Uniaxial Chemical Pressure and Disorder Effects on Magnetic and Dielectric Properties of β′-(BEDT-TTF)₂(ICl₂)_1−x(AuCl₂)_x

Relaxor-like dielectric behaviors in BEDT-TTF-based charge transfer salts have recently been of interest both experimentally^1–3) and theoretically,^4–7) where BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene (also abbreviated as ET). Such an anomalous dielectric polarization coexists with magnetic localized spins characteristic of strongly correlated systems. This is reminiscent of electronic ferroelectricity discovered in inorganic systems^8,9) with a strong coupling of the magnetic and dielectric degrees of freedom, giving rise to multiferroics. Although no overall consensus has yet been reached on the origin of the charge degrees of freedom in organic systems,^10–12) the salt presented here is a good candidate to shed light on this open question.

An organic charge transfer salt, \(\beta'\)-(ET)₂ICl₂, has an alternate stacking structure consisting of a conducting layer composed of donor molecules and an insulating anion layer.¹³⁾ In the conducting layer, two ET molecules with a formal charge of \(+(1/2)e\) form a strong dimer with face-to-face molecular packing, corresponding to one hole carrier per ET dimer, resulting in an anisotropic two-dimensional (2D) effective half-filled electronic band structure. Because the on-site Coulomb repulsion is much larger than the band width, a hole carrier is localized on the dimer, and thus the system becomes an insulating state (a dimer–Mott insulator). In such a dimer–Mott system, there is an \(S=1/2\) localized spin per dimer unit, which antiferromagnetically interacts with each other. This system shows a three-dimensional (3D) antiferromagnetic long-range order below the Néel temperature \(T_{\text{N}}=22\) K¹⁴⁾ and, in addition, a superconducting transition at 14.2 K (under 8.2 GPa), which is the highest among the ET-based salts.¹⁵⁾

Recently, the temperature dependence of the dielectric constant, \(\varepsilon(T)\), has been revealed to be Curie–Weiss-like (a Curie temperature of 67 K) with a frequency-dependent peak structure.³⁾ According to an empirical analysis of the relaxor-like peak structure, a characteristic freezing temperature related to the interaction between electric dipoles (\(T_{\text{VF}}\), as will be discussed later) is estimated to be approximately 23 K, which is almost the same as \(T_{\text{N}}\). This indicates that the system contains a significant coupling between spin and charge degrees of freedom. Additionally, an intralayer pyroelectric current is found to appear below 62 K.³⁾

To verify the spin and charge coupling mechanism, experimental studies of the pressure effect are important. It is, however, difficult to carry out dielectric experiments under pressure because of a possible interruption by a pressure medium in the atmosphere. One possible strategy is to apply chemical pressure by substituting molecular components, which has been one of the most effective methods in organic conductors.¹⁶⁾ The isomorphic salt \(\beta'\)-(ET)₂AuCl₂ is the best candidate. Moreover, alloying the ICl₂ and AuCl₂ anions is a straightforward task because no polymorphic (ET)₂X phases have been found in \(X=\text{ICl$_{2}$}\) or AuCl₂. In this work, we prepare the alloy crystals \(\beta'\)-(ET)₂(ICl₂)\(_{1-x}\)(AuCl₂)_x and observe the magnetic susceptibility and dielectric constant.

