Pressure-induced Jahn-Teller suppression in Rb 2 CuCl 4 „ H 2 O ... 2 : Pseudo-Jahn-Teller effect

1DCITIMAC, Facultad de Ciencias, Universidad de Cantabria, Santander 39005, Spain 2Departmento de Física Aplicada, Universidad de Cantabria, Santander 39005, Spain 3Université Pierre et Marie Curie, B77 4 Place Jussieu 75252 Paris Cedex 05, France 4LURE, Université Paris-Sud, BP34, 91898 Orsay Cedex, France (Received 5 May 2004; revised manuscript received 15 July 2004; published 7 December 2004 )


I. INTRODUCTION
The presence of Cu 2+ ͑3d 9 ͒, [1][2][3][4][5][6][7][8][9] Mn 3+ ͑3d 4 ͒, [9][10][11][12][13][14] or Cr 2+ ͑3d 4 ͒ (Refs.15-17) ions either as a constituent or impurity in insulating materials gives rise to a great variety of coordination geometries, even if the impurity is placed in cubic sites.9][20] In hexacoordinated systems of either homonuclear MX 6 ͑M =Cu,Cr,Mn;X =H 2 O,NH 3 ,O,F,Cl,Br͒ or heteronuclear MX 4 L 2 ͑X =O,F,Cl,Br;L =H 2 O,NH 3 ͒, the observed coordination geometries mostly correspond to low-symmetry elongated octahedra.The occurrence of an elongated geometry can be explained on the basis of electron-phonon coupling between octahedral E g electronic states and e g vibrations: E e JT model.The knowledge of a given symmetry around the JT ion is important since both the distortion and the packing of JT complexes strongly influence the optical, electrical, and magnetic properties of these materials.3][14][15]21 The E e model predicts coordination geometry variations in homonuclear MX 6 JT complexes from elongated to compressed passing through different rhombic intermediates, or even suppression of the JT distortion, applying axial stress or hydrostatic pressure.However no clear evidence of this effect was reported so far using local probes, in spite of the intense activity to achieve this phenomenon using highpressure techniques. 22,23In fact, pressure-induced phase transitions observed in ͓C 2 H 5 NH 3 ͔ 2 CuCl 4 by Raman and optical spectroscopy was initially ascribed to structural changes associated with the suppression of the JT distortion. 23But structural studies performed by x-ray absorption (XAS) and x-ray diffraction (XRD) techniques in the isostructral ͓C 3 H 7 NH 3 ͔ 2 CuCl 4 compound showed that indeed such trans-formations are mainly related to tilts of the CuCl 6 4− octahedra rather than to the JT suppression. 22Also recent structural studies under pressure in LaMnO 3 using XRD (Ref.24) or neutron diffraction (ND) (Ref.25) report controversial results on pressure effects of the JT distortion.
In general, pressure results give evidence of the tendency of CuCl 6 or MnO 6 to preserve their molecular character associated with the JT distortion.In CuCl 6 , it is due to the higher compressibility of the crystal with respect to the local compressibility, whose molecular stiffness is enhanced by the additional JT binding energy of about 0.25 eV. 8 Recent results on NaMnF 4 under pressure also support this idea. 13n this work, we investigate the local structure of homoand heteronuclear CuCl 4 L 2 ͑L:Cl,H 2 O,NH 3 ͒ systems on the basis of the pseudo-Jahn-Teller (PJT) model; 26 the electronphonon coupling is treated in the same manner as homonuclear octahedral complex ͑E e͒, but introducing additional strain terms to describe both the effect of the axial L ligands and the crystal anisotropy.Interestingly, the PJT model can explain the observed coordination geometry of homo-and heteronuclear Cu 2+ systems, as well as its changes induced by stress, hydrostatic pressure or placing the JT ion in low-symmetry sites in impurity systems.In this way, the elongated-octahedron geometry observed for CuCl 6 in the Cu 2+ -doped NaCl (Ref.27) and CsCaCl 3 (Ref.28)(3D cubic) crystals and the A 2 CuCl 4 (Refs.7,8) or Cu 2+ -doped A 2 CdCl 4 (Refs.7,29,30) (2D layer perovskites) crystals forming antiferrodistortive (AFD) structures can be explained on the basis of the PJT model taking into account the axial-stress field is due to the crystal anisotropy.On the other hand, the heteronuclear CuCl 4 ͑H 2 O͒ 2 2− complex, which form intraplane ferrodistortive (FD) and interplane AFD structure associated with the axially-elongated of one Cl-Cu-Cl axis in the Rb 2 CuCl 4 ͑H 2 O͒ 2 crystal (Fig. 1), 31 appears to be stabilized within this model by the ligand-field stress of the water molecules.However the axially-compressed geometry in the CuCl 4 ͑NH 3 ͒ 2 2− complex occurs by the stronger ligand field of the ammonia molecules. 32,33he two-dimensional Rb 2 CuCl 4 ͑H 2 O͒ 2 compound offers the possibility of exploring structural change from the rhombic-elongated geometry to the tetragonal-compressed one by applying pressure.The PJT model foresees the occurrence of such a transition in the CuCl 4 ͑H 2 O͒ 2 2− complex at a weaker axial stress than the transition stress required for homonuclear CuCl 6 4− complexes.The presence of water molecules substantially reduces the energy barrier between the two mutually-orthogonal elongated geometries (see Sec. III B).The suppression of this energy barrier yields stabilization of the D 4h -compressed coordination.The Rb 2 CuCl 4 ͑H 2 O͒ 2 structure involves isolated JT-elongated CuCl 4 ͑H 2 O͒ 2 2− complexes, whose equatorial plane (shortbonded ligands) is formed by two in-plane Cu-Cl bonds and the two out-of-plane Cu-OH 2 bonds (Fig. 1).As a result, the AFD structure can be easily suppressed due to the isolated character of the CuCl 4 ͑H 2 O͒ 2 2− complex and the presence of water ligands.According to the PJT model, the strong axialligand field from water molecules favors the structural requirements to achieve the local structure changes from the initial D 2h -elongated geometry to the D 4h -compressed one.In the latter case, the two-shortest Cu-OH 2 bonds form the fourfold axis, whereas the four Cu-Cl bonds define a new CuCl 4 equatorial plane.This elongated-to-compressed structural change yields disappearance of the AFD structure and, consequently, the electronic ground-state related properties.Such a structural change can be achieved through either an increase of the axial ligand field or an increase of the electron-phonon coupling constant.In the former case, the replacement of H 2 O ligands for the stronger axial-field NH 3 ligands leads directly to the tetragonal compressed CuCl 4 ͑NH 3 ͒ 2 2− complex. 32,33Interestingly, both structural requirements can be achieved by applying pressure.
This work investigates the effect of pressure on Rb 2 CuCl 4 ͑H 2 O͒ 2 through XRD and XAS in the 0 -25 GPa range.The presence of two water ligands exerts an axial compression favoring release of the JT distortion at moderate pressures, i.e., below the metallization pressure.This aspect is important in order to establish correlations between the crystal structure and, the electronic and vibrational structures from optical spectroscopy.Our aim is to elucidate whether the application of pressure mainly induces rotation of the CuCl 4 ͑H 2 O͒ 2 2− D 2h -distorted octahedra or it is able to suppress the AFD structure.This latter case would modify the local structure from an elongated geometry to a compressed situation with four identical Cu-Cl bonds and the shortest Cu-O bond as fourfold axis.The searched transformation implies a modification of the electronic ground state with the unpaired electron changing from mainly d x 2 −y 2 to d 3z 2 −r 2. [32][33][34][35]

