Jahn-Teller Coupling Research Articles

Jahn–Teller coupling in spinel-type crystals doped with transition metal ions

In this article, we report the theoretical evaluation of the vibronic constants for the spinel-type crystals ZnAl 2S 4, ZnAl 2Se 4, CdAl 2Se 4, and CdIn 2S 4 doped with the transition metal ions Cr 3+, Cr 4+, Ti 2+, and Ti 3+. In these crystals the ions Cr 3+, Ti 3+ and Cr 4+, Ti 2+ occupy positions with octahedral and tetrahedral surrounding correspondingly. In the case of a tetrahedral complex the interaction with full symmetric A 1, tetragonal E and two trigonal vibrations T 2 ( 1 ) and T 2 ( 2 ) is considered, while for the octahedral cluster along with the A 1 and E vibrations only one trigonal vibrational mode is taken into account. The examined semiconductor systems are mainly covalent and application of the crystal field point charge model loses proper exactity. For this reason, we employ the exchange charge model for the crystal field that accounts for the covalence effects and provides relatively simple expressions for the crystal field and vibronic parameters keeping at the same time a reasonable level of accuracy. The vibronic coupling constants are numerically calculated and for each case an appropriate multi-mode Jahn–Teller vibronic problem is found out.

A study of the quadratic p2 ⊗ h Jahn–Teller system

A Jahn–Teller (JT) coupling model is developed for the p 2 ⊗ h JT system as a possible model for the doubly charged C 60 2 - dianion. The model described specifically includes second-order electron–vibration interactions which generate minima in the potential energy surface of either D 5 d or D 3 d symmetry depending on the strength of the JT coupling. Expressions are derived for the energies of these minima and linear combinations of the associated states are formulated that represent the vibronic states of the ion at intermediate coupling strengths. The energies of these symmetry-adapted states are given graphically and consideration is also given to the Coulombic interactions between the two electrons. Numerical application is made to the C 60 2 - ion using parameters taken from the literature.

Antisymmetric exchange and pseudo Jahn–Teller instability in spin-frustrated metal clusters

In this article, we analyze the interplay between the antisymmetric (AS) exchange interaction and Jahn–Teller (JT) vibronic coupling in spin-frustrated systems with triangular units. AS exchange in these systems creates a strong first order magnetic anisotropy related to the orbitally degenerate frustrated ground state that is analyzed for the unique structure of the cluster anion present in K 6 [ V 15 IV As 6 O 42 ( H 2 O ) ] · 8 H 2 O (V 15 cluster) exhibiting layers of different magnetization. Spin-frustration inherently related to the orbital degeneracy creates a structural instability that is shown to be competitive to the AS exchange. The vibronic pseudo JT coupling arising from the modulation of the exchange interaction by the double degenerate molecular vibrations is shown to reduce AS exchange giving rise to a restoration of magnetization quenched by AS exchange. This leads to an essential reduction of the magnetic anisotropy in spin-frustrated triangular clusters so that in the limit of strong JT coupling the isotropic exchange model becomes adequate.

On the ground state T g ⊗ εg (T g = 2T 2g, 3T 1g) Jahn–Teller-coupling in hexacyano complexes of 3d-transition metals

The linear and quadratic T g ⊗ ε g Jahn–Teller effect in the T g (T g = 2T 2g, 3T 1g) ground states of low-spin octahedral cyano complexes of 3d-transition metals (M = Ti III, V III, Mn III, Fe III, Cr II, Mn II) has been studied. Vibronic coupling parameters have been derived using density functional theory to calculate energies of Slater determinants, which result from various electron distributions within the t 2 g n configuration due to the metal based t 2g(3d) molecular orbitals ( n = 1, 2, 3, 4). Tetragonal elongations are found in the case of Ti III, Mn III and Cr II, and compressions for V III, Fe III and Mn II, and these establish the metal–ligand π-back donation as the dominant effect and driving force for the geometry distortions and energy stabilizations towards non-degenerate 2 B 2 g ( t 2 g 1 , t 2 g 5 ) and 3 A 2 g ( t 2 g 2 , t 2 g 4 ) ground states. The strength of the Jahn–Teller coupling is very weak and found not to follow a monotonic trend across the transition metal series but is shown to be weakest for Ti III, V III and Fe III, slightly larger for Mn III, increases further to Mn II and is found to be the strongest but is still weak for Cr II.

