Spintronics: The Problem of Efficient Polarized Spin Injection
A. Gabel
Boston University (Introduction to Solid State Physics)
This article gives a broad review of spin-based electronics and focuses specifically on the issue of
injecting spin polarized electrons into a semiconductor. This is currently one of a few major obstacles to creating commercially viable spin-based electronic circuitry. The basis for most spin injection proposals is the fact that ferromagnets have partially polarized conduction electrons, due to
the asymmetry in the density of states between spin up and down electrons. The basic goal discussed in the paper is to pass the spin polarized current in a ferromagnet into a semiconductor.
This article discusses three possible designs. The first is a direct ferromagent to semiconductor
junction. The second is a ferromagnetically doped semiconductor to semiconductor junction, and
the third is a ferrromagnet – insulator – semiconductor junction. All three have serious flaws
which prevent their use in any commercial applications.
Background
Currently, all integrated circuits on
which computers are based depend on the
electrical charge electrons, but ignore the
property of spin, except that it adds to quantum degeneracy. However, utilizing the additional spin degree of freedom could dramatically improve computer performance.
Basing computations on spin, not charge,
has the possibility for decreased volatility,
increased data processing speeds, decreased
power consumption, and increased integrated circuit density. (1) The study of spinbased-electronics, or ‘spintronics,’ has blossomed into an extremely active field of research.
The basic logic component of an
electrical circuit is the transistor switch. In
all transistors, a small applied voltage will
control a large current. For example, zero
applied voltage may allow zero current to
pass through the circuit (the ‘off’ state)
while a small voltage will allow current to
pass as if there is no resistance at all (the
‘on’ the state). (2) A transistor that depended on the spin nature of electrons would be
the basis for any spintronic device.
In a 1990 paper, Datta and Das proposed one of the first designs for a spin
based transistor. (3) Their device proposal
is quite simple, and has thus become a
standard starting point for discussion on spin
transistors. However, in order to understand
the device it is first necessary to understand
spin polarization in ferromagnets.
Ferromagnets exhibit spontaneous
symmetry breaking when they become magnetized. This internal magnetic field splits
the density of states for electrons with spin
along the magnetization and opposite to it.
(See figure 1) This splitting is described by
Figure 1: Asymmetric density of states for a
typical ferromagent. M shows the direction of
magnetization.
Figure 2: Schematic design of Datta and Das spin Transistor. Conductions would flow from left to right with
initial polarization parallel to the direction of motion. The gate electrode is charged to block current and uncharged to allow current.
the Zeeman effect. Polarization is defined
as the fraction of uncompensated spin states
at the Fermi surface.
𝑃𝑜𝑙𝑎𝑟𝑖𝑧𝑎𝑡𝑖𝑜𝑛 = |
𝐷(𝐸𝐹 )𝑢𝑝 − 𝐷(𝐸𝐹 )𝑑𝑜𝑤𝑛
|
𝐷(𝐸𝐹 )𝑢𝑝 + 𝐷(𝐸𝐹 )𝑑𝑜𝑤𝑛
The density of states at the fermi surface is
proportional to the number of conduction
electrons, so the polarization also gives the
fraction of uncompensated spins of conducting charge carriers.
The spin transistor proposed by Datta and Das depends on this polarization effect. The device would consist of a ferromagnetic source and a ferromagnetic drain
electrodes with magnetization along the
same direction for each. (4) These would be
connected by a 2 dimensional semiconductor with a gate electrode placed in between.
(See figure 2) A small voltage on the gate
electrode will create an electric field, and for
carriers confined to an asymmetric quantum
well, this induces an effective magnetic
field, called the Rashba field. (5) This magnetic field causes the electrons to precess. If
the charge carriers precess to 180o out of
phase then they will be anti-aligned with the
drain electrode, and the impedence in the
circuit will be large. However, if the carrier
spins are aligned with the drain, then the
impedence will be low. This device is a
transistor since a small voltage on the gate
electrode will control a relatively large current.
There are four key ingredients to realize a working Datta and Das spin transistor. There must be successful injection of
spin polarized current from the source electrode, spin coherent propagation through the
semiconductor, induced spin precession, and
spin-selective collection of current at the
drain electrode. (5) All four are active areas
of research, but this paper will focus on the
first requirement, successful injection of polarized spin into the semiconductor.
It is also important to note that this
device would also work with a metal in
place of the semiconductor. The motivation
for using semiconductors is that they are already well studied and manufactured for integrated circuits with high purity and expertise.
Optical Detection of Spin Injection
Before discussing different spin injection designs, it is necessary to understand
how to test experimentally if a current is polarized. Currently, the most sensitive technique uses optical methods. A typical set up
is outlined below.
In zincblende semiconductors, like
GaAs, the selection rules for allowed recombination of electrons and holes are spin
dependant. (5) The helicity or polarization
of light coming from spin up electrons will
be opposite that from spin down electrons.
