Pulse EPR
Encyclopedia
Pulsed electron paramagnetic resonance
(EPR) is a spectroscopic technique
related to common nuclear magnetic resonance
(NMR). Its most basic form involves the alignment of the net magnetization vector of the electron spins
in a constant magnetic field
. This alignment is perturbed by applying a short oscillating field, usually a microwave pulse. One can then measure the emitted microwave signal which is created by the sample magnetization. Fourier transform
ation of the microwave signal yields an EPR spectrum in the frequency domain. With a vast variety of pulse sequences it is possible to gain extensive knowledge on structural and dynamical properties of paramagnetic compounds. Pulsed EPR techniques such as electron spin echo
envelope modulation (ESEEM) or pulsed electron nuclear double resonance
(ENDOR) can reveal the interactions of the electron spin with its surrounding nuclear spins
.
in 1958, which came from a solution of sodium in ammonia at room temperature . A magnetic field of 0.62 mT was used requiring a frequency of 17.4 MHz. The first microwave electron spin echoes were reported in the same year by Gordon and Bowers using 23 GHz excitation of dopants in silicon
.
A lot of the pioneering early pulsed EPR was conducted in the group of W. B. Mims at Bell Labs
during the 1960s. In the first decade only a small number of groups worked the field, because of the expensive instrumentation, the lack of suitable microwave components and slow digital electronics. The first observation of electron spin echo envelope modulation (ESEEM) was made in 1961 by Mims, Nassau and McGee . Pulsed electron nuclear double resonance
(ENDOR) was invented in 1965 by Mims . In this experiment, pulsed NMR
transitions are detected with pulsed EPR. ESEEM and pulsed ENDOR continue to be important for studying nuclear spins coupled to electron spins.
In the 1980s, the upcoming of the first commercial pulsed EPR and ENDOR spectrometers in the X band
frequency range, lead to a fast growth of the field. In the 1990s, parallel to the upcoming high-field EPR, pulsed EPR and ENDOR became a new fast advancing magnetic resonance spectroscopy tool and the first commercial pulsed EPR and ENDOR spectrometer at W band
frequencies appeared on the market.
as well as in the rotating frame
. In the laboratory frame the static magnetic field B0 is assumed to be parallel to the z-axis and the microwave field B1 parallel to the x-axis. When an electron spin is placed in magnetic field it experiences a torque which causes its magnetic moment
to precess around the magnetic field. The precession frequency is known as the Larmor frequency
ωL (see page 18 of ref ).
where γ is the gyromagnetic ratio and B0 the magnetic field. The electron spins are characterized by two quantum mechanical states, one parallel and one antiparallel to B0. Because of the lower energy of the parallel state more electron spins can be found in this state according to the Boltzmann distribution
. This results in a net magnetization, which is the vector sum of all magnetic moments in the sample, parallel to the z-axis and the magnetic field. To better comprehend the effects of the microwave field B1 it is easier to move to the rotating frame. EPR experiments usually use a microwave resonator designed to create a linearly polarized
microwave field B1, perpendicular to the much stronger applied magnetic field B0. The rotating frame is fixed to the rotating B1 components. First we assume to be on resonance with the precessing magnetization vector M0.
Therefore the component of B1 will appear stationary. In this frame also the precessing magnetization components appear to be stationary that leads to the disappearance of B0, and we need only to consider B1 and M0. The M0 vector is under the influence of the stationary field B1, leading to another precession of M0, this time around B1 at the frequency ω1.
This angular frequency ω1 is also called the Rabi frequency
. Assuming B1 to be parallel to the x-axis, the magnetization vector will rotate around the +x-axis in the zy-plane as long as the microwaves are applied. The angle by which M0 is rotated is called the tip angle α and is given by:
Here tp is the duration for which B1 is applied, also called the pulse length. The pulses are labeled by the rotation of M0 which they cause and the direction from which they are coming from, since the microwaves can be phase-shifted from the x-axis on to the y-axis. For example, a +y π/2 pulse means that a B1 field, which has been 90 degrees phase-shifted out of the +x into the +y direction, has rotated M0 by a tip angle of π/2, hence the magnetization would end up along the –x-axis. That means the end position of the magnetization vector M0 depends on the length, the magnitude and direction of the microwave pulse B1. In order to understand how the sample emits microwaves after the intense microwave pulse we need to go back to the laboratory frame. In the rotating frame and on resonance the magnetization appeared to be stationary along the x or y-axis after the pulse. In the laboratory frame it becomes a rotating magnetization in the x-y plane at the Larmor frequency. This rotation generates a signal which is maximized if the magnetization vector is exactly in the xy-plane. This microwave signal generated by the rotating magnetization vector is called free induction decay
(FID) (see page 175 of ref ).
