Local structure, zero field splitting and optical absorption of Mn²⁺ doped ZnK₂(SO₄)₂·6H₂O single crystals

Abstract

The Mn²⁺ doped ZnK₂(SO₄)₂·6H₂O (ZKS) single crystal zero field splitting parameters are obtained using the superposition model. The evaluated parameters agree well with those found from EPR. The conclusion of the experiment that in ZKS, the Mn²⁺ ion takes the place of the Zn²⁺ site is verified by theoretical analysis. The crystals’ optical spectra are estimated by utilizing the crystal field parameters obtained from the superposition model and the crystal field analysis computer program. A good agreement between the calculated and experimental band positions is found. Thus, the experimental results are confirmed by the theoretical studies.

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1. Introduction

The EPR of the Mn²⁺ impurity has been widely studied in a variety of single crystals due to the sensitivity of its zero field splitting values to small structural distortions in the lattice.^1,2 A number of studies have been reported on impurities doped into diamagnetic host lattices at room temperature.^3–5

The superposition model (SPM) can be used to model the zero field splitting (ZFS) and crystal field (CF) parameters for use in other studies.^6–10 SPM and the point-charge model^11–13 are commonly used to determine the parameters of the crystal field (CF). SPM was proposed for CF under certain assumptions.¹⁴ (1) The CF at a paramagnetic ion is expressible as an algebraic sum of contributions, from other ions in the crystal. (2) When the paramagnetic ion is located at the origin of a chosen coordinate frame, all the major CF contributions from every single ion in the crystal are axially symmetric with respect to its position vector. (3) Only neighboring or coordinated ions (ligands) need to be counted for their CF contributions. (4) CF contributions from single ligands are transferable across different host crystals. Finding a steady spherical polar coordinate system (R_L, θ_L, Φ_L) for each ligand or ion from the host crystal's X-ray data is crucial for carrying out an SPM analysis on the CF. Ionic charge, ionic size, and inter-ionic bonding mismatches are likely to cause some local distortion when transition metal ions are infused. Critical analysis of the experimental spin-Hamiltonian parameters for Mn²⁺ and Fe³⁺ in CaO and MgO crystals has been done¹⁵ providing the SPM parameters for the EPR data and showing that the CF for 3d ions satisfies the superposition principle. For the alkali earth oxides, sets of SPM intrinsic parameters based on reliable ligand distances have been determined.¹⁶

The crystals with the general formula A₂⁺B²⁺(XO₄)₂·6H₂O are known as Tutton single crystals, where A is a monovalent cation, B is a divalent cation usually a transition metal and X can be sulfur or selenium.^17,18 Tutton salts are a famous isostructural crystal family which shares the same monoclinic symmetry and the space group P2₁/a with two formula units per unit cell Z = 2.¹⁹ The Tutton salts are valuable crystals as they are used extensively in UV filters.²⁰

Zinc potassium sulfate hexahydrate crystals (ZKS) are crystallized in the monoclinic crystal system and belong to the Tutton crystalline salts. These crystals, because of their growth with high purity and suitable crystal sizes and small transparency in the UV region, could be potential candidates for optoelectronic applications.²¹

EPR study of Mn²⁺ doped ZKS has been done at 293.7 K and the spin-Hamiltonian parameters have been obtained.²² From angular variation studies, it is determined that magnetic [Mn(H₂O)₆]²⁺ complexes are created when the Mn²⁺ ion enters the divalent sites of the Tutton salt lattice. The a*bc axis system, where b and c are the crystal axes and a* is perpendicular to b and c, is used to discuss the orientations. The EPR x and z axes deviate by 9° from both the Zn–O(7) and Zn–O(9) directions in ZKS.

