Energy Structure of Yb³⁺-Yb³⁺ Paired Center in LiNbO₃ Crystal

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The subject of the article is calculating the energies of the Stark levels of Yb³⁺-Yb³⁺ pair centers in a lithium niobate doped with Yb³⁺ ions (LiNbO₃:Yb³⁺) crystal, considering the interaction of optical electrons of ytterbium ions forming the pair center. Dexter's theory was used for calculations. A very interesting topic and interesting work. Nowadays, it is rare to find theoretical works on rare earth ions in crystals such as perovskites, e.g. LiNbO₃. On the other hand, we have a lot of experimental works that do not contribute much or nothing new. However, they are published. The discussed work deals with the Stark levels of ion pair Yb³⁺-Yb³⁺ in LiNbO₃ crystal, which is an additional advantage. Ion pairs ion pairs like Yb³⁺-Yb³⁺ in LiNbO₃ single crystal may be important for applications and theoretical results are verified by optical and/or infrared spectroscopy measurements. The data in Table 2 show impressively good agreement on calculated and measured values of the wavelengths of CL at 12 K.

I have a question. The authors write: “However, to our knowledge, no experimental studies have been conducted to measure the absorption of LN: Yb³⁺ crystals in this spectral region.”  (line 185). No such studies were conducted, or were they conducted but no absorption signal from ion pairs was detected? Such a signal may be too weak to be recorded. The number of pairs is a matter of debate, but it is (very) small.

I have noticed a few bugs:

• calculations were performed for Yb³⁺-Yb³⁺ pairs of ions in congruent LN? (see: 1. Abrahams, … 1966…)
• The editor errors in space group, line 41.
• No gaps for new chapter
• Eq 12, first line, it really should be… cm^-1?
• Incomprehensible notation of numbers, e.g.… 10,376.3–11,479.5 cm^-1 (line 147). What does the comma mean here?

Conclusions: the reviewed article is interesting, valuable and worth publishing after correcting a small number of editorial errors. It is an important paper from the theoretical (Dexter's theory) but also experimental side. No re-review is needed.

Comments on the Quality of English Language

I am not competent in English

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses in the attached file and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

The investigation of Yb³⁺ pairs in doped LiNbO₃ crystals are crucial to understand the incorporation of rare earth ions into the crystal lattice and for developing applications based on the electronic transitions of the rare earth ions.  In the article the authors studied the electronic states of Yb-Yb pairs and the transitions between them by theoretical methods (Dexter's theory). The results are consistent with previous experimental data, as shown in Table 2. The theoretical method was described mostly clean, although the text could be a little more detail. Some remarks:

• In line 21 (C_3v6) "6" is not needed.
• In line 24 "5.1483 nm" but it is Â
• In line 25 Li+ the "+" sign needs to be in superscript.
• In line 70 and 71 there are more typos, the vector symbol is missing above the r₁, "cr" is written in subscript of V instead of "CF", in case of H_b  the first index is not "λ" but "μ".
• In line 72 and 73, there is a strange character in the subscript of E and the line number of Stark levels instead of the "λ" and "μ" indexes.
• In line 72 the ψ_bμ needs to be also row vector as in the case of ψ_aλ.
• In line 77 and 104., the authors wrote an expression which is not clear.  The <ψ_a·ψ_b> expression is written instead the full <ψ_aψ_b|V_ab|ψ_aψ_b> term, which describes the extra energy came from the Coulomb interaction between the optical electrons of the neighboring ions.
• Please make Figure 1. much clearer containing only the notations used in the text (e.g. R instead of R_ab, while r_a, r_b1 and Z_e are not needed).
• In line 131 the average notation of "r" went into wrong place (bottom, instead of upper).
• In line 135 it is written "into four and six Kramers" but it needs to be "into four and three Kramers".
• In line 149 there are 2 typos, in the text of "300 cm-1" the "-1" needs to be a superscript, and the "(2.5) and (5.5)" text is "(1,5) and (5,5)" correctly.
• In line 155, in the Table caption, there is an extra ")".
• In the 2 sentences in lines 168-172 the absorption and emission roles have been reversed, please clarify it.
• In line 197, the usage of "(6,5)" instead of "(5,6)" makes the understanding much easier, because the first ion will be excited into the "6" level by the 955 nm photon.
•  In line 199 the term "(1,1):(1,5)" is not good, for the cross-relaxation one needs "(1,5):(1:5)" excited pairs, which are going to the "(1,1):(5,5)" states.
• In line 145 the authors wrote: "As shown in Table 1, the energy levels of the Yb³⁺–Yb³⁺ center are clustered into three distinct regions (last column of Table 1): 0–1545.9 cm⁻¹, 10,376.3–11,479.5 cm⁻¹ , and 20,753.5–21,415 cm⁻¹, separated by approximately 9,000
   cm−1.", which is only the consequence of the electron structure of the single Yb³⁺ ion (summation of the single ion levels in every combination). However, the main result of this work is the shift of the energy levels caused by the Coulomb interaction, which has to be emphasized a bit more in the conclusion.

In a summary I recommend the article for publication after a minor revision taking into account the previous remarks.

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses in the attached file and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

Author Response File: Author Response.docx