Detailed X-band Studies of the π–d Molecular Conductor λ-(BETS)₂FeCl₄: Observation of Anomalous Angular Dependence of the g-value

If there is no exchange interaction between the π- and d-electrons, two EPR signals from each electron, \(S_{\pi} = 1/2\) and \(S_{d} = 5/2\), should be observed separately. However, if a strong interaction exists, the local field is averaged out due to the fast exchange, and the spectra should merge to a single line. This is known as the “exchange narrowing”.^27,28) As reported in the previous ESR study by Kawamata et al., we observed only a single EPR line in the temperature range between \(T_{\text{MI}}\) and room temperature.²¹⁾ This suggests that the π- and d-electrons are strongly coupled in this system. For the case of λ-(BETS)₂FeCl₄, it is also considered that the contribution of the Fe spins in the EPR signal should be dominant in the high temperature phase since the magnetic moment of Fe³⁺ is larger and the π-electrons are itinerant.⁸⁾

The angular dependences of the EPR signal in the \(a^{*}b^{*}\)-plane are obtained for several temperatures, and its g-value and EPR peak-to-peak linewidth are presented in Figs. 3(a) and 3(b), respectively. The raw EPR spectra and the methods of analysis can be found in the supplemental material.²⁹⁾ The relation between the angle θ and the crystal axes can be found in Figs. 1 and 2. As shown as a long-dashed curve in Fig. 3(a), a typical angular dependence of the g-value, which mostly follows the \({g_{\text{eff}} =\sqrt{\smash{g_{\text{max}}^{2}\cos^{2}\theta + g_{\text{min}}^{2}\sin^{2}\theta}\mathstrut}}\) dependence, is observed at 300 K. The maximum and minimum of the g-value are \(g_{\text{max}}\sim 2.05\) and \(g_{\text{min}}\sim 2.04\), and the principal axes of the g-tensor correspond to the \(b'\)- and \(a'\)-axes, respectively. Note that the \(a'\)- and the \(b'\)-axes are defined as the projection of the a- and the b-axes onto the \(a^{*}b^{*}\)-plane, respectively (see also Fig. 1). The principal axes are related to the ligand field of the tetrahedral FeCl₄⁻ anion where \(g_{\text{max}}\) is along the Fe–Cl bond parallel to the \(b'\)-axis (see Fig. 1). Moreover, the ESR signal of λ-(BETS)₂GaCl₄, which consists of only π-electrons, is \(g=1.99{\text{--}}2.02\).²¹⁾ Thus, the g-factor of the BETS molecule is different with the observed g-value. These results confirm that the EPR signal at 300 K comes mainly from the Fe spins.

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Figure 3. (Color online) Angular dependence of (a) the g-value and (b) the peak-to-peak linewidth from the EPR in the \(a^{*}b^{*}\)-plane for 10, 30, 100, 150, 230, 270, 280, and 300 K. The solid lines are eye guide. The long-dashed line for 300 K is the fitting from a typical g-tensor (see text for detail). The definitions of the crystal axes in relation with the angle θ are shown in Figs. 1 and 2.

As the temperature is lowered, a “canine teeth” structure, where two minima of the g-values are observed around \(\theta = 30\) and 90°, starts to develop below 270 K [Fig. 3(a)]. The two minima at 10 K are about \(g_{\text{min}}\sim 1.98\) and 1.99 for \(\theta = 30\) and 90°, respectively. Moreover, the maximum of the g-value, \(g_{\text{max}}\sim 2.05\) around \(\theta = 130\)° at 300 K, increases drastically to 2.11 at 30 K, and the maximum shifts towards \(\theta = 150\)° at 10 K as shown in Fig. 3(a). This suggests the principal axis of \(g_{\text{max}}\) tilts from the \(b'\)-axis toward the \(b^{*}\)-axis by decreasing the temperature. As described later, the tilting of the principal axis might be due to the development of the π–d correlation or the deformation of the FeCl₄⁻ anion with decreasing temperature. In Fig. 3(b), the maximum and the minimum of the EPR linewidth are found nearby the \(a'\)- and \(b'\)-axes, respectively. The linewidth along the \(a'\)-axis, which is parallel to the conducting plane, becomes extremely broad at 10 K as shown in Fig. 3(b). Such kinds of anomalous EPR behavior (i.e., teeth structure and linewidth broadening) suggest that the π–d interaction develops with lowering temperature. The details will be discussed later.

