion layer. As the size of this channel is increased and
ductor and superconductor regions are decreased, the current flowing in the external circuit is increased and decreased, respectively.
separated by an interface at which par- Thus a small magnetic field can extert a large effect on an electric current. This is analogous
ticles can experience potential and to a conventional field effect transistor where an electric field controls the thickness of the
spin-flip scattering. In this approach depletion layer and hence the current.
we need to identify the appropriate
scattering processes and their corre- arated.) These properties give a quan- coherent much longer than even their
sponding magnitudes. We find that al- tum computer the ability to, in effect, already long coherence times in the
though spin conductance shows high operate in parallel—making many bulk. However, to trap a single electron
sensitivity to spin polarization, there computations simultaneously. in a gated quantum dot is a difficult
remains an experimental challenge to Quantum computation requires that task experimentally. In addition, to ap-
directly measure the spin current, the quantum states remain coherent, or ply a local magnetic field on one quan-
rather than the usual charge current. undisturbed by interactions with the tum dot without affecting other neigh-
outside world, for a long time, and the boring dots and trapped spins may also
Computing with Spins states need to be controlled precisely. be impossible in practice.
One of the most ambitious spintronic Because of the requirement of very long We recently showed that in princi-
devices is the spin-based quantum coherence time for a quantum comput- ple it is possible (albeit with great diffi-
computer in solid-state structures. The er, both nuclear spin and electron spin culties) to overcome both of these
use of electron (or nuclear) spin for have been proposed as qubits, since problems. Regarding the difficulty of
these purposes is a manifestly obvious spins inherently have long coherence trapping single electrons in an array of
idea. The particles that physicists call times because they are immune to the quantum dots, Xuedong Hu and I car-
“fermions” have two states of spin and long-range electrostatic Coulomb inter- ried out a multi-electron calculation
so can assume either “up” or “down” actions between charges. I will review and showed that, subject to certain
states, making them natural and intrin- only a few of the representative conditions, an odd number of electrons
sic binary units called quantum bits, or schemes proposed during the past sev- trapped in a quantum dot could effec-
qubits. A qubit, as opposed to a classi- eral years and discuss some recent tively work as a qubit. The problem of
cal binary computing bit, however, is work with my colleagues on electron the local magnetic field may be solved
not restricted to representing just 0 or 1. spin based quantum computation. by the method of quantum error cor-
Because of the quantum property of su- One such scheme uses the spin of a rection. The lack of a purely local mag-
perposition, it may represent arbitrary single electron trapped in an isolated netic field that acts on just a single
combinations of both values—that is, structure called a quantum dot as its qubit is essentially a problem of an in-
an infinite number of possibilities be- qubit. Local magnetic fields are used to homogeneous magnetic field that the
tween 0 and 1. To perform a computa- manipulate single spins, while inter-dot other qubits feel. Such a field may
tion, some initial state is imposed on interaction is used to couple neighbor- come from magnetic impurities or un-
the spins, and this state is allowed to ing qubits and introduce two-qubit en- wanted currents away from the struc-
evolve in time through a process of en- tanglement. A single trapped electron ture. We have done a detailed analysis
tanglement. (Quantum entanglement in a quantum dot implies an extremely and found that there is an error pro-
means that the spins of particles polar- low carrier density, which means very portional to the field inhomogeneity.
ized together remain correlated, even low coupling with the outside world. Using realistic estimates for such an in-
though they may become spatially sep- Thus the electron spins should remain homogeneous magnetic field on
2001 November–December 521

7. nanometer scale quantum dots showed external gate voltages. In addition, the the silicon computer scheme. Another
that the error introduced by the field final measurement is also supplied by potential advantage of a quantum
can actually be corrected (with great the donor electrons by converting spin computer based on silicon is the
difficulty). information into charge information. A prospect of using the vast resources
One of the most influential schemes significant advantage of silicon is that available from the semiconductor chip
is the nuclear spin based quantum its most abundant isotope is spinless, industry.
computer proposed by Bruce Kane, thus providing a “quiet” environment In addition to all the operational
now at the University of Maryland. for donor nuclear spin qubits. In gen- problems discussed above, there is still
Here silicon donor nuclei serve as eral, nuclear spins have very long co- the very hard question of how to reli-
qubits, while donor electrons together herence times because they do not ably measure single electron spins (the
with external gates provide single- strongly couple with their environment readout in quantum computers). Not
qubit (using an external magnetic field) and are thus good candidates for only must one be able to measure single
and two-qubit operations (using elec- qubits. However, this isolation from spin states, but one has to be able to do
tron-nuclear and electron-electron spin the environment also brings with it the it reasonably fast (nanoseconds to mi-
interactions). The donor electrons are baggage that individual nuclear spins croseconds) so that the spin state does
essentially shuttles between different are difficult to control. This is why not decay before readout. Existing spin-
nuclear qubits and are controlled by donor electrons play a crucial role in measurement techniques can at best
measure 500 to 1,000 electron spins, and
extensive experimental exploration is
needed to solve this problem.
Future prospects
Much remains to be understood about
the behavior of electron spins in mate-
rials for technological applications, but
radio frequency much has been accomplished. A num-
ber of novel spin-based microelectronic
devices have been proposed, and the
giant magnetoresistive sandwich struc-
ture is a proven commercial success,
being a part of every computer coming
off the production line. In addition,
spintronic-based nonvolatile memory
elements may very well become avail-
able in the near future. But before we
can move forward into broad applica-
tion of spin-based multifunctional and
novel technologies, we face the funda-
Figure 7. Quantum computing may be possi-
ble one day with spintronic devices. In an
implementation proposed by Bruce Kane,
phosphorus atoms doped into a silicon sub-
strate act as the quantum computing ele-
ments. The diagram shows one part of a
larger array of phosphorus atoms in a hypo-
thetical quantum computer. Each phospho-
rus nucleus embedded in the substrate has
its own nuclear spin and each donates an
electron, which in turn have their own spin.
The state of the nuclear spins can be read
and written by the outer electrodes, called
read read “A gates,” and the nuclear spins can be
out out allowed to interact via the electrons, which
are controlled with the center, or “J gates.”
In a typical series of steps, the nuclear spins
would be set with a pulse of a radio fre-
radio frequency
quency magnetic field (top panel). Next, the
electrons (red spheres) would be activated
with the J gates to move between the phos-
phorus atoms (black circles with arrows),
creating a quantum mechanical “entangled”
state (middle panel). Finally, the gates are
used again to read out the final quantum
state of the array of phosphorus atoms via
the spin state of the electrons (bottom panel).
522 American Scientist, Volume 89

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Acknowledgment er. Physical Review A 61:062301.
The author acknowledges spintronics re- Hu, X., R. De Sousa and S. Das Sarma. 2001. In-
search support from the U.S. Office of terplay between Zeeman coupling and
Naval Research, the Defense Advance Re- swap action in spin based quantum com- Links to Internet resources for
search Projects Agency, the National Se- puter models: Error correction in inhomo- “Spintronics” are available on the
curity Agency and the Advanced Research geneous magnetic fields. Physical Review Let- American Scientist Web site:
ters 86:918.
and Development Activity. He wishes to http://www.americanscientist.org/art
Hu, X., and S. Das Sarma. 2001. Spin-based
thank Jaroslav Fabian, Xuedong Hu and quantum computation in multielectron icles/01articles/dassarma.html
ˇ ´
Igor Zutic for extensive research collabora- quantum dots. Physical Review A 64:042312.
tions leading to the ideas, theories and re- Johnson, M. 1994. The all-metal spin transistor.
sults presented in this article. IEEE Spectrum 31:47.
2001 November–December 523