Theoretical Investigation of the EPR G-Factor for the Axial Symmetry Ce³⁺ Center in the BaWO₄ Single Crystal

Round 1

Reviewer 1 Report

This is an interesting paper, but it doesn't seem to mention how the charge is compensated by the substitution of the Ce3+ ion, presumably at the Ba2+ site. Without discussing that, it is difficult to judge the findings of the paper, because the presence of a charge compensating defect will affect the symmetry of the system. I am assuming this can be done as a 'minor revision' as it may have been included without explanation, but it does need to be considered.

Author Response

Thank you to Reviewer 1 for your comments. Reviewer 1 wrote:

“This is an interesting paper, but it doesn't seem to mention how the charge is compensated by the substitution of the Ce3+ ion, presumably at the Ba2+ site. Without discussing that, it is difficult to judge the findings of the paper, because the presence of a charge compensating defect will affect the symmetry of the system. I am assuming this can be done as a 'minor revision' as it may have been included without explanation, but it does need to be considered.”

 

This is a very interesting comment. It touches on a topic that we have overlooked. This subject is very important. In the literature, it is assumed that dopant ions such as rare earth ions (Re³⁺ like Ce³⁺ or Yb³⁺) substitute in place of barium ions (Ba²⁺) in BaWO₄ single crystal. Hence, two Re_Ba substitutions gives two excess positive charges, which are compensated by one the barium vacancy (V_Ba). Barium vacancies play a key role in explaining the color centers in BWO [1, 2]. The dopant ions (Re³⁺/Ba²⁺) are expected to randomly occupy the site of the barium ions. Dodecahedrons [BaO₈] are connected by its edges. The associated vacancies (V_Ba) do not necessarily affect the surroundings of the dopant ion, dodecahedron [ReO₈]. Thus we obtain a center with axial symmetry [3, 4]. Such centers with axial symmetry occur at low doping of BaWO₄. We investigate low doping monocrystlas: 1) BaWO₄: 0.5 % at. Ce, 2) BaWO₄: 1.0 % at. Ce, 3) BaWO₄: 0.5 % at. Ce, 1.0 % at. Na and 4) BaWO₄: 1.0 % at. Ce, 2.0 % at. Na. At higher doping or simultaneous co-doping, barium vacancy (V_Ba) can appear in neighboring dodecahedron [VO₈] connecting by its edges with dodecahedron [ReO₈]. Thus lowering the symmetries of the center. In addition to the five axial centers, we detected more than ten centers with low symmetry (C₂) in our crystals BWO.

            Two paragraphs were added at the end of the Introduction. The first paragraph describes the monocrystals BaWO₄ (doped and co-doped) that were studied. The second one briefly describes the charge compensation mechanism.A serious description of this issue would require writing a separate article.

 

[1] Haiyan Zhang, Tingyu Liu , Qiren Zhang, Xi’en Wang, Xiaofeng Guo, Min Song, Jigang Yin, First-principles study on electronic structures and color centers in BaWO4 crystal with barium vacancy, Physica B 404 (2009) 1538–1543
[2] Haiyan Zhang, Tingyu Liu, Qiren Zhang, Xi’en Wang, Jigang Yin, Min Song, Xiaofeng Guo, First-principles study on electronic structures of BaWO₄ crystals containing F-type color centers, Journal of Physics and Chemistry of Solids 69 (2008) 1815–1819

[3] Arnab Kumar Dey et al. Journal of Luminescence 211 (2019) 251–257

[4] A.K. Kunti, N. Patra, S.K. Sharma, H.C. Swart, Journal of Alloys and Compounds 735 (2018) 2410-2422

Reviewer 2 Report

As I understand from the letter of Editors, the paper is submitted for publication in the Thematic issue on Tungstate materials. However, I do not see any connection with Tungsten except the presence of tungsten in the considered system. No specific features of registered EPR spectra of impurity Ce3+ ions (which substitute for Ba2+ ions in BaWO4) which might be connected with tungsten in the crystal lattice (for example, a superhyperfine structure due to interactions of a 4f electron with nuclear magnetic moments of the odd isotope 183W) are not revealed. From the very beginning, an approach used by the authors in the analysis of g-factors and crystal field (CF) parameters, based on the Superposition Model (SM), can not bring any information about tungsten ions in the third coordination shell of Ce3+ because SM accounts explicitly for the contributions into the CF from the nearest neighbors (oxygen ions in the first and second coordination shells of an impurity Ce3+ in BaWO4) only. Even more, when using the D2d approximation instead of the real S4 point symmetry, a real orientation of axes of the coordinate frame in the ab-plane is missed, and the coordination factors used in simulations become indefinite. In any case, estimations of the intrinsic parameter A6 of the SM are doubtful because the ground multiplet of Ce3+, 2F5/2, feels the 6th-rank terms in CF Hamiltonian through the spin-orbit coupling only.  