Mn- and Fe- doped GaN for spintronic applications

AbstractIn the context of ferromagnetic spin-coupling in dilute magnetic semiconductors, we present optical investigations on Mg co-doped GaMnN and Fe doped GaN. A complex luminescence feature occurring in Mg co-doped GaMnN around 1 eV was previously attributed to the internal 4T2(F)—4T1(F) transition of Mn4+ involved in different complexes. Selective excitation studies indicate the presence of at least three different complexes. Photoluminescence excitation spectra suggest that the internal Mn3+ transition may represent an excitation mechanism. Magneto photoluminescence spectra indicate equal g values for the ground and excited state. Low temperature infrared absorption spectra of Fe doped GaN allow to unambiguously establish the electronic structure of the Fe2+ center in GaN. Our results suggest that the Fe2+(5T2) state is stabilized against Jahn-Teller coupling by the reduced site-symmetry of the hexagonal lattice.

Domain Formation and Orbital Ordering Transition in a Doped Jahn-Teller Insulator

The ground state of a double-exchange model for orbitally degenerate e(g) electrons with Jahn-Teller lattice coupling and weak disorder is found to be spatially inhomogeneous near half filling. Using a real-space Monte Carlo method we show that doping the half-filled orbitally ordered insulator leads to the appearance of hole-rich disordered regions in an orbitally ordered environment. The doping driven orbital order to disorder transition is accompanied by the emergence of metallic behavior. We present results on transport and optical properties along with spatial patterns for lattice distortions and charge densities, providing a basis for an overall understanding of the low-doping phase diagram of La1 - xCaxMnO3.

Ultrasonic study of Jahn–Teller effect in charge‐ordered Nd1−xCax MnO3 (x = 0.4–0.8) manganites

AbstractThe ultrasonic, magnetic and transport properties of charge‐ordered manganites Nd1−x Cax MnO3 (x = 0.4, 0.5, 0.6, 0.7 and 0.8) were studied between 15 and 300 K. Resistivity and magnetization measurements show that all the samples undergo a charge‐ordering transition at low temperature. Upon cooling from 300 K, an obvious softening of sound velocity above the charge‐ordering transition temperature (T CO) and dramatic stiffening below T CO were observed for all samples. This feature gives clear evidence for strong electron–phonon coupling in these compounds. The Jahn–Teller coupling energy E JT increases with increasing Ca concentration x, and reaches the maximum at around x = 0.6, which is similar in characteristics to the T CO. The results imply that the charge‐ordering in Nd1−x Cax MnO3 is dominated by the Jahn–Teller effect. Our analyses suggested that the type of cooperative Jahn–Teller distortion be Q 2‐mode for x ≤ 0.6, and change to Q 3 mode at around x = 0.6 in the CO state. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Renner-Teller effects inHCO+dissociative recombination

A theoretical description of the dissociative recombination process for the ${\mathrm{HCO}}^{+}$ ion suggests that the nonadiabatic Renner-Teller coupling between electronic and vibrational degrees of freedom plays an important role. This finding is consistent with a recent study of this process for another closed-shell molecule, the ${{\mathrm{H}}_{3}}^{+}$ ion, where Jahn-Teller coupling was shown to generate a relatively high rate. The cross section obtained here for the dissociative recombination of ${\mathrm{HCO}}^{+}$ exhibits encouraging agreement with a merged-beam experiment.

Ultrasonic study of the charge mismatch effect in charge-ordered(Nd0.75Na0.25)x(Nd0.5Ca0.5)1−xMnO3

The resistivity, magnetization and ultrasonic properties of charge-ordered polycrystalline(Nd0.75Na0.25)x(Nd0.5Ca0.5)1−xMnO3 have been investigated from 50 to 300 K. A considerable velocity softening accompanied byan attenuation peak was observed around the charge-ordering transition temperature(TCO) upon cooling. The simultaneous occurrence of the charge ordering (CO) and theultrasonic anomaly implies strong electron–phonon coupling, which originates from thecooperative Jahn–Teller effect. At very low temperature, another broad attenuationpeak was observed, which is attributed to the phase separation (PS) and givesa direct evidence of spin–phonon coupling in the compound. With increasingx,TCO shifts to lower temperature, the magnetization of the system is strengthened and the PS is enhanced.The temperature dependence of the longitudinal modulus shows that the Jahn–Teller coupling energyEJT decreases with increasing Na content. The analysis suggests that the charge mismatch effectmay be the main reason for the suppression of the CO and enhancement of the PS.

