Comment on “State-Dependent Electron Delocalization Dynamics at the Solute-Solvent Interface: Soft-X-Ray Absorption Spectroscopy and Ab initio Calculations”
Experiment IPFY PFY
MCFT XAS PFY
A recent study by Bokarev et al. [1] utilized L edge x-ray absorption spectroscopy (XAS) in an attempt to detect electron delocalization dynamics at solute-solvent interfaces. By observing weaker spectral intensity at some parts of spectra detected using partial fluorescence yield (PFY) compared to the true XAS measured using both the transmission yield and inverse partial fluorescence yield techniques, the authors claim to “quantify unequivocally the state-dependent electron delocalization” with the transition metal 3d orbitals. While their study and conclusions are indeed interesting, here we will show that the observed spectral differences stem from the inherently different cross sections probed by the different techniques. XAS at transition metal L edges is described by a simplified form of Fermi’s second golden rule, expressed as I XAS ðω; ϵÞ ∝
X Γf f
week ending 28 MARCH 2014
PHYSICAL REVIEW LETTERS
PRL 112, 129301 (2014)
jhfjϵ · rjiij2 ; π ðEi þ ω − Ef Þ2 þ Γ2f
(1)
where ω and ϵ are the energy and polarization of the incident photons, r is the position operator, and jii (jfi) is the initial (final) state with energy Ei (Ef ). The final states have an energy width given by Γf. When one attempts to measure L edge XAS using fluorescence yields, however, it has been shown that second order terms often dominate the scattering process [2,3], and the PFY is more appropriately given by rffiffiffiffiffi X X Γn hfjϵ0 · rjnihnjϵ · rjii2 PFY 0 ; (2) I ðω; ϵ; ϵ Þ ∝ π Ei þ ω − En þ iΓn n f where the symbols are as defined above, and now ϵ0 is the polarization of the detected (scattered) photons. The states jni are actually the XAS final states, while jfi are the PFY final states, which are present after the decay of the core hole. Note that this is essentially the Kramers-Heisenberg equation often used for resonant inelastic x-ray scattering [4], but here we integrate over the relevant energy range of the outgoing photons. Accounting for these inherent differences between the two techniques, we can reproduce the experimental observations of Bokarev et al. using multiplet crystal field theory (MCFT) calculations [5], which exclude the electron delocalization effects, as shown in Fig. 1. The trends observed experimentally [1], where the fluorescence yields are weaker in the preedge region, are captured very well simply by using the proper formalisms discussed above. There is excellent agreement in other trends as well, where the L2 intensity is stronger in PFY, for example. While MCFT is not a first-principles method, the model contains all the appropriate atomic multielectron states to account for the differing fluorescence decay rates of the various XAS final states. The good agreement with 0031-9007=14=112(12)=129301(2)
Fe
2+
Fe
3+
Intensity (arb. units)
3
2
1
Co
2+
0
-5
0
5
10
15
20
Excitation Energy (eV)
FIG. 1 (color online). Calculated XAS and PFY using Eqs. (1) and (2), respectively, shown with data digitized from Ref. [1].