      The manuscript is written in a rather perfunctory manner, it contains many grammar errors and typos and wrong notations (in particular, in the total basis of 4f states, the spin-orbit Hamiltonian contains (l*s), not (L*S), in the Zeeman Hamiltonian the magnetic moment contains (l+2s), not g_J*J, in the CF Hamiltonian C_p^k) are spherical tensor operators, not the Stevens operators).   

      I find the results of this work useless and the scientific level too low for a publication in an International physical journal.  

Author Response

Thank you to Reviewer 2 for your comments, although we disagree with most of them.

“As I understand from the letter of Editors, the paper is submitted for publication in the Thematic issue on Tungstate materials. However, I do not see any connection with Tungsten except the presence of tungsten in the considered system.”

Nevertheless, tungsten is present in the barium tungstate (BaWO₄) single crystal, belonging to a broader group of the scheelite structure crystals, tungstate AWO₄ (A = Ba, Sr, Ca, Pb We disagree with the reviewer here and believe that our article on paramgentic cetenr with axial symmetry in the BaWO₄ single crystal fits into the issue on Tungstate materials.

“No specific features of registered EPR spectra of impurity Ce3+ ions (which substitute for Ba2+ ions in BaWO4) which might be connected with tungsten in the crystal lattice (for example, a superhyperfine structure due to interactions of a 4f electron with nuclear magnetic moments of the odd isotope 183W) are not revealed. From the very beginning, an approach used by the authors in the analysis of g-factors and crystal field (CF) parameters, based on the Superposition Model (SM), can not bring any information about tungsten ions in the third coordination shell of Ce3+ because SM accounts explicitly for the contributions into the CF from the nearest neighbors (oxygen ions in the first and second coordination shells of an impurity Ce3+ in BaWO4) only.”

One of the basic assumptions of the SPM model is that it only takes into account the impact of the nearest neighbors. The cerium ion is substituted for the barium ion. The Ba²⁺ ion is coordinated by eight O^2- ions in the form of dodecahedron [BaO₈]. The influence of ions from other coordination shell is not taken into account. In the references, I have accumulated 46 entries, thirty-some of which relate to the application of the SPM model to various rare earth ions (Ce, Yb, Er) in similar oxygen environments. Many others I have omitted, I believe. Of course, everyone is entitled to their own opinion.

 

“Even more, when using the D2d approximation instead of the real S4 point symmetry, a real orientation of axes of the coordinate frame in the ab-plane is missed, and the coordination factors used in simulations become indefinite.”

Some authors make careful distinctions between so called symmetry adopted axis system (SAAS, with axes, let’s say: X, Y, Z) and crystal axis system (CAS with axes a, b, c). This makes sense for systems with low symmetry, where the axes (or one axis) are not perpendicular to each other. However, scheelite structure BaWO₄ has a tetergonal strukture of a space group I4₁/a (C⁶_4h). So, in this case, we assumed that SAAS = CAS or alternatively X || a, Y || b, and Z || c. Wu Shao-Yi and Dong Hui-Ning did the same by analyzing the erbium ion (Er³⁺) in BaWO₄ single crystals [2]. There is nothing new. Therefore, we do not agree that “…a real orientation of axes of the coordinate frame in the ab-plane is missed, and the coordination factors used in simulations become indefinite.”

 

“In any case, estimations of the intrinsic parameter A6 of the SM are doubtful because the ground multiplet of Ce3+, 2F5/2, feels the 6th-rank terms in CF Hamiltonian through the spin-orbit coupling only.”

The obtained values of parameters A2, A4, and A6 were compared to the values of the same parameters from other works. We examine the Ce³⁺ in BaWO₄ single crystals. We find only one paper about Ce³⁺ in similar environment, YPO₄ and LuPO₄ crystals [1], and one about rare earth ion (Er³⁺) in BaWO₄ [2]. The calculated values of intrinsic parameters (rank second, fourth and sixth) should be considered as reasonable and contained within the range of data. It should be added that optical studies would be very useful. So far, we have not found any results of such measurements.

 

     “The manuscript is written in a rather perfunctory manner, it contains many grammar errors and typos and wrong notations (in particular, in the total basis of 4f states, the spin-orbit Hamiltonian contains (l*s), not (L*S), in the Zeeman Hamiltonian the magnetic moment contains (l+2s), not g_J*J, in the CF Hamiltonian C_p^k) are spherical tensor operators, not the Stevens operators).”

