Pressure-induced Jahn-Teller suppression and simultaneous high-spin to low-spin transition in the layered perovskite CsMnF4

The interplay between the orbital ordering and the spin state in Jahn-Teller Mn3+ governing the optical, magnetic, and transport properties in the layered CsMnF4 perovskite is investigated. Such electronic effects are strongly coupled to the lattice and thus can be modified by external pressure. However, there is very little understanding of the structural conditions which are required to attain spin crossover in connection with the electronic structure of Mn3+. The distortion, spin state, and tilting of MnF6 3− octahedra in the insulating ferromagnet CsMnF4 are jointly studied by high-pressure optical spectroscopy. The insulating character of CsMnF4 allowed us to explore the electronic structure associated with the 3d levels of Mn 3+ in the 0–46 GPa pressure range, an information which is obscured in most oxides due to metallization at high pressure. We show that the spin-crossover transition, related to the spin change, S=2→1, in Mn3+, takes place at 37 GPa with the simultaneous suppression of the axially elongated distortion associated with the Jahn-Teller effect. The wide stability pressure range of the Jahn-Teller distortion and high-spin state is explained in terms of crystalfield models including the Jahn-Teller stabilization energy. On this basis, we discuss the interplay between spin transition and Jahn-Teller effect comparing present findings with other results attained in Mn3+, Ni3+, and Co3+ systems.


I. INTRODUCTION
The magnetic moment of transition-metal ions can be abruptly reduced upon compression as a result of the increase in electronic energy dispersion caused by the electronelectron and electron-lattice interactions. 1For octahedral ͑O͒ transition-metal ions of a given electronic configuration d n ͑4 ഛ n ഛ 5͒, the transition from high-spin ͑S = n /2͒ to lowspin ͓S = ͑6−n͒ /2͔, or from S = ͑n −5͒ /2 to S = ͑n −6͒ /2 if ͑6 ഛ n ഛ 8͒, is governed by the competition between the crystal field, which splits the 3d levels into a low-lying t 2 triplet and an excited e doublet in ⌬, and the interelectronic repulsion and exchange energies for pairwise occupation of d orbitals, U ͑Fig. 1͒.If ⌬ϾU, the low-spin configuration is more favorable than the high-spin configuration.Strictly speaking, the spin transition in condensed matter systems will occur if the low-spin free energy is smaller than the high-spin free energy.2][3][4][5][6][7][8][9] Current research of this kind is focused on materials involving transition-metal complexes with C, O, or N ligands.][4] Similar to Earth's interior conditions, high-pressure techniques have emerged as efficient tools to attain structural conditions for spin change, even dealing with systems where ⌬Ӷ⌬ SCO .Although we know the relevance of the spin state of Fe 2+ in ͑Mg,Fe͒O, the second most abundant phase in lower mantle, on the radiative conductivity 5,6 or that highspin Fe 3+ ͑S =5/2͒ transits to the low-spin state ͑S =1/2͒ in Fe 2 O 3 at pressures around 50 GPa, 7,8 the problem of predicting spin-crossover pressures in materials science is still a challenge.A comprehensive characterization of high-spin to low-spin ͑or intermediate spin͒ 1 phenomena requires knowledge of the electronic structure of materials, a major problem because optical absorption measurements in extreme conditions are tricky. 6Besides, the influence of the particular d n configuration and site symmetry on the spin state must also be considered.][11] As a result, the interplay between the Jahn-Teller distortion and the spin state strongly affects both the magnetic moment and local structure of the transition-metal ion, and thus the associated physical properties of the material.Perovskitetype Mn 3+ oxides and fluorides exhibit a great variety of structures illustrating this effect. 