Critical Exponents

Magnetic materials generally undergo a phase transition lowering temperature below the transition temperature. At the transition temperature physical properties e.g. magnetic susceptibility, heat capacity and magnetic entropy shows singular behavior. The singularities are characterized by the set critical exponents. The value of critical exponent are universal in nature for type of exchange interaction. The singularity in physical quantities is observed in physical properties at critical temperature that are governed by the spin correlation function. Whereas, evolution of homogeneous (anti)ferromagnetic phases generally deal with the class of universality of critical exponent. We extended our analysis about magnetization by collecting information about the critical exponent β (associated with the spontaneous magnetization), γ (associated with the initial susceptibility) and δ (denotes the critical magnetization isotherms) observed from the isotherm magnetization measurement.

According to scaling hypothesis, the spontaneous magnetization $M_S(T)$ below $T_C$, inverse $χ–1_0 (T)$ above $T_C$ and measured magnetization at $T_C$ are characterized by β, γ and δ. They are defined as:

χ–1_0(T) = (h0/M0)ε^γ , ε > 0,

M= A0(H)^(1/δ) , ε = 0,

MS(T) =M0(–ε)^β , ε < 0,

Where ε ≡ (T–Tc), Tc , M0, h0, M0, h0, and A0 are critical amplitudes.

This analysis requires isotherms magnetization around the transition temperature. A complete set of critical exponent

offers detail information about magnetization-field-temperature when TC is approached

from above and below.

Figure 1: Arrott plot and modified Arrotto plot are presented.