The Reviewer has right. SH may be expressed in the extended Stevens operators as:

where,  – are extended Stevens operators.

SH may be expressed also in the Wybourne notation as:

where  - there are Racah spherical tensor operators. ,  – there are crystal field parameters, not the same but proportional, multipliers are tabulated. The error in equation 4 has been corrected.

“For a free Ce³⁺, the electron configuration is 4f¹, with 2F_5/2 ground state and a 2F_7/2 excited state.” [1]. This is correct, I think. The rest is a labeling difference. However, I would insist on capital letters because we have the case of the rare earth ion and for example spin-orbit coupling term should be written as:

 

“I find the results of this work useless and the scientific level too low for a publication in an International physical journal.”

 

We disagree with this conclusion. It seems that the Reviewer a priori rejects the use of the SPM model in this case. On the contrary based on broad literature from the last 50 years, we think that the SPM model can and should be applied to this system as well.

 

[1] H.G. Liu, W.C. Zheng and W.L. Feng, Philosophical Magazine Letters, Vol. 89, No. 4 (2009) 306-311

[2] Wu Shao-Yi and Dong Hui-Ning, Spectrochimica Acta Part A 60 (2004) 1991–1994

Author Response File: Author Response.docx

Reviewer 3 Report

Peer-reviewing the article (crystals-1261878):

“Theoretical investigation of the EPR g-factor for the axial symmetry Ce³⁺ center in the BaWO4 single crystal” in the Crystals journal.

After carefully reading this article, I got a certain impression and also there were a number of questions to the authors, which I will share below.

1. In the introduction, the authors describe the advantages and potentials of using crystals with a scheelite-type structure, namely BaWO, doped with trivalent rare-earth ions (Re³⁺) as solid state lasers and X-ray phosphor or for different photocatalysis, scintillation applications and ect. But the authors are very obscure about the advantages of introducing cerium ions into the BaWO structure, noting that the impurity leads to greatly increases further possibility of application as luminescence and solid-state laser materials without any references! At the end of the introduction, the authors declare an extremely uncertain aim of this article and it is completely unclear what question the researchers efforts with theoretical calculations will be aimed at finding out? The author's declaration that "It is interesting to compare our results with the results from these papers" is groundless and further in the article, no stated comparisons are given. It is also worth noting that the text of the introduction traces the repetition of the thoughts (whole sentences) given by the authors from their previous articles. Therefore, the relevance of the theoretical study of the g-factor shift using the specifically approach of complete diagonalization procedure of energy matrix, and not another, as well as the applicability in the future of the results obtained in this article is poorly justified and requires serious revision.
2. To calculate the g-factors, the complete diagonalization procedure of energy matrix was chosen, for which it is necessary to know the parameters of the crystal field. To calculate the parameters of the crystal field, the initial values were taken with an approximation from other articles (the spin-orbit coupling constant and power law exponent) or by estimating the difference in the ionic radii of cerium and barium (the distance to the ligands). The experimentally determined value of the g-factor is given without an error (confidence interval) and it is not clear with what accuracy it was determined. The authors should take into account that the goniometer used to set the orientation of the crystal always (without exception) has a backlash (free rotation), which gives an error in the angles of at least 1-2 degrees or more. For the EPR spectrum of cerium in the X-range with a line width of 15-20 Gauss, the change in the g-factor value in the third sign should give only a weak shift in the field, which may be within their error-bars. Therefore, taking into account all possible errors, experimental inaccuracies and theoretical approximations, the authors' result that they found a deviation of the polar angle of 1 degree causes strong distrust. If the authors are going to show such accurate calculations, then all instrumental and experimental errors and theoretical approximations should be properly commented on.
3. The authors state that the cerium impurity on the barium position leads to a change in the local environment, namely, a modify in the polar angle by 1 degree. However, changes in the polar angle should lead to a lowering in the crystal symmetry, at least in the near order. In the EPR spectra, this should affect the appearance of new absorption lines, at least two, which will confirm a real decrease in the symmetry of the local environment in the cerium position. How can the authors comment on this?
4. The authors state that in their previous work they determined a change in the polar angle by 4 degrees in the exactly same material (Ce³⁺-doped BaWO₄ crystal). However, the authors do not comment at all on why such a significant difference arises and which of the values (1 or 4 degree) is more correct.
5. Why the fitting does not show the full selection of angles, although up to 5-6 degrees, to show the trend of the g-factor more fully?
6. Unfortunately, the general conclusions are also unclear. The authors do not emphasize the significance and real applicability (with references) of the polar angle deviation by 1 degree in various scientific and technical applications.

