Scaling Theory for Critical Phenomena in Coupled Magnetic Systems —Critical Exponents of πd Antiferromagnets—

Abstract

The scaling theory for critical phenomena is extended to coupled magnetic systems that consist of two subsystems, and some extended relations of critical exponents are derived. It is shown that the extended theory practically reduces to the conventional scaling theory in ferromagnets and in non-ferromagnetic systems with β 1 = β 2 ; however, the extended form of the theory can be relevant otherwise, where β 1 and β 2 are exponents of the order parameters in subsystems 1 and 2, respectively. The theory is applied to a model of the organic πd antiferromagnet λ-(BETS) 2 FeCl 4 , which contains πand d-spin subsystems, where BETS stands for bis(ethylenedithio)tetraselenafulvalene. It is shown that an effective Hamiltonian for the π spins is reduced to the two-dimensional Ising model in the vicinity of the critical temperature T c . This supports a conjecture from a recent experimental observation. Consequently, β 1 = 1/8 is obtained, where subsystems 1 and 2 correspond to the πand d-spin systems, respectively. Additional relations α = 1 − β 1 − β 2 and β 1 = β 2 ≡ β are derived from specific features of the λ-(BETS) 2 FeCl 4 system. These relations result in α = 1 − 2β, which was previously obtained in a free-energy functional model. Critical exponents below T c are obtained as α = 3/4, β = 1/8, γ = 1, δ = 9, ψ = 1/5, and ν = 5/8. The value of α is close to a recent experimental result of α = 0.77 in λ-(BETS) 2 FeCl 4 .