Proximity effects in conical-ferromagnet/superconductor bilayers
Proximity effects in conical-ferromagnet/superconductor bilayers
复制标题
锥形铁磁体/超导双层中的邻近效应
DOI：
10.1103/physrevb.86.184517
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发表时间：
2012
影响因子：
3.7
通讯作者：
Klaus Halterman
中科院分区：
文献类型：
--
作者：
Chien;O. Valls;Klaus Halterman
我们研究的各个方面的邻近效应在$F/S$（铁磁体/超导体）双层，其中$F$有一个螺旋磁纹理，如发现在钬，铒和其他材料，和$S$是一个传统的s波超导体。我们数值求解Bogoliubov-德Gennes（BdG）方程自洽和使用的解决方案来计算这些双层的邻近效应相关的数量。通过求解线性化的BdG方程，得到了超导转变温度T_c与磁性层厚度d_F之间的关系。我们发现$T_c（d_F）$曲线包含多重振荡。此外，该系统可能是重入不仅与$d_F$的情况下，当磁铁是均匀的，但与温度$T$：超导性消失在一定范围内的$d_F$或$T$。当d_F$大于锥形交换场的空间周期时，出现T$重入。从完整的BdG方程计算了凝聚自由能和熵，发现结果与线性化得到的T_c值一致。磁体的不均匀性使得所有奇数三重态配对分量都可能被感应。我们研究了它们的性质，发现与单重态振幅相比，$m=0$和$m=\pm 1$三重态分量都表现出长程穿透。对于纳米尺度的双层膜，也获得了两层的邻近长度。这些长度与$d_F$振荡，他们被发现是长期的两侧。这些结果与最近的实验结果是一致的。我们还计算了由三维局部磁化描述的反向邻近效应和局部DOS，这揭示了与邻近效应相关的重要能量分辨签名。
We study various aspects of proximity effects in $F/S$ (Ferromagnet/Superconductor) bilayers, where $F$ has a spiral magnetic texture such as that found in Holmium, Erbium and other materials, and $S$ is a conventional s-wave superconductor. We numerically solve the Bogoliubov-de Gennes (BdG) equations self-consistently and use the solutions to compute quantities relevant to the proximity effects in these bilayers. We obtain the relation between the superconducting transition temperature $T_c$ and the thicknesses $d_F$ of the magnetic layer by solving the linearized BdG equations. We find that the $T_c(d_F)$ curves include multiple oscillations. Moreover, the system may be reentrant not only with $d_F$, as is the case when the magnet is uniform, but with temperature $T$: the superconductivity disappears in certain ranges of $d_F$ or $T$. The $T$ reentrance occurs when $d_F$ is larger than the spatial period of the conical exchange field. We compute the condensation free energies and entropies from the full BdG equations and find the results are in agreement with $T_c$ values obtained by linearization. The inhomogeneous nature of the magnet makes it possible for all odd triplet pairing components to be induced. We have investigated their properties and found that, as compared to the singlet amplitude, both the $m=0$ and $m=\pm 1$ triplet components exhibit long range penetration. For nanoscale bilayers, the proximity lengths for both layers are also obtained. These lengths oscillate with $d_F$ and they are found to be long range on both sides. These results are shown to be consistent with recent experiments. We also calculate the reverse proximity effect described by the three dimensional local magnetization, and the local DOS, which reveals important energy resolved signatures associated with the proximity effects.