Another assumption we have made was the exact resonance condition, in which the Larmor frequency is equal to the microwave frequency. In reality EPR spectra have many different frequencies and not all of them can be exactly on resonance, therefore we need to take off-resonance effects into account. The off-resonance effects lead to three main consequences. The first consequence can be better understood in the rotating frame. A π/2 pulse leaves magnetization in the xy-plane, but since the microwave field (and therefore the rotating frame) do not have the same frequency as the precessing magnetization vector, the magnetization vector rotates in the xy-plane, either faster or slower than the microwave magnetic field B1. The rotation rate is governed by the frequency difference Δω.
If Δω is 0 then the microwave field rotates as fast as the magnetization vector and both appear to be stationary to each other. If Δω>0 then the magnetization rotates faster than the microwave field component in a counter-clockwise motion and if Δω<0 then the magnetization is slower and rotates clockwise. This means that the individual frequency components of the EPR spectrum, will appear as magnetization components rotating in the xy-plane with the rotation frequency Δω. The second consequence appears in the laboratory frame. Here B1 tips the magnetization differently out of the z-axis, since B0 does not disappear when not on resonance due to the precession of the magnetization vector at Δω. That means that the magnetization is now tipped by an effective magnetic field Beff, which originates from the vector sum of B1 and B0. The magnetization is then tipped around Beff at a faster effective rate ωeff.
This leads directly to the third consequence that the magnetization can not be efficiently tipped into the xy-plane because Beff does not lie in the xy-plane, as B1 does. The motion of the magnetization now defines a cone. That means as Δω becomes larger, the magnetization is tipped less effectively into the xy-plane, and the FID signal decreases. In broad EPR spectra where Δω > ω1 it is not possible to tip all the magnetization into the xy-plane to generate a strong FID signal. This is why it is important to maximize ω1 or minimize the π/2 pulse length for broad EPR signals.
So far the magnetization was tipped into the xy-plane and it remained there with the same magnitude. However, in reality the electron spins interact with their surroundings and the magnetization in the xy-plane will decay and eventually return to alignment with the z-axis. This relaxation process is described by the spin-lattice relaxation time T1, which is a characteristic time needed by the magnetization to return to the z-axis, and by the spin-spin relaxation time T2, which describes the vanishing time of the magnetization in the xy-plane. The spin-lattice relaxation results from the urge of the system to return to thermal equilibrium after it has been perturbed by the B1 pulse. Return of the magnetization parallel to B0 is achieved through interactions with the surroundings, that is spin-lattice relaxation. The corresponding relaxation time needs to be considered when extracting a signal from noise, where the experiment needs to be repeated several times, as quickly as possible. In order to repeat the experiment, one needs to wait until the magnetization along the z-axis has recovered, because if there is no magnetization in z direction, then there is nothing to tip into the xy-plane to create a significant signal.
The spin-spin relaxation time, also called the transverse relaxation time, is related to homogeneous and inhomogeneous broadening. An inhomogeneous broadening results from the fact that the different spins experience local magnetic field inhomogeneities (different surroundings) creating a large number of spin packets characterized by a distribution of Δω. As the net magnetization vector precesses, some spin packets slow down due to lower fields and others speed up due to higher fields leading to a fanning out of the magnetization vector that results in the decay of the EPR signal. The other packets contribute to the transverse magnetization decay due to the homogeneous broadening. In this process all the spin in one spin packet experience the same magnetic field and interact with each other that can lead to mutual and random spin flip-flops. These fluctuations contribute to a faster fanning out of the magnetization vector.
All the information about the frequency spectrum is encoded in the motion of the transverse magnetization. The frequency spectrum is reconstructed using the time behavior of the transverse magnetization made up of y- and x-axis components. It is convenient that these two can be treated as the real and imaginary components of a complex quantity and use the Fourier theory to transform the measured time domain signal into the frequency domain representation. This is possible because both the absorption (real) and the dispersion (imaginary) signals are detected.