As shown in Fig. 4, the temperature dependence of the EPR signal for \(\theta=20\)°, which is around the g-value minimum in Fig. 3(a), also shows a distinct feature. The g-value starts to decrease below 150 K, and a sudden increase is observed below 12 K. In turn, the linewidth gradually increases by lowering temperature, and a steep linewidth broadening is observed below 12 K. We suppose the gradual decrease of the g-value and the gradual linewidth broadening between 12 and 150 K are due to the development of the spin correlation between π- and d-electrons. In contrast, the drastic g-shift and the linewidth broadening below 12 K are typical of EPR above the Néel temperature, which are due to the development of the antiferromagnetic spin correlation. Let us also note that, consistent with previous studies, the EPR intensity starts to diminish around 12 K and disappears in the AFI phase.^{8,9,15,16,29)}

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Figure 4. (Color online) Temperature dependence of the g-value and the peak-to-peak linewidth at \(\theta = 20\)°. The solid lines are eye-guide.

In general, microscopic information surrounding the magnetic ions can be obtained from the angular dependence of the g-value since the g-tensor reflects the symmetry of the ligand field, and its angular dependence behaves as \(g_{\text{eff}} =\sqrt{\smash{g_{\text{max}}^{2}\cos^{2}\theta + g_{\text{min}}^{2}\sin^{2}\theta}\mathstrut}\) (i.e., rotational ellipsoid). Therefore, the observation of the “canine teeth” structure in the angular dependence of the g-value in the low temperature region is quite unconventional.

The two-minima of the teeth structure are observed around \(\theta=30\) and 90°. The direction of the minimum at \(\theta = 30\)° appears to be along the projection of two cation-anion contacts, S⋯Cl (3.836 [3.696] Å, #2) and S⋯Cl (3.650 [3.526] Å, #4) contacts, in the \(a^{*}b^{*}\)-plane which are shown as purple and orange dotted lines in Fig. 1, respectively. The values in the parentheses are their inter-atomic distances at room temperature (italic values for 7 K), and the label of the corresponding cation-anion contact in Fig. 1. Note that the labels of the cation-anion contacts are according to the paper by Mori et al.⁴⁾ In this paper, they estimated the exchange interactions of these π–d couplings from the crystal structure at room temperature, and its values are 0.39 K for #2 and 0.50 K for #4.⁴⁾ Meanwhile, the minimum at \(\theta=90\)° mostly corresponds to the projection of the S⋯Cl (3.647 [3.553] Å, #1) and Se⋯Cl (3.539 [3.465] Å, #6) contacts shown as green and blue dotted lines in Fig. 1, respectively. The estimated exchange couplings for these contacts are 1.44 and 14.14 K, respectively.⁴⁾ Let us note that there is no g-value anomaly when the magnetic field is along the S⋯Cl (3.424 [3.389] Å, #5) contact, and contacts #3 and #7 are omitted for clarity in Fig. 1 since they are the second smallest and the smallest π–d couplings, respectively.⁴⁾ Hence, it is interesting that the two-minima of the g-value are observed along the projection of cation-anion contacts with noticeable exchange interaction.

Let us now discuss what makes the “canine teeth” structure in the low temperature region. In the transition metal coordination compounds, it is well known that the “covalent” character of the metal–ligand bond appears in the ligands such as halides, oxides, and sulfides.²⁷⁾ This covalency of the metal–ligand bond can induce the nephelauxetic effect, where the name “nephelauxetic” comes from the Greek meaning “cloud-expanding”. In such a case, the spin density of the central metal ion spread out to the surrounding non-magnetic ions. The expansion of the spin density from the central ion has two main effects: (i) the decrease of the spin–orbit coupling and (ii) the increase of interaction with the surrounding atoms. The former affects the g-value to be close to the g-value of the free spin (i.e., \(g=2\)), and the latter broadens the EPR linewidth since the contribution of the super hyperfine coupling increases.²⁷⁾ The latter effect also contributes to the super exchange interaction if adjacent magnetic ions are present.^30,31) The ligand field of isolated FeCl₄⁻ anion was studied both theoretically and experimentally, and it was shown that the spin–orbit coupling is reduced by the nephelauxetic effect, and the expansion of the Fe³⁺ spin density affects the g-value and the single ion anisotropy.^32,33)

