Sylwia
Kiczka
,
Stanislaw K.
Hoffmann
*,
Janina
Goslar
and
Ludoslawa
Szczepanska
Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, PL-60179, Poznan, Poland. E-mail: skh@ifmpan.poznan.pl; Fax: +48-61-8684-524; Tel: +48-61-8612-407
First published on 27th November 2003
Cd(HCOO)2·2H2O single crystals weakly doped with Cu(II) ions have been studied by cw-EPR (4.2–300 K) and by electron spin echo – ESE (4.2–60 K). Copper(II) ions substitute Cd(II) in two different sites forming Cu(HCOO)6–Cuf and Cu(HCOO)2(H2O)4–Cuw octahedral complexes with strong preference to Cuf as shown by the intensity ratio of the EPR spectra (up to 20∶1). Despite different molecular structures both complexes have nearly identical EPR parameters at rigid lattice limit with gz=
2.429, gy
=
2.092, gx
=
2.064, Az
=
120, Ay
=
32 and Ax
=
12
×
10−4 cm−1 for Cuf. This fact as well as strong axial deformation of the crystal field at Cu(II) sites indicate that the strong Jahn–Teller effect operates producing three wells in the potential surface with one having much lower energy than the others. In the Cuf complex the dynamic J–T-effect has been observed as a vibronic averaging of the two g and A parameters (along z and y axes). It indicates that only one of the higher energy wells is thermally accessible and the Silver–Getz model leads to the average energy difference between the two lowest energy wells δ12
=
500(60) cm−1. The δ12 is temperature dependent. For Cuw complex no vibronic effects were observed in EPR spectra indicating that higher energy wells are not populated up to 300 K. The spin–lattice relaxation time T1 and phase memory time TM were measured up to 60 K only, because for higher temperatures the ESE decay was too fast. Spin–lattice relaxation is governed by two-phonon Raman processes which allow one to determine the Debye temperature of the crystal as ΘD
=
193 K. The ESE decay was described as V(2τ)
=
V0exp(−τ/b
−
mτ2) indicating the contribution of the spectral diffusion (quadratic term). The ESE dephasing rate 1/TM is governed by spectral diffusion below 15 K. For higher temperatures the T1-processes and excitations to the higher vibronic levels of energy Δ
=
166 cm−1 give comparable contributions.
Dihydrated formates of divalent metal ions, like Cd, Cu, Zn, Fe, Mn and Ni are monoclinic and isostructural with a layered structure determining their two-dimensional properties. The formates of magnetic ions have two magnetic sublattices with relatively strong superexchange coupling transmitted via formate molecules (J=
33 cm−1 for copper formate7) and display a transition to the antiferromagnetic ordering at subhelium temperatures.8,9
The diamagnetic cadmium(II) formate dihydrate, Cd(HCOO)2·2H2O, which has been studied in this work, crystallizes in P21/c symmetry with unit cell dimensions: a=
0.8981, b
=
0.7391, c
=
0.9760 nm, β
=
97.32° and Z
=
4.10 A specific feature of the structure is the existence of two chemically and crystallographically distinct cadmium(II) sites: I-Cdf and II-Cdw with octahedral coordination of six oxygens. The structural unit is shown in Fig. 1. The Cdf is coordinated by six formate molecules with nearly uniform Cd–O distances (0.2248–0.2301 nm), whereas Cdw through four water oxygens and two formates with slightly less uniform Cd–O distances, varying from 0.2243–0.2326 nm. Thus, the centrosymmetric CdO6-octahedra are weakly tetragonally distorted with elongation along Cd–O of Cdf–Cdw bridging formate molecule as marked by z-axes in Fig. 1. There is also a small rhombic distortion of the main coordination plane differentiating the in-plane Cd–O bonds. The Cdf are linked by the four formate ligands into two-dimensional layers parallel to the bc-plane. The layers are sandwiched by Cdw complexes with two bridging formate molecules. This polymeric network is further strengthened by hydrogen bonds of about 0.275 nm length between water molecules and each of the formate oxygens.