II. EXPERIMENT
Single crystals of Rb 2 CuCl 4 ͑H 2 O͒ 2 were grown by slow evaporation from alcoholic solutions following the procedure given elsewhere. 7he XAS experiments under pressure were performed at the absorption setup XAS10 of the D11 beamline at LURE (Orsay).The extended x-ray absorption fine structure (EXAFS) spectra of the investigated Rb 2 CuCl 4 ͑H 2 O͒ 2 were measured at the Cu K-edge ͑E 0 = 8.98 keV͒ at room temperature using dispersive EXAFS in the 8.9-9.3 keV range.This experimental setup has been proved to be very sensitive for obtaining suitable EXAFS oscillations in a wavelength range where the diamond anvil absorption is very strong.XRD experiments under pressure were done in the energy dispersive setup WDIS of the DW11A beamline at LURE.The XRD and XAS data were analyzed by means of the FULL- PROF (Ref.36) and the WINXAS package programs, respectively.
In both experiments the pressure was applied with a membrane-type diamond anvil cell employing silicon oil as pressure transmitter.The pressure was measured from the R-line shift of Ruby.lated to the different local structure around Cu 2+ (Fig. 2, right). 34igure 3 shows the variation of XAS and XRD of Rb The analysis of the XRD data has been limited to the lattice cell parameters, i.e., the Bragg angles, since the measured peak intensity is inadequate for a proper Rietveld analysis.Within the experimental accuracy, the energydispersive XRD diagrams of Rb 2 CuCl 4 ͑H 2 O͒ 2 were explained according to the P4 2 / mnm crystal structure in the 0 -15 GPa range.Above 15 GPa, the splitting of the (220) Bragg peak evidences a structural phase transition.On the other hand, reliable variations of the local bond distances with pressure were obtained from the EXAFS oscillations according to the following procedure.First, we derive the Debye-Waller factors, the electron mean-free path parameter together with the Cu-Cl and Cu-O bond lengths of the CuCl 4 ͑H 2 O͒ 2 2− complex at ambient pressure from the accurate ambient-pressure XAS using three neighbor shells (Fig. 2 and Table II).Secondly, we use the so-obtained parameters as input parameters for the next pressure XAS analysis.Due to the few EXAFS oscillations attained in diamond anvil cell (Fig. 3), an accurate XAS fit at a given pressure was accomplished allowing bond-distance variation but keeping the Debye-Waller and the electron mean-free path as fixed parameters.

