Normal-state bubbles and lamellae in type-I superconductors
Normal-state bubbles and lamellae in type-I superconductors
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I 型超导体中的常态气泡和片层
DOI：
10.1103/physrevb.72.014513
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
T. Okada
中科院分区：
文献类型：
--
作者：
A. Cēbers;C. Gourdon;V. Jeudy;T. Okada
我们报告了对 I 型超导体中正常态域形成的广泛研究。首先从理论上考虑域模式。磁域之间的磁相互作用在“电流环路”模型的框架中描述：中间状态由一组围绕磁域的屏蔽电流环路建模，并像在自由空间中一样相互作用。该系统在形式上等效于一组均匀磁化的磁域。提出了电流环路模型的扩展，以考虑超导区域磁屏蔽的约束。我们确定了圆柱域（气泡）的六角形阵列和无限长且平行的条纹的晶格的自由能。正相体积分数和磁畴尺寸的平衡值作为磁场的函数计算。当正相的体积分数约为 0.3 时，预计会发生气泡到条纹的转变。实验上，利用高分辨率磁光成像技术研究了正常态域。观察到的图案包括共存的气泡和无序的迷宫式片层结构。我们展示了固定对域接口位置的贡献的证据。然后分析片层的平均宽度作为所施加磁场的函数，发现其增加与预测非常一致。相反，气泡的平均直径保持恒定：它几乎独立于磁域之间的磁相互作用。磁性键合数与孤立气泡的平衡直径有超过三十倍的一致性。所提出的约束电流环模型被证明可以提供比电流环模型更准确的预测，特别是对于小磁性键合数。此外，正如理论上所预测的那样，增加正相的体积分数会导致气泡到薄片的转变。
We report an extensive study of the formation of normal-state domains in type-I superconductors. Domain patterns are first considered theoretically. The magnetic interaction between domains is described in the framework of the ``current-loop'' model: the intermediate state is modeled by a set of loops of screening current encircling the domains and interacting as in the free space. This system is shown to be formally equivalent to a set of uniformly magnetized domains. An extension of the current-loop model is proposed to take into account the constraint of the magnetic shielding by the superconducting regions. We determine the free energy of a hexagonal array of cylindrical domains (bubbles) and of a lattice of infinitely long and parallel stripes. The equilibrium values of both the volume fraction of the normal phase and the domain size are calculated as functions of the magnetic field. A bubble-to-stripe transition is predicted to occur for a volume fraction of the normal phase about 0.3. Experimentally, normal-state domains are studied with the high-resolution magneto-optical imaging technique. The observed patterns consist in coexisting bubbles and disordered labyrinthine lamellae structures. We show evidence of the contribution of pinning on the position of domain interfaces. The average width of the lamellae is then analyzed as a function of the applied magnetic field and found to increase in good agreement with the predictions. In contrast, the average diameter of bubbles remains constant: it is almost independent of the magnetic interaction between domains. A very good agreement, over three decades of the magnetic Bond number, is found with the equilibrium diameter of an isolated bubble. The proposed constrained current-loop model is shown to provide significantly more accurate predictions than the current-loop model, in particular for small magnetic Bond numbers. Additionally, increasing the volume fraction of the normal phase results in a bubble-to-lamella transition, as predicted theoretically.