![]() | ||
Fig. 1 The structural unit consists of two centrosymmetric Cd-octahedra: I-Cd(formate)6![]() ![]() ![]() ![]() |
Paramagnetic ions introduced into a diamagnetic formate lattice substitute host divalent ions and allow separate EPR studies of electronic structure and dynamics of the two sublattice constituents. Such EPR studies have been performed for Cu(II) in Zn(HCOO)2·2H2O,7 Co(II) in Zn(HCOO)2·2H2O,11 Mn(II) in Zn(HCOO)2·2H2O,12,13 Mn(II) in Cd(HCOO)2·2H2O,14 VO(II) in Cd(HCOO)2·2H2O and in Pb(HCOO)2·2H2O,15 and hot ions Cd(I) in Cd(HCOO)2·2H2O.14 Radiation defects (formate radicals) have also been studied by EPR and ENDOR in various formates.16,17 The results of EPR studies of Cu(II) in Cd(HCOO)2·2H2O single crystals have already been published.18 Because of clear experimental errors (the crystal orientation was incorrect, thus the b-axis was not the symmetry axis of the angular dependence in the ab-plane; weak lines from Cuw complexes were missing because of a low crystal quality and strong background EPR line) and incorrect interpretation, the results (two inequivalent sites of Cuf complexes were interpreted as Cuf and Cuw sites) are not reliable and this had motivated us to perform detailed EPR studies of this system and to enrich them with electron spin echo relaxation measurements.
It is well known that Cu(II) ions in a high-symmetry environment undergo the Jahn–Teller effect.3 Thus, for Cu(II) in Cd(HCOO)2·2H2O crystals such an effect can be expected, since both types of the CdO6-octahedra are only weakly distorted from a regular structure. A very small rhombic distortion suggests that we can deal with a specific pseudo-Jahn–Teller effect in a three well potential having one deep well and two excited wells of approximately the same energy. Thus, in this crystal an unique possibility exists to study two different environments of Jahn–Teller active Cu(II) ions in the same lattice and to observe the influence of their dynamics on spin relaxation of the unpaired electrons. In this paper we present the results of cw-EPR and pulsed EPR (electron spin echo) studies of electronic structure and dynamics of Cu(II)-complexes in the temperature range 4–300 K.
Cw-EPR measurements were performed on a Radiopan SE/X-2547 spectrometer with an Oxford ESR900 flowing helium cryostat, and pulsed EPR experiments were performed on a Bruker ESP380E FT/CW spectrometer with an Oxford CF935 cryostat, in the temperature range 4–300 K. Single crystal EPR rotational data were collected at 77 K in the reference frame a, b, c*=
a
×
b with alignment of the crystal under optical microscope prior to the experiments. The temperature dependence of the EPR spectrum was measured along the principal directions of the g2-tensor.
Electron spin relaxation experiments were performed on single crystals by excitation of the single hyperfine line mI=
−3/2 in the crystal orientation close to the z-axis of the g2-tensor. The short tp
=
16 ns pulses with spectral bandwidth 1.207/tp
=
75 MHz
=
2.68 mT19 were used, since they were able to excite the whole line having linewidth ΔBpp
=
0.9 mT at this crystal orientation. The spin–lattice relaxation time T1 was determined using the saturation recovery method with the 16 ns saturation pulse. The full saturation was achieved in the whole temperature range. The magnetization recovery was monitored by the Hahn-type ESE signal generated by two 16 ns pulses with interpulse interval 176 ns. The electron spin echo dephasing described by the phase memory time TM was determined from Hahn echo amplitude decay, after excitation by two 16 ns pulses. The decay was strongly modulated with NMR frequencies of surrounding magnetic nuclei and was approximated by two-component exponential decay function with details described below.
