A theoretical investigation of crystal field parameters (CFP) and zero-field splitting (ZFS) parameter D of Mn2+ doped guanidine zinc sulphate (GZS) crystals at room temperature (RT) is done with the help of superposition model and the perturbation theory. The ZFS parameter D determined here is in good agreement with the experimental value reported earlier. The conclusion of experimental study that Mn2+ substitutes for Zn2+ in GZS is supported by our theoretical investigation. The values of D without and with local distortion are 11174.3×10-4 cm-1 and 702.4 ×10-4 cm-1, respectively, while the experimental value is 702.0×10-4 cm-1

Kripal, Ram

Shukla, Lal Chandra

Tripathi, Upendra Mani

English

Scitech Research Journals

                                                                                                                                        Journal of                                                                                                                                          ISSN   Volume 8, Issue 1 available at www.scitecresearch.com/journals/index.php/bjmp                                                         18|       Boson Journal of Modern Physics                           E-ISSN: 2454-8413 Zero field splitting parameter of Mn2+ doped guanidine zinc sulphate crystal -a theoretical study Ram Kripal, Lal Chandra Shukla, Upendra Mani Tripathi  EPR Laboratory, Department of Physics, University of Allahabad, Allahabad-211002, India E-mail: ram_kripal2001@rediffmail.com      Received: March 02, 2021; Accepted: March 19, 2021; Published: March 29, 2021  _______ Cite this article: Kripal, R., Shukla, L. C., & Tripathi, U. M. (2021). Zero field splitting parameter of Mn2+ doped guanidine zinc sulphate crystal -a theoretical study. Boson Journal of Modern Physics, 8(1), 18-23. Retrieved from http://www.scitecresearch.com/journals/index.php/bjmp/article/view/2032.    Abstract  This study      1.  Introduction       Electron paramagnetic resonance (EPR) studies are useful for the knowledge of structural distortions and local site symmetry of transition ions in crystals [1-7]. EPR spectra of these ions are frequently analyzed with the help of microscopic spin-Hamiltonian (MSH) theory. Using this theory, the spin Hamiltonian (SH) parameters from EPR can be correlated with optical absorption and structural parameters. Both the experimental and theoretical studies indicate that the spin Hamiltonian parameters of transition ions (d5 (6S)) in crystals are very sensitive to local distortion. Therefore, the SH theory is widely used in crystals. The crystal-field (CF) parameters of d5 ion are obtained using superposition model (SPM) [8, 9]. The zero field splitting (ZFS) parameters are determined using CF parameters [10]. Mn2+ ion is important as its ground state is 6S5/2 [11-15]. The electron spin is affected by high order interaction of crystalline electric field and in external magnetic field the orientation of spins is free [16]. As S state ions have large spin–lattice relaxation time, Mn2+ ion gives well resolved EPR lines [15-19] at room temperature (RT). In the present paper, the CF parameters are determined using SPM and these parameters with MSH theory give ZFS parameter for Mn2+ ion at the substitutional Zn2+ site in guanidine zinc sulphate (GZS) crystal at RT. 2. Crystal Structure  The crystal structure of GZS, Zn[C(NH2)3]2(SO4)2 belongs to space group dI 24 with unit cell dimensions a = 0.9515 nm and c = 1.4351 nm, and there exist four molecules per unit cell (Z = 4) [20]. A network of zinc and sulphate ions constitutes the main feature of the structure. Four oxygen ions form a distorted tetrahedral environment around the Mn2+ ion, as shown in Fig. 1.  Scitech Research  Organisation  Abstract.  A theoretical investigation of crystal field parameters (CFP) and zero-field splitting (ZFS) parameter D of Mn2+ doped guanidine zinc sulphate (GZS) crystals at room temperature (RT) is done with the help of superposition model and the perturbation theory. The ZFS parameter D determined here is in good agreement with the experimental value reported earlier. The conclusion of experimental study that Mn2+ substitutes for Zn2+ in GZS is supported by our theoretical investigation. The values of D without and with local distortion are 11174.3×10-4 cm-1 and 702.4 ×10-4 cm-1, respectively, while the experimental value is 702.0×10-4 cm-1. Keywords: A. Organic compounds; A. Single crystal; D. Crystal fields; D. Optical properties; D. Electron paramagnetic resonance.  Boson Journal of Modern Physics Vol 8,1 - 2021 E-ISSN: 2454-8413                                                                                                                                         Journal of                                                                                                                                          ISSN   Volume 8, Issue 1 available at www.scitecresearch.com/journals/index.php/bjmp                                                         19|       Boson Journal of Modern Physics                           E-ISSN: 2454-8413  Fig. 1 Environment around Mn2+ ion. 3. Theoretical Investigation The Mn2+ ion in GZS crystal substitutes at Zn2+ site [21]. The SH of 3d5 ion in crystal field of axial symmetry is given as [2, 22, 23] +  D{Sz2-31S(S+1)}                    ℋ =                                                                                       +                                                                                                            (1) where the first term gives electronic Zeeman interaction, B is the external magnetic field, g is the spectroscopic splitting factor and μB is Bohr magneton. The second, third, and fourth terms represent the second order axial, fourth-rank cubic and fourthrank axial ZFS terms [2]. The fifth term provides the hyperfine interaction term. S, D, a, F are the effective spin vector, second order axial, fourth-rank cubic and fourth-rank axial ZFS parameters, respectively. An isotropic approximation for the electronic Zeeman interaction is used in case of Mn2+ ions [2, 24, 25].  