CN110275293B - Method for analyzing influence of praseodymium ion doping on magneto-optical performance of terbium gallium garnet - Google Patents

Method for analyzing influence of praseodymium ion doping on magneto-optical performance of terbium gallium garnet Download PDF

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CN110275293B
CN110275293B CN201910563556.4A CN201910563556A CN110275293B CN 110275293 B CN110275293 B CN 110275293B CN 201910563556 A CN201910563556 A CN 201910563556A CN 110275293 B CN110275293 B CN 110275293B
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蔡伟
杨志勇
许友安
李敏
王振业
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Rocket Force University of Engineering of PLA
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Abstract

The invention relates to a method for doping praseodymium (Pr) in Terbium Gallium Garnet (TGG)3+) An analysis method for the influence of magneto-optical properties of crystal after ion. Solving a long-term equation according to a perturbation theory to obtain Tb under the super-exchange action among spin-orbit coupling, a crystal field, an effective field and ions3+、Pr3+Energy level shift and wave function of the ions; and further solve Tb3+、Pr3+Transition electric dipole moment of ions from the ground state 4f to 5d, distribution probability on each energy level and average magnetic moment; finally, the Verdet constant and the magnetic susceptibility of the Pr TGG crystal, the Verdet constant and the Pr are obtained3+The relationship between the ion doping amounts. The invention proves that the Verdet constant of the crystal is obviously improved and the Verdet constant and Pr are obviously improved through calculation and analysis3+The ion content is in a linear relation, and basically coincides with Pr: the inverse magnetic susceptibility of TGG is linear with temperature and has paramagnetic property.

Description

Method for analyzing influence of praseodymium ion doping on magneto-optical performance of terbium gallium garnet
Technical Field
The invention belongs to the technical field of magneto-optical modulation and Faraday magneto-optical effect, and relates to praseodymium (Pr) doped Terbium Gallium Garnet (TGG)3+) An analysis method for the influence of magneto-optical properties of crystal after ion.
Background
In 1845, Faraday discovered that the polarization plane of incident light is deflected by a specific material under the action of an external magnetic field. The magneto-optical material with the magneto-optical effect is used in various fields such as magneto-optical modulators, optical fiber current sensors, optical information processing and the like. Among them, the TGG crystal has the most extensive applications because of its advantages of high thermal conductivity, stable physicochemical properties, good size expandability, etc.
Since the 80 s of the 20 th century, a great deal of research has been conducted on TGG crystals at home and abroad. TGG crystals were obtained and the diffraction data were indexed by Liulin et al, institute of physical sciences, of the Chinese academy of sciences (Liu L, Yu Y D1985J Synthetic Crystal 127(inChinese) [1985 Artificial Crystal school 127 ]]) Chenjian Bin et al performed more complete magneto-optical property tests on TGG crystals (Chen J B, Lin Y, Li G H, Chen J S, Teng S, Yao Y G2014J Synthetic Crystal 438(in Chinese) [2014 Artificial Crystal declaration 438)]) Xujialin, Longyon and Chaoyang respectively research the defect, eccentric growth and volatilization mechanism of TGG crystal (Xu J L, Dong W L, Peng H Y, Liu W, Jin W Z, Lin H, Li C2015 JChangchun Univ Techno 320(in Chinese)2015 university of Catharan science 320]Long Y, Xu Y, Shi Z B, Ding Y T, Wang J, Fu C L2015 Piezoelectric and sound and light 37277(in Chinese)2015 Piezoelectric and acousto-optic 37277, Fei G Q, Zhang Y, Liu Z P2015 Journal of Synthetic Crystals 44885(in Chinese)2015 intraocular lenses report 44885). Longyong et al used a homemade JGD-800 type automatic pulling furnace to grow large-sized TGG crystals (L Y, Shi Z B, Ding Y D2016 Piezoelectrics)&Acousto-optic 38433(in Chinese)2016 Piezo and Acousto-optic 38433), and Yttrium Iron Garnet (YIG), Ce-doped Yttrium iron garnet (Ce: YIG), apatite crystals (Sr)2Tb8(SiO4)6O2) Compared with magneto-optical materials, pure TGG crystal has a low Verdet constant, and cannot meet the requirements of high-power Faraday isolators, rotators, magnetic switches and other partial devices. To solve this problem, the document "wavelet dependency of Verdet constant of Pr doped cubic gallium nitride crystal" grows Pr with good performance from the process level: TGG crystal 9(Chen Z, Yang L, Wang X Y, Hang Y2016 opt. mater 62475). However, due to the complex interaction inside the crystal, no relevant theoretical analysis report is found at present about the intrinsic mechanism of the influence of doped praseodymium ions on the magneto-optical performance of the TGG crystal.