Magnetic and orbital order in the A-phase of manganites

The A-phase of La 1 - x Ca x MnO 3 , stable for small x, is studied using a mean-field slave–boson formulation for e g -electrons in two orbitals with excluded multiple occupancy. The classical t 2 g -spins are ordered ferromagnetically (F) in the xy planes, which are antiferromagnetically (AF) coupled along the z -direction. All 3d-electrons are coupled F via Hund's rule. The F double-exchange, competing with the AF superexchange, can lead to a lattice distortion via Jahn–Teller coupling of the e g -electrons to the lattice degrees of freedom. Conditions for staggered orbital long-range order are discussed.

Jahn-Teller Solitons, Structural Phase Transitions, and Phase Separation

It is demonstrated that under common conditions a molecular solid subject to Jahn-Teller interactions supports stable Q-ball-like nontopological solitons. Such solitons represent a localized lump of excess electric charge in periodic motion accompanied by a time-dependent shape distortion of a set of adjacent molecules. The motion of the distortion can correspond to a true rotation or to a pseudorotation about the symmetric shape configuration. These solitons are stable for Jahn-Teller coupling strengths below a critical value; however, as the Jahn-Teller coupling approaches this critical value, the size of the soliton diverges signaling an incipient structural phase transition. The soliton phase mimics features commonly attributed to phase separation in complex solids.

Instabilities and insulator-metal transitions in half-doped manganites induced by magnetic-field and doping

We discuss the phase diagram of the two-orbital model of half-doped manganites by calculating self-consistently the Jahn-Teller (JT) distortion patterns, charge, orbital and magnetic order at zero temperature. We analyse the instabilities of these phases caused by electron or hole doping away from half-doping, or by the application of a magnetic-field. For the CE insulating phase of half-doped manganites, in the intermediate JT coupling regime, we show that there is a competition between canting of spins (which promotes mobile carriers) and polaronic self-trapping of carriers by JT defects. This results in a marked particle-hole asymmetry, with canting winning only on the electron doped side of half-doping. We also show that the CE phase undergoes a first-order transition to a ferromagnetic metallic phase when a magnetic-field is applied, with abrupt changes in the lattice distortion patterns. We discuss the factors that govern the intriguingly small scale of the transition fields. We argue that the ferromagnetic metallic phases involved have two types of charge carriers, localised and band-like, leading to an effective two-fluid model.

Pseudo-Jahn-Teller origin of geometry and pseudorotations in second row tetra-atomic clusters X4 (X=Na,Mg,Al,Si,P,S)

Experimentally determined or ab initio calculated molecular geometries carry no information about their origin. Employing the Jahn-Teller (JT) vibronic coupling effects as the only source of instability and consequent distortions of high-symmetry molecular configurations, we have worked out a procedure that allows us to trace the origin of particular geometries and determine the detailed electronic mechanism of their formation. This procedure is illustrated by considering a series of X(4) clusters with X=Na, Mg, Al, Si, P, and S. It shows explicitly why Na(4), Si(4), and Al(4) have a rhombic geometry in the ground state, while Mg(4) and P(4) are tetrahedral, whereas S(4) is a trapezium. Even when the minimum-energy geometries are the same (as in the case of rhombic Na(4), Si(4), and Al(4)), the electronic mechanism of their formation is quite different. In particular, in Na(4) and Si(4) the rhombic minima are produced by a strong pseudo JT coupling between two excited states in the square-planar configuration (different in the two cases) that stabilizes one of them and makes it the ground state by rhombic distortions. The rhombic configuration of Al(4) is due to the pseudo JT effect in its ground-state square-planar configuration, and the trapezium in S(4) is formed by two pseudo JT couplings essentially involving excited states. In several cases this analysis shows also the tunneling paths between equivalent configurations.

The relativistic E × E Jahn–Teller effect revisited

The vibronic Hamiltonian describing linear Jahn–Teller coupling as well as spin–orbit coupling in systems of trigonal symmetry is derived in the diabatic spin–orbital representation, employing the microscopic (Breit–Pauli) spin–orbit coupling operator in the single-electron approximation. The analysis generalizes previous treatments based on more phenomenological models of spin–orbit coupling. It is shown that an alternative time-reversal symmetry adapted diabatic representation exists, in which the 4 × 4 Jahn–Teller spin–orbit vibronic Hamiltonian is block-diagonal. The adiabatic electronic wave functions are obtained in explicit form. The topological phases (Berry’s phases) of all four adiabatic electronic basis states are calculated. As found previously for the special case of systems with D 3h symmetry, the topological phases depend on the radius of the loop of integration.