9,10The occurrence of given properties is driven by strong correlation effects associated with electron-electron interactions, the Jahn-Teller effect, spin state and tilting of Mn 3+ octahedra.Such effects are coupled to the lattice, and thus can be modified by external pressure.Magnetic transformation from ferromagnetic to antiferromagnetic in CsMnF 4 ͑Refs.11-13͒, metal to insulator transition phenomena in LaMnO 3 ͑Ref.14͒, or colossal magnetoresistance and spintronics in Sm 0.55 Sr 0.45 MnO 3 or La 2−2x Sr 1+2x Mn 2 O 7 ͑Refs.15 and 16͒ are examples, for which reason they have received considerable attention.Our interest in fluorides stems from their advantage over oxides when obtaining the electronic structure in extreme conditions.In particular, the Jahn-Teller distortion, its associated electronic structure and stabilization energy ͑E JT ͒, the spin state, and orbital ordering of Mn 3+ ions can be jointly studied by optical absorption spectroscopy under high-pressure conditions. 11,12,17

II. EXPERIMENT
Single crystals of CsMnF 4 were obtained from dehydration of the CsMnF 4 .͑H 2 O͒; its tetragonal P4/n crystal structure was checked by x-ray diffraction with lattice parameters of a = 7.947͑3͒ Å and c = 6.340͑3͒Å.A Merril-Basset diamond anvil cell, Diamond Optics, Inc., was employed for high-pressure optical absorption spectroscopy.Every experiment was done loading a suitable single-crystal platelet ͑150ϫ 100ϫ 30 m 3 ͒ of CsMnF 4 in the diamond anvil cell with several ruby chips for pressure calibration.Dow-Corning 200 silicone oil was employed as pressuretransmitter medium, as it provides a suitable operation for optical spectroscopy at high pressures ͑P Ͼ 20 GPa͒.In order to estimate contributions from non hydrostatic components, we have measured the variation of the Ruby linewidth as a function of pressure in several Ruby chips.The R1 linewidth of 0.6 nm is almost constant in the range 0 -20 GPa, and increases continuously from 0.6 to about 1.0 nm in the 20-46 GPa range.The high-pressure spectroscopy setup has been described elsewhere. 17The absorption spectra were taken with the light propagating perpendicular to the c lay-ers, and are nearly isotropic as corresponds to antiferrodistortive layers of ͑MnF 6 ͒ 3− even in the monoclinic highpressure phase.

A. Structural correlations in "MnF 6 … 3− systems:
Pressure effects on CsMnF 4 Here, we investigate the interplay between the Jahn-Teller effect, spin state, and tilting of ͑MnF 6 ͒ 3− octahedra in the layer perovskite CsMnF 4 as a function of pressure.The aim is to elucidate whether pressure induces tilts of the ͑MnF 6 ͒ 3− octahedra preserving the Jahn-Teller distortion and high spin, as occurs along the AMnF 4 series upon volume reduction, 11,13 or whether it mainly reduces their axial distortion toward O symmetry, the latter modification favoring low-spin stabilization.The electronic spectrum of CsMnF 4 and its variation with pressure in the 0 -46 GPa range are shown in Fig. 2. At ambient pressure, it consists of three broadbands, E 1 = 1.89 eV, E 2 = 2.26 eV, and E 3 = 2.79 eV, corresponding to interelectronic transitions within d 4 from the 5 B 1 ground state to the 5 A 1 , 5 B 2 , and 5 E excited states, respectively, according to the energy level diagram of Figs.1-3.Their energy provides the d-splitting pattern due to the D 4 -elongated Jahn-Teller distortion of ͑MnF 6 ͒ 3− .Note that in O, the spectrum would consist of a single broadband ͑ 5 E → 5 T 2 ͒, whose energy is ⌬. 