Pulsed EPR techniquesBasic concepts

Pulsed EPR course material provided by Sabine Van DoorslaerPhysics Department, University of Antwerp

Etienne Goovaerts, Physics Department, University of Antwerp

Course at CAB, San Carlos de Bariloche, Argentina, 6/12/2012

Relaxation mechanisms

We work on a macroscopic scale -> different electron spins form an “ensemble”

-> typically paramagnetic phase, ± dilute spin system

We measure not of a single spinbut the magnetization

i

iVμM 1

bs-big

pulse EPR methods

In thermal equilibriumBoltzmann distribution

between spin statesM along z (if B0 is on) -> M0

0BMM

dtd

If M out of equilibriumWe get a precession of the magnetization

because of torque on each of the magnetic moments

Relaxation mechanisms

pulse EPR methods

SITUATION 1

System returns to equilibrium -> characteristic time T1(spin-lattice or longitudinal relaxation time)

Mz= 0 Mz = -M0

Mz= M0(1-e-t/T1) Mz= M0(1-2e-t/T1)

Relaxation mechanisms

We bring magnetization out of equilibrium, such thatthe system is saturated (Mz = 0)

or the magnetization is inversed (Mz = -M0)

pulse EPR methods

SITUATION 2

We turn the magnetization in the xy plane

Magnetization B0 -> rotation with Larmor frequency

At thermal equilibrium: magnetization in planeshould be 0 -> system will try to return to this situation

Mxy = Mxy,0 e-t/T2 Characteristic timeT2

Transversal or spin-spin relaxation

“pure” T2Molecular interactions

throughinhomogeneous field

1/T2* = 1/T2 + 1/T2,inhom

pulse EPR methods

Combination of transversal and

longitudinal relaxation

pulse EPR methods

Spin dynamics: classical pictureSpin dynamics: classical pictureSpin dynamics: classical picture

pulse EPR methods

The ‘rotating frame’:

pulse EPR methods

In the rotating frame:pulse EPR methods

Pulsed microwaves:

pulse EPR methods

Pulse EPR: FT EPRPulse EPR: FT EPRPulse EPR: FT EPR

Single pulse: free induction decay (FID)

pulse EPR methods

Pulse EPR: FT EPRPulse EPR: FT EPRPulse EPR: FT EPR

pulse EPR methods

Pulse EPR: need for echo detectionPulse EPR: need for echo detectionPulse EPR: need for echo detectionLine broadening + spectral hole burning

pulse EPR methods

Pulse EPR: Electron Spin Echo (ESE)Pulse EPR: Electron Spin Echo (ESE)Pulse EPR: Electron Spin Echo (ESE)Primary (or Hahn) echo or 2-pulse ESE

pulse EPR methods

Pulse EPR: ESEPulse EPR: ESEPulse EPR: ESEPhase cycling:

pulse EPR methods

Pulse EPR: ESEPulse EPR: ESEPulse EPR: ESE

Multiple applications: relaxation times T1 , T2

resolution enhancement:– field-swept echo

– modulated echo: ESEEM:ESE envelope modulationnuclear hyperfine interactions

2D- spectroscopiescorrelation between nuclei

pulse EPR methods

Measuring nuclear interactions ESEEMElectron spin echo envelope modulation

S=1/2 coupled to nuclear spin Iby hf interaction

Need for density matrix description(not fully developed here)

pulse EPR methods

/2 pulse creates electron coherence= in-plane rotating electron magnetization

Specific vector contributions in 4x4 density matrix

/2)x

S=1/2, I=1/2

21

34

| ½ -½ >| ½ ½ >

| -½ ½ >

| -½ -½ >

ECa

ECf

What happens after a /2 pulse ?

x

z

y

x

z

y

M/2)x

x

z

y

Different rotation frequencies among spins?

ECa

pulse EPR methods

In ESEEM, we use a series of microwave pulses

General outline of an ESEEM experiment

evolutionevolutionmixingpreparation detection

n

EC, NCEP, NP

ECEPNPECNC

EPNPECNC

detection of spin echo vs. inter-pulse distance

time domain frequency domainF.T.

pulse EPR methods

Two-pulse ESEEMS=1/2, I=1/2

1 2

34

| ½ -½ > | ½ ½ >

| -½ ½ >| -½ -½ >

(1,3)

x

yx

z

y

/2)x x

evolution

detectionpreparation mixing

EC EC EC EC

1 2 3 4

1

pulse EPR methods

Two-pulse ESEEM

/2)x x

evolution

detectionpreparation mixing

EC EC EC EC

1 2 3 4

2

x

y

(1,3)

