the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Oct 2024
Electron spin dynamics during microwave pulses studied by 94 GHz chirp and phase-modulated EPR experiments
Abstract. Electron spin dynamics during microwave irradiation are of increasing interest in electron paramagnetic resonance (EPR) spectroscopy, as locking electron spins into a dressed state finds applications in EPR and dynamic nuclear polarization (DNP) experiments. Here, we show that these dynamics can be probed by modern pulse EPR experiments that use arbitrary waveform generators to produce shaped microwave pulses. We employ phase-modulated pulses to measure Rabi nutations, echoes, and echo decays during spin locking of a BDPA radical at 94 GHz EPR frequency. Depending on the initial state of magnetization, different types of echos are observed. We analyze these distinct coherence transfer pathways and measure the decoherence time T2ρ, which is a factor 3–4 longer than Tm. Furthermore, we use chirped Fourier transform EPR to detect the evolution of magnetization profiles. Our experimental results are well reproduced using a simple density matrix model that accounts for T2ρ relaxation in the spin lock (tilted) frame. The results provide a starting point for optimizing EPR experiments based on hole burning, such as electron-nuclear double resonance or ELDOR-detected NMR.
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RC1: 'Comment on mr-2024-16', Anonymous Referee #1, 24 Oct 2024
The paper by Lenjer et al. investigates phase-modulated pulses during spin-locking as well as chirp pulses for hole-burning at W-band for a model system consisting of a BDPA radical, including a first demonstration of phase-modulated pulses at this frequency. Their experimental work is complemented by an in-depth analysis of observed effects at several levels of theory, from Bloch equations to advanced spin dynamics simulations. The experimental and theoretical work is carefully performed, the manuscript is well-written, and the results are presented in detailed and informative figures. The authors helpfully include thorough descriptions of the experimental implementation, and the scripts used to perform the described simulations.
This work covers many interesting aspects and constitutes a valuable addition to the literature. However, the current manuscript is quite long and very dense, which is not too surprising given the complexity of the topic, but, in my view, a couple of small changes could be made to improve readability for a wider audience.I would recommend considering the following points:
- The paper discusses both phase-modulated pulses during spin-locking as well as frequency- and amplitude-modulated chirp pulses, and shows that the theoretical treatment developed for the first case is valuable for the analysis of the excitation profiles of long chirp microwave pulses. The motivation for performing both classes of experiments and the exact connection between them could be made much clearer. In particular in the results, the transition from one to the other is quite abrupt at the moment.
- An overview figure showing all of the pulse sequences employed (before they are discussed in the Materials and Methods and Results sections) and a clearer summary explaining the motivation for each in the introduction would be extremely helpful for making this paper more accessible to a general audience.
- The thorough explanation of the theoretical basis is very instructive and really makes this section easier to follow for non-experts. For this purpose, I would recommend also explaining more explicitly why the transformation into the tilted frame is necessary for describing spin relaxation in section 2.1.2. It would also be useful to already include the notation of dressed and bare state in the theoretical description section rather than only starting to use it in the Results section.
- Can the authors specify more clearly what systems their results and insights are applicable for? Is it just for S=1/2 systems with narrow and featureless spectra? In section 3.5, TEMPOL is mentioned as a sample measurements have also been performed on, but it is unclear what the results were and if they matched the results for BDPA (e.g. the surprising low MW intensity for the chirp pi pulse). (At the moment it sounds like the optimization was done on TEMPOL, but in the subsequent paragraph the results seem to be discussed for BDPA?)
- It would be useful to more clearly point out the differences between the simulations performed with home-written routines by the authors and with Spinach, and when and why each is better, i.e. what results can only be reproduced if MW inhomogeneity is taken into account or if powder averaging is included, and how using a Gaussian distribution of resonance offsets compares to modeling the spectrum with artificial g-anisotropy. E.g. it seems like the inclusion of MW inhomogeneity is necessary for the accurate simulation of Rabi nutations, but the corresponding excitation profiles for different pulse lengths seem to no longer require this based on the good agreement of the Spinach simulations with experiment in Fig. 5. Is there a single approach that is able to model every experimentally observed effect accurately (in SL Rabi nutations, SL echo, Rabi nutations and excitation profiles) and what would that entail?
Minor comments and typos:
- Both echos and echoes are used in different parts of the manuscript.
- In the introduction, where decoherence during spin locking is discussed, it might be useful to include a reference to 10.5194/mr-2024-17.
- p. 3, line 57, their respective interaction frames
- p. 3, line 58, clarify this is sufficient for the simple system used in this paper, unless this is really general.
- Consider adding the transformation operator for the transformation into the nutating frame before equation 6 for completeness.
- Hyphenation in so-called, spin-locked, Boltzmann-populated.