11On the basis of correlations established elsewhere, 11,17 the three transition energies in D 4 ͑four in D 2 ͒ are related to the equatorial Mn-F distance, R eq , and the tetragonal and rhombic normal coordinates, Q and Q , describing the low-symmetry distortion of the ͑MnF 6 ͒ 3− octahedra ͑Fig.1͒.In fact, E 1 , E 2 , and E 3 provide the socalled equatorial crystal-field parameter, ⌬͑eq͒ = E 2 , and the tetragonal splitting of the parent octahedral e and t 2 orbitals, ⌬ e = E 1 =4E JT , and ⌬ t = E 3 − E 2 ͑Ref.11͒.The narrow peaks, E SP1 = 2.39 eV and E SP2 = 2.88 eV, correspond to spin-flip transitions: 5 , the transition mechanism of which is activated by the Mn-F-Mn exchange interaction, 12,17 similar to the K 2 CrCl 4 ferromagnet involving the isoelectronic Cr 2+ ͑Ref.18͒.Their intensity decreases with the Mn-F-Mn bending angle as it is confirmed through the variation of the optical spectrum along the series AMnF 4 ; A: Cs→ Tl→ Na ͑Fig.3͒, and thus can probe tilting phenomena.0][21] The dependence of the spin-flip intensity with as −0.9+ 2.1 cos 2 ͑͒Ϸcos͑2͒ supports this view ͑Fig.3͒.Note, however, that the exchange mechanism is weaker in the axially F-sharing linear chains of ͑MnF 6 ͒ 3− units ͑AMnF 5 series͒ or in ͑MnF 6 ͒ 3− isolated systems ͑A 3 MnF 6 ͒, and, consequently, the spin-flip peaks are missed in their corresponding OA spectra ͑Fig.4͒.Hence, spin-flip transitions appear as efficient probes for exploring tilting phenomena in CsMnF 4 , as already suggested in previous pressure studies in NaMnF 4 ͑Ref.17͒.Although departures of from 180°in AMnF 4 ͑A :Cs→ Tl→ Na͒ reduce the spin-flip intensity, the E 1 , E 2 , and E 3 energies are similar according to the same local structure of ͑MnF 6 ͒ 3− ͑Ref.11͒.Nevertheless, a substantial variation in these energies is attained if the coordination geometry around Mn 3+ is modified by crystal anisotropy, as occurs in K 3 MnF 6 , Tl 2 MnF 5 .H 2 O, and CsMnF 4 , where ͑MnF 6 ͒ 3− units appear independent, in chains, and forming layers, respectively ͑Fig.4͒.The Jahn-Teller splitting obtained from the absorption spectra, ⌬ e and ⌬ t , both depend linearly on Q with ⌬ e / ⌬ t = 3.7.This noteworthy result indicates that the Jahn-Teller electron-ion coupling E e is four times bigger than the T e coupling, which explains the greater axial distortions exhibited by Jahn-Teller systems involving e electrons instead of t 2 .Thus, E 1 , E 2 , and E 3 together with spin-flip peaks provide a useful probe for exploring electronic properties and hence the Jahn-Teller effect of Mn 3+ in pressure experiments.

B. Spin transition and Jahn-Teller suppression in CsMnF 4
Two relevant features are observed in the evolution of the CsMnF 4 spectrum with pressure in Fig. 2: first, the Jahn-Teller-related triple-broadband structure is observed up to 36 GPa, and second, the 5 B 1 → 3 B 1 spin-flip peaks decrease from ambient pressure to around 36 GPa.Both features indicate that pressure mainly induces ͑MnF 6 ͒ 3− tilts below 37 GPa, still preserving the Jahn-Teller distortion.Above 37 GPa, the triple-broadband structure sharply transforms into a single broadband located at 2.5 eV, whereas spin-flip peaks completely disappear.The abrupt transition at 37 GPa involves a marked piezochromism with a color change of the crystal from light brown to pinkish red.We associate this change with the simultaneous suppression of the Jahn-Teller distortion and the spin transition ͑S =2→ 1͒ in Mn 3+ .The collapse of the low-symmetry 3d-splitting pattern into one single electronic band, which is basically related to the t 2 → e one-electron transition as expected in O, supports the suppression of the Jahn-Teller distortion ͑Fig.2͒.The band energy at 40 GPa corresponds to ⌬ = 2.5 eV, and, as we dem-onstrate below, is in agreement with the proposed model.
