Interplay of Magnetic and Superconducting Proximity Effects in Ferromagnet-Superconductor-Ferromagnet Trilayers

Abstract

We present theoretical results on the interplay of magnetic and superconducting orders in diffusive ferromagnet-superconductor-ferromagnet trilayers. The induced triplet superconducting correlations throughout the trilayer lead to an induced spin magnetization. We include self-consistency of the order parameter in the superconducting layer at arbitrary temperatures, arbitrary interface transparency, and any relative orientation of the exchange fields in the two ferromagnets. We propose to use the torque on the trilayer in an external magnetic field as a probe of the presence of triplet correlations in the superconducting phase.The importance of triplet pairing correlations in the interface region between a singlet superconductor and a ferromagnet recently became the focus of research in the field of spintronics [1,2,3,4]. In contrast to clean triplet p-wave superconductors and superfluids, for diffusive materials p-wave correlations are suppressed and triplet correlations have s-wave orbital symmetry, but are odd in frequency [1]. In the case of a homogeneous magnetization of the ferromagnet, the spin projection of the triplet correlations on the quantization axis of the exchange field is zero. If, on the other hand, the distribution of the exchange field in the ferromagnet is inhomogeneous in space, then under suitable conditions [5] also triplet correlations with non-zero spin projection (equal spin pairs) are induced [1,2,3]. Triplet pairing correlations induce in turn a spin magnetization both in the ferromagnet and in the superconductor [6,7].An important question is how to experimentally find good fingerprints of the triplet superconducting correlations. Theoretical work has been focused on calculations of T c [5,8,9], the local density of states (LDOS) [4, 10, 11], or to search for unconventional Josephson couplings [3,12]. Experimentally, no smoking gun has been found although recently magnetization changes were observed through neutron reflectometry on multilayers of YBa 2 Cu 3 O 7 and La 2/3 Ca 1/3 MnO 3 [13]. Various other properties of FS heterostructures that could be influenced by triplet superconducting correlations have been measured, as for example a negative Josephson coupling (π junctions) [14], and LDOS modulations [15].In the following we present results for the induced triplet correlations and corresponding changes of the magnetization in a ferromagnet-superconductorferromagnet (FSF) trilayer with arbitrary misalignment of the exchange fields in the two F layers. We put forward signatures of triplet correlations that can be measured experimentally.The FSF trilayer we consider is sketched in Fig. 1. We denote the layer thicknesses by d F 1 , d S , and d F 2 respectively. The x-axis is directed perpendicular to the layer interfaces with the origin at the center of the superconductor. The z-axis is aligned with the exchange field J 1 in the left ferromagnet. The angle between the exchange fields J 1 and J 2 is denoted θ J . We also assume translational invariance in the y-z-plane.We use the qu...

Observation of Anomalous Meissner Screening in Cu/Nb and Cu/Nb/Co Thin Films

“…[21]) with J z the exchange field directed along the z-axis and ω n the Matsubara frequencies defined by ω n = πk B T (2n + 1) with k B the Boltzmann constant, n integer and the maximum allowed frequency given by the Debye frequency. Furthermore, σ i and τ i are the Pauli matrices of the spin space and Nambu space respectively.…”

Theoretical Study of Magnetism Induced by Proximity Effect in a Ferromagnetic Josephson Junction with a Normal Metal

“…Within the quasiclassical Green's function theory, the magnetization M y(z) (d, θ) (θ : superconducting phase difference between S1 and S2) induced inside the N is given by 25,62) M…”

“…[59][60][61] As well as the detection of STC by measuring the Josephson critical current and T C as mentioned above, the spin-dependent transport of STC in S/F hybrid junctions gives a direct evidence of spin in the STC . 22,29,[62][63][64][65][66][67][68] One of the simplest quantity induced by the spin of the STC is a magnetization induced by the proximity effect of STC . 22,29,62,65,67) In F/S junctions, the STC is also induced to S by the inverse proximity effect.…”

“…22,29,[62][63][64][65][66][67][68] One of the simplest quantity induced by the spin of the STC is a magnetization induced by the proximity effect of STC . 22,29,62,65,67) In F/S junctions, the STC is also induced to S by the inverse proximity effect. [69][70][71][72][73] The magnetization induced by spin of STC is a good fingerprint to establish the existence of STC.…”

“…22,62,63) To detect the magnetization induced by the STC, recently, a rather complex ferromagnetic Green's function theory. Assuming that the magnetization in F 2 is fixed along the z direction perpendicular to the junction direction (x direction), we show that i) the x component of the magnetization in the N is always zero, ii) the y component becomes exactly zero when the magnetizations in F 1 and F 2 are collinear, and iii) the z component is generally finite for any magnetization alignment between F 1 and F 2.…”