^{1,a)}and Fernando Rodríguez

^{1}

### Abstract

This work investigates the influence of electron-phonon coupling associated with and Jahn–Teller (JT) effect in different transition-metal (TM) ions on de-excitation phenomena through nonradiative multiphonon relaxation, i.e., photoluminescence(PL) quenching. We developed a configurational curve model which is able to predict from the absorptionspectrum whether a given JT-TM ion is PL or quenched. The prediction is made on the basis of an adapted Dexter–Klick–Russell parameter for JT systems, defined in terms of spectroscopic parameters through , where refers to the splitting of the parent octahedral states by the JT distortion in or , and is the energy of the first absorption band involving electronic transition between and . We show that PL in any JT-TM ion occurs whenever or is quenched if . This result is noteworthy since it allows us to establish structural requirements for the JT-TM ion and the host crystal to be PL. Although PLproperties of materials containing TM ions depend on a variety of structural factors such as the electronic configuration, the site symmetry, and the crystal field produced by neighboring atoms, the present model achieves this goal through a simple spectroscopic parameter: . In this work we correlated the PLproperties of different sixfold-coordinated JT systems such as , , , , , , and in halides and oxides with obtained from their respective absorption spectra. From this analysis we conclude that depending on the nature of the JT coupling and its strength, PL is either strongly favored or quenched in while it is mostly quenched in systems due to the larger JT distortion.

We thank Professor M. C. Marco de Lucas, Professor R. Valiente, Dr. F. Aguado, and Dr. S. Garcia-Revilla for helpful discussions and collaborations in some previous works connected to Jahn–Teller systems. Financial support from the Spanish Ministerio de Ciencia e Innovación (Project No. MAT2008-06873-C02-01/MAT) and the MALTA–Consolider Ingenio 2010 (Ref. No. CSD2007-00045) are acknowledged. M.N.S.O. thanks for a FPU research grant (Ref. No. AP-2004-5954).

I. INTRODUCTION

II. RESULTS AND DISCUSSION

A. Radiative versus nonradiative de-excitation processes in Jahn–Teller systems

1. Configurational curves for Jahn–Teller systems

2. The Jahn–Teller model

3. JT effect

4. Jahn–Teller effect

III. CONCLUSIONS

### Key Topics

- Photoluminescence
- 77.0
- Jahn Teller effect
- 55.0
- Excited states
- 29.0
- Absorption spectra
- 23.0
- Copper
- 14.0

## Figures

PL scheme in a single-coordinate, , configuration diagram, for the excited and ground electronic states. Within a semiclassical description nonradiative de-excitation by multiphonon relaxation is associated with an activation energy (see text for an explanation). The DKR criterion for PL quenching requires the intersection point to be below the vertical excitation point : . Note that although harmonic models are unrealistic to predict real activation energies, nonradiative processes are blocked by increasing . The critical point for the onset of PL quenching corresponds to , or equivalently . Parameters are explained in the text.

PL scheme in a single-coordinate, , configuration diagram, for the excited and ground electronic states. Within a semiclassical description nonradiative de-excitation by multiphonon relaxation is associated with an activation energy (see text for an explanation). The DKR criterion for PL quenching requires the intersection point to be below the vertical excitation point : . Note that although harmonic models are unrealistic to predict real activation energies, nonradiative processes are blocked by increasing . The critical point for the onset of PL quenching corresponds to , or equivalently . Parameters are explained in the text.

Single-coordinate, , configuration diagram of the parent octahedral and electronic states as a function of the tetragonal normal coordinate . The ground and excited states exhibit a JT coupling and , respectively. Note that the corresponding configurational energy curves have been plotted using electron-phonon coupling constants and with [Eqs. (10)–(13) in text]. The equilibrium geometry is given by and for the ground and excited states, respectively. Vertical arrows represent electronic transitions associated with JT split states in absorption and emission. The ground-state JT energy is given by . Other parameters are explained in text.

Single-coordinate, , configuration diagram of the parent octahedral and electronic states as a function of the tetragonal normal coordinate . The ground and excited states exhibit a JT coupling and , respectively. Note that the corresponding configurational energy curves have been plotted using electron-phonon coupling constants and with [Eqs. (10)–(13) in text]. The equilibrium geometry is given by and for the ground and excited states, respectively. Vertical arrows represent electronic transitions associated with JT split states in absorption and emission. The ground-state JT energy is given by . Other parameters are explained in text.