Disclosure of Invention
In view of the above-mentioned state of the art, the present invention aims to: by passingThe calculation and inference method of quantum theory clearly shows that the doped Pr3+Ion post, interaction of physical quantities in the TGG crystal interior, explain Pr3+Intrinsic mechanism of ion impact on the magneto-optical properties of TGG crystals; analysis of Pr3+Influence of ion doping on Verdet constant and magnetic susceptibility of TGG crystal, and Verdet constant and Pr3+And calculating an optimal value according to the dependence relationship among the ion doping amounts, and providing a basis for practically preparing the magneto-optical material with the high Verdet constant.
In order to achieve the purpose, the invention starts from quantum theory, firstly, a long-term equation is solved according to perturbation theory to obtain Tb under the super-exchange action among spin-orbit coupling, crystal field, effective field and ions3+、Pr3+Energy level shift and wave function of the ions; and further solve Tb3+、Pr3+Transition electric dipole moment of ions from the ground state 4f to 5d, distribution probability on each energy level and average magnetic moment; finally, the Verdet constant and the magnetic susceptibility of the Pr TGG crystal, the Verdet constant and the Pr are obtained3+The relation between the ion doping amount mainly comprises the following steps:
step 1: solving for Tb3+、Pr3+Energy level and wave function of ions
Step 1.1: solving energy level displacement and wave function under the action of crystal field and spin-orbit coupling
Will be provided with
Figure BDA0002108933320000021
As a perturbation quantity, wherein
Figure BDA0002108933320000022
In order to act on the crystal field,
Figure BDA0002108933320000023
for spin-orbit coupling, the crystal field is obtained by the following long-term equation and Tb is obtained under the effect of spin-orbit coupling3+、Pr3+Crystal field energy level and wave function of ions
Figure BDA0002108933320000024
In the formula psii1、ψj1As an unperturbed eigenwave function, Ea1For spin-orbit coupling and ground state energy level shift induced by the crystal field, Eb1Is an excited state energy level shift;
step 1.2: solving energy level displacement and wave function under effective action
Hamiltonian of effective field
Figure BDA0002108933320000025
Viewed as the perturbation of the spin-orbit coupling and crystal field, at a first approximation the effective field induced ground state energy level shift is
Ea2＝μBHe·[ψi2|(L+2S)|ψj2>+2νχ<ψi2|S|ψj2>] (2)
In the formula psii2、ψj2Respectively, the ground wave function, H, of the crystal field and of the spin-couplingeThe magnitude of an external magnetic field, L is orbital angular momentum, S is spin angular momentum, v is a molecular field coefficient, and χ is magnetic susceptibility;
step 1.3: solving for Tb3+Ion and Pr3+Energy level shift and wave function under superexchange action between ions
Solving the following long-term equation according to the theory of degeneracy perturbation to obtain the energy level displacement and wave function caused by super-exchange
Figure BDA0002108933320000031
In the formula
Figure BDA0002108933320000032
Hamiltonian, ψ, caused for superexchangei3、ψj3The eigen wave functions after the action of the crystal field, spin-orbit coupling and effective field, Ea3、Eb2Are respectively Tb3+、Pr3+Ground state caused by superexchange between ionsAnd excited state energy level shift;
the ground state has a final energy level of Ea＝Ea1+Ea2+Ea3，Tb3+、Pr3+The final energy level of the excited state of the ion is Eb(Tb3+)＝Eb1+Eb2+38462cm-1、Eb(Pr3+)＝Eb1+Eb2+63580cm-1
Step 2: calculating Pr: verdet constant of TGG and Pr3+Relationship between ion doping amounts