The density functional theory (DFT) studies elucidate the electronic structure regulation in Ru–NiCo₂O₄ and the modification of the d-band center optimizes H* adsorption energy, which considerably increased the hydrogen production efficiency.²³ A Mo-doped CoN is coupled with NiFe-LDH for preparing a Mott–Schottky heterojunction, addressing the enhanced hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and urea oxidation reaction (UOR) compared with the individual counterparts.²⁴ This process for varying the local electron density could be a promising route to obtain low-energy consumption green hydrogen generation. DFT calculations were performed to further understand the catalytic mechanism and to assess the influence of Mo doping and heterointerfaces on the HER and OER performance of Mo–CoN coupled with NiFe-LDH. The incorporation of Mo and the fabrication of the composite with NiFe-LDH improve the electrocatalytic activity by modulating the electronic structure [JEC]. The above studies motivated us to perform a theoretical study on the local structure, zero field splitting and optical absorption of Mn²⁺ doped ZKS.

In this study, the ZFS parameters D and E are determined for the Mn²⁺ ion in ZKS at 293.7 K (room temperature, RT) taking CF parameters obtained from SPM and perturbation equations.²⁵ The goal is to locate the Mn²⁺ ion and the distortion that is taking place in the ZKS crystal. The results obtained for the Mn²⁺ ion at the substitutional Zn²⁺ site in the ZKS crystal with local distortion show good agreement with the EPR experimental values. The crystal field analysis (CFA) program and CF parameters are used to calculate the optical spectra of the Mn²⁺ doped ZKS single crystals. The calculated positions of the optical energy bands agree reasonably well with those obtained from the experiment. A further aim of the study is to find the extent to which CF theory and SPM analysis can be applied to Mn²⁺ ions in ZKS crystals in order to generate an SPM parameter database. This will determine molecular nanomagnet (MNM) design and computer simulation of their magnetic and spectroscopic characteristics. The transition ion-based MNM class currently includes single-molecule magnets (SMMs),²⁶ single-chain magnets (SCMs),²⁷ and single ion magnets (SIMs).²⁸ Because of the interesting magnetic properties of MNMs, such as magnetization's macroscopic quantum tunneling and possible uses in high-density information storage and quantum computing, the above systems have attracted large attention from scientists and researchers.^26,27 There are several synthesized SCM or SMM systems with Mn²⁺ and Cr³⁺ ions.²⁹ Since model calculations for simpler crystal systems can be used as a basis for more complex ones, the parameters of the model obtained in this case may be used for ZFS parameter calculations for Mn²⁺ ions at similar sites in MNM. This work's modeling can be extended to investigate various crystals of scientific and industrial interest in a number of other ion-host systems.

2. Crystal structure

The crystal structure of Tutton salt ZKS is monoclinic with space group P2₁/a.^21,30 The unit cell's parameters are as follows: Z = 2, β = 104.78°, a = 9.044, b = 12.194 and c = 6.151 Å. All other divalent cations in the unit cell are in general positions, with the two inequivalent ones located at points (0, 0, 0) and (1/2, 1/2, 0). Each divalent cation is surrounded by a slightly distorted octahedron of water molecules.³⁰Fig. 1 shows the symmetry adopted axis system (SAAS) and ZKS crystal structure.

Fig. 1 The room-temperature ZKS crystal structure and the symmetry-adopted axis system (SAAS).

3. Crystal field and zero field splitting parameter calculations

The EPR spectra can be analyzed with the spin Hamiltonian:⁷where B, μ_B, g, D and E are the applied magnetic field, Bohr magneton, splitting factor, second rank axial, and second rank rhombic ZFS parameters.^31,32 The modified crystallographic a*, b and c axes (a* is normal to axes b and c) and the (x, y, z) laboratory axes are shown in Fig. 1. The directions of metal–ligand bonds being mutually perpendicular are referred to as the symmetry adopted axes (SAA) or the local symmetry axes of the site. As shown in Fig. 1, the axis-Z of SAAS is along the crystal axis-c, and (X, Y) are perpendicular to the axis-Z. When Mn²⁺ ions are introduced in the ZKS crystal, they substitute at Zn²⁺ (1) sites with some local distortion in the lattice.³³