Two-channel semiclassical S-matrix for the E × E Jahn–Teller problem including spin–orbit coupling

An exact analytical solution of the time-dependent semiclassical equations is obtained for the relativistic E × E Jahn–Teller problem, which includes linear vibronic coupling and spin–orbit splitting of the degenerate electronic state in a molecular system with three-fold symmetry axis. The configurational displacements from the point of intersection are assumed to be linear functions of time. The analytical solution of the nonstationary problem is obtained with the use of the ordered exponential operator method. The asymptotic analysis of the exact solution in the limits t → ± ∞ yields the two-channel S-matrix, which gives the transition amplitude of the problem. The results derived in this work reveal explicitly the dependence of the nonadiabatic transition amplitude on the Jahn–Teller coupling parameter and the spin–orbit splitting.

Mössbauer study of the relationship between magnetic properties and Jahn–Teller distortion in La1–xBax(Mn,Fe)O3 perovskites

AbstractThe local structural distortion and its effect on the magnetic and magnetotransport properties of the Fe‐doped La1–xBaxMnO3 (0.00 ≤ x ≤ 0.35) compounds were investigated by means of X‐ray diffraction, Mössbauer spectroscopy, and magnetization measurements. The Mössbauer spectra show clear evidence of the local structural distortion of the Mn(Fe)O6 octahedron on the basis of non‐zero nuclear quadrupole interactions for high‐spin Fe3+ ions. It was found that the local structural distortion decreases significantly with the introduction of a few per cent of Ba, reaches a minimum around x = 0.13, and then increases slightly on further increasing the Ba concentration. The Ba‐concentration dependence of the Jahn–Teller coupling strength estimated from the Mössbauer results was found to be consistent with the magnetic properties. Consequently, the connection between this local structural distortion and the colossal magnetoresistive behavior of this family of materials can be well explained. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

FiniteE⊗βJahn-Teller systems: A continued-fraction approach

A recursive method is developed to treat electrons coupled to phonons. It is applied to small systems with $E\otimes\beta$ Jahn-Teller coupling. Two cases are considered, a model with one electron and two orbitals on a single site (related to the Rabi Hamiltonian) and a model with two electrons on two sites. The corresponding Green's functions are represented by rational functions. It is found that the spectra change substantially when one phonon couples to the electron but are relatively robust under an increasing number of phonons.

Doping and Field-Induced Insulator-Metal Transitions in Half-Doped Manganites

We argue that many properties of the half-doped manganites may be understood in terms of a new two-(${e}_{g}$ electron)-fluid description, which is energetically favorable at intermediate Jahn-Teller (JT) coupling. This emerges from a competition between canting of the core spins of Mn promoting mobile carriers and polaronic trapping of carriers by JT defects, in the presence of magnetic (CE), orbital and charge order. Using it we explain features of the doping and magnetic-field-induced insulator-metal transitions such as the electron-hole asymmetry and the smallness of the transition fields.

Jahn-Teller vibronic coupling in II–VI compounds with Cr 2+ ion

A theoretical study of the vibronic Jahn-Teller interaction in a series of II–VI crystals doped with Cr 2+ ion is reported. The vibronic coupling parameters for the tetrahedrally coordinated Cr 2+ ion (high-spin d 4 configuration) are evaluated in the framework of the exchange charge model of the crystal field accounting for the exchange and covalence effects. The calculations demonstrate the leading role of the trigonal vibrations for the 5T 2 term although the contribution of tetragonal modes is also important; the full symmetric and tetragonal vibrations for the 5E term significantly contribute to the phonon broadening of the absorption and emission bands related to the 5E ↔ 5T 2 transition in Cr 2+ ion.

A new theory of doped manganites exhibiting colossal magnetoresistance

Rare earth manganites doped with alkaline earths, namely $Re_1_-_xAxMnO_3$, exhibit colossal magnetoresistance, metal insulator transitions, competing magnetic, orbital and charge ordering, and many other interesting but poorly understood phenomena. In this article I outline our recent theory based on the idea that in the presence of strong Jahn-Teller, Coulomb and Hund's couplings present in these materials, the low-energy electronic states dynamically reorganize themselves into two sets: one set (l) which are polaronic, i.e., localized and accompanied by large local lattice distortion, and another (b) which are non-polaronic and band-like. The coexistence of the radically different l and b states, and the sensitive dependence of their relative energies and occupation upon doping x, temperature T, magnetic field H, etc., underlies the unique effects seen in manganites. I present results from strong correlation calculations using dynamical mean-field theory and simulations on a new 2-fluid model which accord with a variety of observations.