Magnetisation as a function of time and field.

A non-Ohmic current that grows exponentially with the square root of applied electric field is well known from thermionic field emission (the Schottky effct), electrolytes (the second Wien effct) and semiconductors (the Poole-Frenkel effect). It is a universal signature of the attractive Coulomb force between positive and negative electrical charges, which is revealed as the charges are driven in opposite directions by the force of an applied electric field. Here we apply thermal quenches to spin ice to prepare metastable populations of bound pairs of positive and negative emergent magnetic monopoles at millikelvin temperatures. We find that the application of a magnetic field results in a universal exponential-root field growth of magnetic current, thus confirming the microscopic Coulomb force between the magnetic monopole quasiparticles and establishing a magnetic analogue of the Poole-Frenkel effect. At temperatures above 300 mK, gradual restoration of kinetic monopole equilibria causes the non-Ohmic current to smoothly evolve into the high field Wien effect for magnetic monopoles, as confirmed by comparison to a recent and rigorous theory of the Wien effect in spin ice. Our results extend the universality of the exponential-root field form into magnetism and illustrate the power of emergent particle kinetics to describe far-from equilibrium response in complex systems.The data comprises magnetisation as a function of time (up to Research results based upon these data are available at http://doi.org/10.1038/nphys3704随外加电场平方根呈指数增长的非欧姆电流，已在热离子场发射（肖特基效应，Schottky effect）、电解质体系（第二维恩效应，second Wien effect）以及半导体材料（普尔-弗伦克尔效应，Poole-Frenkel effect）中被广泛报道。该现象是正负电荷间库仑吸引力的普适特征——当外加电场的作用力将两类电荷沿相反方向驱动时，这一微观库仑力便会显现出来。 本研究通过对自旋冰（spin ice）实施热淬冷处理，在毫开尔文（millikelvin）温度下制备出正负涌现磁单极子（emergent magnetic monopoles）束缚对的亚稳态种群。我们发现，施加外磁场后会出现磁流随磁场平方根呈指数增长的普适行为，由此证实了磁单极准粒子（quasiparticle）间的微观库仑力，并确立了普尔-弗伦克尔效应的磁学类比形式。 当温度高于300毫开尔文时，磁单极子动力学平衡的逐步恢复会使非欧姆电流逐渐演变为磁单极子的高场维恩效应（Wien effect），这一结论通过与近期发表的自旋冰中维恩效应的严谨理论对比得到了验证。本研究将平方根指数场依赖形式的普适性拓展至磁学领域，并展示了涌现粒子动力学在描述复杂系统远离平衡态响应时的强大能力。 本数据集包含磁化强度随时间的变化关系（原文此处内容疑似缺失）。基于本数据集的研究成果可通过下述链接获取：http://doi.org/10.1038/nphys3704