Stable phase separation and heterogeneity away from the coexistence curve

Abstract

Phase separation, i.e., the coexistence of two different phases, is observed in many systems away from the coexistence curve of a first-order transition, leading to a stable heterogeneous phase or region. Examples include various quantum ferromagnets, heavy-fermion systems, rare-earth nickelates, and others. These observations seem to violate basic notions of equilibrium thermodynamics, which state that phase separation can occur only on the coexistence curve. We show theoretically that quenched disorder allows for phase separation away from the coexistence curve even in equilibrium due to the existence of stable minority-phase droplets within the majority phase. Our scenario also answers a related question: How can a first-order transition remain sharp in the presence of quenched disorder without violating the rigorous lower bound ν ≥ 2/d for the correlation-length exponent? We discuss this scenario in the context of experimental results for a large variety of systems.

Quantum ferromagnet in the proximity of the tricritical point

“…Finally, the possibility of crossing the TCP by means of pressure or composition allows one to perform detailed investigation of the basic thermodynamics related to phase separation in the immediate proximity of the QPT. This is of particular importance, since contrary to expectations on the basis of basic thermodynamic considerations it is known that phase separation in some quantum ferromagnets and other systems can occur away from the coexistence curve of a first-order phase transition [11].…”

Restoration of quantum critical behavior by disorder in pressure-tuned (Mn,Fe)Si

“…8,9 This behavior matches the results in pure MnSi, except for the effect of helical spin correlations, which adds a weakly first-order character to the thermal transition before the TCP is reached, and phase separation at p* < p, which cannot be expected for ideally thermodynamic behavior in systems without disorder. 36,37 In their recent studies, 36,37 quenched disorder was suggested as a possible origin for the phase separation observed in pure MnSi. This situation is illustrated in Fig.…”

“…8,9,[34][35][36][37] Considering the effect of a negative m 3 ln(m) term of the magnetization m (order parameter) on the free energy in itinerant ferromagnets due to soft modes and particle-hole excitations, they proposed that the second-order thermal transition in ferromagnets is replaced by a first-order transition at a tricritical point (TCP) when approaching the quantum critical point (QCP), as illustrated in Fig. 1b.…”

Anomalous Transport Behavior in Quantum Magnets

“…Candidates for such fluctuations have been observed in the nonmagnetic phase of MnSi [24] and discussed as a possible origin of the observed T 3/2 behavior [30]. Or, weak quenched disorder may provide droplets of the ordered phase within the disordered one (and vice versa) [31]. This explains the widespread observation of phase separation away from the coexistence curve of a first-order of a first-order phase transition, and it also provides a way for scattering mechanisms that are germane to the magnetic phase to persist in parts of the disordered phase.…”

“…In order for this mechanism to explain the anomalous transport behavior on either side of the first-order QPT, the droplet formation discussed in Ref. [31] is crucial.…”