The Pr to TGG is represented as TbxPryGazO12(x + y ≈ 3, z ≈ 5), when x ≧ y, there is only an equal amount of Tb3+Ion and Pr3 +The ions are super-exchanged, so the Verdet constant is expressed as
V(Pr:TGG)＝{y[V1(Tb3+)+V1(Pr3+)]+(x-y)V2(Tb3+)}/(x+y) (4)
When y is<x is equivalent to doping Tb in pure PrGG crystal3+Ion, Verdet constant expressed as
V(Pr:TGG)＝{x[V1(Tb3+)+V1(Pr3+)]+(y-x)V2(Pr3+)}/(x+y) (5)
In the formula V1(Tb3+)、V1(Pr3+) Denotes the Verdet constant, V, after the occurrence of the superexchange2(Tb3+)、V2(Pr3+) Represents the Verdet constant without superexchange;
and step 3: solving Pr: magnetic susceptibility of TGG
In the same way as the calculation of the verdet constant, Pr: the magnetic susceptibility of TGG can be seen as Tb3+Ion and Pr3+Sum of ion contributions
Figure BDA0002108933320000033
Middle X type1(Tb3+)、χ1(Pr3+) After the occurrence of the superexchangeMagnetic susceptibility of2(Tb3+)、χ2(Pr3+) Indicating the magnetic susceptibility without superexchange.
Drawings
FIG. 1: wavelength characteristics of Verdet constant
FIG. 2: verdet constant with Pr3+Variation of the ion content (y)
(a) Theoretical relationship, (b) data validation.
FIG. 3: temperature characteristic of magnetic susceptibility
Detailed Description
Referring now to the drawings, an analysis of the intrinsic mechanism of the effect of praseodymium ion doping on the magneto-optical properties of TGG crystals is provided3+Influence of ion doping on Verdet constant and magnetic susceptibility of TGG crystal, and Verdet constant and Pr3+Analyzing the dependence relationship among the ion doping amounts, calculating an optimal value, and providing a basis for actually preparing the magneto-optical material with the high Verdet constant, wherein the method specifically comprises the following steps:
step 1: tb3+、Pr3+Solution of ion energy level and wave function
The total Hamiltonian of the crystal is
Figure BDA0002108933320000041
In the formula
Figure BDA0002108933320000042
In order to make the coulomb interaction,
Figure BDA0002108933320000043
for the purpose of spin-orbit coupling,
Figure BDA0002108933320000044
in order to act on the crystal field,
Figure BDA0002108933320000045
in order for the effective field to act on the ions,
Figure BDA0002108933320000046
magnetic interactions (negligible);
step 1.1: solving energy level displacement and wave function under the action of crystal field and spin-orbit coupling
Will be provided with
Figure BDA0002108933320000047
As the perturbation quantity, Tb was obtained by the following long-term equation3+、Pr3+Crystal field energy level and wave function of ions
Figure BDA0002108933320000048
Considering the coupling of 4f and 5d multiple states, the reference state of 4f is used7F6For the zero of the energy level, the energy level shift is calculated as shown in table 1,
TABLE 1 energy level shift (cm) under the action of crystal field and spin orbit-1)
Table 1.Energy level shift under the action of crystal field and spin orbit.(cm-1)
Figure BDA0002108933320000049
Step 1.2: solving energy level displacement and wave function under effective action
Under the influence of the effective field, the 4f ground state energy level will produce Zeeman splitting, and the effect of the effective field on 5d is negligible due to the higher excited state energy level. Taking into account the additional magnetic field HνActing only on spins, the Hamiltonian of the effective field is
Figure BDA0002108933320000051
Effective field
Figure BDA0002108933320000052
It can be regarded as spin-orbit couplingAnd perturbation of crystal field, under the first approximation, the ground state energy level shift caused by effective field is
Ea2＝μBHe·[ψi2|(L+2S)|ψj2>+2νχ<ψi2|S|ψj2>] (2)
The ground state energy level split calculated from equation 4 is shown in Table 2
TABLE 2 energy level splitting (cm-1)