Author Response

Thank you to Reviewer 3 for your valuable comments. Let me answer these comments one by one:

1. As we mentioned in one of the previous our papers [10], the BaWO₄:Ce single crystals obtained by Czochralski growth, do not emit any luminescence at ambient pressure under near-UV (325 nm) excitation. Efficient green light is emitted only at high pressure and low temperature. The luminescence is of excitonic character, since the lowest Ce³⁺ 5d level is degenerate with the conduction band also under hydrostatic pressures. So direct application of the material to generate laser action seem to be improper. Although, doping of BaWO₄ single crystals with Ce ions does not activate Ce³⁺ luminescence at any pressure and any temperature, their presence may contribute to the efficiency of exciton formation. It is observed that in crystals doped with Ce³⁺ the intensity of the excitonic emission is significantly higher than that in pure crystals. Moreover, applying another methods of growth, e.g. co-precipitation method with controlled pH environment, the Ce³⁺ doped AWO₄ (M=Ca, Sr and Ba) phosphor shows broad PL excitation band in the UV region having peak at 280 nm. Phosphor excited by 280 nm shows broad emission band in the visible region (400–650 nm) having peak in the blue region at around 465 nm which is the characteristic of (WO₄)₂ The intensity of PL emission is enhanced with an increase in the concentration of Ce³⁺ up to 5 mol% and then the intensity decreases [K.V. Dabre , S.J. Dhoble, Jyoti Lochab, “Synthesis and luminescence properties of Ce³⁺ doped MWO₄ (M=Ca, Sr and Ba) microcrystalline phosphor”, J. Lumin., 19 (2014) 348]. As one can see, doping with Ce³⁺ ions has an important influence on luminescence properties of AWO₄ (M=Ca, Sr and Ba) phosphor.
2. This comment applies to the specific accuracy of spin Hamiltonian parameters, and numerical calculations. Spin Hamiltonian parameters, like g -factors, are calculated from the EPR spectra. Exactly on the basis of the roadmap of EPR spectra recorded in two, better three, planes. You stick the sample on the goniometer, inserted into the resonance chamber, make measurements, peel it off and stick it on again, and so on. An accuracy of 1 or 2 degrees is very, very good. I know this procedure well, I have been doing it for years. I understand that the Reviewer is also an experimental physicist. After all we have calculated parameters of spin Hamiltonian with error of course. A shift of one or two degrees is a change in the third or fourth decimal place. Practically meaningless, in the error limit.

Let's look at the unit cell of the BaWO₄ single crystals. The Ba²⁺ ion is coordinated by eight O^2- ions in the form of dodecahedron [BaO₈] made of two rotated, interpenetrated tetrahedrons. Dodecahedrons [BaO₈] are connected by its edges. Each oxygen ion (O^2-) belongs to two or three dodecahedrons. This is a rigid structure, neglecting, for example, thermal vibrations. Doping is the introduction of another ion, with a different radius and valence. Tetrahedrons rotate, but only by one degree. This is the result of the SPM model. Sometimes, an angular distortion of one, two degrees is very much.

Results of angular distortion for other rare earth elements in crystals with similar structure:

1. Cerium! Ce³⁺ in Y₃Al₅O₁₂ and Lu₃Al₅O₁₂garnets

Hong-Gang Liu, Yang Mei, Wen-Chen Zheng, Link between EPR g-factors and local structure of the orthorhombic Ce³⁺ center in Y₃Al₅O₁₂ and Lu₃Al₅O₁₂ garnets, Chemical Physics Letters 554 (2012) 214–218,

angular distortion:  

1. Er³⁺ in BaWO4 crystal, the same crystal!

Wu Shao-Yi and Dong Hui-Ning, Theoretical investigations of the EPR g factor and the local structure for Er³⁺ in BaWO₄, Spectrochimica Acta Part A 60 (2004) 1991–1994  [25]

angular distortion:  

1. c) Yb³⁺ in Na₃Sc₂V₃O₁₂ garnet

H.G. Liu, W.C. Zheng, and W.L. Feng, Spin-Hamiltonian parameters of Yb³⁺ ions in trigonally-distorted octahedral sites of Na₃Sc₂V₃O₁₂ garnet, Philosophical Magazine, Vol. 88, No. 25, 1 September 2008, 3075–3080

angular distortion:

 

The obtained angular distortion is significant and the results are consistent with others. The calculations show that the spin Hamilotnian parameter (g - factors) values are very sensitive to even small changes in the polar angles. The remark about errors is correct. The reported values have been supplemented with error,

We have two types of data: 1) crystallographic, experimetall data for a pure BaWO₄ crystal, including dodecahedron [BaO₈] and b) experimetall g-factors data for doped BaWO₄:Ce, origineted from Ce³⁺ ion surrounded by eight oxygen ions - dodecahedron [CeO₈]. The SPM model combines these data, proving that small changes in polar angles give correct values of the experimental parameter values of the g-factors. This is the great advantage of this model.