III. RESULTS AND DISCUSSION
Interestingly, the pressure behavior of complex and crystal shown in Fig. 4(b) is rather different.This phenomenon reflects the stiffness of the Cu-Cl and Cu-O bonds of the JT distorted complex, whose local compressibility is an order of magnitude smaller than the crystal compressibility.This conclusion is based on the different bulk modulus obtained by fitting the volume variations, V Comp ͑P͒ and V Cryst ͑P͒, with pressure to a Murnaghan equation of state [Fig.4(b)].Note that the error bar of V Comp corresponds to the absolute error, which is an order of magnitude higher than the error of the volume change induced by pressure, ⌬V = V Comp ͑P͒ -V Comp ͑0͒, i.e., EXAFS provides accurate distance variations ͑ϳ0.01 Å͒ although the absolute errors for distance determinations may be significantly bigger.Therefore we obtain a local bulk modulus, B loc = 240 GPa, with an accuracy of about 10% taking the V Comp ͑0͒ value derived from x-ray data.
A similar result was found for CuCl 6 4− in ͓C 3 H 7 NH 3 ͔ 2 CuCl 4 . 22However, the abrupt change experienced by the long Cu-Cl distance at 15 GPa is noteworthy [Fig.4(c)].The XAS analysis reveals that the short Cu-Cl distance slightly increases with pressure ͑‫ץ‬R / ‫ץ‬P = 0.0003 Å GPa −1 ͒ whereas the long Cu-Cl bond ͑‫ץ‬R / ‫ץ‬P = −0.008Å GPa −1 ͒ reduces to a common distance, R = 2.27 Å.This abrupt variation was evidenced by the divergence of the XAS fit using the D 2h -elongated CuCl 4 ͑H 2 O͒ 2 2− complex distances as input parameters above 15 GPa.The fit provides axial Cu-Cl distances, which are physically meaningless   We therefore associate the pressure-induced structural transformation at 15 GPa with the disappearance of the AFD structure, which is related to the suppression of the in-plane JT distortion.The Cu 2+ coordination changes with pressure from an rhombic-elongated structure to a tetragonalcompressed situation.The associated bond distances change from 2.72 Å and 2.26 Å for Cu-Cl, and 1.97 Å for Cu-O, in the low-pressure phase, to 2.25 Å and 1.96 Å for Cu-Cl and Cu-O, respectively, in the high-pressure JT-suppressed phase.This change is also accompanied by a crystal phasetransition.It must be noted that we were not able to resolve the crystal space group above 16 GPa due to the poor XRD resolution, thus no structural data could be included in Fig. 4 in this pressure range.However, the complex volume experiences an abrupt jump of 16%; i.e., V comp reduces from 16 Å 3 to 13.5 Å 3 at 16 GPa, thus approaching the variation of the crystal volume with pressure, in agreement what is expected in the high-pressure limit.
It is worth noting that pressure induces an increase of Cu-O distance above 16 GPa as 0.015 Å GPa −1 .This slight lengthening of the Cu-O bond together with the almost unmodified Cu-Cl bonds, R Cu-Cl = 2.25 Å, likely reflect an intrato intermolecular charge-transfer electron, whose main effect is to soften the Cu-O bond.

