Influence of pair breaking effects on the long-range odd triplet superconductivity in a ferromagnet/superconductor bilayer

Thanasit  Rachataruangsit; Suthat  Yoksan

Authors

Thanasit Rachataruangsit Physics Department, Faculty of Science, Burapha University, Chonburi 20131
Suthat Yoksan Physics Department, Faculty of Science, Srinakharinwirot University, Bangkok 10110

Keywords:

odd triplet superconductivity, ferromagnetism, proximity effect, transition temperature, impurity scattering, spin-orbit scattering

Abstract

The spin-dependent potential together with magnetic impurity and the spin-orbit scatterings were incorporated into the de Gennes-Takahashi-Tachiki theory of a diffusive superconductor-and-ferromagnetic metal to derive a formulation of the odd triplet superconductivity proximity effect. It is found that when the spin exchange interaction is inhomogeneous, i.e., the Neel spiral magnetic order, a new type of triplet condensate is generated, due to the broken time-reversal invariance. The triplet amplitude still contains the s-wave state, similar to the conventional singlet pairing, but the frequency symmetry must be odd to obey the Pauli's exclusion principle. As a result, the self-consistent order parameter contains only the singlet pair amplitude. The superconducting critical temperature of the bilayer is obtained in the single mode approximation and takes the form of the Abrikosov-Gorkov formula. The necessary condition for the occurrence of the induced long-range triplet component in the ferromagnet layer is characterized by the modulation of the pair amplitudes in the transverse direction. The possibility of the cryptoferromagnetic state, corresponding to the finite value of the spiral wave vector, is demonstrated in favor of the superconductivity. In addition, the influence of the magnetic impurity and the spin-orbit scattering is to decrease the decay length and to increase the oscillation period of the pair amplitudes which in turn enhances the critical temperature but in a less pronounced non-monotonicity manner.

References

Abrikosov, A.A., & Gorkov, L.P. (1961). Contribution to the theory of superconducting alloys with paramagnetic impurities. Sov. Phys. JETP, 12(6), 1243-1253.

Auvil, P.R., Ketterson, J.B., & Song, S.N. (1989). Generalized de Gennes-Takahashi-Tachiki proximity effect theory. J. Low. Temp. Phys, 74(1/2), 103-117.

Baladie, I., Buzdin, A.I., Ryzhanova, N., & Vedyayev, A.V. (2001). Interplay of superconductivity and magnetism in superconductor/ferromagnet structures. Phys. Rev. B, 63, 054518.

Baladie, I., & Buzdin, A.I. (2003). Thermodynamic properties of ferromagnet/superconductor/ferromagnet nanostructures. Phys. Rev. B, 67, 014523.

Berezinskii, V.L. (1974). New model of the anisotropic phase of superfluid He3. JETP Lett., 20(9), 287-289.

Buzdin, A.I., Vedyayev, A.V., & Ryzhanova, N.V. (1999). Spin orientation dependent superconductivity in S/F/S structures. Europhys. Lett., 48(6), 686-691.

Barsic, P.H., Valls, O.T., & Halterman, K. (2007). Thermodynamic and phase diagrams of layerd superconductor/ferromagnet nanostructures. Phys. Rev. B, 75, 104502.

Champel, T., & Eschrig, M. (2005). Effect of an inhomogeneous exchange field on the proximity effect in disordered superconductor-ferromagnet hybrid structures. Phys. Rev. B, 72, 054523.

de Gennes, P.G. (1966). Superconductivity of Metals and Alloys, New York, USA: Benjamin.

Faure, M., Buzdin, A.I., & Gusakova, D. (2007). On the theory of ferromagnet/ superconductor heterostructures. Physica C, 454, 61-69.

Halterman, K., & Valls, O.T. (2005). Nanoscale ferromagnet-superconductor-ferromagnet switches controlled by magnetization orientation. Phys. Rev. B, 72, 060514(R).

Jiang, J.S., Davidovic, D., Reich, D.H., & Chein, C.L. (1995). Oscillatory superconducting transition temperature in Nb/Gd multilayers. Phys. Rev. Lett., 74(2), 314-317.

Jiang, J.S., Davidovic, D., Reich, D.H., & Chein, C.L. (1996). Superconducting transition in Nb/Gd/Nb trilayers. Phys. Rev. B, 54(9), 6119-6121.

Krunavakarn, B., Sritrakool, W., & Yoksan, S. (2004). Nonmonotonic critical temperature in ferromagnet/ superconductor/ferromagnet trilayers. Physica C, 406, 46-52.

Krunavakarn, B., & Yoksan, S. (2006). Upper critical fields of ferromagnet/ superconductor layered structures. Physica C, 440, 25-34.

Kuboya, K., & Takanaka, K. (1998). Upper critical field and transition temperature of superconducting/ferromagnetic superlattices. Phys. Rev. B, 57(10), 6022-6028.

Obi, Y., Ikebe, M., & Fujishiro, H. (2005). Evidence for zero-and pi-phase order parameters of superconducting Nb/Co tri-and pentalayers from the oscillatory behavior of the transition temperature. Phys. Rev. Lett., 94, 057008.

Proshin, Y.N., Zimin, A., Fazleev, N.G., & Khusainov, M.G. (2006). Hierarchy of critical temperatures in four-layered ferromagnet/superconductor nanostructures and control devices. Phys. Rev. B, 73, 184514.

Radovic, Z., Ledvij, M., Dobrosavljevic-Grujic, L., Shelukhin, V., Tsukernik, A., Karpovski, M., Blum, Y., Efetov, K.B., Volkov, A.F., Champel, T., Eschrig, M., Lofwander, T., Schon, G., & Palevski, A. (2006). Observation of periodic pi-phase shifts in ferromagnet-superconductor multilayers. Phys. Rev. B, 73, 174506.

Tagirov, L.R. (1999). Low-field superconducting spin switch based on a superconductor/ ferromagnet multilayers. Phys. Rev. Lett, 83(10), 2058-2061.

Takahashi, S., & Tachiki, M. (1986). Theory of the upper critical field of superconducting superlattices. Phys. Rev. B, 33(7), 4620-4631.

Usadel, K.D. (1970). Generalized diffusion equation for superconducting alloys. Phys. Rev. Lett., 25(8), 507-509.

You, C.-Y., Bazaliy, Ya.B., Gu, J.Y., Oh, S.-J., Litvak, L.M., & Bader, S.D. (2004).Magnetization-orientation dependence of the superconducting transition temperature calculated for F/S/F trilayer structures. Phys. Rev. B, 70, 014505.