![]() | ||
Fig. 2 EPR spectra recorded at liquid nitrogen temperature 77 K: (a) Single crystal spectrum along the crystal b-axis. Hyperfine quartets from two different type complexes are marked. The intensity of the Cuf spectrum is about 20 times stronger than that for Cuw-complexes. The Cuf-complex spectrum is complicated by forbidden transition lines close to the perpendicular orientation. (b) Powder EPR spectrum showing the lines from Cuf-complexes. |
Cu(formate)6-complex I | ||||||
---|---|---|---|---|---|---|
EPR parameters | Direction cosines | Angles/degree | ||||
a | b | c* | a | b | c* | |
g
x
![]() ![]() ![]() ![]() |
±0.1888 | 0.6707 | ±0.7173 | 79 | 48 | 44 |
g
y
![]() ![]() ![]() ![]() |
0.4448 | ±0.5988 | −0.6713 | 64 | 53 | 132 |
g
z
![]() ![]() ![]() ![]() |
0.8755 | ∓0.4458 | 0.1864 | 29 | 64 | 80 |
Bond directions | ||||||
CdI–O(2) | 0.4064 | −0.8115 | −0.4199 | 66 | 36 | 65 |
CdI–O(1) | 0.2845 | −0.3148 | −0.9055 | 74 | 72 | 162 |
CdI–O(4) | 0.8563 | 0.5144 | −0.0454 | 31 | 59 | 92 |
Cu(formate)2(H2O)4-complex II | ||||||
---|---|---|---|---|---|---|
g
x
![]() ![]() ![]() ![]() |
±0.7892 | −0.3475 | ∓0.5063 | 38 | 110 | 120 |
g
y
![]() ![]() ![]() ![]() |
−0.5823 | ∓0.1616 | −0.7968 | 126 | 99 | 143 |
g
z
![]() ![]() ![]() ![]() |
−0.1951 | ∓0.9236 | 0.3300 | 101 | 157 | 71 |
Bond directions | ||||||
CdII–O(5) | −0.9547 | −0.0447 | 0.2940 | 17 | 87 | 73 |
CdII–O(6) | 0.2548 | 0.3757 | 0.8910 | 75 | 68 | 27 |
CdII–O(3) | −0.1929 | 0.9202 | −0.3404 | 101 | 23 | 70 |
The EPR lines are relatively broad at room temperature (linewidth ΔBpp=
3.3 mT) producing a badly resolved spectrum. The lines narrow considerably on cooling thus, angular variation of the spectrum was recorded at 77 K (linewidth ΔBpp
=
0.9 mT) and it is shown in Fig. 3. Fitting of the angular variation data to the g2 and gA2g-tensors with second order corrections gives solid lines in Fig. 3 and spin-Hamiltonian parameters listed in Table 1.
![]() | ||
Fig. 3 Angular variations of hyperfine EPR line positions at 77 K for Cuf and Cuw complexes. The solid lines are plotted using g-factors and A-splittings of Table 1. Inset shows the single crystal habit. |
The g-factors and hyperfine splittings A are unexpectedly almost identical for both the sites Cuf and Cuw. This is clearly visible in the powder spectrum (Fig. 2b), where the lines of two complexes are superimposed. The large axial deformation of both complexes (gz≫
gy, gx) indicates that the deformation is produced by the strong Jahn–Teller effect. The nearly octahedral host Cd–O6 octahedra are strongly tetragonally distorted when Cd(II) is substituted by Cu(II). Thus, Cu(II) ions readjust the molecular environment but surprisingly in such a way, that despite the different molecular structure of the Cuf and Cuw complexes they display the same crystal field strength and symmetry. It is worth noting, that the g-factors and A-splittings are very similar to those of Cu(II) in Tutton salt crystals in the rigid lattice limit (for example: gz
=
2.432, gy
=
2.105, gx
=
2.074, Az
=
120, Ay
=
14, Ax
=
37
×
10−4 cm−1 for Cu(II) in (NH4)2Mg(SO4)2·6H2O;22gz
=
2.443, gy
=
2.134, gx
=
2.069, Az
=
112, Ay
=
10, Ax
=
46
×
10−4 cm−1 for Cu(II) in Cs2Zn (SO4)2·6H2O23), which are known as undergoing the strong Jahn–Teller effect with static complex deformation at low temperatures. This suggests that the geometry of the doped Cu(II) complexes is determined mainly by the Jahn–Teller effect with the strong vibronic coupling.