The alloy crystals were grown by the conventional electrochemical oxidation method. The mole ratio of a supporting electrolyte n-tetrabutylammonium dichloroaurate (TBA∙AuCl₂) to TBA∙ICl₂, \(x_{0}\), was varied from 0 to 1. The crystal quality was independent of \(x_{0}\) and no deterioration by alloying was found. This can be confirmed from the \(R1\)-value of the X-ray structure refinement.^13,17,18) To examine the Au:I ratio of the prepared crystals, x, FE-SEM with EDX (JEOL JSM6500F) was performed. As a result, for example, the crystals used for X-ray structural analysis have x (\(x_{0}\)) = 0.15 (0.09), 0.27 (0.29), 0.45 (0.6), 0.47 (0.5), 0.66 (0.7), and 0.81 (0.8), revealing that \(x_{0}\) is almost comparable to the Au content x of the crystals. The X-ray crystal structure data were obtained at room temperature on a Rigaku Mercury 375R/M CCD (XtaLAB mini) diffractometer using Mo-Kα radiation. The structure was solved by direct methods and refined on the basis of a full-matrix least-squares refinement (SHELX-97). The magnetic susceptibility χ was measured using a SQUID magnetometer (Quantum Design MPMS-XL). The c-axis (corresponding to the magnetic easy axis) of a single crystal was aligned along the magnetic field. The contribution of the core diamagnetization was subtracted from the magnitudes of χ. The dielectric constant measurement was carried out by the 2-terminal capacitance method using an LCR meter (HP4284A) with \(V_{\text{ac}}=100\) mV parallel to the \(a^{*}\)-(interlayer) axis. As previously reported,¹³⁾ the \(\beta'\)-salts are semiconductive; the low conductivity is also seen in all the alloys (typically \(10^{-6}\)–\(10^{-7}\) S cm⁻¹ at 100 K), which supports the validity of the capacitance measurement.

The structure of \(\beta'\)-(ET)₂(ICl₂)\(_{1-x}\)(AuCl₂)_x has a triclinic crystal system with space group of \(P\bar{1}\). Figures 1(a) and 1(b) show the lattice parameters¹⁷⁾ as a function of x. The lattice length of the a-axis (interlayer) decreases almost linearly with increasing x from 0 to 1, leading to a slight shrinkage of the unit cell volume V by ∼1.5% [Fig. 1(c)]. The decrease in the a-axis length caused by the AuCl₂ substitution for ICl₂ is due to the smaller ionic radius of Au than of I. Although the b- and c-axes (intralayer) do not vary with x, the bc conducting layer is slightly distorted as reflected in the α-angle, which is the most prominent of the three angles [Fig. 1(b)]. To confirm whether the effect of alloying on the 2D electronic structure is present, we evaluate transfer integrals between the ET molecules in the bc-layer displayed in Fig. 1(d). The transfer integral (t) was calculated using HOMO orbitals obtained from the extended Hückel LCAO approximation.¹⁹⁾ As shown in Fig. 1(e), t is almost insensitive to x within the accuracy of the structure analysis, suggesting that alloying leads to a negligible effect on the 2D structure. Taking account of the lattice parameters and transfer integrals, we determine that uniaxial chemical pressure along the a-axis is fairly introduced into the system by the anion substitution. The magnitude of pressure for inducing the variation of V by 1.5% is approximately estimated to be ∼1 kbar.²⁰⁾ In addition to chemical pressure, however, we note that the randomness of the anions significantly affects the magnetic property, as mentioned below.

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Figure 1. (a) Lattice lengths, (b) angles, and (c) cell volume of \(\beta'\)-(BEDT-TTF)₂(ICl₂)\(_{1-x}\)(AuCl₂)_x at room temperature. The data of the \(x=0\) and 1 salts are cited from the literature^13,18) (open symbols). (d) Intralayer donor molecular arrangement and (e) magnitude of transfer integrals as a function of x.

The temperature dependence of the paramagnetic susceptibility of the \(x=0.47\) alloy in the field of 5 T is shown in Fig. 2(a). The broad peak structure at approximately 110 K is almost the same as those of the ICl₂ (\(x=0\)) and AuCl₂ (\(x=1\), not shown in figure) salts. These \(\chi(T)\) curves are well explained on the basis of a 2D square-lattice \(S=1/2\) Heisenberg antiferromagnetic model, giving the intralayer exchange interaction \(J=59\) K.¹⁴⁾ Figure 2(b) shows the susceptibilities in the magnetic field parallel to the c-axis for several alloys at low temperatures. There is no trace of any impurity such as a Curie term in all the specimens. With decreasing temperature, \(\chi(T)\) at 0.5 T (filled circles) indicates a kink at \(T_{\text{N}}\) and gradually approaches approximately zero because the c-axis corresponds to the magnetic easy axis and the applied field is smaller than the spin-flop field \(H_{\text{sf}}=1.1\) T (\(x=0\) and 1).¹⁴⁾ Additionally, the data at 5 T (open circles) deviate from \(\chi(T)\) at 0.5 T below \(T_{\text{N}}\) as a typical response of the canted spins above \(H_{\text{sf}}\). The x dependence of \(T_{\text{N}}\) is plotted in the inset of Fig. 2(b); \(T_{\text{N}}\) is almost constant in \(0\leq x\leq 0.5\) and then increases in \(x\geq 0.5\).