However, the asymmetric anisotropy of the g-value with the “canine teeth” structure observed in λ-(BETS)₂FeCl₄ is quite different from the one observed in the previous studies which shows a typical g-anisotropy.^32,33) We suppose the difference comes from the magnetic interactions surrounding the FeCl₄⁻ anion since the previous studies examined isolated anions.^32,33) Considering that (i) the two-minima of the g-value are observed along the Se/S⋯Cl contacts with noticeable interactions, and (ii) its g-value is close to \(g=2\) and linewidth maximum is also observed (i.e., suggesting the reduction of the spin–orbit coupling), the “canine teeth” structure might be a result of the nephelauxetic effect where the spin density of the central metal ion is expanded toward the p-orbital of the Cl⁻ which has significant exchange path with the BETS molecule. The elongated spin density of the central metal ion along the indirect exchange path is previously observed in IrCl₆²⁻ by neutron diffraction.³¹⁾ Hence, the observation of the “canine teeth” structure with \(g\sim 2\) at \(\theta=30\) and 90° might indicate that the π–d interaction is strong along these directions.

It is also interesting that the “canine teeth” structure develops with decreasing temperature as shown in Figs. 3(a) and 4. The decrease of the g-value towards \(g\sim 2\) suggests that the spin–orbit coupling gradually reduces and the spin density of Fe³⁺ expands with decreasing the temperature. If the above argument is correct, there should be some increase of the π–d correlation with decreasing the temperature. Hence, we verified whether the inter-atomic distance of the Se/S⋯Cl contacts and the bond angles of the FeCl₄⁻ anion are affected by temperature. The inter-atomic distances of typical Se/S⋯Cl contacts and the Cl–Fe–Cl bonds angles as a function of temperature are shown in Figs. 5(a) and 5(b), respectively. The inset in Fig. 5(a) is the zoomed crystal structure around the FeCl₄⁻ anion with the typical Se/S⋯Cl contacts. In Fig. 5(a), the S⋯Cl contacts #3 and #7 are not shown again for clarity since they are the two smallest π–d couplings. The Se/S⋯Cl contacts is normalized with the one at room temperature.⁴⁾ It is found that inter-atomic distances of the S⋯Cl contacts #2 and #4 become much shorter than other Se/S⋯Cl contacts with decreasing temperature as shown in Fig. 5(a). It suggests that the π–d couplings #2 and #4 are more enhanced as the temperature decreases. Let us remind that the S⋯Cl contacts #2 and #4 are related with the g-value minimum observed around \(\theta=30\)°. On the other hand, the S⋯Cl contact #1 and Se⋯Cl contact #6, which are related to the g-value minimum at \(\theta=90\)°, show a modest contraction of the inter-atomic distance in Fig. 5(a). However, the bond angles of the FeCl₄⁻ anion show significant changes in the Cl(2)–Fe–Cl(1) and Cl(2)–Fe–Cl(4) bond angles with temperature as shown in Fig. 5(b). The changes of these two bond angles suggest that the Fe–Cl(2) bond is pointing toward the Se(7) of the BETS molecule with decreasing temperature. Indeed, the bond angle of Fe–Cl(2)–Se(7) changes from 160.2° at 300 K to 162.5° at 7 K, enhancing the π–d coupling #6. Therefore, we conclude the enhancement of the “canine teeth” structure in the low temperature region is owing to the development of the π–d coupling in λ-(BETS)₂FeCl₄.

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Figure 5. (Color online) Temperature dependence of (a) the ratio of the inter-atomic distance of the typical Se/S⋯Cl contacts compared with the distance at room temperature, and (b) the Cl–Fe–Cl bond angles in the FeCl₄⁻ anion. The inset in (a) shows the typical Se/S⋯Cl contacts surrounding the FeCl₄⁻ anion.

