We measured the specific heat of λ-BETS₂FeCl₄ and nonmagnetic λ-BETS₂GaCl₄ by the thermal relaxation method. The specific heat of FeCl₄ and GaCl₄salts are indicated by open and closed circles in Figure 1, respectively. The specific heat of FeCl₄ salt shows a sharp peak at the MI transition temperature (T_MI ~ 8.3 K) and has a larger value than that of GaCl₄ salt at the entire temperature region. In order to study the excess components of the FeCl₄ salt in detail, we first estimated its lattice and electronic specific heat. We assumed that the specific heat of isostructural GaCl₄ salt was equivalent to the lattice specific heat of FeCl₄ salt.

The electronic specific heats of these two salts were clearly different since the GaCl₄ salt exhibited superconductivity at 5.5 K, while the FeCl₄ salt underwent an MI transition at 8.3 K. Around 5.5 K, the GaCl₄ salt exhibited superconductivity of the BCS type and showed the specific heat jump 1.43 γT J/mol·K [12]. Considering the difference in these electronic specific heats, we obtained the excess specific heats ΔC (shown in Figure 2) by subtracting the lattice and electronic specific heats in the PM phase, and subtracting the lattice contribution in the AFI phase, respectively.

The open circles in Figure 2 show the excess specific heat ΔC obtained by subtraction of the lattice and electronic specific heat estimated for the GaCl₄ salt from the total specific heat of the FeCl₄ salt. A sharp peak was observed at 8.3 K. It should be noted that a broad hump that appears to be a Schottky-type anomaly was found in a lower temperature side of the sharp peak. If the π and 3d spins cooperatively align antiferromagnetically below T_MI, as was expected for the present system, the larger peak of the specific heat would only exist at T_MI, followed by a rapid reduction without the formation of the hump. This behavior is completely different from that of ΔC in Figure 2. We can speculate that the Schottky-type specific heat is derived from the paramagnetic 3d spin under the internal magnetic field induced by the π-d interaction.

Since the Schottky-type anomaly occurs for 3d or π spin systems only under the influence of a magnetic field, we calculated the temperature dependence of the specific heat of the 3d spin s_d = 5/2 and π spin s_π = 1/2 systems for paramagnetic states and obtained the best fit for the excess specific heat ΔC in the case of the Fe³⁺ 3d spin. The energies at s_d = 5/2 were split into six levels by the Zeeman splitting under an internal magnetic field H_πd ascribed to the π-d interactions, as shown in the inset of Figure 2. On the basis of the results of the energy splitting, we estimated the internal magnetic field H_πd from the π spin to the 3d spin as 4.0 T, while the internal magnetic field H_dπ caused by the 3d spin to the π electron was estimated as H_dπ = 33 T from the experimental results of the field-induced superconductivity [4,13]. We consider that this disagreement is mainly due to the different origins (s_π and s_d) of H_πd and H_dπ.

The integration of ΔC/T was performed to estimate the entropy S, which derives information about the degrees of freedom, as shown in Figure 3. The resulting entropy was close to a value of Rln6 (Rln6 = 14.9 J/mol·K), i.e., the spin degrees of freedom for the 3d spin (Rln(2s_d + 1), s_d = 5/2). These experimental results suggest that the 3d spin degrees of freedom give a large contribution to the sharp peak as well as the Schottky-type hump. It should be noted that about 80% of the 3d spin degrees of freedom is sustained just below T_MI.

At MI transition, π electron system transfers from the Pauli paramagnetic metal state having the entropy of π electron S_π = γT to the antiferromagnetic insulator with S_π = 0 because of the strong π-π exchange interaction J_ππ/k_B = 448 K, which is much larger than the metal-insulator transition temperature T_MI [14]. The entropy difference ΔS_π in both phases corresponds to the γT_MI = 0.014 × 8.3 = 0.17 J/mol·K by assuming that the electronic density of the states at Fermi level is the same with that of GaCl₄ salt [12]. Its value is much smaller than the observed 3d contribution Rln6. From this result of entropy, we could not detect the large reductions of Rln2 ~ 5.7 J/mol·K accompanied with the AF ordering of π spin (s_π = 1/2). Combining the metal-insulator transition is a remarkable feature of this novel AF spin alignment.

The magnetic susceptibility provides information about the direction and magnitude of the internal magnetic field H_πd. To clarify the origin of the splitting of the 3d spin state, we examined the magnetic susceptibility. Figure 4 illustrates the magnetic susceptibility observed under application of an external field H of 0.1 T along the c-axis. Above T_MI, the magnetic susceptibility M/H shows Curie-Weiss-type behavior for s_d = 5/2. At T_MI, it shows a sharp step down, and subsequently, M/H reduces with decreasing temperature. We also find that M/H has a shoulder-shaped anomaly below T_MI. This characteristic shoulder is observed in the curve at low temperatures, corresponding to the region where the Schottky-type specific heat anomaly is also observed. These findings suggest a common origin of the shoulder in the magnetic susceptibility curve and the Schottky-type specific heat.