The FID signal decays away and for very broad EPR spectra this decay is rather fast due to the inhomogeneous broadening. To obtain more information one can recover the disappeared signal with another microwave pulse to produce a Hahn echo
. After applying a π/2 pulse (90°), the magnetization vector is tipped into the xy-plane producing an FID signal. Different frequencies in the EPR spectrum (inhomogeneous broadening) cause this signal to "fan out", meaning that the slower spin-packets trail behind the faster ones. After a certain time t, a π pulse (180°) is applied to the system inverting the magnetization, and the fast spin-packets are then behind catching up with the slow spin-packets. A complete refocusing of the signal occurs then at time 2t. An accurate echo caused by a second microwave pulse can remove all inhomogeneous broadening effects. After all of the spin-packets bunch up, they will dephase again just like an FID. In other words, a spin echo is a reversed FID followed by a normal FID, which can be Fourier transformed to obtain the EPR spectrum. The longer the time between the pulses becomes, the smaller the echo will be due to spin relaxation. When this relaxation leads to an exponential decay in the echo height, the decay constant is the phase memory time TM, which can have many contributions such as transverse relaxation, spectral, spin and instantaneous diffusion. Changing the times between the pulses leads to a direct measurement of TM as shown in the spin echo decay animation below.
are widely-used echo
experiments, in which the interaction of electron spins with the nuclei in their environment can be studied and controlled. Quantum computing and spintronics
, in which spins are used to store information, have led to new lines of research in pulsed EPR.
One of the most popular pulsed EPR experiments currently is double electron-electron resonance (DEER), which is also known as pulsed electron-electron double resonance (ELDOR). This uses two different frequencies to control different spins in order to find out the strength of their coupling. The distance between the spins can then be inferred from their coupling strength, which is used to study structures of large bio-molecules.
Electron paramagnetic resonance
Electron paramagnetic resonance or electron spin resonance spectroscopyis a technique for studying chemical species that have one or more unpaired electrons, such as organic and inorganic free radicals or inorganic complexes possessing a transition metal ion...
(EPR) is a spectroscopic technique
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...
related to common nuclear magnetic resonance
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
(NMR). Its most basic form involves the alignment of the net magnetization vector of the electron spins
Electron magnetic dipole moment
In atomic physics, the electron magnetic dipole moment is the magnetic moment of an electron caused by its intrinsic property of spin.-Magnetic moment of an electron:...
in a constant magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
. This alignment is perturbed by applying a short oscillating field, usually a microwave pulse. One can then measure the emitted microwave signal which is created by the sample magnetization. Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
ation of the microwave signal yields an EPR spectrum in the frequency domain. With a vast variety of pulse sequences it is possible to gain extensive knowledge on structural and dynamical properties of paramagnetic compounds. Pulsed EPR techniques such as electron spin echo
Spin echo
In magnetic resonance, a spin echo is the refocusing of precessing spin magnetisation by a pulse of resonant radiation. Modern nuclear magnetic resonance and magnetic resonance imaging rely heavily on this effect....
envelope modulation (ESEEM) or pulsed electron nuclear double resonance
Electron nuclear double resonance
Electron nuclear double resonance is a magnetic resonance technique for obtaining detailed molecular and electronic structure of paramagnetic species. In the standard continuous wave experiment, a microwave field is first applied, followed by irradiation with a radio frequency field...
(ENDOR) can reveal the interactions of the electron spin with its surrounding nuclear spins
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
.
Scope
Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) is a spectroscopic technique widely used in biology, chemistry, medicine and physics to study systems with one or more unpaired electrons. Because of the specific relation between the magnetic parameters, electronic wavefunction and the configuration of the surrounding non-zero spin nuclei, EPR and ENDOR provide information on the structure, dynamics and the spatial distribution of the paramagnetic species. However, these techniques are limited in spectral and time resolution when used with traditional continuous wave methods. This resolution can be improved in pulsed EPR by investigating interactions separately from each other via pulse sequences.Historical overview
R. J. Blume reported the first electron spin echoSpin echo
In magnetic resonance, a spin echo is the refocusing of precessing spin magnetisation by a pulse of resonant radiation. Modern nuclear magnetic resonance and magnetic resonance imaging rely heavily on this effect....
in 1958, which came from a solution of sodium in ammonia at room temperature . A magnetic field of 0.62 mT was used requiring a frequency of 17.4 MHz. The first microwave electron spin echoes were reported in the same year by Gordon and Bowers using 23 GHz excitation of dopants in silicon
Silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...
.
