Electric dipole spin resonance (EDSR) is a method to control the magnetic moments inside a material using quantum mechanical effects like the spin–orbit interaction.
Mainly, EDSR allows to flip the orientation of the magnetic moments through the use of electromagnetic radiation at resonant frequencies.
EDSR allows to use the electric component of AC fields to manipulate both charge and spin.
, results in electron paramagnetic resonance, that is, the signal gets absorbed strongly at this frequency as it produces transitions between spin values.
sees, according to the Lorentz transformations of special relativity, a complementary magnetic field
This coupling is known as the spin–orbit interaction and gives corrections to the atomic energies about the order of the fine-structure constant squared
,[2] and this product is larger for massive atoms, already of the order of unity in the middle of the periodic table.
This enhancement of the coupling between the orbital and spin dynamics in massive atoms originates from the strong attraction to the nucleus and the large electron speeds.
While this mechanism is also expected to couple electron spin to the electric component of electromagnetic fields, such an effect has been probably never observed in atomic spectroscopy.
The ratio of the spin–orbit splitting of the bands to the forbidden gap becomes a parameter that evaluates the effect of spin–orbit coupling, and it is generically enhanced, of the order of unity, for materials with heavy ions or with specific asymmetries.
The coupling to the external electric field can be found by substituting the momentum in the kinetic energy as
, is much shorter than all characteristic lengths of solid state physics, EDSR can be by orders of magnitude stronger than EPR driven by an AC magnetic field.
EDSR is usually strongest in materials without the inversion center where the two-fold degeneracy of the energy spectrum is lifted and time-symmetric Hamiltonians include products of the spin related Pauli matrices
In narrow-gap semiconductors with inversion center EDSR can emerge due direct coupling of electric field
However, for transitions between Kramers conjugate bound states, its intensity is suppressed by a factor
The mechanism of its generically high efficiency is illustrated below as applied to electrons in direct-gap semiconductors of the InSb type.
The physical mechanism behind the enhancement is based on the fact that inside crystals electrons move in strong field of nuclei, and in the middle of the periodic table the product
is of the order of unity, and it is this product that plays the role of the effective coupling constant, cf.
However, one should bear in mind that the above arguments based on effective mass approximation are not applicable to electrons localized in deep centers of the atomic scale.
[5][6] EDSR was first observed experimentally with free carriers in indium antimonide (InSb), a semiconductor with strong spin–orbit coupling.
Observations made under different experimental conditions allowed demonstrate and investigate various mechanisms of EDSR.
In a dirty material, Bell[7] observed a motionally narrowed EDSR line at
MacCombe et al.[8] working with high quality InSb observed isotropic EDSR driven by the
by Dobrowolska et al.[9] spin–orbit coupling in n-Ge that manifests itself through strongly anisotropic electron g-factor results in EDSR through breaking translational symmetry by inhomogeneous electric fields which mixes wave functions of different valleys.
EDSR with free and trapped charge carriers was observed and studied at a large variety of three-dimensional (3D) systems including dislocations in Si,[13] an element with notoriously weak spin–orbit coupling.
Principal applications of EDSR are expected in quantum computing and semiconductor spintronics, currently focused on low-dimensional systems.
One of its main goals is fast manipulation of individual electron spins at a nanometer scale, e.g., in quantum dots of about 50 nm size.
Time-dependent magnetic fields practically cannot address individual electron spins at such a scale, but individual spins can be well addressed by time dependent electric fields produced by nanoscale gates.
[15][16][17] For achieving fast qubits operated by EDSR[18] are needed nanostructures with strong spin–orbit coupling.
[19] A different way for achieving fast spin qubits based on quantum dots operated by EDSR is using nanomagnets producing inhomogeneous magnetic fields.