- In the paragraph after equation 13, consider starting from the general expression for rho(0) (missing ') and then explaining what has been used in the calculation and why.
- p. 6, line 144, non-resolved -> unresolved
- In section 3.2, it would be useful to specify how exactly LO leakage is minimized on the spectrometer. Does it include active compensation of the amplitude imbalance of the I and Q channels of the SpinJet AWG?
- Inconsistency between use of MW and mw.
- p. 8, line 213, featured -> structured?
- p. 8, line 222, these non-ideal conditions
- p. 9, line 237, Bodenhausen
- p. 9, line 245, prohibited -> prevented
- p. 13, line 362, turning angles ... were not optimized ...
- p. 15, line 382, microwave power dependence
- Fig. 4, (c) and (d) labels swapped? Wrong part of figure referenced in section A12 of the SI.
- In the captions to Fig. 4 and 5 it would be useful to mention that experiment and simulation are offset, the slightly offset y scales are not immediately obvious. Also, is this really necessary or could the data also be shown with matching scales?
- Legends or clear labels for the different colored lines in the Fig. 4 and 5 would be useful rather than having to rely on the caption (in particular for the light blue lines).
- Specify the type of fit used to model saturation effects (shown in Fig. A3).
- Including an intermediate graph would be useful in Fig. A5, to more clearly and visibly show how the probability distribution is obtained from the recorded experimental data. Also, using nu_PM instead of nu_set might be clearer and more consistent with the rest of the manuscript.
- It would be useful to also include the real part of the signal in Fig. A 10 again in the same figure (in addition to being shown in the main text).
- Fig. A14 caption: omega -> nu
- p. 38, line 688: is/was overestimated
- Fig. A 16, inclusion of the experimental spectrum in (a) would be usefulCitation: https://doi.org/10.5194/mr-2024-16-RC1 -
AC1: 'Reply on RC1', Marvin Lenjer, 07 Nov 2024
We thank Anonymous Referee #1 for the extensive, helpful comments and the general appreciation of our work. We particularly appreciate the meticulous documentation of the minor mistakes and typos. We agree that the manuscript is quite extensive and, therefore, are grateful for the suggestions on how to make it more accessible and readable. In particular, we will include an overview figure in the introduction.
Citation: https://doi.org/10.5194/mr-2024-16-AC1
-
RC2: 'Comment on mr-2024-16', Anonymous Referee #2, 28 Oct 2024
Lenjer et al. present an investigation of electron spin dynamics and relaxation behavior under microwave irradiation at 94 GHz. Periodic phase modulations are used to manipulate locked spins and chirp echo EPR spectroscopy (CHEESY) excitation profiles are measured. All experiments are performed on a commercial spectrometer and the manuscript gives a good impression of the applicability of pulse shaping on this instrument. Accompanying simulations are presented.
The work is suitable for publication in Magnetic Resonance, but it would be appropriate to address the following points.
- The expression for the transformation to the nutating frame should be given.
- In the experiments without a preparation pulse (Figure 2d), the phases of individual signals do not reproduce if the experiment is repeated. Could the cause be instability of the microwave excitation? Savitsky et al. (https://doi.org/10.1016/j.jmr.2014.02.026) characterized the phase-noise and the frequency-stability of the 84.5 GHz PLL Gunn diode in their Bruker ElexSys E680 spectrometer and found it advantageous for long-term EPR experiments to replace it with a dielectric resonator oscillator. The 84.5 GHz Gunn is likely the source of the phase noise shown in Figure A2.
- The discussion of the echoes observed without a preparation pulse on p. 13 is hard to follow. Is it possible that these echoes are due to off-resonance effects? If omega_eff is near parallel to the z-axis, preparation pulses are typically not needed for a "spin-lock".
- In Figure 3 on p.15 the T_2rho is plotted as a function of nu_1. The authors note that the results agree well with low-field results by Wili et al. Why is this expected? Wili et al. investigated bis-trityl rulers, not BDPA in polystyrene, at considerably lower field and with much higher Rabi frequency.
- How do the T_2rho values compare to T_m measured with a CPMG sequence?
- According to Figure 3b, the value of T_m (measured with a Hahn echo) is independent of the Rabi frequency. Is instantaneous diffusion negligible?
- The reason for the tilting of the frame in the Spinach simulations has to be explained better. Tilted interaction frames are commonly used to derive an effective Hamiltonian. But since Spinach executes the propagation numerically in small time steps, this does not seem to be the reason here. Is the purpose to get the correct relaxation mechanics?
- In Eq. A2 a subscript p is missing after Delta t. I suggest to remove the exclamation mark as in some programming languages != means not equal to.