The Hamiltonian for a d5 ion is given as ℋ = ℋ 0+ ℋ cf + ℋ so                                                                                                                                                                                                                                                                                               Journal of                                                                                                                                          ISSN   Volume 8, Issue 1 available at www.scitecresearch.com/journals/index.php/bjmp                                                         20|       Boson Journal of Modern Physics                           E-ISSN: 2454-8413  where ℋ cf  = kqkqkqCB                                                                                                               (2) gives the crystal field Hamiltonian. ℋ 0 and ℋ so represent free ion Hamiltonian and spin-orbit (SO) coupling, respectively. Since the spin-spin coupling is very small [26-28], its contribution has been neglected in Eq. (2). The crystal field of SO interaction is considered as perturbation term [29,30]. The strong-field scheme calculation for F-state ions was given by Macfarlane [31]. The SO contribution to the ZFS parameter D for 3d5 ions in axial symmetry is given by [30]                                          (3)                         where P = 7(B+C), G = 10B+5C and D = 17B+5C. P, G, and D represent the energy separations between the excited quartets and the ground sextet. Racah parameters B and C give the electron-electron repulsion. Only fourth order term is taken in Eq. (3) as other perturbation terms are negligible [32]. The parameters B, C and ξ, in terms of the average covalency parameter N, are given as, B = N4B0, C = N4C0 and ξ = N2 ξ0, where B0 and C0 are the Racah parameters and ξ0, the spin-orbit coupling parameter, for free ion [33, 34]. B0 = 960 cm-1, C0 = 3325 cm-1, ξ0 = 336 cm-1 [2] for Mn2+ ion are used here. N can be obtained with the help of equation            ,                                                                                                     (4)  By using SPM the CF parameters for Mn2+ in GZS crystal are calculated and substituting these in Eq. (3) ZFS parameter D is obtained. Similar method has been used for finding ZFS parameters by many other workers [35]. To understand the crystal-field splitting, the SPM is effectively used. This model has also been applied for 3dn ions [8, 32, 36]. The crystal field parameters, using this model, are found from the equations [37]              22220021100220 42ttRRRARRRAB                                                (5)                         44220041100440 1216ttRRRARRRAB                                                (6)                         42200444 702tRRRAB                                                                                        (7)  in which R0 is the reference distance, in general chosen as the average value of all four bond lengths (for axial symmetry). 4. Results and Discussion  The average value of two out of four Mn2+-O bond lengths are given as R10 = 0.20936 nm and the average value of the rest two bond lengths are also given as R20 = 0.20936 nm. ΔR1 and ΔR2 represent the distortion parameters. 2A , 4A and tk are the intrinsic parameter and power law exponent, respectively. In tetrahedral                                                                                                                                         Journal of                                                                                                                                          ISSN   Volume 8, Issue 1 available at www.scitecresearch.com/journals/index.php/bjmp                                                         21|       Boson Journal of Modern Physics                           E-ISSN: 2454-8413 coordination, )(RA 04 =  Dq 27/16-   [10]. For 3d5 ions, 42AAis in the range 8-12 [32, 36]. The power law exponent for Mn2+ ion is taken as t2 = 3, t4 = 7. Semi-ab initio calculations are performed for other transition metal ions to obtain the intrinsic parameter values in SPM, The values of B, C and Dq are obtained (for oxygen ligands) [38] using optical study [39] as 917, 2254 and 756 cm-1, respectively. First no local distortion is considered and the value of D is estimated. For this, taking 42AA= 8 and R0 = 0.215 nm, the sum of ionic radii of Mn2+ = 0.08 nm and O2- = 0.135 nm, which is slightly larger than the average distance of four ligands; the Bkq parameters are obtained as: B20 = -66319.5 cm-1, B40 = 43026.6 cm-1, B44 = 25713.3 cm-1 and the value of D as: D = 11174.3×10-4 cm-1. EPR study gives the experimental value of D as: D = 702.0×10- 4 cm-1 [40]. From above it is found that the theoretical value is larger than the experimental one. Now, taking local distortions as ΔR1 = 0.04794 nm and ΔR2 = 0.00002 nm, R0 = 0.215 nm and ratio 42AA = 8, the Bkq parameters are obtained as: B20 = -56109.5 cm-1, B40 = 24233.6 cm-1, B44 = 25696.1 cm-1and the value of D as: D = 702.4×10-4 cm-1, in reasonable agreement with the experimental one: D = 702.0×10-4 cm-1. 5. Conclusions Axial symmetry zero-field splitting parameter D for Mn2+ in GZS crystal has been determined using superposition model and perturbation theory. The theoretical D is in reasonable agreement with the experimental one when local distortion is taken into consideration. This theoretical investigation suggests that Mn2+ ion occupies substitutional Zn2+ site supporting the conclusion drawn from the experimental EPR study. ACKNOWLEDGEMENT                 The authors are thankful to the Head, Department of Physics, University of Allahabad for providing the facilities of the department.      References [1] C. Rudowicz, S. K. Misra, SPIN-HAMILTONIAN FORMALISMS IN ELECTRON MAGNETIC      RESONANCE (EMR) AND RELATED SPECTROSCOPIES, Appl. Spectrosc. Rev. 36 (2001)11-63. [2] Z. Y. Yang, C. Rudowicz, Y. Y. Yeung, Microscopic spin-Hamiltonian parameters and crystal field energy levels for the low C3 symmetry Ni2+ centre in LiNbO3 crystals, Physica B 348 (2004) 151-159. [3] Z. Y. Yang, Y. 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Zero field splitting parameter of Mn2+ doped guanidine zinc sulphate crystal -a theoretical study

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Zero field splitting parameter of Mn2+ doped guanidine zinc sulphate crystal -a theoretical study

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