A lot of the pioneering early pulsed EPR was conducted in the group of W. B. Mims at Bell Labs
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...
during the 1960s. In the first decade only a small number of groups worked the field, because of the expensive instrumentation, the lack of suitable microwave components and slow digital electronics. The first observation of electron spin echo envelope modulation (ESEEM) was made in 1961 by Mims, Nassau and McGee . Pulsed electron nuclear double resonance
Electron nuclear double resonance
Electron nuclear double resonance is a magnetic resonance technique for obtaining detailed molecular and electronic structure of paramagnetic species. In the standard continuous wave experiment, a microwave field is first applied, followed by irradiation with a radio frequency field...
(ENDOR) was invented in 1965 by Mims . In this experiment, pulsed NMR
NMR
NMR may refer to:Applications of Nuclear Magnetic Resonance:* Nuclear magnetic resonance* NMR spectroscopy* Solid-state nuclear magnetic resonance* Protein nuclear magnetic resonance spectroscopy* Proton NMR* Carbon-13 NMR...
transitions are detected with pulsed EPR. ESEEM and pulsed ENDOR continue to be important for studying nuclear spins coupled to electron spins.
In the 1980s, the upcoming of the first commercial pulsed EPR and ENDOR spectrometers in the X band
X band
The X band is a segment of the microwave radio region of the electromagnetic spectrum. In some cases, such as in communication engineering, the frequency range of X band is rather indefinitely set at approximately 7.0 to 11.2 gigahertz . In radar engineering, the frequency range is specified...
frequency range, lead to a fast growth of the field. In the 1990s, parallel to the upcoming high-field EPR, pulsed EPR and ENDOR became a new fast advancing magnetic resonance spectroscopy tool and the first commercial pulsed EPR and ENDOR spectrometer at W band
W band
The W band of the microwave part of the electromagnetic spectrum ranges from 75 to 110 GHz. It sits above the U.S. IEEE designated V band in frequency, yet overlaps the NATO designated M band...
frequencies appeared on the market.
Principle
The basic principle of pulsed EPR is similar to NMR spectroscopy. Differences can be found in the relative size of the magnetic interactions and in the relaxation rates which are orders of magnitudes larger in EPR than NMR. A full description of the theory is given within the quantum mechanical formalism, but since the magnetization is being measured as a bulk property, a more intuitive picture can be obtained with a classical description. For a better understanding of the concept of pulsed EPR let us consider the effects on the magnetization vector in the laboratory frameLaboratory frame of reference
In physics, the laboratory frame of reference, or lab frame for short, is a frame of reference centered on the laboratory in which the experiment is done. This is the reference frame in which the laboratory is at rest...
as well as in the rotating frame
Rotating reference frame
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. A rotating frame of reference is a special case of a non-inertial reference...
. In the laboratory frame the static magnetic field B0 is assumed to be parallel to the z-axis and the microwave field B1 parallel to the x-axis. When an electron spin is placed in magnetic field it experiences a torque which causes its magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
to precess around the magnetic field. The precession frequency is known as the Larmor frequency
Larmor precession
In physics, Larmor precession is the precession of the magnetic moments of electrons, atomic nuclei, and atoms about an external magnetic field...
ωL (see page 18 of ref ).
where γ is the gyromagnetic ratio and B0 the magnetic field. The electron spins are characterized by two quantum mechanical states, one parallel and one antiparallel to B0. Because of the lower energy of the parallel state more electron spins can be found in this state according to the Boltzmann distribution
Boltzmann distribution
In chemistry, physics, and mathematics, the Boltzmann distribution is a certain distribution function or probability measure for the distribution of the states of a system. It underpins the concept of the canonical ensemble, providing its underlying distribution...
. This results in a net magnetization, which is the vector sum of all magnetic moments in the sample, parallel to the z-axis and the magnetic field. To better comprehend the effects of the microwave field B1 it is easier to move to the rotating frame. EPR experiments usually use a microwave resonator designed to create a linearly polarized
Linear polarization
In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation...
microwave field B1, perpendicular to the much stronger applied magnetic field B0. The rotating frame is fixed to the rotating B1 components. First we assume to be on resonance with the precessing magnetization vector M0.
Therefore the component of B1 will appear stationary. In this frame also the precessing magnetization components appear to be stationary that leads to the disappearance of B0, and we need only to consider B1 and M0. The M0 vector is under the influence of the stationary field B1, leading to another precession of M0, this time around B1 at the frequency ω1.
This angular frequency ω1 is also called the Rabi frequency
Rabi frequency
The Rabi frequency is the frequency of population oscillation for a given atomic transition in a given light field. It is associated with the strength of the coupling between the light and the transition. Rabi flopping between the levels of a 2-level system illuminated with resonant light, will...