- and -polarized absorption spectra of at 10 K and the corresponding band assignment: , , and (adapted from Ref. 12). The vibrational progression of the first absorption band gives a Huang–Rhys parameter . Within a singlet-to-singlet transition , the DKR parameter is . (Top left) Energy variation of the vibrational component with the derived from the second derivative spectrum shown below. Note the weak anharmonicity of the vibrational mode derived by fitting the vibronic energy to linear and quadratic terms of : , being the vibrational quantum number of the excited state. (Top right) One electron energy level diagram of in and spin-allowed crystal-field transitions. The crystal structure of is shown in the right side.

- and -polarized absorption spectra of at 10 K and the corresponding band assignment: , , and (adapted from Ref. 12). The vibrational progression of the first absorption band gives a Huang–Rhys parameter . Within a singlet-to-singlet transition , the DKR parameter is . (Top left) Energy variation of the vibrational component with the derived from the second derivative spectrum shown below. Note the weak anharmonicity of the vibrational mode derived by fitting the vibronic energy to linear and quadratic terms of : , being the vibrational quantum number of the excited state. (Top right) One electron energy level diagram of in and spin-allowed crystal-field transitions. The crystal structure of is shown in the right side.

Single-coordinate , configuration diagram for the parent octahedral and electronic states as a function of the tetragonal normal coordinate . The ground and excited states exhibit a JT coupling and , respectively. Note that the corresponding configurational energy curves have been plotted using electron-phonon coupling constants and with [Eqs. (22)–(25) in text]. The equilibrium geometry is given by and for the ground and excited states, respectively (see text for explanation). Vertical arrows represent electronic transitions associated with JT split states in absorption and emission. The ground-state JT energy is given by . Other parameters are explained in text.

Single-coordinate , configuration diagram for the parent octahedral and electronic states as a function of the tetragonal normal coordinate . The ground and excited states exhibit a JT coupling and , respectively. Note that the corresponding configurational energy curves have been plotted using electron-phonon coupling constants and with [Eqs. (22)–(25) in text]. The equilibrium geometry is given by and for the ground and excited states, respectively (see text for explanation). Vertical arrows represent electronic transitions associated with JT split states in absorption and emission. The ground-state JT energy is given by . Other parameters are explained in text.

Excitation and emission spectra of at 297 K (adapted from Ref. 22). Both bands consist of two Gaussian components according to the energy diagrams shown on both sides of the figure. The energy separation, and , corresponds to the JT-related splitting of the parent octahedral orbitals at the equilibrium geometry of the excited state and to the parent octahedral orbitals at the equilibrium geometry of the ground state , with , respectively, as shown in the energy level diagrams on the top left (emission) and right (excitation). The corresponding equilibrium geometries for the excited and ground states on the basis of the JT effect are also included.

Excitation and emission spectra of at 297 K (adapted from Ref. 22). Both bands consist of two Gaussian components according to the energy diagrams shown on both sides of the figure. The energy separation, and , corresponds to the JT-related splitting of the parent octahedral orbitals at the equilibrium geometry of the excited state and to the parent octahedral orbitals at the equilibrium geometry of the ground state , with , respectively, as shown in the energy level diagrams on the top left (emission) and right (excitation). The corresponding equilibrium geometries for the excited and ground states on the basis of the JT effect are also included.

## Tables

Spectroscopic parameters for TM ions in different crystals, including the absorption energy and the JT splittings ( and ) derived from the optical spectra given in the reference therein. The last two columns collect the JT-DKR parameter and the PL behavior.

Spectroscopic parameters for TM ions in different crystals, including the absorption energy and the JT splittings ( and ) derived from the optical spectra given in the reference therein. The last two columns collect the JT-DKR parameter and the PL behavior.

Spectroscopic parameters for TM ions in different crystals, including the absorption energy and the JT splittings ( and ) derived from the optical spectra given in the reference therein. The last two columns collect the JT-DKR parameter and the PL behavior.

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