In a typical spin injection detection experiment (see figure 3) a GaAs/AlGaAs heterostructure is placed in contact with the semiconductor (GaAs) which is in contact with
the ferromagnetic injector. When current is
driven through the system, the electrons
which have passed through the ferromagnet
into the semiconductor layer combine with
holes being driven by the current in the opposite direction. The light emitted from
these recombinations will have polarization
proportional to the polarization of the electrons, according to the spin-dependant recombination rules. By measuring the polarization of the emitted light, we can determine the spin polarization of the injected
electron current. (6)
Other current polarization techniques
are often used which require only electronics
and no optics, and are, thus, easier to implement. However, the optical technique is
linearly sensitive to polarization, while other
techniques are sensitive only to the polarization squared. (7) This is particularly useful
since the effects being measured are often
quite small.
Spin Injection Schemes
With a way to test a spin polarized
injection mechanism, we now look at specific designs. The simplest design is that proposed by Datta and Das for their spin transistor. In there design, current is driven
through a ferromagnet directly into a semiconductor. Unfortunately, experiment has
shown that this injection technique has low
efficiency, 1-2%. (8) This was explained
with a theoretical framework by Schmidt et
al, which assumes that the electrons propagate by diffusion. (9) The polarization of
current at the interface is given by
𝑃=
𝑃0
1 + (1 − 𝑃02 )
𝜎𝐹 𝜆𝑆𝐶
𝜎𝑆𝐶 𝜆𝐹
Where P0 is the polarization far inside the
ferromagnet; σF and σSC are the conductivity
of the ferromagnet and semiconductor, respectively; and λF and λSC are the mean distances travelled by spin carriers before a
spin flipping scattering occurs. The important feature to notice in this equation is
the ratio of conductivities in the denominator. Conducting ferromagnets, like Fe, typically have conductivities on the order of 103
greater than typical semiconductors. The
huge number in the denominator drives the
spin polarization to zero. This problem is
referred to as ‘conductivity mismatch.’ It
can only be overcome with a bulk ferromagnetic polarization, P0, at or extremely close
to one. Then the otherwise large term in the
Figure 3: Design for optical measuring polarization. Electrons are driven from top to bottom, where they recombine
with holes, in the heterostructure to emit left or right circularly polarized light, depending on their spins.
denominator is offset by the small (1-P02)
factor. Unfortunately, the experimentally
measured polarizations for some typical
metals are far too low at 44% for Fe, 34%
for Co, and 11% for Ni. (5)
An alternative, which addresses the
issue of ‘conductivity mismatch,’ is to use a
ferromagnetically doped semiconductor in
place of the ferromagnet. In this scenario,
the conductivities of both materials are extremely close so the ratio of σF/σSC is close
to 1.
In fact, polarization of injected spins
from a ferromagnetically doped semiconductor into an undoped semiconductor has
been measured between 90-100%. (10) (11)
However, this comes with some major limitations. A large external magnetic field (on
the order of 1.5 Tesla) must be applied to
achieve any appreciable polarization, P0.
Also, the injection is only efficient at extremely low temperatures. The injected spin
polarization drops to between 0-10% for
temperatures above 40K. These limitations
are substantial, and would preclude any
commercially viable applications.
There is another method which does
not suffer from ‘conductivity mismatch’ or
the need for extreme external fields and
temperatures. It is an injector comprised of
a ferromagent/insulator/semiconductor junction. Current would pass through the insulator from the ferromagnet to the semiconductor. Because the transport is due to a tunneling mechanism and not diffusion, our former
analysis does not apply. This was first observed experimentally by Alvarado et al. for
spin polarized electrons tunneling from a
ferromagnetic STM tip, through vacuum,
into a semiconductor sample. (12) Since
then, experiment has detected polarizations
across and a tunneling junction of up to 2%
at room temperature (13) and as high as 30%
polarization at temperature of 5K. (14) A
theoretical framework has been worked out
that predicts the spin injector efficiency will
increase, as the insulator or barrier layer increases in thickness. (1) But a larger barrier
leads to greater impedence in the circuit. So
employing a tunneling junciton for spin injection implies a trade-off. One can achieve
high polarization efficiency at the cost of
either a low current density in the semiconductor or the need for a high current density
in the ferromagnet. These are not ideal
characteristics for in integrated circuit.
Conclusions
The use of spin in electronic circuitry
is a tantalizing method to increase computer
performance. But so far, this has only been
realized as a vague theory, not in actual application. The spin transistor was first proposed by Datta and Das close to 20 years
ago, and a working model has never been
successfully built.
High efficiency spin injection is definitely an obstacle, and so far all of the proposed solutions have been lacking. The
three specific injection systems discussed in
this paper have serious drawbacks in their
present form which would preclude them
from useful applications.
There are still many new ideas that
this paper did not address, and these may be
the key to unlocking the spin transistor puzzle. Whether spintronics is possible is still
an open question.
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