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Figure 2. (Color online) Temperature dependence of the magnetic susceptibility of \(\beta'\)-(BEDT-TTF)₂(ICl₂)\(_{1-x}\)(AuCl₂)_x. (a) Data of the \(x=0.47\) (filled circles) and \(x=0\) (open circles) salts. (b) Enlargement of the susceptibility at low temperatures. The data are shifted for clarity. The magnetic fields of 0.5 (filled circles) and 5 (open circles) T were applied parallel to the c-axis. The arrows indicate the Néel temperature. The data of the \(x=0\) and 1 salts are cited from the literature,¹⁴⁾ where the open triangles indicate the data observed in the field of 0.5 T perpendicular to the c-axis. The upper inset shows the Néel temperature as a function of x. The broken line \(T_{\text{N}}^{li}(x)\) is the linear interpolation between \(x=\) 0 and 1. The lower inset shows a normalized difference g between \(T_{\text{N}}\) and \(T_{\text{N}}^{li}\). The solid curve is a parabolic fitting (see text).

The x dependence of \(T_{\text{N}}\) is well understood from the viewpoint of uniaxial chemical pressure and anion disorder. The 3D long-range order at \(T_{\text{N}}\) is induced by the strong 2D correlation J developing in the bc-plane with the weak interlayer interaction \(J'\) along the a-axis. As reflected in t (Fig. 1) and J, the intralayer magnetic structure of the \(x=1\) salt is almost the same as that of the \(x=0\) salt. Thus, the high \(T_{\text{N}}\) of 28 K of the \(x=1\) salt is attributed to the short interlayer distance and the large \(J'\) compared with those of the \(x=0\) salt. In the alloy crystals, although the partial AuCl₂ substitution for ICl₂ gives uniaxial chemical pressure along the interlayer direction, disorder in the anion layer will disturb the uniform paths of J and \(J'\). The magnitude of disorder most likely becomes apparent at \(x\approx 0.5\), and thus \(T_{\text{N}}\) is suppressed toward low temperatures from the linear interpolation as a first-order approximation of \(T_{\text{N}}(x)\) [indicated by \(T_{\text{N}}^{li}(x)\) in the upper inset of Fig. 2(b)], which would appear if the a-axis of the \(x=0\) salt were uniformly compressed in the low-pressure regime (∼1 kbar). Here, we define the normalized difference \(g=[T_{\text{N}}(x)-T_{\text{N}}^{li}(x)]/T_{\text{N}}^{li}(x=0.5)\), which reflects the suppression of \(T_{\text{N}}\) after subtracting the effect of chemical pressure and thus extracts only the contribution of the randomness. As shown in the lower inset of Fig. 2(b), the x dependence of g is well fitted with a parabolic function: \(g(x)=0.366x(x-1.02)+2.70\times 10^{-3}\). The symmetrical shape at \(x=0.5\) ensures that the randomness of the anions certainly suppresses \(T_{\text{N}}\).