experiment was obtained from Eq. (2) straightforwardly employing common empirical parameters proven to be successful for the transition metal ion systems studied. Note that the use of an ab initio or semiempirical interpretation is irrelevant here: the same intra-atomic electron correlations which lead to the very presence of multiplets in L-edge spectra are responsible for the strongly varying decay rates and subsequent PFY distortions. In summary, we have shown that the variations pointed out by Bokarev et al. in the comparison of PFY and XAS at L edges and attributed to electron delocalization effects are instead natural consequences of the different physical processes that underlie the two techniques. Another Comment by Föhlisch et al. [6] and the Reply by Bokarev et al. [7] have been published concurrently. R. J. Green,1 D. Peak,2 A. J. Achkar,3 J. S. Tse,1 A. Moewes,1 D. G. Hawthorn3 and T. Z. Regier4,* 1
Department of Physics and Engineering Physics University of Saskatchewan Saskatoon, Saskatchewan, Canada S7N 5E2 2 Department of Soil Science College of Agriculture and Bioresources University of Saskatchewan Saskatoon, Saskatchewan, Canada S7N 5A8 3 Department of Physics and Astronomy University of Waterloo Waterloo, Ontario, Canada N2L 3G1 4 Canadian Light Source, Inc. Saskatoon, Saskatchewan, Canada S7N 2V3 Received 9 September 2013; published 28 March 2014 DOI: 10.1103/PhysRevLett.112.129301 PACS numbers: 31.15.vj, 31.70.Dk, 32.80.Aa, 78.70.En
129301-1
© 2014 American Physical Society
PRL 112, 129301 (2014) *
PHYSICAL REVIEW LETTERS
[email protected] [1] S. I. Bokarev, M. Dantz, E. Suljoti, O. Kuhn, and E. F. Aziz, Phys. Rev. Lett. 111, 083002 (2013). [2] F. M. F. de Groot, M. A. Arrio, Ph. Sainctavit, Ch. Cartier, and C. T. Chen, Solid State Commun. 92, 991 (1994). [3] R. Kurian, K. Kunnus, P. Wernet, S. M. Butorin, P. Glatzel, and F. M. F de Groot, J. Phys. Condens. Matter 24, 452201 (2012). [4] L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Rev. Mod. Phys. 83, 705 (2011).
week ending 28 MARCH 2014
[5] F. de Groot and A. Kotani, Core Level Spectroscopy of Solids (CRC Press, Taylor & Francis Group, Boca Raton, FL, 2008). [6] A. Föhlisch, F. M. F. de Groot, M. Odelius, S. Techert, and Ph. Wernet, preceding Comment, Phys. Rev. Lett. 112, 129302 (2014). [7] S. I. Bokarev, M. Dantz, E. Suljoti, K. Atak, B. Winter, O. Kühn, and E. F. Aziz, following Reply, Phys. Rev. Lett. 112, 129303 (2014).
129301-2
Experiment IPFY PFY
MCFT XAS PFY
A recent study by Bokarev et al. [1] utilized L edge x-ray absorption spectroscopy (XAS) in an attempt to detect electron delocalization dynamics at solute-solvent interfaces. By observing weaker spectral intensity at some parts of spectra detected using partial fluorescence yield (PFY) compared to the true XAS measured using both the transmission yield and inverse partial fluorescence yield techniques, the authors claim to “quantify unequivocally the state-dependent electron delocalization” with the transition metal 3d orbitals. While their study and conclusions are indeed interesting, here we will show that the observed spectral differences stem from the inherently different cross sections probed by the different techniques. XAS at transition metal L edges is described by a simplified form of Fermi’s second golden rule, expressed as I XAS ðω; ϵÞ ∝
X Γf f
week ending 28 MARCH 2014
PHYSICAL REVIEW LETTERS
PRL 112, 129301 (2014)
jhfjϵ · rjiij2 ; π ðEi þ ω − Ef Þ2 þ Γ2f
(1)
where ω and ϵ are the energy and polarization of the incident photons, r is the position operator, and jii (jfi) is the initial (final) state with energy Ei (Ef ). The final states have an energy width given by Γf. When one attempts to measure L edge XAS using fluorescence yields, however, it has been shown that second order terms often dominate the scattering process [2,3], and the PFY is more appropriately given by rffiffiffiffiffi X X Γn hfjϵ0 · rjnihnjϵ · rjii2 PFY 0 ; (2) I ðω; ϵ; ϵ Þ ∝ π Ei þ ω − En þ iΓn n f where the symbols are as defined above, and now ϵ0 is the polarization of the detected (scattered) photons. The states jni are actually the XAS final states, while jfi are the PFY final states, which are present after the decay of the core hole. Note that this is essentially the Kramers-Heisenberg equation often used for resonant inelastic x-ray scattering [4], but here we integrate over the relevant energy range of the outgoing photons. Accounting for these inherent differences between the two techniques, we can reproduce the experimental observations of Bokarev et al. using multiplet crystal field theory (MCFT) calculations [5], which exclude the electron delocalization effects, as shown in Fig. 1. The trends observed experimentally [1], where the fluorescence yields are weaker in the preedge region, are captured very well simply by using the proper formalisms discussed above. There is excellent agreement in other trends as well, where the L2 intensity is stronger in PFY, for example. While MCFT is not a first-principles method, the model contains all the appropriate atomic multielectron states to account for the differing fluorescence decay rates of the various XAS final states. The good agreement with 0031-9007=14=112(12)=129301(2)
Fe
2+
Fe
3+
Intensity (arb. units)
3
2
1
Co
2+
0
-5
0
5
10
15
20
Excitation Energy (eV)
FIG. 1 (color online). Calculated XAS and PFY using Eqs. (1) and (2), respectively, shown with data digitized from Ref. [1].