Upon pressure release, a reversible abrupt change occurs at about 30 GPa, yielding the high-spin phase.Both the large hysteresis ͑Ͼ5 GPa͒ and observed piezochromism indicate that the simultaneous Jahn-Teller suppression and spin change likely involve a first-order structural-phase transition in CsMnF 4 .However, it must be pointed out that although the pressure hysteresis can be affected by the pressuretransmitter medium, we have verified that the Ruby lines show no hysteresis effect in the same pressure range.Therefore, under the assumption that there is no residual strain in the crystal left on the pressure release, the high-spin to lowspin transition must be fully associated with a first-order phase transition in CsMnF 4 .

C. Interplay between spin transition and Jahn-Teller effect:
Crystal-field model In contrast to Ni 3+ ͑t 2 6 e 1 ; S =1/2͒ and Co 3+ ͑t 2 6 e 0 ; S =0͒, with a strong tendency to form a low-spin ground state, 1,[22][23][24][25][26][27][28][29] Mn 3+ in fluorides and oxides exhibits a high-spin ground state ͑t 2 3 e 1 ; S =2͒ in spite of ⌬ Ϸ 2 eV being similar for all these ions. 3,4,29Within O, the spin crossover for Mn 3+ ͓t 2 3 e 1 ͑ 5 E͒ ↔ t 2 4 e 0 ͑ 3 T 1 ͔͒ and Ni 3+ ͓t 2 5 e 2 ͑ 4 T 1 ͒ ↔ t 2 6 e 1 ͑ 2 E͔͒ takes place typically at ⌬ SCO Ϸ 2.7 and 2.1 eV, respectively. 3,4,30ctually, spin crossover occurs if the associated free energy of the high-spin state becomes greater than that of the low- FIG. 3. ͑Color online͒ Optical absorption spectra of NaMnF 4 , TlMnF 4 , and CsMnF 4 single crystals.R ax and R eq are 2.15, 1.82 Å for TlMnF 4 and 2.17, 1.84 Å for NaMnF 4 and CsMnF 4 .The Mn-F-Mn bond angle is indicated on the right. 13The three spin-allowed crystalfield transitions, E 1 , E 2 , and E 3 , and the spin-flip peaks, E SP1 and E SP2 , are indicated by vertical and horizontal arrows, respectively.The spin-flip integrated peak intensity decreases with the tilting angle, = 180− , being the Mn-F-Mn bond angle.Its variation is linear with cos 2 = cos 2 , showing the exchange-induced electric-dipole mechanism of the spin-flip transitions ͑Refs.12, 17, and 18͒.The errors are 0.05 and 0.005 for the relative intensity and cos 2 , respectively.spin state.Therefore, the effective energy for spin crossover ⌬ SCO is thus released by the lattice-relaxation energy E LR , due to the electron-lattice coupling between low-spin and high-spin states in O. Interestingly, E LR can be obtained from optical spectroscopy and is given approximately by Sប Ϸ 0.1-0.3eV for trivalent transition-metal ions. 3,4,12Additionally, this energy can be either reduced or increased depending on whether the high-spin or low-spin states exhibit a strong Jahn-Teller effect associated with e electrons ͑E e͒.Within the d 4 high-spin configuration ͑t 2 3 e 1 ͒, the lone e electron is responsible for the strong axial distortion exhibited by the ͑MnF 6 ͒ 3− octahedra, 11 whose electronic structure is sketched in Fig. 1.As a result, the energy separation between the e electron ͑a 1 ͒ and t 2 electrons ͑b 2 + e͒, which is ⌬ in O, reduces approximately by E 1 / 2 = 0.9 eV ͑Ref.11͒ in D 4 , yielding high-spin stabilization.This gain of electronic energy is, nevertheless, accompanied by an increase in elastic energy associated with the axial distortion.According to E e theory, 11,17 the energy gain, E JT , is given by E 1 /4 = 0.45 eV/ Mn 3+ in AMnF 4 ͑Fig.3͒.An opposite situation is attained for Ni 3+ since the low-spin