Stochastic Collision Theory of Magnetism in Radical Fluids

Abstract

How stochastic, microscopic events generate deterministic, macroscopic properties is a fundamental question in physics. We address this question by developing a quantum master equation model for concentrated radical solutions, where random molecular collisions govern the magnetic properties of the system. Our theory reveals a simple mechanism: the first-order exchange contribution averages to zero over collisions, while the second-order term survives as an effective ferromagnetic coupling that enhances magnetization. The model captures the experimentally observed trends in magnetic behavior that deviate from conventional theories. Because the mechanism arises from statistical averaging, it may apply to a broader class of soft matter phenomena, including liquid crystals.

Figures (4)

• Figure 1: Stochastic exchange interactions arising from molecular collisions in a fluid. (a) The model assumes that molecules undergo a series of discrete, pairwise collisions with varying partners. (b) Each collision event generates an exchange interaction, $J_{ij}$, which is treated as a random variable fluctuating in both magnitude and sign (we take $J_{ij}$ to be Gaussian with zero mean in the model). This stochastic nature reflects the complex and unpredictable dynamics of molecular encounters in the fluid phase.
• Figure 2: Effect of the first-order term (full model) on spin equilibration and magnetization. (a) Time evolution of the spin populations $\uprho_{00}$ (orange) and $\uprho_{11}$ (blue) toward equilibrium. (b) The resulting magnetization curve $M$ (cyan line) satisfies $|M| > |M_0|$ compared to the ideal paramagnetic magnetization $M_0$ (red line), indicating enhancement from the interaction. Shaded area in (a) denotes the standard deviation.
• Figure 3: Effect of the second-order term (simplified model) on spin equilibration and magnetization. (a) Time evolution of the spin populations $\uprho_{00}$ (orange) and $\uprho_{11}$ (blue) toward equilibrium. (b) The resulting magnetization curve $M$ (cyan line) satisfies $|M| > |M_0|$ compared to the ideal paramagnetic magnetization $M_0$ (red line), demonstrating the significant contribution of the second-order term. Shaded area in (a) denotes the standard deviation.
• Figure 4: Temperature and concentration dependence of magnetic susceptibility. (a) Magnetic susceptibility $\upchi$ as a function of temperature under a magnetic flux density of 0.3 T (vertical axis: $\upchi$). The black dots represent the simulation data. The red solid line shows the susceptibility of non-interacting spins ($\upchi_0$). The blue dashed line represents the best fit using the standard Curie-Weiss law ($\uptheta$ = constant), while the cyan solid line shows the fit with the modified Curie-Weiss law incorporating a temperature-dependent Weiss constant ($\uptheta(T) = aT+b$). (b) Concentration dependence at 300 K and 0.3 T (vertical axis: $\Updelta\upchi$). The quantity is plotted against radical concentration on a log-log scale.