experiment was obtained from Eq. (2) straightforwardly employing common empirical parameters proven to be successful for the transition metal ion systems studied. Note that the use of an ab initio or semiempirical interpretation is irrelevant here: the same intra-atomic electron correlations which lead to the very presence of multiplets in L-edge spectra are responsible for the strongly varying decay rates and subsequent PFY distortions. In summary, we have shown that the variations pointed out by Bokarev et al. in the comparison of PFY and XAS at L edges and attributed to electron delocalization effects are instead natural consequences of the different physical processes that underlie the two techniques. Another Comment by Föhlisch et al. [6] and the Reply by Bokarev et al. [7] have been published concurrently. R. J. Green,1 D. Peak,2 A. J. Achkar,3 J. S. Tse,1 A. Moewes,1 D. G. Hawthorn3 and T. Z. Regier4,* 1
Department of Physics and Engineering Physics University of Saskatchewan Saskatoon, Saskatchewan, Canada S7N 5E2 2 Department of Soil Science College of Agriculture and Bioresources University of Saskatchewan Saskatoon, Saskatchewan, Canada S7N 5A8 3 Department of Physics and Astronomy University of Waterloo Waterloo, Ontario, Canada N2L 3G1 4 Canadian Light Source, Inc. Saskatoon, Saskatchewan, Canada S7N 2V3 Received 9 September 2013; published 28 March 2014 DOI: 10.1103/PhysRevLett.112.129301 PACS numbers: 31.15.vj, 31.70.Dk, 32.80.Aa, 78.70.En
129301-1
© 2014 American Physical Society
PRL 112, 129301 (2014) *
PHYSICAL REVIEW LETTERS
[email protected] [1] S. I. Bokarev, M. Dantz, E. Suljoti, O. Kuhn, and E. F. Aziz, Phys. Rev. Lett. 111, 083002 (2013). [2] F. M. F. de Groot, M. A. Arrio, Ph. Sainctavit, Ch. Cartier, and C. T. Chen, Solid State Commun. 92, 991 (1994). [3] R. Kurian, K. Kunnus, P. Wernet, S. M. Butorin, P. Glatzel, and F. M. F de Groot, J. Phys. Condens. Matter 24, 452201 (2012). [4] L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Rev. Mod. Phys. 83, 705 (2011).
week ending 28 MARCH 2014
[5] F. de Groot and A. Kotani, Core Level Spectroscopy of Solids (CRC Press, Taylor & Francis Group, Boca Raton, FL, 2008). [6] A. Föhlisch, F. M. F. de Groot, M. Odelius, S. Techert, and Ph. Wernet, preceding Comment, Phys. Rev. Lett. 112, 129302 (2014). [7] S. I. Bokarev, M. Dantz, E. Suljoti, K. Atak, B. Winter, O. Kühn, and E. F. Aziz, following Reply, Phys. Rev. Lett. 112, 129303 (2014).
129301-2
