Revealing the one-dimensional (1-D) Heisenberg antiferromagnetic state in pyrochlore α-Cu2V2O7 from critical exponent analysis

Low-dimensional magnets provide avenues to explore novel excitations and critical behaviour that are not typically found in their higher-dimension analogues. Herein, we investigate the critical behaviour of the canted antiferromagnet α-Cu₂V₂O₇ in the vicinity of magnetic phase transition by measuring isothermal magnetization curves. The α-Cu₂V₂O₇ sample is synthesized using the conventional solid-state route, and it stabilizes in an orthorhombic crystal structure with the Fdd2 space group, as determined from X-ray diffraction analysis. Critical exponents (β = 0.283(8), γ = 2.418(6) and δ = 9.16) obtained using the modified Arrott plot (MAP) suggest that α-Cu₂V₂O₇ does not belong to any of the existing magnetic universality classes. The reliability and self-consistency of the estimated exponents are further validated using Widom scaling relation and scaling analysis equations. To link the above obtained critical exponents to the underlying spatial-dimensionality (d) and spin-dimensionality (n) of the system, we used the renormalization group theory approach to estimate a set of critical exponents spanning various spin and spatial dimensions. Notably, the critical exponents obtained from renormalization group theory analysis by considering that (d(spatial-dimensionality) : n(spin-dimensionality)) = (1 : 3) closely matches with the value derived from MAP, revealing that α-Cu₂V₂O₇ can be considered a 1-D Heisenberg antiferromagnetic system. Finally, critical behaviour analysis testifies that α-Cu₂V₂O₇ exhibits long-range type exchange interaction J(r), which decays with r as J(r) ∼ r^−1.84.