To summarize this subsection, a characteristic angular dependence of g-value, which has a “canine teeth” structure, has been observed in λ-(BETS)₂FeCl₄ below 270 K. The structure is enhanced especially below 150 K. The g-value minima are the results of the asymmetric nephelauxetic effect where the spin density expands along the direction of significant indirect exchange paths, and the development of the “canine teeth” structure is related to the enhancement of the π–d exchange couplings as a consequence of the deformation of the tetrahedral coordination in FeCl₄⁻ and the development of several significant S(Se)⋯Cl⋯Fe exchange paths with decreasing temperature.

The results of the measurements for \(B\parallel\text{$a^{*}b^{*}$-plane}\) in the previous section indicate that the crystal axes can be identified by the minimum and the maximum of the g-values within the \(a^{*}b^{*}\)-plane. The \(b^{*}\)-axis corresponds to the maximum of the g-value, and the \(a^{*}\)-axis to one of the minima of the g-value at about 120° from the \(b^{*}\)-axis [see Fig. 3(a)]. Hence, the \(b^{*}\)-axis is defined from the g-value in the \(a^{*}b^{*}\)-plane rotation, and it is possible to perform the EPR measurement in the \(b^{*}c\)-plane by using a triangular prism jig as shown in Fig. 2(b). The angle ϕ indicates the direction of the applied magnetic field, and the sample was set so that the directions of \(\phi = 90\) and 180° are along the c- and \(b^{*}\)-axes, respectively. The direction of the magnetic field in the crystal structure is shown in Fig. 6(a).

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Figure 6. (Color online) (a) Crystal structure of λ-(BETS)₂FeCl₄ and the direction of the magnetic field projected to the \(b^{*}c\)-plane. The thick dotted lines are the same short Se/S⋯Cl contacts as Fig. 2. (b) Angular dependence of the g-value and linewidth within the \(b^{*}c\)-plane at 10 K. The red box is the area where AFMR is observed at 4.5 K [see Fig. 7(a)].

Figure 6(b) shows angular dependence of the g-value and the linewidth within the \(b^{*}c\)-plane measured at 10 K. In this case, an asymmetric canine teeth structure of the g-value is observed. The g-value minima are 2.01 and 2.03 at \(\phi = 30\) and 100°, respectively. Similarly to the results of the \(a^{*}b^{*}\)-plane rotation, a broad EPR linewidth is observed around the g-value minima (i.e., suggesting the nephelauxetic effect). Many projections of the π–d contacts, such as Se⋯Cl (#6, blue dotted line), S⋯Cl (#1, green dotted line), and S⋯Cl (#2, purple dotted line) contacts, correspond to the minimum at \(\phi = 30\)° [see Fig. 6(a)]. They are the same contacts that contributed to the g-value minima in the \(a^{*}b^{*}\)-plane. On the other hand, there is no corresponding projection of the Se/S⋯Cl contact around \(\phi=100\)°, where the g-value dip is about 2.03, and no minimum of the g-value is observed along the projection of the S⋯Cl contact (#4, orange dotted line), where the projection is around \(\phi=150\)°. In contrast to the \(a^{*}b^{*}\)-plane rotation which shows two minima with \(g\sim 2\), the minimum value for \(\phi=100\)° is around \(g\sim 2.03\). The difference of the effective g-value from \(g=2\) is due to the effect of the spin–orbit coupling, therefore, it seems that the spin–orbit coupling is still effective at \(\phi=100\)° (\(g\sim 2.03\)) in comparison with \(\phi=30\)° (\(g\sim 2.01\)). Considering that there is no projection of the Se/S⋯Cl contact and the g-value is about 2.03 at \(\phi=100\)°, the minimum of the g-value at \(\phi=100\)° might not be due to the cation-anion interaction but due to the minimum of the g-tensor reflecting the ligand field of FeCl₄⁻ anion. Furthermore, the lack of g-value anomaly along \(\phi=150\)° might suggest the absence of the nephelauxetic effect for the S⋯Cl contact #4. Hence, the S⋯Cl contact #2 might be the main origin of the g-value minimum at \(\theta=30\)° in the \(a^{*}b^{*}\)-plane. It is not clear why there is no sign of the nephelauxetic effect for the S⋯Cl contact #4 despite that the exchange coupling is finite, 0.50 K at room temperature.⁴⁾

It is known from the magnetic torque measurement by Sasaki et al. that the easy-axis of the antiferromagnetic state forms an angle of about 30° with respect to the c-axis and an angle of about 120° with respect to the \(b^{*}\)-axis within the \(b^{*}c\)-plane.²²⁾ In our configuration, this angle corresponds to \(\phi = 60\)° where a linewidth maximum of the EPR line is observed as shown in Fig. 6(b). In general, the maximum/minimum of the EPR linewidth is related with the magnetic anisotropy, and it is understandable that the antiferromagnetic easy-axis appears at the linewidth maximum. Therefore, the easy-axis mode of AFMR should be observed if the magnetic field is applied nearby \(\phi = 60\)° below \(T_{\text{MI}}\) in the AFI phase.