The Mn²⁺ ion spin Hamiltonian can be written as,³⁴

[script letter H] = [script letter H]_o + [script letter H]_so + [script letter H]_ss + [script letter H]_c (2)

where B_kq, in Wybourne notation, represent the CF parameters and C^(k)_q, the spherical tensor operators. B_kq ≠ 0 in the orthorhombic symmetry crystal field only for k = 2, 4; q = 0, 2, 4. Employing SPM, the CF parameters B_kq are computed.³⁴

The symmetry of the local field about Mn²⁺ ions in the ZKS crystal is taken to be orthorhombic (OR-type I),⁷ where the ZFS parameters D and E are found as follows:³⁵

Here P = 7B + 7C, G = 10B + 5C, D′ = 17B + 5C. B and C represent Racah parameters and ς is the spin–orbit coupling parameter. In terms of average covalency parameter N, B = N⁴B₀, C = N⁴C₀, ς = N²ς₀, where ς₀ gives the free ion spin–orbit coupling parameter and B₀ and C₀ are Racah parameters for the free ion.^34,36ς₀ = 336 cm⁻¹, B₀ = 960 cm⁻¹ and C₀ = 3325 cm⁻¹ for free Mn²⁺ ions.⁷

The covalency parameter N is found from using Racah parameters (B = 850 cm⁻¹, C = 2970 cm⁻¹) obtained from optical analysis of the Mn²⁺ ion in zinc cesium sulphate hexahydrate where ligands are oxygens,³⁷ as no optical absorption of Mn²⁺ doped ZKS has been reported.

The CF parameters using SPM are determined,^14,35 in terms of co-ordination factor K_kq(θ_j,φ_j) and intrinsic parameter , as

is found fromwhere the ligand's distance from the dⁿ ion is denoted by R_j, is the intrinsic parameter, R₀ is the reference distance of the ligand from the metal ion and t_k gives the power law exponent. For Mn²⁺ doped crystals, t₂ = 3 and t₄ = 7 were used earlier,³⁵ the same values are taken here. Since the co-ordination about the Mn²⁺ ion is octahedral, is obtained from the relation³⁸

From optical study,³⁷Dq = 790 cm⁻¹. Therefore, . For 3d⁵ ions the ratio falls in the range 8–12.^34,39,40 With , .

4. Results and discussion

Using SPM and the ligand configuration about the Mn²⁺ ion shown in Fig. 1, the CF parameters of the Mn²⁺ ion at the Zn²⁺ (1) sites are estimated. Table 1 provides atoms’ coordinates in the ZKS single crystal with bond length R (both with and without distortion) and angles θ, φ for site I. The ZFS and CF parameters together with reference distance R₀ are presented in Table 2. Table 2 shows that R₀ = 0.200 nm, being slightly less than the sum of the radii of the ions (0.223 nm) of Mn²⁺ = 0.083 nm and O²⁻ = 0.140 nm with no distortion and provide ZFS parameter values at octahedral substitutional site I different from the EPR experimental ones.²² Experimental parameters of ZFS |D| and |E| (in unit of 10⁻⁴ cm⁻¹) for site I from EPR are 355.8, 57.2, respectively. |E|/|D| is obtained as 0.160 being smaller than the standard value 0.33.³² |D| and |E| estimated theoretically without distortion are larger than the EPR experimental values. The value of |E|/|D| is also larger than the standard value 0.33.³² Therefore, local distortion is included into the calculation. For local distortion an iterative procedure has been used by changing R, θ and φ to minimize the difference between calculated and experimental D and E and E/D near to standard value 0.33³² keeping in mind the minimum lattice strain. Using the above value of R₀ and local distortion, the ZFS parameters for substitutional octahedral sites I are determined for and are given in Table 2. The ZFS parameter values are smaller than the experimental ones (error 19.84%) for and larger for (error 23.02%, |E|/|D| is also larger than the standard value 0.33) while these are in good agreement with the EPR experimental values for .²² Hence seems to be appropriate. The parameters t₂ = 3 and t₄ = 7 with transformation S2 for standardization³² are employed to get an |E|/|D| ratio near to 0.33 and calculated ZFS parameters close to the experimental values from EPR. A similar value of has been used for Mn²⁺ doped diglycine calcium chloride tetrahydrate⁴¹ and Fe³⁺ doped BiVO₄.³⁴