Citation: https://doi.org/10.5194/mr-2024-16-RC2 -
AC2: 'Reply on RC2', Marvin Lenjer, 07 Nov 2024
We thank Anonymous Referee #2 for the positive feedback and the helpful comments. In particular, we appreciate the suggestion to compare our relaxation measurements with CPMG and to assess the effect of instantaneous diffusion, which we will include in the revised manuscript.
A detailed answer to all reviewer comments will be given upon resubmission of the revised manuscript.
Citation: https://doi.org/10.5194/mr-2024-16-AC2
-
AC2: 'Reply on RC2', Marvin Lenjer, 07 Nov 2024
Status: closed
-
RC1: 'Comment on mr-2024-16', Anonymous Referee #1, 24 Oct 2024
The paper by Lenjer et al. investigates phase-modulated pulses during spin-locking as well as chirp pulses for hole-burning at W-band for a model system consisting of a BDPA radical, including a first demonstration of phase-modulated pulses at this frequency. Their experimental work is complemented by an in-depth analysis of observed effects at several levels of theory, from Bloch equations to advanced spin dynamics simulations. The experimental and theoretical work is carefully performed, the manuscript is well-written, and the results are presented in detailed and informative figures. The authors helpfully include thorough descriptions of the experimental implementation, and the scripts used to perform the described simulations.
This work covers many interesting aspects and constitutes a valuable addition to the literature. However, the current manuscript is quite long and very dense, which is not too surprising given the complexity of the topic, but, in my view, a couple of small changes could be made to improve readability for a wider audience.I would recommend considering the following points:
- The paper discusses both phase-modulated pulses during spin-locking as well as frequency- and amplitude-modulated chirp pulses, and shows that the theoretical treatment developed for the first case is valuable for the analysis of the excitation profiles of long chirp microwave pulses. The motivation for performing both classes of experiments and the exact connection between them could be made much clearer. In particular in the results, the transition from one to the other is quite abrupt at the moment.
- An overview figure showing all of the pulse sequences employed (before they are discussed in the Materials and Methods and Results sections) and a clearer summary explaining the motivation for each in the introduction would be extremely helpful for making this paper more accessible to a general audience.
- The thorough explanation of the theoretical basis is very instructive and really makes this section easier to follow for non-experts. For this purpose, I would recommend also explaining more explicitly why the transformation into the tilted frame is necessary for describing spin relaxation in section 2.1.2. It would also be useful to already include the notation of dressed and bare state in the theoretical description section rather than only starting to use it in the Results section.
- Can the authors specify more clearly what systems their results and insights are applicable for? Is it just for S=1/2 systems with narrow and featureless spectra? In section 3.5, TEMPOL is mentioned as a sample measurements have also been performed on, but it is unclear what the results were and if they matched the results for BDPA (e.g. the surprising low MW intensity for the chirp pi pulse). (At the moment it sounds like the optimization was done on TEMPOL, but in the subsequent paragraph the results seem to be discussed for BDPA?)
- It would be useful to more clearly point out the differences between the simulations performed with home-written routines by the authors and with Spinach, and when and why each is better, i.e. what results can only be reproduced if MW inhomogeneity is taken into account or if powder averaging is included, and how using a Gaussian distribution of resonance offsets compares to modeling the spectrum with artificial g-anisotropy. E.g. it seems like the inclusion of MW inhomogeneity is necessary for the accurate simulation of Rabi nutations, but the corresponding excitation profiles for different pulse lengths seem to no longer require this based on the good agreement of the Spinach simulations with experiment in Fig. 5. Is there a single approach that is able to model every experimentally observed effect accurately (in SL Rabi nutations, SL echo, Rabi nutations and excitation profiles) and what would that entail?
Minor comments and typos:
- Both echos and echoes are used in different parts of the manuscript.
- In the introduction, where decoherence during spin locking is discussed, it might be useful to include a reference to 10.5194/mr-2024-17.
- p. 3, line 57, their respective interaction frames
- p. 3, line 58, clarify this is sufficient for the simple system used in this paper, unless this is really general.
- Consider adding the transformation operator for the transformation into the nutating frame before equation 6 for completeness.
- Hyphenation in so-called, spin-locked, Boltzmann-populated.
- In the paragraph after equation 13, consider starting from the general expression for rho(0) (missing ') and then explaining what has been used in the calculation and why.
- p. 6, line 144, non-resolved -> unresolved
- In section 3.2, it would be useful to specify how exactly LO leakage is minimized on the spectrometer. Does it include active compensation of the amplitude imbalance of the I and Q channels of the SpinJet AWG?
- Inconsistency between use of MW and mw.
- p. 8, line 213, featured -> structured?
- p. 8, line 222, these non-ideal conditions
- p. 9, line 237, Bodenhausen
- p. 9, line 245, prohibited -> prevented
- p. 13, line 362, turning angles ... were not optimized ...