Structural correlations and equation of state
The bulk modulus, B 0 , and corresponding derivative, BЈ, were obtained by fitting the measured complex and cell volumes to a Murnaghan's equation-of-state [Fig.4(b)].The comparison between variations of the crystal volume and the complex volume indicates that the complex is much less compressible ͑B 0 = 240 GPa; BЈ =6͒ than the crystal ͑B 0 = 20.5 GPa; BЈ = 5.8͒.Furthermore, the lattice parameters vary differently with pressure.Parameters defining the FD plane, a and b, reduce with pressure slightly shorter than c, which is proportional to the interplanar distance.This behavior, which is shown in Fig. 4(a), reflects weakly pressureinduced crystal anisotropy.According to the PJT theory, the associated strain together with the isostatic reduction of the crystal volume can influence significantly the occurrence of the structural transition associated with the in-plane JT suppression and, therefore, the interplane AFD structure.In fact, crystal anisotropy and isostatic compression increase the effective axial stress along the O -Cu-O fourfold axis, yielding destabilization of the mainly x 2 − y 2 hole state in favor of the 3z 2 − r 2 state.The associated structural change is accompanied by a reduction of the long axial Cu-Cl bonds towards a compressed complex.This behavior is precisely described within the PJT model, where the effects of the water molecules and crystal anisotropy are treated simultaneously through external axial-stress terms.
B. The pseudo-Jahn-Teller effect in the MX 4 L 2 complex: Electron-phonon coupling E ‹ e, axial stress, and isostatic compression

Jahn-Teller model E ‹ e in homonuclear MX 6 systems
The local coordination geometry of an octahedral MX 6 complex involving JT ions (M :Cu 2+ ,Cr 2+ ,Mn 3+ ,Ni 3+ [lowspin configuration] ) can be effectively treated on the basis of the electron-ion coupling, i.e., between the electronic state of E g symmetry and ligand-field distortions (either static or dynamic) related to e g normal coordinates (JT E e model).On the assumption that the complex distortion is either tetragonal ͑D 4h ͒ or rhombic ͑D 2h ͒, what is the usual case for the JT MX 6 complex, then the cubic-perturbed Hamiltonian can be described as a function of the octahedral e g and a 1g normal coordinates of the X ligands within the harmonic approximation as 7,13 where H O h is the cubic Hamiltonian at the equilibrium geometry, R = R 0 , and ⌬H is the Hamiltonian perturbation.The normal coordinates are defined as follows: where R ax is the axial M -X distance of an elongated octadron complex, R eq = 1 2 ͑R eq1 + R eq2 ͒ is the average of the two equatorial distances and R 0 is the average M -X distance.Within the E e JT theory, the parameter = ͱ Q 2 + Q 2 describes the radius of distortion in ͑Q , Q ͒-space in the six-coordinate complex. 1,2,7,13he representation matrices of ⌬H for the parent octahedral T 2g ͑xy , xz , yz͒ and E g ͑3z 2 − r 2 , x 2 − y 2 ͒ states are then given by for T 2g and, The parameter A 1 i ͑i = e , t͒ is the linear JT electron-ion coupling coefficient, which is quite different for the e g and t 2g one-electron wave functions (or analogously the T 2g and E g states). 14Note that A 1 e as defined in Eq. ( 2) is one-half the corresponding linear coupling constant employed elsewhere. 1,2f we limit our analysis to the E g state (E e model), and we introduce the polar coordinates, and ␣ defined as Q = cos͑␣͒ and Q = sin͑␣͒, then the energy becomes 2 k e 2 .The ± refers to the B 1g ͑x 2 − y 2 ͒ and A 1g ͑3z 2 − r 2 ͒ states in elongated D 4h , and an appropriate combination of both states in D 2h .The B 1g stabilization energy is just the JT energy, which is given within this scheme by E JT =− 1 4 A 1 e 0 .Where 0 = A 1 e /2k e with k e = 2 (Refs.7 and 13) corresponds to the equilibrium geometry of the E − surface [Fig.5(a)].In first-order electron-ion terms, the ground-state energy-surface in (Q , Q )-space is the wellknown Mexican hat potential energy surface.In this approximation, it corresponds to any point around the ͑Q , Q ͒-space circumference of radius 0 .This means that structures going from the axially elongated octahedron ͑Q = 0 , Q =0͒ to the axially compressed octahedron ͑Q = − 0 , Q =0͒, passing through different tetragonal and rhombic intermediate structures ͑Q 0,Q 0͒, are equally probable provided that the M-X i distance deviations, Obviously the linear approximation does not reflect any real situation.Actual coordination geometries are accounted for within this model including second-order JT terms and anharmonicity in Eq. (1).These terms are given, respectively, by The energy is thus given by diagonalizing the matrix 5,20,26 The presence of only anharmonic terms ͑A 2 =0;A 3 0͒, is enough to account for the usual elongated-octahedron geometries of D 4h , or nearly D 4h , usually found in JT systems.The ground-state energy-surface is then given by which is similar to 0 when A 1 e ӷ A 3 0 2 .It is worth mentioning that although each minimum represents a local D 4h -symmetry complex, the system keeps the overall cubic symmetry.In dynamical JT systems, the timeaveraged symmetry is cubic, while for static JT systems, the cubic symmetry is related to the averaged symmetry of the three-equivalent statically-distorted JT complexes along x, y, and z (topological degeneracy).Thus the criterion for static and dynamic JT regimes relies on the experiment time scale.Within this model, the mean jumping time of the system among the three equivalent minima is proportional to the overlap between vibronic wave functions centered in the three minima.Therefore, the occurrence of a given JT regime strongly depends on the separation of the minima in ͑Q , Q ͒-space, the vibrational e g -mode energy and the energy barrier between wells, i.e., the energy difference between minima and saddle points.This latter energy is according to Eq. ( 5) given approximately by ⌬E act =2␤ with .