3. “…However, changes in the polar angle should lead to a lowering in the crystal symmetry, at least in the near order.”

This is not necessarily true. A symmetric and the same change in the polar angles of the two tetrahedrons does not lead to a decrease in symmetry. The symmetry remains the same, only the oxygen ions lie closer to the axis of dodecahedron (see Fig. 2). In other words, the Ce³⁺ ion remains on the axis and in the center of dodecahedron [CeO₈]. An asymmetric change in the polar angles will lead to a reduction in symmetry. For example, if one or two oxygen ions move differently. In this case the Ce³⁺ ion moves off the axis and out of the center of the dodecahedron [CeO₈]. Both types of centers are recorded. We discovered five axial symmetry centers and 11 low symmetry centers (C₂) in our measurements of the BaWO₄: Ce single crystals. This article focuses on the strongest axial center, found in all the crystals studied.

1. “The authors state that in their previous work they determined a change in the polar angle by 4 degrees in the exactly same material (Ce³⁺-doped BaWO₄ crystal). However, the authors do not comment at all on why such a significant difference arises and which of the values (1 or 4 degree) is more correct.”

In previous work, we used a simplified Newman model, proposed by him in 1977. We obtained an angular displacement of the polar angles of 4 degrees. In the present work, we used the full superposition model (SPM model) and obtained an angular distortion of one degree. The result obtained from the superposition model is correct. However, if one does not want to get into complicated calculations, one can use a simplified model. The results obtained are quite a good, qualitative approximation.

1. “Why the fitting does not show the full selection of angles, although up to 5-6 degrees, to show the trend of the g-factor more fully?”

A mathematical model was applied but to a physical system. Theoretically, one can imagine changing angles of 5, 10, or 25 degrees. However, the positions of the ions in the unit cell are rigidly fixed. Doping, that is, substitution of another ion, changes these positions, but the changes cannot be large. I must confess that I studied changes of angles in the range of +-10 degrees. The best fit was for angular distortion 1 degree. This result is consistent with physical intuition and with other results for rare earth ions in a similar environment. It also confirms that the SPM model is correct.

6. “Unfortunately, the general conclusions are also unclear. The authors do not emphasize the significance and real applicability (with references) of the polar angle deviation by 1 degree in various scientific and technical applications.”

The reviewer is right. I don't give “significance and real applicability (with references) of the polar angle deviation by 1 degree in various scientific and technical applications” because I don't know them. On the other hand, someone puts a sample into an EPR spectrometer, measures the spectra, and determines the parameters of the spin Hamiltonian. What is the relationship between the spin Hamiltonian parameters and, for example, the laser action of that sample? Obviously, some relationship is there, but it is not a direct relationship. From the analysis of the EPR spectra, conclusions can be taken about the environment of the paramagnetic ion. These conclusions may or may not have practical implications. This work is a theoretical work. It describes the effects, in the immediate environment, of replacing the Ba²⁺ ion with a Ce³⁺ ion. In my opinion, it gives some knowledge. Will this knowledge be meaningful, when and for whom? I know I should say yes. Yes, yes of course! To be honest I really don't know.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

I am not satisfied with the authors answer on my comments and questions. The authors argumentation is not physically grounded, the authors insist on wrong equations (Hamiltonian of the Zeeman interaction (2) can not operate in the total basis of 4f^1 states, the spin-orbit interaction in the presented form can be used for Ce3+ but not for any rare-earth ion) and statements. In particular, the authors write now explicitly about the crystallographic system of coordinates (X||a, Z||c), this demonstrates that they do not read attentively even the paper [44] from the list of references, where (page 3725) it is clearly written "...the new x and y axes should be defined" to use the D2d approximation. The authors follow a flow of useless papers by Wu Shao-Yi, W.C. Zheng and their coworkers disseminated in a lot of journals where the Superposition Model has been used to analyze published earlier data of EPR and optical studies. However, it is necessary to understand the approximations involved, and that this model gives no information about mechanisms of crystal-field formation or specific features of a studied compound.

Reviewer 3 Report

I am quite happy with the answers to my questions. After revision's article looks pretty good and may be accepted.