Table 2.Energy level splitting under the action of effective field.(cm-1)
Figure BDA0002108933320000053
Step 1.3: solving for Tb3+Ion and Pr3+Energy level shift and wave function under superexchange action between ions
Doping Pr in TGG crystal3+After ionization, Tb3+、Pr3+Strong superexchange between the orbital and spin angular momentum between ions occurs, and the Hamilton quantity of the orbital-spin related term of the shell electron can be expressed as
Figure BDA0002108933320000054
Wherein i, j and Tb are3+、Pr3+Ion correlation, mi、mjRepresenting the ground state orbit, mi′、mj' represents an excited orbital, J (m)i′,mj′,mi,mj)＝<mi′,mj′|J(i,j)|mi,mj>Representing the mixed orbital angular momentum, Si、SjRepresenting the spin angular momentum of both ions. Solving the following long-term equation according to the theory of degeneracy perturbation to obtain the energy level displacement and wave function caused by super-exchange
Figure BDA0002108933320000055
Tb3+、Pr3+The ground state and excited state energy level shifts caused by the superexchange between ions are shown in Table 3
TABLE 3 energy level shifts (cm-1)
Table 3.Energy level shift under the action of super-exchange interaction.(cm-1)
Figure BDA0002108933320000056
Figure BDA0002108933320000061
The ground state has a final energy level of Ea＝Ea1+Ea2+Ea3，Tb3+、Pr3+The energy level spacing between the excited 5d state and the ground 4f state of the ion is 38462cm-1、63580cm-1And thus the final energy level of the excited state is Eb(Tb3+)＝Eb1+Eb2+38462cm-1、Eb(Pr3+)＝Eb1+Eb2+63580cm-1；
Step 2: calculation of Verdet constant and Pr3+Relationship between ion doping amounts
Step 2.1: calculation of Verdet constants
Paramagnetic and diamagnetic Verdet constants are respectively
Figure BDA0002108933320000062
Figure BDA0002108933320000063
In the formula
Figure BDA0002108933320000064
Ln＝[(n2+2)/3]2Is Lorentz-Lorenz correction term, N is ion number in unit volume, N is average refractive index, e, m are electron charge and mass, omega is incident light frequency, omegaabIs the frequency between the excited and ground states,abis the line width of the optical fiber,
Figure BDA0002108933320000065
the wave vector is the wave vector,
Figure BDA0002108933320000066
(± represents right-handed and left-handed respectively) is the probability that an electron transits from the ground state to the excited state;
for Tb3+Ions, the crystal field is non-singlet, the diamagnetic verdet constant is negligible,
Figure BDA0002108933320000067
but is singlet to the crystal field, Pr3+Ion, diamagnetic Verdet constant is as important as paramagnetic Verdet constant,
Figure BDA0002108933320000068
the Pr to TGG is represented as TbxPryGazO12(x + y ≈ 3, z ≈ 5), when x ≧ y, there is only an equal amount of Tb3+Ion and Pr3 +The ions are super-exchanged, so the Verdet constant is expressed as
V(Pr:TGG)＝{y[V1(Tb3+)+V1(Pr3+)]+(x-y)V2(Tb3+)}/(x+y) (4)
When y is<x is equivalent to doping Tb in pure PrGG crystal3+Ion, Verdet constant expressed as
V(Pr:TGG)＝{x[V1(Tb3+)+V1(Pr3+)]+(y-x)V2(Pr3+)}/(x+y) (5)
Assuming that the temperature T is 298K, the external magnetic field HeTaking the wavelength variation range of 400-1500nm as 0.1T, respectively calculating pure TGG (x is 3, y is 0,z ═ 5) and 5% Pr: the verdet constants of TGG (x-2.926, y-0.073, z-5.03) at different wavelengths are shown in table 4
TABLE 4 Verdet constants V (rad/m. T) at different wavelengths
Table 4.Verdet constant at different wavelengths.(rad/m·T)
Figure BDA0002108933320000071
Note: vcCalculated for the Verdet constant herein, VeIs an experimental value
See FIG. 1
Analysis of the variation of Verdet constant with wavelength:
