In the organic π–d hybrid conductor λ-(BETS)₂FeCl₄ [BETS = bis(ethylenedithio)tetraselena-fulvalene], the π-electrons and localized d-spins play roles reversed from those in conventional π–d systems, leading to anomalous critical phenomena. In normal Ruderman–Kittel–Kasuya–Yosida (RKKY) compounds, π-electrons support antiferromagnetic (AF) ordering of localized d-spins, and the specific heat exhibits the logarithmic divergence characteristic of two-dimensional (2D) AF order. In contrast, in λ-(BETS)₂FeCl₄, the π-electrons themselves form an AF order, generate an internal field 𝐻_int, align the d-spins, and then polarize them. This first role reversal produces critical behavior far beyond what is expected in π–d coupled magnets and naturally leads to a “reverse RKKY” interaction.

The transition occurs at a relatively high temperature, and the specific heat shows a sharp peak with an anomalously large exponent 𝛼=0.77, far exceeding the logarithmic behavior of 2D AF systems. A Schottky-type shoulder appears at lower temperatures, indicating that most of the d-spin entropy remains active even after ordering. Since the π-electron system transitions from a metallic state, very little specific‑heat anomaly is expected from the π-electrons. Instead, the π-electron–induced polarization of the d-spins reduces the d-spin entropy, making the d-spins the dominant contributors to both the transition anomaly and the low-temperature specific heat. Thus, unlike conventional systems in which the component controlling the order also produces the main thermodynamic anomaly, this system exhibits a second role reversal: the π-electron system drives the AF transition, while the “supporting” d-spins provide the main thermodynamic contribution.

To examine these anomalous critical phenomena, we constructed a reverse RKKY model in which the spontaneous magnetization of the π-spin system follows 𝑀_𝜋∝(𝑇𝑐−𝑇)^𝛽, with 𝛽=1/8 for a 2D AF order, generating the 𝐻_int that polarizes the d-spins. The model reproduces the sharp specific‑heat peak from the modest initial alignment of the d‑spins along 𝐻_int at the transition, and the Schottky‑type shoulder from their gradual low‑temperature polarization. Under these reversed roles, the specific‑heat exponent naturally becomes an induced critical exponent, given by 𝛼=1−2𝛽, yielding 𝛼=0.75, in good agreement with the observed value 𝛼=0.77. This demonstrates that the anomalous exponent is a quantitative signature of the reverse RKKY interaction. The reverse RKKY mechanism may arise in multicomponent systems where low dimensionality, frustration and/or poor nesting of the Fermi surface suppress conventional magnetic order. This work shows that even within a conventional universality class, a twofold reversal between π-electrons and d-spins can induce a power‑law divergence in specific heat with an exponent not previously reported.
(Written by Yutaka Nishio on behalf of all authors.)

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