͑6͒
Note that only anharmonic terms have been considered in this equation.JT distortions of rhombic or compressed octahedron symmetry can also be explained on the basis of present model, but including second-order JT terms in the Hamiltonian [Eq.( 4)]: A 2 0. The competition between A 2 and A 3 parameters finally determines the JT complex distortion.In this context, it must be noted that whereas both elongated and compressed geometries have been observed for CuF 6 (Refs.3-6,26,35,37) and CuO 6 , 1,38 a compressed coordination has never been so far observed in CuCl 6 , whose coordination geometries correspond to elongated nearly-D 4h .Unfortunately, the criterion to predict whether a complex will exhibit a given coordination geometry is still unsolved in spite of the efforts carried out to explain the microscopic dependence of A 2 and A 3 with the complex structure through density functional theory (DFT) calculations. 39

Pseudo-Jahn-Teller model in heteronuclear MX 4 L 2
The present E e model can also be applied for heteronuclear complexes, MX 4 L 2 , on the basis that the L-ligand effects with respect to the homonuclear MX 6 complex, are described by an effective axial-stress term whose tetragonal and rhombic components are 1 2 A 1 e s cos͑␣ s ͒ and 1 2 A 1 e s sin͑␣ s ͒. 1,26,37 The addition of the axial-stress term in A and C [Eq. ( 4)] leads to the so-called PJT model. 26,43The achievement of PJT theory has been checked in diff erent Cu 2+ complexes like CuCl 6 for explaining the variation of the gyromagnetic-tensor components with temperature. 40,41Furthermore, the introduction of an axial-stress term in Eqs.(4) is useful to deal simultaneously with either homo-or heteronuclear complexes under external axial compression, hydrostatic pressure or low-symmetry crystal-field strains associated with the crystal anisotropy.Thus Eq. (5) transforms to where E JT is the JT energy, ␤ Ϸ A 2 0 2 + ͉A 3 ͉ 0 3 and S = 1 2 A 1 e s .The parameters s and ␣ s indicate the stress-induced deformation, due to the crystal anisotropy or the nonoctahedral ligand field in heteronuclear complexes.Experimental values of ␤ vary from near zero for Cu 2+ -doped MgO, 5 -meV for Cu 2+  = 5.2 eV Å −1 ͒. 14 Figure 6 shows the effect of applying a compressive stress along the X-M-X axis ͑␣ s = ͒ starting from an elongated-D 4h situation ͑S =0͒ for the homonuclear MX 6 complex.The stress gradually destabilizes the potential well, which is associated with the axially elongated M-X bond pointing along the stress, with respect to the other two wells.The stress range, 0 Ͻ S Ͻ 9␤, corresponds to the two-dimensional JT regime (2D).As Fig. 6 shows, the potential-well destabilization is accompanied by a decrease of the energy barrier, ⌬E act , connecting the two equivalent ground-state wells, from ⌬E act =2␤ for S =0 (elongated octahedron) to ⌬E act =0 for S =9␤ (compressed octahedron coordination).
The AFD structure displayed by layered perovskites A 2 CuCl 4 (Ref.and 6 ).In these systems, the layered-crystal anisotropy provides the axial-stress field.Interestingly, further increase of the axial stress around 9␤ causes a progressive approach of the two ground-state wells in ͑Q , Q ͒-space for S =9␤ (Fig. 6).Above this critical value, the two wells collapse into a single well at Ϸ 0 and ␣ = , which corresponds to the compressed-D 4h complex, whose fourfold X-M-X axis is along the stress.In terms of electron-ion interaction, the stress increases the electronic repulsion in the 3z 2 -r 2 orbital making the electronic ground state to be mixed between x 2 − y 2 and 3z 2 − r 2 .Further increase of S reduces the stressed M-X bond distance, yielding destabilization of the 3z 2 − r 2 with respect to the x 2 − y 2 along the transition from elongated to compressed D 4h .

Elongated-to-compressed transition in MX 4 L 2 : Pressure estimates
The external stress, either axial or hydrostatic, within a given complex can lead to similar coordination-geometry variations.However, there is no evidence of such structural changes at a local level using external stress, in spite of the intense work devoted to achieve such a goal.In the case of homonuclear complexes, it is likely due to the high-pressure requirements to attain the critical stress S crit =9␤.In A 2 CuCl 4 , the critical pressure was estimated above 30 GPa. 22 Nevertheless, the elongated-to-compressed structural change can be easier tackled in hydrostatic pressure experiments provided that we start from an axially-stressed complex like CuCl 4 ͑H 2 O͒ 2 .Moreover, the parameters associated with the potential energy surface of this complex are known from electron paramagnetic resonance (EPR) experiments.41 They are S H 2 O = 25 meV and ␤ = 12 meV for CuCl 4 ͑H 2 O͒ 2 at ambient conditions (S D 2 O = 70 meV for the deuterated complex). 42It implies that an external axial stress localizes the surface minimum at a compressed tetragonal geometry ͑␣ = ͒ whether the condition S ext Ͼ 9␤ is fulfilled.This requirement can be achieved by applying hydrostatic pressure due to either an enhancement of the axial stress induced by pressure in anisotropic crystals, or by decreasing the energy barrier, 2␤, in nearly isotropic systems.The pressure-induced axial stress is inversely proportional to the Cu-O distance provided that the pressure produces a nearly isostatic strain in the complex.In fact, this is the case since the relative decrease of the a and c lattice parameters is: ⌬c / c Ϸ ⌬a / a [inset of Fig. 4(a)].Consequently, the water molecules provide an axial stress that can be estimated on the basis of the stress value at ambient conditions ͑R Cu-O = 1.97 Å͒ and the pressure-induced axial-stress, through where c 0 and c͑P͒ are the lattice parameter at ambient pressure and P, respectively, and S ext = 25 meV is the effective axial stress due to H 2 O at ambient pressure. 41Note that this expression is valid on the assumption that the water stress is proportional to the interatomic distance reduction along the Cu-O bond direction, thus the crystal strain along c.According to XRD data (Fig. 4) and crystal-field theory ͑m Ϸ 3-5͒, 43,46 we estimate an axial stress at 15 GPa of S ext ͑15͒ = 31-36 meV.This value is still far from the critical stress: S crit =9␤ = 108 meV, provided that ␤ does not change appreciably with pressure.However, the latter condition is hard to concile in high-pressure experiments since, according to Eq. (6), the energy barrier mainly depends on the equilibrium coordinate, m , hence on the complex volume.In fact, a main effect of hydrostatic pressure on CuCl 4 ͑H 2 O͒ 2 2− is to reduce the energy barrier.We can roughly estimate its pressure dependence following Eq.(6).The ␤ parameter relies mainly on the electron-ion coupling, A 1 e , and the e g -vibration frequency, .Both parameters depend on the crystal-volume as A 1 e = A 1 e ͑0͒͑V 0 / V͒ n and = 0 ͑V 0 / V͒ ␥ , where A 1 e ͑0͒, V 0 , and 0 are the electron-ion coupling parameter, the volume, and the phonon frequency at zero pressure, respectively, and n is an exponent close to 1 (see below), and ␥ is the Grüneisen parameter.Therefore, we obtain or, analogously,