as can be seen from FIG. 1, doped with Pr3+After ionization, the Verdet constant of the crystal is obviously improved, and the Videt constant is 313.4 rad/m.T, 191.2 rad/m.T and 60.4 rad/m.T at the wavelengths of 532nm, 632.8nm and 1064nm respectively. This is due to: (1) pr (Pr) of3+Transition matrix element of ion is Tb3+Ion is large and Pr3+Ions also contain diamagnetic FR moieties, giving rise to large faraday rotation angles; (2) doped Pr3+After ionization, Tb3+Ion and Pr3+Strong superexchange action is generated between ions, and further energy level splitting is caused;
step 2.2: verdet constant and Pr3+Relationship between ion doping amount
Taking wavelength lambda as 532nm, 632.8nm and 1064nm, calculating Pr of TGG crystal in different Pr3+The Verdet constants at the ion contents (y) are given in Table 5
TABLE 5 different Pr3+Vierde constant V (rad/m. T) at ion content (y)
Table 5.Verdet constant under different Pr3+ions content(rad/m·T)
Figure BDA0002108933320000072
See FIG. 2
Pr:TGGVerdet constant and Pr of crystal3+Analysis of the relationship between the ion contents (y):
FIG. 2(a) shows the Verdet constant and Pr of the crystal of Pr TGG3+The theoretical relationship between the ion contents, fig. 2(b) is a comparison verification of the existing experimental data and the calculated values. The three curves in FIG. 2(a) show different wavelength values, and as can be seen from FIG. 2(a), the Verdet constant and Pr of the Pr TGG crystal3+The ion content is in a piecewise linear relation, and the more the number of ions subjected to super exchange is, the higher the Verdet constant of the crystal is; when y is 1.5, i.e. Tb in crystal3+Ion and Pr3+When the ion content is equal, the maximum value of 2913.4 rad/m.T is reached. As can be seen from Table 5 and FIG. 2(a), Tb is doped in PrGG compared with Pr TGG crystal3+Ions can theoretically obtain larger Verdet constants;
the solid line in fig. 2(b) is a curve fitted to the experimental data and the dotted line represents the calculated values herein. As can be seen, the solid line and the dotted line have the same variation trend, and the Verdet constant and Pr3+The ion contents are in a linear relation and basically coincide, which shows that the calculation result in the text is feasible;
and step 3: calculation of magnetic susceptibility
The relationship between magnetic susceptibility and magnetization is
Figure BDA0002108933320000081
Wherein N is the number of ions per unit volume,
Figure BDA0002108933320000082
the average magnetic moment of single 4f ion is obtained by calculating the electron distribution probability
Figure BDA0002108933320000083
In the same way as the calculation of the verdet constant, Pr: the magnetic susceptibility of TGG can be seen as Tb3+Ion and Pr3+Sum of ion contributions
Figure BDA0002108933320000084
Assuming a wavelength λ of 1064nm and a temperature variation range of 10-300K, pure TGG and 5% Pr were calculated, respectively: the reciprocal 1/chi of the magnetic susceptibility of TGG at different temperatures is shown in Table 6
TABLE 6 inverse magnetic susceptibility 1/χ at different temperatures
Table 6.Inverse magnetic susceptibility at different temperatures.
Figure BDA0002108933320000085
Figure BDA0002108933320000091
Note: 1/chicCalculated herein, 1/χeIs an experimental value
See FIG. 3
The variation of magnetic susceptibility with temperature is analyzed:
as can be seen from fig. 3, in common with pure TGG crystals, Pr: the reciprocal of the magnetic susceptibility of TGG has a linear relation with temperature, meets the Currie-weiss law, and has paramagnetic property. However, Pr: TGG has a large magnetic susceptibility and a small temperature dependence due to Tb3+Ion and Pr3+The outer electrons of the ions have spin-orbit angular momentum coupling, the internal magnetic moment of the crystal is increased, and the effective magnetic moment reaches 9.92 mu at 10KBAs can be seen from equation 11, the magnetic susceptibility increases as the magnetic moment increases.