. Assuming B1 to be parallel to the x-axis, the magnetization vector will rotate around the +x-axis in the zy-plane as long as the microwaves are applied. The angle by which M0 is rotated is called the tip angle α and is given by:
Here tp is the duration for which B1 is applied, also called the pulse length. The pulses are labeled by the rotation of M0 which they cause and the direction from which they are coming from, since the microwaves can be phase-shifted from the x-axis on to the y-axis. For example, a +y π/2 pulse means that a B1 field, which has been 90 degrees phase-shifted out of the +x into the +y direction, has rotated M0 by a tip angle of π/2, hence the magnetization would end up along the –x-axis. That means the end position of the magnetization vector M0 depends on the length, the magnitude and direction of the microwave pulse B1. In order to understand how the sample emits microwaves after the intense microwave pulse we need to go back to the laboratory frame. In the rotating frame and on resonance the magnetization appeared to be stationary along the x or y-axis after the pulse. In the laboratory frame it becomes a rotating magnetization in the x-y plane at the Larmor frequency. This rotation generates a signal which is maximized if the magnetization vector is exactly in the xy-plane. This microwave signal generated by the rotating magnetization vector is called free induction decay
Free induction decay
In Fourier Transform NMR, free induction decay is the observable NMR signal generated by non-equilibrium nuclear spin magnetisation precessing about the magnetic field ....
(FID) (see page 175 of ref ).
Another assumption we have made was the exact resonance condition, in which the Larmor frequency is equal to the microwave frequency. In reality EPR spectra have many different frequencies and not all of them can be exactly on resonance, therefore we need to take off-resonance effects into account. The off-resonance effects lead to three main consequences. The first consequence can be better understood in the rotating frame. A π/2 pulse leaves magnetization in the xy-plane, but since the microwave field (and therefore the rotating frame) do not have the same frequency as the precessing magnetization vector, the magnetization vector rotates in the xy-plane, either faster or slower than the microwave magnetic field B1. The rotation rate is governed by the frequency difference Δω.
If Δω is 0 then the microwave field rotates as fast as the magnetization vector and both appear to be stationary to each other. If Δω>0 then the magnetization rotates faster than the microwave field component in a counter-clockwise motion and if Δω<0 then the magnetization is slower and rotates clockwise. This means that the individual frequency components of the EPR spectrum, will appear as magnetization components rotating in the xy-plane with the rotation frequency Δω. The second consequence appears in the laboratory frame. Here B1 tips the magnetization differently out of the z-axis, since B0 does not disappear when not on resonance due to the precession of the magnetization vector at Δω. That means that the magnetization is now tipped by an effective magnetic field Beff, which originates from the vector sum of B1 and B0. The magnetization is then tipped around Beff at a faster effective rate ωeff.
This leads directly to the third consequence that the magnetization can not be efficiently tipped into the xy-plane because Beff does not lie in the xy-plane, as B1 does. The motion of the magnetization now defines a cone. That means as Δω becomes larger, the magnetization is tipped less effectively into the xy-plane, and the FID signal decreases. In broad EPR spectra where Δω > ω1 it is not possible to tip all the magnetization into the xy-plane to generate a strong FID signal. This is why it is important to maximize ω1 or minimize the π/2 pulse length for broad EPR signals.
So far the magnetization was tipped into the xy-plane and it remained there with the same magnitude. However, in reality the electron spins interact with their surroundings and the magnetization in the xy-plane will decay and eventually return to alignment with the z-axis. This relaxation process is described by the spin-lattice relaxation time T1, which is a characteristic time needed by the magnetization to return to the z-axis, and by the spin-spin relaxation time T2, which describes the vanishing time of the magnetization in the xy-plane. The spin-lattice relaxation results from the urge of the system to return to thermal equilibrium after it has been perturbed by the B1 pulse. Return of the magnetization parallel to B0 is achieved through interactions with the surroundings, that is spin-lattice relaxation. The corresponding relaxation time needs to be considered when extracting a signal from noise, where the experiment needs to be repeated several times, as quickly as possible. In order to repeat the experiment, one needs to wait until the magnetization along the z-axis has recovered, because if there is no magnetization in z direction, then there is nothing to tip into the xy-plane to create a significant signal.