This internal magnetic field H_πd is generated by the exchange interaction J_πd with the AF-ordered π spin system. The π-d interaction having the shortest contact was found to be the strongest coupling between several π-d couplings [14]. Assuming that this coupling dominates the internal magnetic field H_πd, we may ignore the other weak couplings and propose a possible spin structure in the AFI phase, as shown in Figure 5a. In this case, the internal magnetic field on the 3d spin induced by the nearest neighbor π spin is alternately oriented in the opposite direction. Since the alternating internal magnetic field begins to align the 3d spins as the temperature decreases, the magnetization of the 3d spin system will be canceled out, and so will gradually decrease in the AFI phase.

Next, we tried to reproduce the characteristic shoulder in the magnetic susceptibility on the basis of this spin model. Under the weak external field H = 0.1 T (<< spin-flop field H_SF ~ 1 T [6]), the π spin system forms AF alignment along the easy axis and produces the internal magnetic fields +H_πd and −H_πd on the Fe 3d spin at sites A and B, respectively, where the effective magnetic field H_eff^± becomes H_eff^± = H ± H_πd, as shown in Figure 5b. We calculated the magnetizations M_d⁺ and M_d⁻ at sites A and B, respectively, using the Brillouin function B_s(x) as

In this study, the external magnetic field is applied along the c-axis. According to the torque measurement by Sasaki et al. [16], the c-axis is tilted by about θ = 30° from the easy axis. Considering the tilt angle θ, the total magnetization component M_d parallel to H can be obtained as

where the angles α between H and H_eff⁺ and β between H and H_eff⁻ can be determined from θ, H_πd, and H (see Figure 6b). The calculated magnetic susceptibility M_d/H can well reproduce the resulting data, as shown by the solid curve in Figure 4, using the following parameter values: H = 0.1 T, θ = 25°, and H_πd = 4 T. The strength of this internal field is in good agreement with the value estimated from the Schottky specific heat. In addition, Waerenborgh et al. observed sextet Fe Mössbauer signals generated by an internal magnetic field H_πd, which supports the paramagnetic model of the Fe 3d spin [17].

In the high-temperature metallic phase, the magnetic susceptibility follows the Curie-Weiss law with 3d spin s_d = 5/2, as shown by the dashed curve in Figure 4. It is notable that over the entire temperature range studied, the Fe 3d spin paramagnetic states dominate the magnetic susceptibility and specific heat. Because we can expect that for the π spin system, the temperature-independent Pauli paramagnetic susceptibility χ_Pauli is approximately 3 × 10⁻⁴ emu, which is three orders of magnitude smaller than that for Fe 3d predicted by the Curie-Weiss law, assuming that the electronic density of states at the Fermi level is the same as that for λ-BETS₂GaCl₄ [12].

At T_MI, the paramagnetic metal PM-AFI transition causes a sharp step down. In the metallic region, the interaction working on the 3d spins is of the Ruderman-Kittel-Kasuya-Yoshida (RKKY) type via the conduction π electrons [18]. Across the MI transition, this spin network will be cut off by the localization of π electrons. Therefore, the magnetic susceptibility curve of 3d spin changes from following the Curie-Weiss law (dashed curve in Figure 4) to the present paramagnetic model (solid curve in Figure 4). The 3d spin dominates the step down at T_MI and the slow reduction in the AFI phase.

Figure 6a shows the specific heats of mixed crystals λ-BETS₂Fe_xGa_1−xCl₄ (0.4 < x ≤ 1) and λ-BETS₂GaCl₄. The specific heats of λ-BETS₂Fe_xGa_1−xCl₄ show sharp peaks at T_MI or SC-AFI transition temperature T_SCI and broad humps below these sharp peaks, while non-magnetic λ-BETS₂GaCl₄ does not exhibit these anomalies. Because the specific heat of λ-BETS₂Fe_xGa_1−xCl₄ in the metallic phase was close to that of λ-BETS₂GaCl₄ in the metallic phase, we assumed that the lattice and electronic specific heats of isostructural λ-BETS₂GaCl₄ were equivalent to those of λ-BETS₂Fe_xGa_1−xCl₄. We obtained the excess specific heats ΔC (shown in Figure 6b) by subtracting the estimated lattice and electronic specific heat in the metal phase, and subtracting the lattice contribution in the AFI phase, respectively. In Figure 6a, broad humps are found below sharp peaks for all mixed crystals. This large value for ΔC in the low-temperature AFI phase suggests that a majority of the spin degrees of freedom in this system were maintained even after transition to the AFI phase was achieved. These anomalies in the AFI ground state of the mixed crystals contrast the critical behavior that in π-d system κ-BETS₂FeBr₄, Fe 3d spin (s_d = 5/2) takes place at AF transition at Neel temperature [19,20].