Assuming D2h crystal field symmetry, the Cu(II) orbitals in the MO-approximation can be written as:24
ψ1(Ag)![]() ![]() ![]() ![]() ![]() ![]() ψ2(Ag) ψ3(B1g) ψ4(B2g) ψ5(B3g) | (1) |
![]() | (2) |
![]() | (3) |
![]() | (4) |
α | β 21 | β 2 | β′2 | κ | E xy | E xz | E xz |
---|---|---|---|---|---|---|---|
0.88(5) | 0.84(5) | 0.84(5) | 0.60(5) | 0.33(6) | 11![]() |
13![]() |
13![]() |
![]() | ||
Fig. 4 Temperature dependence of the g-factors and hyperfine splittings A for Cu(formate)6 complexes. The solid lines are plotted according to the Silver–Getz model describing vibronic averaging of spin-Hamiltonian parameters. |
The model describing the g-factor averaging by vibronic dynamics in the dynamic Jahn–Teller effect has been proposed by Silver and Getz28 and Riley et al.29 The model assumes that the observed g-factors are weighted averages of the three potential wells produced by Jahn–Teller effect. When fractional populations of the wells are N1, N2 and N3
(N1+
N2
+
N3
=
1) then experimental g-factors can be calculated as:22,30
gz![]() ![]() ![]() ![]() ![]() ![]() gy gx | (5) |
Moreover, the model assumes that: (a) the g-factors are identical in all three configurations and reorientations result in an interchange of the x, y, and z-axes only; (b) the population of the wells is described by Boltzmann statistics; (c) the shape of adiabatic potential surface and thus, the energy difference between the wells are temperature independent. Thus, the populations are:
![]() | (6) |
For the Cuf complex we can assume N3=
0, and by taking the gzi
=
2.429 and gyi
=
2.092 (i
=
1, 2) from Table 1, the g-factor temperature dependences and energy difference δ12 can be calculated. The results are shown as lines in Fig. 4a and the average energy value is δ12
=
500 (±60) cm−1. Assuming that A-splittings are influenced by g-factor variations only the plots of the A(T) dependences are shown in Fig. 4b. The calculated δ12 values are shown in Fig. 5 for temperatures higher than 100 K, where the variations in g and A parameters are measurable. It is clearly seen that δ12 is not constant over the whole temperature range, indicating a restricted validity of the used model which assumes temperature independence of δ12. Moreover, a few vibronic levels of energy lower than δ12 are expected in the deepest potential well with typical splitting order of 100 cm−1.29 As a result the overbarrier jumps or phonon induced tunneling to the higher energy well can appear via few intermediate states modifying effective δ12-value. As one can see from Fig. 4b the average value of Az and Ay decreases slightly with temperature. It can be a result of the increase in unpaired electron delocalisation (a decrease in the α2 MO coefficient) in the ground state. Thus, the phonon induced tunneling is more probable as in the case of K2Zn(SO4)2·6H2O: Cu(II).27
![]() | ||
Fig. 5 Energy difference δ12 between the two lowest energy potential wells vs. temperature, calculated from Silver–Getz model. |
![]() | (7) |
![]() | ||
Fig. 6 Temperature dependence of the spin–lattice relaxation rate. The inset shows magnetization recovery after saturation, monitored by ESE amplitude, with exponential fit (solid line) at 32 K. |
The second term with characteristic T9-dependence describes a Raman two-phonon relaxation process for Kramers transitions with I8 being the transport integral over the whole phonon spectrum.32 Assuming the Debye-type phonon spectrum with cut-off temperature ΘD the transport integral can be written as
![]() | (8) |
for x=
0.1–16.6
I8![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
and for x=
16.6–40.0
I8![]() ![]() ![]() ![]() ![]() ![]() |
The best fit to eqn. (7) using these expressions (written in Y-script) and the fitting subroutine of ORIGIN 7.0 has given parameters a, b and ΘD summarized in Table 3. The fits are shown as solid lines in Fig. 6.
Spin–lattice relaxation |
|||
---|---|---|---|
Complex | a/K−1 s−1 | b/K−9 s−1 | Θ D/K |
I![]() ![]() |
12 | 1.3![]() ![]() |
193 |
II![]() ![]() |
85 | 0.7![]() ![]() |
193 |
Phase relaxation |
|||
---|---|---|---|
Complex | (1/TM)0/s−1 | c/s−1 | Δ/cm−1 |
I![]() ![]() |
1.7![]() ![]() |
5.7![]() ![]() |
166(3) |
II![]() ![]() |
0.4![]() ![]() |
1.3![]() ![]() |
166(3) |
As it was expected the fits display identical Debye temperature 193 K for Cuf and Cuw but slightly different a and b parameters. The higher b-value for Cuf and thus, faster relaxation at high temperatures is due to the larger electron–phonon coupling for Cu(formate)6 complexes located within the formate layers as compared to the hydrated Cuw complex linked to those layers. The larger a-coefficient value for Cuw indicates a larger disorder in the sublattice of the hydrated Cu-complexes.