The spin-spin relaxation time, also called the transverse relaxation time, is related to homogeneous and inhomogeneous broadening. An inhomogeneous broadening results from the fact that the different spins experience local magnetic field inhomogeneities (different surroundings) creating a large number of spin packets characterized by a distribution of Δω. As the net magnetization vector precesses, some spin packets slow down due to lower fields and others speed up due to higher fields leading to a fanning out of the magnetization vector that results in the decay of the EPR signal. The other packets contribute to the transverse magnetization decay due to the homogeneous broadening. In this process all the spin in one spin packet experience the same magnetic field and interact with each other that can lead to mutual and random spin flip-flops. These fluctuations contribute to a faster fanning out of the magnetization vector.
All the information about the frequency spectrum is encoded in the motion of the transverse magnetization. The frequency spectrum is reconstructed using the time behavior of the transverse magnetization made up of y- and x-axis components. It is convenient that these two can be treated as the real and imaginary components of a complex quantity and use the Fourier theory to transform the measured time domain signal into the frequency domain representation. This is possible because both the absorption (real) and the dispersion (imaginary) signals are detected.
The FID signal decays away and for very broad EPR spectra this decay is rather fast due to the inhomogeneous broadening. To obtain more information one can recover the disappeared signal with another microwave pulse to produce a Hahn echo
Spin echo
In magnetic resonance, a spin echo is the refocusing of precessing spin magnetisation by a pulse of resonant radiation. Modern nuclear magnetic resonance and magnetic resonance imaging rely heavily on this effect....
. After applying a π/2 pulse (90°), the magnetization vector is tipped into the xy-plane producing an FID signal. Different frequencies in the EPR spectrum (inhomogeneous broadening) cause this signal to "fan out", meaning that the slower spin-packets trail behind the faster ones. After a certain time t, a π pulse (180°) is applied to the system inverting the magnetization, and the fast spin-packets are then behind catching up with the slow spin-packets. A complete refocusing of the signal occurs then at time 2t. An accurate echo caused by a second microwave pulse can remove all inhomogeneous broadening effects. After all of the spin-packets bunch up, they will dephase again just like an FID. In other words, a spin echo is a reversed FID followed by a normal FID, which can be Fourier transformed to obtain the EPR spectrum. The longer the time between the pulses becomes, the smaller the echo will be due to spin relaxation. When this relaxation leads to an exponential decay in the echo height, the decay constant is the phase memory time TM, which can have many contributions such as transverse relaxation, spectral, spin and instantaneous diffusion. Changing the times between the pulses leads to a direct measurement of TM as shown in the spin echo decay animation below.
Applications
ESEEM and pulsed ENDORElectron nuclear double resonance
Electron nuclear double resonance is a magnetic resonance technique for obtaining detailed molecular and electronic structure of paramagnetic species. In the standard continuous wave experiment, a microwave field is first applied, followed by irradiation with a radio frequency field...
are widely-used echo
Spin echo
In magnetic resonance, a spin echo is the refocusing of precessing spin magnetisation by a pulse of resonant radiation. Modern nuclear magnetic resonance and magnetic resonance imaging rely heavily on this effect....
experiments, in which the interaction of electron spins with the nuclei in their environment can be studied and controlled. Quantum computing and spintronics
Spintronics
Spintronics , also known as magnetoelectronics, is an emerging technology that exploits both the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-state devices.An additional effect occurs when a spin-polarized current is...
, in which spins are used to store information, have led to new lines of research in pulsed EPR.
One of the most popular pulsed EPR experiments currently is double electron-electron resonance (DEER), which is also known as pulsed electron-electron double resonance (ELDOR). This uses two different frequencies to control different spins in order to find out the strength of their coupling. The distance between the spins can then be inferred from their coupling strength, which is used to study structures of large bio-molecules.
See also
- Electron paramagnetic resonanceElectron paramagnetic resonanceElectron paramagnetic resonance or electron spin resonance spectroscopyis a technique for studying chemical species that have one or more unpaired electrons, such as organic and inorganic free radicals or inorganic complexes possessing a transition metal ion...
- Spin echoSpin echoIn magnetic resonance, a spin echo is the refocusing of precessing spin magnetisation by a pulse of resonant radiation. Modern nuclear magnetic resonance and magnetic resonance imaging rely heavily on this effect....
- Nuclear magnetic resonanceNuclear magnetic resonanceNuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
- Electron nuclear double resonanceElectron nuclear double resonanceElectron nuclear double resonance is a magnetic resonance technique for obtaining detailed molecular and electronic structure of paramagnetic species. In the standard continuous wave experiment, a microwave field is first applied, followed by irradiation with a radio frequency field...
External links
- Pulse EPR Bruker BioSpin