Figure 7 shows the excess entropies obtained by integrating ΔC/T over temperature. The resulting total entropies were close to the values of xR ln6 (dashed line in Figure 7) expected for the degrees of freedom of 3d high spins (s_d = 5/2) per molecular formula. These experimental results suggest that the 3d spin degrees of freedom contributed substantially to the sharp peaks as well as the Schottky-type humps for all mixed crystals. During transition, π spin resulted in AF ordering and produced a strong internal magnetic field at the nearest neighboring Fe sites. At the transition temperature, an increase in the intensity of the internal magnetic field at the Fe sites caused a rapid reduction in 3d spin entropy, indicated by sharp peaks in the specific heats.

To discuss the origin of this transition, we investigated the dependence of excess specific heat on Fe content. Figure 8a indicates excess specific heats normalized by Fe content ΔC/x. The maximum of these broad humps gradually shifts to a lower temperature with decreasing x. The broad humps of all mixed crystals could be fitted to the calculated Schottky specific heats of s_d = 5/2 (solid curves in Figure 8a).

As we approach the transition temperature, the experimental data deviate from the solid curves because of the formation of sharp peaks. The sharp peaks are attributed to the rapid enhancement of the internal magnetic field at the Fe sites accompanied with the development of spontaneous magnetization in the π spin system. When the π magnetization reaches saturation, ΔC follows the calculated Schottky curves under fixed internal magnetic fields H_πd. The intensity of H_πd estimated from the agreement between the ΔC data and the calculated curves were proportional to the x values, as shown in Figure 8b. However, these experimental results are very puzzling because the high density of paramagnetic Fe 3d spin increased the internal magnetic field H_πd, owing to the saturation magnetization of the AF ordered π spin and increased the PM-AFI transition temperature. These results clarify that the Fe 3d spin plays a crucial role in stabilizing AF ordering in the π spin system. Further analysis of the sharp peaks enables a measurement of the strong temperature dependence of the internal magnetic field in the vicinity of the transition temperature and gives information about a characteristic critical behavior of the spontaneous magnetization in the low-dimensional π spin system. The detailed studies of this critical behavior will be reported in our next paper.

Figure 9 shows a plot of ΔC/x versus the temperature normalized by each internal magnetic field k_BT/gμ_BH_πd. These normalized data fit to one of the curves obtained at the temperatures studied. The sharp peaks as well as the Schottky-type broad humps could be normalized in the high Fe-content region of x > 0.5, where the PM-AFI transition occurs [9]. In the low Fe-content region (0.3 < x < 0.5), the Schottky term could be reduced to the same universal curve; however, the sharp peak at the phase transition could not be normalized, because at peak temperatures, the SC-AFI transition occurred instead of the PM-AFI transition (see the inset of Figure 9). It should be noted that at the PM-AFI transition, the phase transition temperatures as well as the Schottky specific heats could be scaled by internal magnetic field H_πd. These scaling rules clarify that the internal magnetic field drove the PM-AFI transition.

We have a possible explanation for the role of Fe 3d spins in PM-AFI transitions and propose a mechanism for this peculiar phase transition, in which the fluctuation of the π spin system is suppressed by magnetic anisotropy introduced by Fe 3d spin via the π-d interaction. Magnetic susceptibility measurements suggested that the π spin system, which exhibits isotropic magnetic properties in ordinary organic conductors, has finite anisotropy in λ-BETS₂FeCl₄ [5]. A decrease in Fe content weakens the anisotropic magnetic properties, i.e., the spin-flop fields H_SF in magnetization [21]. These results suggest that the magnetic anisotropy of the π spin system originates from the anisotropic crystal field surrounding the Fe 3d spin system through the π-d interaction; this Fe-induced anisotropy suppresses two-dimensional fluctuation in the present π spin system and increases the PM-AFI transition temperature.

We have studied the critical behavior of the PM-AFI transition for the λ-BETS₂FeCl₄ system, measuring the excess magnetic specific heat. We estimated the critical process of the spontaneous magnetization of π spin in the vicinity of the transition temperature. We could observe the low dimensional criticality of the magnetization of π spin. We considered that the magnetic anisotropy induced by π-d interactions transfer the π spin from the two-dimensional (2D) Heisenberg spin system to the 2D Ising one having the easy axis. Antiferromagnetic order cannot be established in 2D Heisenberg spin systems. In contrast, 2D Ising spin system exhibits long-range magnetic order. To find unambiguous evidence for 2D long-range ordering in the AFI phase, a more detailed study on the criticality of this phase transition is now in progress.