state has one electron in the e orbitals, and thus exhibits a strong Jahn-Teller effect in contrast to its high-spin state.Consequently, ⌬ SCO for Ni 3+ is smaller than that for Mn 3+ to encompass spin transition.Therefore, the effective ⌬ SCO increases or decreases by E JT depending on whether we are dealing with Mn 3+ or Ni 3+ , respectively.In other words, the energy balance between low-spin and high-spin states is given by where U = 2.7 and 2.1 eV for Mn 3+ and Ni 3+ , respectively.Taking E JT = 0.4 eV and E LR = 0.2 eV for both ions, we obtain ⌬ SCO = 2.9 and 1.5 eV, respectively, which explains why the Jahn-Teller effect stabilizes Mn 3+ high-spin and Ni 3+ lowspin at ambient pressure.In fact, Ni 3+ is low spin ͑ 2 E͒ in RNiO 3 perovskites ͑R: rare earth͒, 24,25 Ni 3+ -doped LaAlO 3 ͑Ref.22͒, and CsCaNiF 6 ͑Ref.30͒, whereas corresponding Mn 3+ compounds are high spin at ambient conditions.The present model foresees that in the eventual case of Jahn-Teller suppression by pressure ͑E JT =0͒, the spin crossover in CsMnF 4 would occur at ⌬ SCO = 2.5 eV as is observed in Fig. 2.

IV. CONCLUSIONS
Our observations demonstrate that the pressure-induced Jahn-Teller suppression leads to a sharp spin crossover in CsMnF 4 taking place at 37 GPa.The spin transition occurs if the high-spin 5 E free energy surpasses the low-spin 3 T 1 free energy, which is attained for ⌬ SCO Ϸ 2.5 eV, once the axial distortion is suppressed ͑E JT =0͒.The low-spin phase is stable at least to 46 GPa, the highest pressure applied in the present studies.Upon pressure release, a reversible abrupt change occurs at about 30 GPa, yielding the high-spin phase.Both the large hysteresis ͑Ͼ5 GPa͒ and observed piezochromism indicate that the simultaneous Jahn-Teller suppression and spin change involve a first-order structural-phase transition in CsMnF 4 .These results are noteworthy since they go a long way to explaining some essential features related to the spin state of transition-metal ions in oxides and fluorides, and have to be considered when discussing the cooperative Jahn-Teller effect in complex systems where electron delocalization or high-pressure conditions play a key role.

FIG. 1 .
FIG. 1. ͑Color online͒ ͑Left͒ Diagram of the d levels of Mn 3+ in octahedral ͑O͒ and elongated tetragonal ͑D 4 ͒ coordinations, showing the E e Jahn-Teller high-spin and O low-spin configurations.͑Right͒ Variation of the state energies ͑Tanabe-Sugano diagram͒ for 3d 4 ions calculated for C / B = 4.6 as a function of the crystal-field energy in terms of the Racah parameter B ͑Ref. 11͒.Some states have been omitted in the diagram for the sake of clarity.The 5 E ↔ 3 T 1 crossover crystal field ͑⌬ / B͒ SCO is 27; B Ϸ 0.1 eV for Mn 3+ in fluorides and oxides ͑Refs.2-4͒.The splittings of the 5 E and 5 T 2 states due to the Jahn-Teller effect are given as a function of the normal coordinate Q , keeping a ratio ⌬ e / ⌬ t = 3.7 ͑Ref.11͒.The crystal structure of the layered perovskite CsMnF 4 ͑space group: P4/n͒, showing the in-layer and intralayer views, together with the elongated ͑MnF 6 ͒ 3− complex, with axial and equatorial Mn-F distances, R ax , R eq1 and R eq2 , are given bottom left.The normal coordinates, Q and Q , representing the tetragonal and rhombic distortions, respectively, are given as a function of the three Mn-F distances.R eq =1/2͑R eq1 + R eq2 ͒.Note the antiferrodistortive structure shown by the ͑MnF 6 ͒ 3− octahedra in the a , b layer.