- p. 15, line 382, microwave power dependence
- Fig. 4, (c) and (d) labels swapped? Wrong part of figure referenced in section A12 of the SI.
- In the captions to Fig. 4 and 5 it would be useful to mention that experiment and simulation are offset, the slightly offset y scales are not immediately obvious. Also, is this really necessary or could the data also be shown with matching scales?
- Legends or clear labels for the different colored lines in the Fig. 4 and 5 would be useful rather than having to rely on the caption (in particular for the light blue lines).
- Specify the type of fit used to model saturation effects (shown in Fig. A3).
- Including an intermediate graph would be useful in Fig. A5, to more clearly and visibly show how the probability distribution is obtained from the recorded experimental data. Also, using nu_PM instead of nu_set might be clearer and more consistent with the rest of the manuscript.
- It would be useful to also include the real part of the signal in Fig. A 10 again in the same figure (in addition to being shown in the main text).
- Fig. A14 caption: omega -> nu
- p. 38, line 688: is/was overestimated
- Fig. A 16, inclusion of the experimental spectrum in (a) would be usefulCitation: https://doi.org/10.5194/mr-2024-16-RC1 -
AC1: 'Reply on RC1', Marvin Lenjer, 07 Nov 2024
We thank Anonymous Referee #1 for the extensive, helpful comments and the general appreciation of our work. We particularly appreciate the meticulous documentation of the minor mistakes and typos. We agree that the manuscript is quite extensive and, therefore, are grateful for the suggestions on how to make it more accessible and readable. In particular, we will include an overview figure in the introduction.
Citation: https://doi.org/10.5194/mr-2024-16-AC1
-
RC2: 'Comment on mr-2024-16', Anonymous Referee #2, 28 Oct 2024
Lenjer et al. present an investigation of electron spin dynamics and relaxation behavior under microwave irradiation at 94 GHz. Periodic phase modulations are used to manipulate locked spins and chirp echo EPR spectroscopy (CHEESY) excitation profiles are measured. All experiments are performed on a commercial spectrometer and the manuscript gives a good impression of the applicability of pulse shaping on this instrument. Accompanying simulations are presented.
The work is suitable for publication in Magnetic Resonance, but it would be appropriate to address the following points.
- The expression for the transformation to the nutating frame should be given.
- In the experiments without a preparation pulse (Figure 2d), the phases of individual signals do not reproduce if the experiment is repeated. Could the cause be instability of the microwave excitation? Savitsky et al. (https://doi.org/10.1016/j.jmr.2014.02.026) characterized the phase-noise and the frequency-stability of the 84.5 GHz PLL Gunn diode in their Bruker ElexSys E680 spectrometer and found it advantageous for long-term EPR experiments to replace it with a dielectric resonator oscillator. The 84.5 GHz Gunn is likely the source of the phase noise shown in Figure A2.
- The discussion of the echoes observed without a preparation pulse on p. 13 is hard to follow. Is it possible that these echoes are due to off-resonance effects? If omega_eff is near parallel to the z-axis, preparation pulses are typically not needed for a "spin-lock".
- In Figure 3 on p.15 the T_2rho is plotted as a function of nu_1. The authors note that the results agree well with low-field results by Wili et al. Why is this expected? Wili et al. investigated bis-trityl rulers, not BDPA in polystyrene, at considerably lower field and with much higher Rabi frequency.
- How do the T_2rho values compare to T_m measured with a CPMG sequence?
- According to Figure 3b, the value of T_m (measured with a Hahn echo) is independent of the Rabi frequency. Is instantaneous diffusion negligible?
- The reason for the tilting of the frame in the Spinach simulations has to be explained better. Tilted interaction frames are commonly used to derive an effective Hamiltonian. But since Spinach executes the propagation numerically in small time steps, this does not seem to be the reason here. Is the purpose to get the correct relaxation mechanics?
- In Eq. A2 a subscript p is missing after Delta t. I suggest to remove the exclamation mark as in some programming languages != means not equal to.
Citation: https://doi.org/10.5194/mr-2024-16-RC2 -
AC2: 'Reply on RC2', Marvin Lenjer, 07 Nov 2024
We thank Anonymous Referee #2 for the positive feedback and the helpful comments. In particular, we appreciate the suggestion to compare our relaxation measurements with CPMG and to assess the effect of instantaneous diffusion, which we will include in the revised manuscript.
A detailed answer to all reviewer comments will be given upon resubmission of the revised manuscript.
Citation: https://doi.org/10.5194/mr-2024-16-AC2
-
AC2: 'Reply on RC2', Marvin Lenjer, 07 Nov 2024
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Electron spin dynamics during microwave pulses studied by 94 GHz chirp and phase-modulated EPR experiments Marvin Lenjer https://doi.org/10.25625/B11CUC
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