Table 1 Atoms’ coordinates, bond length R (both with and without distortion) and angles θ, φ in the ZKS single crystal (site I)

Mn^2+ position	Ligands	x (Å)	y (Å)	z (Å)	Spherical polar coordinates of ligands
					R (nm)		θ°		φ°
Without distortion
Site: substitutional	O7	0.1723	0.1080	0.1683	0.20741	R 1	85.34	θ 1	85.22	φ 1
Zn(1)	O8	−0.1629	0.1113	0.0351	0.20598	R 2	89.02	θ 2	94.53	φ 2
(0.0000, 0.0000, 0.0000)	O9	−0.0007	−0.0676	0.3024	0.20362	R 3	81.46	θ 3	90.02	φ 3
	O7′	−0.1723	−0.1080	−0.1683	0.20741	R 4	94.65	θ 4	94.78	φ 4
	O8′	−0.1723	0.3920	0.6683	0.67733	R 5	84.34	θ 5	91.46	φ 5
	O9′	0.1723	0.6080	0.3317	0.77278	R 6	87.54	θ 6	88.72	φ 6
With distortion
I	O7				0.28741		66.34		86.72
	O8				0.28598		70.02		92.53
	O9				0.26007		62.46		88.02
	O7′				0.30901		86.65		90.78
	O8′				0.79733		82.34		91.46
	O9′				0.85778		89.54		90.72

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Table 2 The Mn²⁺ doped ZKS crystal's CF and ZFS parameters

Site	Crystal-field parameters (cm^−1)						Zero-field splitting parameters (× 10^−4 cm^−1)
	R 0 (nm)	B 20	B 22	B 40	B 42	B 44	|D|	|E|	|E|/|D|
Without distortion site I
	0.200	−17 062.3	−21 071.6	5249.723	5583.833	8072.755	3295.6	1679.4	0.509
	0.200	−21 327.9	−26 339.5	5249.723	5583.833	8072.755	4724.9	2421.1	0.512
	0.200	−25 593.5	−31 607.4	5249.723	5583.833	8072.755	6458.7	3314.3	0.513
With distortion site I
	0.200	−5618.94	2495.683	−133.084	−19.7999	2948.929	285.2	75.7	0.265
	0.200	−7023.67	3119.604	−133.084	−19.7999	2948.929	355.8	109.3	0.307
Exp.							355.8	57.2	0.160
	0.200	−8428.4	3743.524	−133.084	−19.7999	2948.929	437.7	148.9	0.340

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The CFA program⁴² and B_kq parameters (with distortion) are used to calculate the optical spectra of Mn²⁺ doped ZKS single crystals. By diagonalizing the full Hamiltonian, the positions of the energy bands of the Mn²⁺ ion are evaluated. Table 3 shows the energy band positions (experimental and calculated) for substitutional site I.³⁷ From the position and the nature of the bands observed, they have been ascribed to a Mn²⁺ ion in octahedral symmetry.^37,43 Ligand field bands are sharp when the energy expressions for the transitions are independent of Dq, since the number of t_2g electrons is the same in both the excited and the ground states.⁴³ The sharp bands are therefore assigned to the [⁴A_1g(G), ⁴E_g(G)] and the ⁴E_g(D) states, respectively. The broad bands are assigned to ⁴T_1g(G) and ⁴T_2g(G), respectively. These bands are broad as their transitions involve a change of configuration from (t_2g)³(e_g)² to (t_2g)⁴(e_g). The remaining bands are assigned to ⁴T_2g(G), ⁴T_1g(P) and ⁴T_1g(F) states, respectively. The CFA program⁴² can perform diagonalization of the complete Hamiltonian within the 3d^N basis of states in the intermediate crystal field coupling scheme providing not only the CF energy levels but also the state vectors. The Hamiltonian incorporated in the CFA program contains the Coulomb interaction (in terms of the Racah parameters B and C), Trees correction (α), the spin–orbit interaction (ς), the crystal field Hamiltonian, the spin–spin interaction (M₀), and the spin-other orbit interaction (two parameters: M₀₀, M₂₂). The adjusted values of the free-ion parameters used in the CFA calculations are (in cm⁻¹): B = 850 and C = 2970, α = 76, ς₀ = 336 cm⁻¹, M₀ = 0.2917, M₂ = 0.0229, M₀₀ = 0.2917, and M₂₂ = 0.0229. Though the whole Mn²⁺ spectra consist of 120 degenerate states, we present only a few energy levels based on intensity.⁴⁴ The transitions associated with ⁴E_g(G), ⁴A_1g(G), ⁴T_2g(D), ⁴E_g(D) and ⁴A_2g(F) are well predicted while the transitions associated with ⁴T_1g(G), ⁴T_2g(G), ⁴T_1g(P) and ⁴T_1g(F) show larger deviation. The reasons for these deviations may be electron correlation effects, vibronic coupling or limitations of the CF model.³³