͑9͒
with ␤͑0͒ = 12 meV at ambient pressure.Therefore, the critical stress, S crit =9␤, decreases with pressure if n Ͻ 2␥.Al-though ␤͑P͒ is difficult to calculate 5 since the n and ␥ exponents are not known for Rb 2 CuCl 4 ͑H 2 O͒ 2 , we can roughly estimate it taking the equation-of-state (Fig. 4), and the exponents usually found in other JT systems: n Ϸ 1 (Refs.13,40) and ␥ Ϸ 1. 41,44,45 So that we obtain ␤͑15͒ = ␤͑0͓͒465/ 350͔ −3 = 5.1 meV and, consequently, the critical stress reduces to S crit =9␤ = 46 meV at 15 GPa.Precisely, we can obtain the critical pressure, P crit , on the basis of Eqs.(8) and (9).At P crit , c and V must verify the structural constraint c 0 / c͑P crit ͒ = 1.63͑V / V 0 ͒.According to the equation-of-state of Rb 2 CuCl 4 ͑H 2 O͒ 2 (Fig. 4), that condition yields a critical pressure: P crit Ϸ 20 GPa.Although this value strongly depends on the particular choice of n and ␥, the present estimate provides a fair agreement with the experimental critical pressure, P = 16 GPa (Fig. 4).
It is worth noting that the experimental critical pressure in Rb 2 CuCl 4 ͑H 2 O͒ 2 is one-half the estimated critical pressure for CuCl 6 4− in A 2 CuCl 4 . 22Within PJT model this difference is likely due to the larger ␤ value ͑Ϸ50 meV͒ and the weaker axial stress attained in homononuclear complexes, even in anisotropic crystals.Both effects yield larger strain and higher pressure conditions to achieve the change of coordination geometry in CuCl 6 4− .A complete structural study on the pressure-induced variation of the coordination geometry in layered perovskites A 2 CuCl 4 (A = Rb, R-NH 3 : R-alkyl groups) is currently in progress.

IV. CONCLUSIONS
Throughout this work, we demonstrate that the JT distortion in Cu 2+ can be efficiently suppressed in axially-stressed complexes.In the present case, this situation is attained through the heteronuclear CuCl 4 ͑H 2 O͒ 2 2− complex, whose water ligands favor the elongated-to-compressed localstructure transformation at moderate pressures.In fact, water molecules provide an intermediate axial ligand-field between that attained in the homonuclear CuCl 6 4− complex, associated with an x 2 − y 2 unpaired electron, and the heteronuclear tetragonal-compressed CuCl 4 ͑NH 3 ͒ 2 2− complex with 3z 2 − r 2 ground state.The ammonium axial ligand-field leads directly to a D 4h -compressed coordination beyond 2D JT elongateddistortion associated with the Cl ligands.High hydrostatic pressure on Rb 2 CuCl 4 ͑H 2 O͒ 2 favors an increase of the axial strain along the Cu-O bond, yielding stabilization of the D 4h -compressed CuCl 4 ͑H 2 O͒ 2 2− coordination geometry.The observed structural change can be explained within the PJT model, assuming that the hydrostatic pressure exerts an increasingly axial strain along c favored by the crystal anisotropy.Finally, this work clearly demonstrates the adequacy of the PJT model to explain the structural variation found through XAS and XRD techniques, and highlights the usefulness of heteronuclear complexes to achieve the foreseen elongated-to-compressed structural changes.

2
CuCl 4 ͑H 2 O͒ 2 as a function of pressure.The corresponding variations of Cu-Cl and Cu-O bond lengths derived from XAS and the lattice parameters from XRD are plotted in Figs.4(a) and 4(c).In Fig. 4(b), the variation of the complex volume with pressure is compared with the variation of the cell volume in order to analyze the local and crystal compressibility in Rb 2 CuCl 4 ͑H 2 O͒ 2 .