Next, we describe the dielectric properties. The dielectric constant of the \(x=1\) salt with the electric field parallel to the \(a^{*}\)-axis is shown in Fig. 3(a). The temperature and frequency dependences of \(\varepsilon/\varepsilon_{0}\) are quantitatively similar to the data of the \(x=0\) salt;³⁾ the broad peak temperature \(T_{\text{max}}\) strongly depends on the measurement frequency f, and the maximum amplitude of \(\varepsilon/\varepsilon_{0}\approx 20\) at 0.5 kHz and the f-independent \(\varepsilon_{\text{const}}/\varepsilon_{0}\approx 6\) at the lowest temperature are comparable to those of the \(x=0\) salt. It is difficult to verify the Curie–Weiss law because of the low S/N ratio at frequencies lower than 0.5 kHz in our apparatus. Nevertheless, from the similarity between \(\varepsilon(T,f)\) values of the \(x=0\) and 1 salts, we conclude that the chemical pressure does not affect the dielectric property. This indicates that the origin of the electric dipole is attributed to the intralayer element composed of the dimerized donor molecules, such as a charge fluctuation induced by the ac electric field. The dielectric moment originating from the interlayer constituents such as a donor-anion coupling, if ever, might be markedly affected by the uniaxial compression.

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Figure 3. (a) Temperature dependence of the dielectric constant of \(\beta'\)-(BEDT-TTF)₂AuCl₂, where the data at 0.5 to 500 kHz are overlaid. (b) Dielectric constant of \(\beta'\)-(BEDT-TTF)₂(ICl₂)\(_{1-x}\)(AuCl₂)_x at 5 kHz, shifted for clarity. The arrows indicate the peak temperature \(T_{\text{max}}\). (c) \(T_{\text{max}}\) as a function of x at several frequencies.

Figure 3(b) shows the \(\varepsilon(T)\) values of several alloys at 5 kHz, which are subtracted by \(\varepsilon_{\text{const}}\) at the lowest temperature. The broad peak apparently shifts toward lower temperatures in all the alloys. The amplitudes of \(\varepsilon(T)\) are almost similar, and thus we find no systematic variation in the peak height or \(\varepsilon_{\text{const}}\) with x, probably owing to the uncertainty of the sample form factor. As shown in Fig. 3(c), the concave shape of \(T_{\text{max}}(x)\) is found at all the frequencies examined and has a minimum at \(x\approx 0.5\). The remarkable suppression of \(T_{\text{max}}\) in the alloy crystals evidently arises from the randomness of the anions. Before discussing this point in detail, let us investigate the frequency dependence of \(T_{\text{max}}\).

As reported in the \(x=0\) salt,³⁾ the relaxor-like peak temperature \(T_{\text{max}}\) is well described on the basis of the Vogel–Fulcher (VF) empirical law:²¹⁾ \(f=f_{0}\exp[-E_{\text{VF}}/(T_{\text{max}}-T_{\text{VF}})]\), where \(f_{0}\) is the frequency in the high-temperature limit, \(E_{\text{VF}}\) is the corresponding activation energy, and \(T_{\text{VF}}\) is the VF temperature. The main panel of Fig. 4 is the semi-log plot of the measurement frequency vs \(1/(T_{\text{max}}-T_{\text{VF}})\) with the best fit results displayed by the solid lines. The fitting parameters of \(f_{0}\) and \(E_{\text{VF}}\) are shown in the right-upper and middle insets of Fig. 4, respectively. The magnitudes of \(f_{0}\) and \(E_{\text{VF}}\) of the \(x=0\) and 1 salts are almost the same within the statistical error. \(T_{\text{VF}}\) adopted in the analysis is also represented in the right-lower inset. The extrapolation to the longitudinal axis in the main panel contains an ambiguity due to a lack of a clear peak structure higher than 10 kHz; nevertheless, a systematic variation of the fitting parameters \(f_{0}\) and \(E_{\text{VF}}\) is clearly obtained. As shown in the left inset of Fig. 4, \(T_{\text{VF}}\) is entirely equivalent to \(T_{\text{N}}\) obtained from \(\chi(T)\). The reason for the correspondence between \(T_{\text{VF}}\) and \(T_{\text{N}}\) has been pointed out in terms of an antiferroelectric interaction mechanism related to the antiferromagnetic interactions (J and \(J'\)).³⁾ The linear relationship obtained between \(T_{\text{VF}}\) and \(T_{\text{N}}\) supports this explanation.