Claims (1)

1. A method for analyzing the influence of praseodymium ion doping on the magneto-optical performance of terbium gallium garnet is characterized by comprising the following steps: resolving a long-term equation according to a perturbation theory to obtain Tb under the super-exchange action among spin-orbit coupling, a crystal field, an effective field and ions3+、Pr3+Energy level shift and wave function of the ions; finally obtaining the Verdet constant and the Verdet of the Pr TGG crystalConstant and Pr3+The relation between the ion doping amount comprises the following steps:
step 1: solving for Tb3+、Pr3+Energy level and wave function of the ions;
step 1.1: solving energy level displacement and wave function under the action of crystal field and spin-orbit coupling;
will be provided with
Figure FDA0002699871020000011
As a perturbation quantity, wherein
Figure FDA0002699871020000012
In order to act on the crystal field,
Figure FDA0002699871020000013
for spin-orbit coupling, the crystal field is obtained by the following long-term equation and Tb is obtained under the effect of spin-orbit coupling3+、Pr3+Crystal field energy level and wave function of ions
Figure FDA0002699871020000014
In the formula psii1、ψj1As an unperturbed eigenwave function, Ea1For spin-orbit coupling and ground state energy level shift induced by the crystal field, Eb1Is an excited state energy level shift;
step 1.2: solving energy level displacement and wave function under effective action;
hamiltonian of effective field
Figure FDA0002699871020000015
Viewed as the perturbation of the spin-orbit coupling and crystal field, at a first approximation the effective field induced ground state energy level shift is
Ea2＝μBHe·[<ψi2|(L+2S)|ψj2>+2νχ<ψi2|S|ψj2>] (2)
In the formula psii2、ψj2Respectively, the ground wave function, H, of the crystal field and of the spin-couplingeThe magnitude of an external magnetic field, L is orbital angular momentum, S is spin angular momentum, v is a molecular field coefficient, and χ is magnetic susceptibility;
step 1.3: solving for Tb3+Ion and Pr3+Energy level shift and wave function under superexchange action between ions
Solving the following long-term equation according to the theory of degeneracy perturbation to obtain the energy level displacement and wave function caused by super-exchange
Figure FDA0002699871020000016
In the formula
Figure FDA0002699871020000017
Hamiltonian, ψ, caused for superexchangei3、ψj3The eigen wave functions after the action of the crystal field, spin-orbit coupling and effective field, Ea3、Eb2Are respectively Tb3+、Pr3+Ground state and excited state energy level shifts caused by the super exchange between ions;
step 2: calculating Pr: verdet constant of TGG and Pr3+The relationship between the ion doping amounts is as follows:
the Pr to TGG is represented as TbxPryGazO12(x + y ≈ 3, z ≈ 5), when x ≧ y, there is only an equal amount of Tb3+Ion and Pr3+The ions are super-exchanged, so the Verdet constant is expressed as
V(Pr:TGG)＝{y[V1(Tb3+)+V1(Pr3+)]+(x-y)V2(Tb3+)}/(x+y) (4)
When y is<x is equivalent to doping Tb in pure PrGG crystal3+Ion, Verdet constant expressed as
V(Pr:TGG)＝{x[V1(Tb3+)+V1(Pr3+)]+(y-x)V2(Pr3+)}/(x+y) (5)
In the formula V1(Tb3+)、V1(Pr3+) Denotes the Verdet constant, V, after the occurrence of the superexchange2(Tb3+)、V2(Pr3+) Denotes the Verdet constant without superexchange, where V1(Tb3+) And V2(Tb3+) Tb obtainable according to step 13+Ion energy level and wave function solution, V1(Pr3+) And V2(Pr3+) Pr obtainable according to step 13+And solving the ion energy level and the wave function to obtain the ion energy level and the wave function.
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