͑R ӷ 3
Å͒.However, a fairly good convergence is obtained taking the compressed CuCl 4 ͑H 2 O͒ 2 2− geometry as starting fit parameters.It must be noted that the compressed coordination geometry, which involves only two fit parameters, i.e., the Cu-Cl distance and the Cu-O distance, accounts for XAS in the 15-30 GPa range.Nevertheless, it fails for P Ͻ 15 GPa, where only the elongated geometry with two different Cu-Cl distances and one Cu-O distance, provides suitable convergence.

FIG. 3 .
FIG. 3. Variation of XRD (a) and XAS (b) for Rb 2 CuCl 4 ͑H 2 O͒ 2 as a function of pressure.Arrows in (a) indicate the Bragg peaks used for obtaining the lattice parameters given in Fig. 4(a).(c) Fourier transform (FT) of the EXAFS oscillations as a function of pressure.The corresponding bond distances, Cu-Cl and Cu-O, derived from the FT data are plotted in Fig. 4(c).

FIG. 5 .
FIG. 5. (Color online) (a) Ground-state energy surface and projection in ͑Q , Q ͒-space, corresponding to the E e Jahn-Teller (JT) effect for MX 6 octahedral complex in the linear approximation ͑A 3 = A 2 =0͒: Mexican hat surface.(b) Ground-state energy-surface and corresponding projection including JT second-order ͑A 2 0͒ and anharmonic ͑A 3 Ͻ 0͒ terms.Note the formation of threeequivalent potential wells (warped Mexican hat surface: Tricorn).The parameters involved in the E e JT model are indicated.

FIG. 6 .
FIG. 6. (Color online) Effect of the axial stress in the ground-state energy in ͑Q , Q ͒-space.The effective axial stress produced by the axial ligands in homo-and heteronuclear MX 4 L 2 systems ͑X =Cl;L =Cl,H 2 O,NH 3 ͒ is indicated with the associated coordination geometries.The ͑Q , Q ͒-space ground-state energy surface is shown on the left.Note the evolution from elongated-to-compressed coordination geometry upon increasing the axial stress.The collapse into the compressed geometry takes place at S crit =9␤.The CuCl 4 L 2 series ͑L =Cl→ H 2 O → NH 3 ͒ illustrates the effect of axial stress induced by crystal anisotropy (homonuclear) or axial ligand-field (heteronuclear) in real complexes at ambient conditions.

A. Local and crystal structure of Rb 2 CuCl 4 "H 2 O… 2 1. EXAFS and XRD analysis Figure
1 shows the crystal structure of the Rb 2 CuCl 4 ͑H 2 O͒ 2 and the corresponding anhydrous Rb 2 CuCl 4 .Note the different coordination geometry of Cu 2+ in each structure as well as the distinct character of the AFD structure.In Rb 2 CuCl 4 ͑H 2 O͒ 2 , the Cu 2+ complexes are isolated and do not share any common ligand in contrast to Rb 2 CuCl 4 .The XRD and XAS data of Rb 2 CuCl 4 ͑H 2 O͒ 2 at room temperature are given in Fig. 2 and Tables I and II.The results are compared with those of Rb 2 CuCl 4 .Apart from differences in XRD, which are associated with the tetragonal P4 2 / mnm ͓Rb 2 CuCl 4 ͑H 2 O͒ 2 ͔ and the orthorhombic Cmca ͑Rb 2 CuCl 4 ͒ structures, a salient feature is the different XANES signal observed for each compound, which is re- FIG. 2. XRD and XAS results obtained for CuCl 4 ͑H 2 O͒ 2 2− and CuCl 6 4− -in Rb 2 CuCl 4 ͑H 2 O͒ 2 ͑P4 2 / mnm͒ and Rb 2 CuCl 4 ͑Cmca͒, respectively, at ambient conditions.

TABLE I .
Structural data of Rb 2 CuCl 4 ͑H 2 O͒ 2 at ambient conditions.The lattice parameters and cell volume correspond to the tetragonal P4 2 / mnm space group.The reduced atomic coordinates and the metal-ligand bond distances around Cu 2+ are included.