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Figure 4. (Color online) Vogel–Fulcher plot of the measurement frequency against inverse temperature \(1/(T_{\text{max}}-T_{\text{VF}})\). The right insets show the x-dependences of \(f_{0}\), \(E_{\text{VF}}\), and \(T_{\text{VF}}\). The error bars indicate the statistical error. The broken line \(\widetilde{E_{\text{VF}}}\) is the mean value between \(x=0\) and 1. The solid curve is calculated as \(\widetilde{E_{\text{VF}}}[1+g(x)]\). The left inset shows the \(T_{\text{VF}}\) vs \(T_{\text{N}}\) plot.

In contrast to the magnetic property, in which the variation of \(T_{\text{N}}\) is governed by chemical pressure and anion disorder, the dielectric response does not show the effect of chemical pressure, but instead, is dominated by the randomness of the anions. As a reasonable interpretation of the relaxor-like property in the \(x=0\) salt, a polar glassy domain picture with thermally activated fluctuations is proposed.³⁾ Such a dynamical domain picture provides an explanation of the broad peak at \(T_{\text{max}}\); at high temperatures, the polarization of the domain responds to the ac electric field, giving a Curie–Weiss-type behavior in \(\varepsilon(T)\). The volume of the polar domain increases with decreasing T and then the polarization (or domain wall motion) cannot keep up with the measurement frequency, resulting in the peak at \(T_{\text{max}}\). In the alloy crystals, \(E_{\text{VF}}\) and \(f_{0}\) as functions of x are explained in terms of this scenario, taking account of anion disorder. The randomness of the anions disturbs the periodic potential in the donor layer and suppresses the growth of the polar domain. The \(x=0.5\) alloy leads to the maximum degrees of randomness giving the smallest average of the domain, in which the activation energy for the polarization flipping, \(E_{\text{VF}}\), and the characteristic flipping frequency \(f_{0}\) take minimum and maximum values, respectively. These qualitative behaviors are very similar to the result of X-ray irradiation²²⁾ in κ-(ET)₂Cu₂(CN)₃, where the anion site is partly destroyed by prolonged X-ray irradiation.

In particular, the suppression of \(E_{\text{VF}}\) from \(\widetilde{E_{\text{VF}}}\) is a key to estimating the effect of the randomness quantitatively, where \(\widetilde{E_{\text{VF}}}=782\) K is the mean value between \(x=0\) and 1. The solid curve shown in the right-middle inset in Fig. 4 is described as \(E_{\text{VF}}(x)=\widetilde{E_{\text{VF}}}[1+g(x)]\), where \(1+g(x)\) is the suppression factor by the randomness evaluated from \(T_{\text{N}}(x)\). Note that there is no fitting parameter in this curve. The good agreement with the experimental result proves that the randomness equally disturbs the magnetic long-range order and the growth of the polar domain.

At first glance, the difference between \(T_{\text{VF}}\) values of the \(x=0\) and 1 salts seems to contradict the dielectric response independent of chemical pressure. However, we propose the following scenario; \(T_{\text{VF}}\) is completely related to \(T_{\text{N}}\) and the increase in \(T_{\text{N}}\) with x arises from the increase in \(J'\). Therefore, the x-dependent \(T_{\text{VF}}\) is attributed to the interlayer magnetic interaction \(J'\), probably reflecting the interlayer interaction between the polar domains. In other words, the variation of \(T_{\text{VF}}\) may be derived from an indirect pressure effect via the spin-charge coupling. To further uncover the relationship between the spin and charge degrees of freedom in detail, other experimental studies will be needed, such as determining the dielectric constant at low frequency to confirm the Curie temperature and pyroelectric current measurements.

In summary, we have studied the dimer–Mott insulator \(\beta'\)-(BEDT-TTF)₂(ICl₂)\(_{1-x}\)(AuCl₂)_x. The lattice length of the a-axis decreases with increasing x, while the b- and c-axes do not vary. Taking into account the intralayer t insensitive to x, the present alloying leads to uniaxial chemical pressure with a negligible effect on the 2D structure. The variation of the Néel temperature as a function of x is understood from the viewpoint of uniaxial chemical pressure accompanied by disorder. On the other hand, the dielectric response does not indicate the effect of chemical pressure but is governed by the randomness of the anions.

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