After time magnetization has gained phase

S=1/2, I=1/2

S(1,3)=(13‐mw)

pulse EPR methods

Two-pulse ESEEM

/2)x x

evolution

detectionpreparation mixing

EC EC EC EC

1 2 3 4

pulse inducesflip of magnetization but also

redistribution of electron coherence

x

y(1,3)

(2,3)(1,4)

(2,4)

S=1/2, I=1/2

3

pulse EPR methods

Two-pulse ESEEM

/2)x x

evolution

detectionpreparation mixing

EC EC EC EC

1 2 3 4

x

y(1,3)

(2,3)(1,4)

(2,4)

3

1 2

34

| ½ -½ > | ½ ½ >

| -½ ½ >

| -½ -½ >

S=1/2, I=1/2

pulse EPR methods

Two-pulse ESEEM

/2)x x

evolution

detectionpreparation mixing

EC EC EC EC

1 2 3 4

After time the magnetization M(i,j) have gained

a phase

(S(i,j) - S

(1,3)) = (ij – 13)

S=1/2, I=1/2

4

x

y(1,3)

(2,3)

(1,4) (2,4)

12

34 -

pulse EPR methods

Two-pulse ESEEM

/2)x x

evolution

detectionpreparation mixing

EC EC EC EC

1 2 3 4

4

Example:(S

(1,4) - S(1,3)) = (14 – 13)= 34

1 2

34

| ½ -½ > | ½ ½ >

| -½ ½ >

| -½ -½ >

x

y(1,3)

(2,3)

(1,4) (2,4)

12

34 -

34

S=1/2, I=1/2

pulse EPR methods

Two-pulse ESEEM

/2)x x

evolution

detectionpreparation mixing

EC EC EC EC

1 2 3 4

4

Example:(S

(1,4) - S(1,3)) = (14 – 13)= 34

x

y(1,3)

(2,3)

(1,4) (2,4)

12

34 -

S=1/2, I=1/2

Changing pulse interval

Echo modulates with nuclear frequencies !

pulse EPR methods

�/2 �

� �

FTNZ

A

Q

Two-pulse ESEEMpulse EPR methods

Two-pulse ESEEM

V2p() = 1 - (k/4)[2-2cos()-2cos()+cos()+cos()]

Modulation formula for an S=1/2, I=1/2 system

No ESEEM for isotropic hyperfine or hyperfine principal directions

-> no ESEEM for a molecule in a non-viscous solution at room temperature

(|12|=, |34|=)

pulse EPR methods

Two-pulse ESEEM

Advantage of 2-pulse ESEEM

Very fast method

Drawbacks of 2-pulse ESEEM

1. Overlap of signals: one-dimensional technique + line broadening

2. Depends on electron spin-spin relaxation which is often very short, so that one has broad signals

pulse EPR methods

/2 /2 /2

TEvolution time

3-pulse ESEEM sequence

Note : in three-pulse ESEEM no - and + are found !-> simpler spectrum than two-pulse ESEEM

For = 2n/(n = 0,1, ...) blind spots in spectrum

Eliminate this artefact with sum over - values(but more measurements needed!!)

pulse EPR methods

Phase cycling is needed to remove unwanted echoes

(Measurement on ‐irradiated quartz (G. Jeschke))

pulses

detection

-yy-yy

x-xx-x

2

xx-x-x

3

xxxx

HE=Hahn echo or primary echoRE=refocused echoSE=stimulated echo

pulse EPR methods

Advantage of 3-pulse ESEEM

1. only basic frequencies2. T1 dependence of signal -> narrower lines

ESEEM

3-pulse ESEEM sequence

2-pulse ESEEM

3-pulse ESEEM

Ferric cytoglobin

pulse EPR methods

2D-ESEEM sequence: HYSCOREHyperfine sublevel correlation spectroscopy

1

2

F.T.

/2 /2 /2

t1 t2

t1t2

pulse EPR methods

Pulse EPR: HYSCOREPulse EPR: HYSCOREPulse EPR: HYSCOREusing 4-pulse sequence:

pulse EPR methods

Pulse EPR: 2D ESEEMPulse EPR: 2D ESEEMPulse EPR: 2D ESEEMpulse EPR methods

Nanosecond mw pulses, kW amplificationfast spectroscopy (ns steps)

-> technically only possible from the 80s-> commercially available since early 90s

Relaxation times -> solids or frozen solutions

Pulsed EPR did not replace CW EPRNot possible to excite total spectrum

with one pulse

pulse EPR methods