Table 3 Both calculated and experimental energy bands of the single crystal of ZKS doped Mn²⁺

Transition from ^6A1g(S)	Observed band (cm^−1)	Calculated band (cm^−1) I
^4T1g(G)	18 436	23 327, 23 343, 23 513, 23 592, 23 759, 23 843
^4T2g(G)	22 815	23 979, 24 000, 24 363, 24 402, 24 445, 24 485
^4Eg(G)	24 783	24 828, 24 856, 24 865, 24 872
^4A1g(G)	24 850	24 880, 24 889
^4T2g(D)	28 003	26 582, 26 639, 27 214, 27 274, 28 565, 28 578
^4Eg(D)	29 870	29 249, 29 305, 29 730, 29 828
^4T1g(P)	32 435	31 477, 31 502, 34 913, 35 045, 35 148, 35 264
^4A2g(F)		36 656, 36 961
^4T1g(F)	41 460	40 843, 40 559, 40 678, 40 730, 40 790, 40 799

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It is evident from Table 3 that the calculated and experimental energy band positions agree fairly well. Therefore, the theoretical results verify the EPR experimental one^22,37 that Mn²⁺ ions enter the ZKS crystal at the substitutional Zn²⁺ (1) octahedral site. The model parameters determined may be utilized in ZFS parameter estimations for Mn²⁺ ions at similar molecular nanomagnet sites.

5. Conclusions

To determine the zero field splitting parameters, the superposition model and perturbation theory are utilized for ZKS single crystals infused with Mn²⁺ ions. The calculated ZFS parameters match well with the experimental values from EPR for . The computed optical spectra are discussed. The calculated positions of the optical energy bands agree reasonably well with those obtained from the experiment. Thus, the experimental result is supported by the theoretical analysis that Mn²⁺ ions substitute at Zn²⁺ (1) sites in ZKS. The model parameters evaluated in this study may be utilized for ZFS parameter determinations for Mn²⁺ ions at similar sites in MNM. The present modeling technique may be useful in finding various crystals of a number of scientific and industrial applications.

Ethical approval

There were no human or animal subjects in this study, and it wasn’t conducted in any protected or private locations. Corresponding locations did not require any special permissions.

Author contributions

Vikram Singh and Maroj Bharati prepared the figure, wrote the manuscript, and carried out the computations. Ram Kripal: concept and oversight. The manuscript has been reviewed by all authors.

Conflicts of interest

The authors affirm that no known conflicting financial interests or personal relationships could have influenced any of the work presented in this paper.

Data availability

Data will be made available on request.

Acknowledgements

The authors are grateful to the Head of Physics Department of Allahabad University, Allahabad for giving facilities of the department and to Prof. C. Rudowicz of Faculty of Chemistry, Adam Mickiewicz University, Poznan, Poland for the CFA program.

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