![]() | ||
Fig. 7 Electron spin echo amplitude decay for Cu(formate)2(H2O)4 complex at 15.8 K. Strong modulations of the decay arise from the proton 1H and 111,113Cd magnetic nuclei surrounding Cu-centres, as shown by the FT-ESE spectrum in the inset. The dotted line is the decay function V(τ)![]() ![]() ![]() ![]() |
The decay function was exponential and well fit to the expression
![]() | (9) |
An effective phase memory time resulting from two-component decay of ESE is defined as the time when V(t) dependence falls down to the V0/e value. This TM was determined from experimental results with relatively a low accuracy owing to the strong modulation, with the error of about 15% at low temperatures and of about 30% at high temperatures, where most of the decay is hidden in the dead time of the spectrometer.
After subtraction of Vdecay from the total decay function the modulation function was obtained. Its Fourier transform delivers the pseudo-ENDOR spectrum containing peaks at main and harmonic frequencies of nuclei surrounding the paramagnetic centre. The FT-ESE spectrum for the Cuw-complex is shown as the inset in Fig. 7. The spectrum displays peaks at proton frequencies around 12.7 MHz with splittings at 2.44 and 5.13 MHz from the nearest protons and overtones around 25.9 MHz. Moreover, weaker peaks are located at low frequencies at 2.9 MHz with overtone at 5.6 MHz and can be identified as due to magnetic isotopes 111,113Cd with total natural abundance of about 25%.
The phase memory time varies with temperature and the dephasing rate 1/TM is shown in Fig. 8 and Fig. 9 for Cuf and Cuw complexes, respectively, where they are compared with the spin–lattice relaxation rate. 1/TM depends more weakly on temperature than 1/T1. After the temperature independent region below 15 K, where the mτ2 term in decay function dominates, the ESE dephasing accelerates on heating. In this temperature range 1/T1 approaches 1/TM, being one order of magnitude shorter only at about 50 K. Thus, a contribution from T1-type relaxation processes is expected. Moreover, molecular motions can also contribute.33–35 Matrix molecule motion is expected to produce an averaging of the local magnetic fields on heating producing spin-packet narrowing and thus, slowing down the dephasing rate. This has not been observed in our crystal. Thermal motions of paramagnetic centres can produce an opposite effect. For considerable g-factor and A-splitting anisotropy, like for Cu(II) ions, the jumps, rotations or librations of Cu(II) complex can produce time dependent shifts Δg(t) and ΔA(t) resulting in broadening of the spin-packet on heating observed as an acceleration of the dephasing rate. Thus, the temperature dependence of the dephasing rate can be written as
![]() | (10) |
![]() | ||
Fig. 8 ESE dephasing rate 1/TM and spin–lattice relaxation rate 1/T1vs. temperature for Cuf-complex. The dashed line indicates the contribution of T1-processes to ESE dephasing. |
![]() | ||
Fig. 9 ESE dephasing rate 1/TM and spin–lattice relaxation rate 1/T1vs. temperature for Cuw-complex. The dashed line indicates the contribution of T1-processes to ESE dephasing. |
Fits to eqn. (10) give solid lines at 1/TM plots in Fig. 8 and Fig. 9 where the dashed lines show contributions from 1/T1. It should be noted that ESE decay due to T1-processes is clearly described as V(2τ)=
Voexp(−τ/b)k with k
=
1, whereas existing theories predict k
=
2 or k
=
3/2.37–39 The parameters for Cuf and Cuw complexes are summarized in Table 3. One can see that contributions from spin–lattice relaxation processes and from Cu-complex dynamics are comparable. The parameters (1/TM)0, c and Δ are not strongly different for both complexes and are typical for Cu(II) complexes exhibiting the Jahn–Teller effect, as we had observed previously.22,27,34,40 The same value of Δ
=
166 cm−1 for both types of Cu-complexes suggests that the dynamic process producing ESE dephasing operates in the deepest potential well but not between the wells, since for Cuw the higher energy well is not accessible at room temperature, whereas for Cuf the higher energy well is populated as we observed by vibronic g-factor averaging. Thus, we can conclude that the Δ is not an energy barrier but rather the splitting of the vibronic levels.
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