Free energy and phase diagram of chromium alloys

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Abstract
The phase diagram of chromium alloys is remarkably rich. At the Néel temperature of 310 K, pure chromium undergoes a weakly first-order phase transition into an incommensurate spin-density wave (SDW) state. When doped with more than 0.2% manganese, this transition becomes second order and the SDW becomes commensurate. Over 25 years ago, Koehler et al. and Komura, Hamaguchi, and Kunitomi observed a first-order commensurate-to-incommensurate (CI) transition in CrMn alloys. The temperature of this CI transition decreased to zero as the manganese concentration increases from about 0.2% to about 1.5%. Using mean-field theory, we have constructed the free energy and phase diagram of chromium alloys in the presence of electron scattering. In the absence of scattering, the phase diagram allows a first-order phase transition from the incommensurate to the commensurate states with decreasing temperature. But if the damping is sufficiently large, the phase-separation curve flips from the right side of the tricritical point to the left. So within a small window of manganese concentrations, the commensurate state undergoes a first-order transition into the incommensurate state with decreasing temperature, in agreement with the experiments of Koehler et al. At zero temperature, we find a first-order phase transition from the incommensurate to the commensurate state with manganese doping, in agreement with the work of Komura, Hamaguchi, and Kunitomi. In the absence of damping, the zero-temperature energy gap Δ(0) in the commensurate regime is independent of manganese concentration. But in the presence of damping Δ(0) becomes an increasing function of the manganese concentration.