The angular dependence of the ESR spectrum in the high field region (550–1350 mT) at 4.5 K, namely in the AFI phase, is presented in Fig. 7(a). For X-band ESR, EPR is observed around 330 mT for the temperature above \(T_{\text{MI}}\) (i.e., paramagnetic metal phase), however, no EPR is observed at 4.5 K as mentioned above. Instead, two ESR signals are observed around 950 and 1150 mT at \(\phi = 60\)°, and more clear and stronger signals are observed for \(\phi = 65\)° as shown in Fig. 7(a). At \(\phi = 55\)° or 70°, the ESR intensity rapidly decreases, and the two ESR lines merge to a single line. Then, ESR completely disappears at \(\phi = 50\) and 80°. This suggests that the two ESR signals only appear for the magnetic field orientation between \(\phi = 60\) and 65°. The temperature dependence of the ESR spectrum at \(\phi = 65\)° is presented in Fig. 7(b). Although the higher ESR signal does not shift with temperature, the lower ESR signal shifts to lower field as the temperature increases. Meanwhile, the intensity for both ESR signals decreases with increasing temperature. Note that the resonance field for the higher ESR signal, 1150 mT, corresponds to the spin-flop field as previously reported.^9,16,22)

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Figure 7. (Color online) (a) ESR spectra in the high field region for \(\phi = 50\), 55, 60, 65, 70, and 80° at 4.5 K. (b) Temperature dependence of ESR spectrum at \(\phi = 65\)°. The low- and high-field ESR signals are attributed to the easy-axis mode of AFMR and the spin-flop resonance, respectively. The broken arrow is an eye-guide for the resonance shift of the easy-axis mode with temperature.

From above-mentioned typical behavior, these two ESR lines observed in the AFI phase are ascribed to the easy-axis mode of AFMR and the spin-flop resonance. The behavior of AFMR lines is consistent with previous studies.^9,15,16) Since the easy-axis mode and the spin-flop resonance were observed, our results suggest that the antiferromagnetic easy-axis corresponds to \(\phi = 60{\text{--}}65\)°. This result, where the antiferromagnetic easy-axis is about 30° from the c-axis to the \(b^{*}\)-axis, is consistent with the magnetic torque measurements.²²⁾ Interestingly, this angle area of \(\phi = 60{\text{--}}65\)° corresponds to the area where the maximum of the EPR linewidth is observed at 10 K as shown in the solid red box in Fig. 6(b). Hence, the antiferromagnetic easy-axis can be assigned from the maximum of the EPR linewidth in the \(b^{*}c\)-plane rotation.

It is also worth to mention that the spin-flop resonance of AFMR is observed below 11 K, which is higher than the temperature of the MI transition, \(T_{\text{MI}}\). The intensity of AFMR is rather small at 11 K, suggesting the antiferromagnetic transition is only partial, and the intensity is enhanced as temperature decreases. Furthermore, as it can be seen in the spin-flop resonance of 4.5 and 7 K in Fig. 7(b), a fine double peak structure of the spin-flop resonance, two identical signals with different linewidth, is observed below \(T_{\text{MI}}\). The double peak structure is also observed in the easy-axis mode of AFMR at 4.5 K in Fig. 7(b). This double peak structure suggests that two kinds of antiferromagnetic spin states exist. It should be noted that splitting of the sextets is observed from 8.3 K down to 3.2 K in the ⁵⁷Fe Mössbauer spectra, which indicates two different environments for the Fe sites.³⁴⁾ Although only one Fe site is crystallographically independent down to 7 K, we think the fine double peak structure of AFMR is related to the magnetic splitting observed in the Mössbauer measurements.³⁾ The two different environments might be due to the metastable state of the π-electrons as discussed in the next section.