Abstract
Renormalization group theory does not restrict the form of continuous variation of critical exponents which occurs in presence of a marginal operator. However, the continuous variation of critical exponents, observed in different contexts, usually follows a weak universality scenario where some of the exponents (e.g., β, γ, ν) vary keeping others (e.g., δ, η) fixed. Here we report ferromagnetic phase transition in (Sm1−yNdy)0.52Sr0.48MnO3 (0.5 ≤ y ≤ 1) single crystals where all three exponents β, γ, δ vary with Nd concentration y. Such a variation clearly violates both universality and weak universality hypothesis. We propose a new scaling theory that explains the present experimental results, reduces to the weak universality as a special case, and provides a generic route leading to continuous variation of critical exponents and multi-criticality.
Highlights
Study of critical phenomena is based on two concepts: one is universality[1,2] which states that the associated critical exponents and scaling functions are universal up to symmetries and space dimensionality, and another is scaling theory[3] that describes the general properties of the scaling functions and relates different critical exponents
Sr1−zCazRuO3 from (β ≈ 0.5, γ ≈ 1, δ ≈ 3) for z = 0 to (β ≈ 1, γ ≈ 0.9, δ ≈ 1.6) for z = 0.6. They have suggested that the evolution of exponents may be originating from orthorhombic distortions or additional quantum fluctuations associated with quantum phase transition at z = 0.7 whether there is a quantum critical point in
The variation of exponents is not new to critical phenomena as it can be generated by a marginal interaction, but most examples in both theoretical and experimental studies satisfy the weak universality[14] where (β, γ, ν) vary but (η, δ) are fixed
Summary
Study of critical phenomena is based on two concepts: one is universality[1,2] which states that the associated critical exponents and scaling functions are universal up to symmetries and space dimensionality, and another is scaling theory[3] that describes the general properties of the scaling functions and relates different critical exponents. Anomalous ferromagnetic (FM) transition has been observed in mixed valance manganites, RE1−xAExMnO3 (RE: rare earth ions, AE: alkaline earth ions) either as a discontinuous transition or a continuous transition with a set of critical exponents that does not belong to any known universality or the weak www.nature.com/scientificreports/. The nature of phases and transitions strongly depend on the bandwidth and disorder (namely quenched disorder) arising due to the size mismatch between A-site cations[50,51]. Such disorder reduces the carrier mobility and the formation energy for lattice polarons[52], in effect TC reduces, rendering the FM transition towards first-order. The first-order transition is extremely sensitive to external pressure, magnetic field, A-/B-site substitution, oxygen isotope exchange, etc. - with the application of external and internal pressure (chemical substitution) beyond a critical threshold, the transition becomes continuous[43,44,45,53]
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