Theory for Intrinsic Magnetic Field in Chiral Superconductor Measured by \muSR: Case of Sr_2RuO_4

Abstract

The local magnetic field induced by ${\mu }^{+}$ trapped at an interstitial site in a chiral superconductor with $p$-wave symmetry, such as Sr${}_2$RuO${}_4$, is discussed by solving the Bogoliubov-de Gennes equation on the two-dimensional square lattice. In the model Hamiltonian, the effect of the trapped ${\mu }^{+}$ extracting the electrons at surrounding Ru sites is phenomenologically taken into account as a non-magnetic impurity potential which locally destroys the chiral superconducting order with $p$-wave symmetry giving rise to local circulating current around ${\mu }^{+}$ site. It is shown that the size of the induced local magnetic field in the case with periodic boundary condition is far smaller compared to the case with open boundary condition without ${\mu }^{+}$, in which the surface current induced by destruction of superconducting order at the surface boundary gives contribution corresponding to the intrinsic angular momentum of the order of $\hslash N_{\mathrm{s}}/2$, with $N_{\mathrm{s}}$ being the number of superconducting electrons. This result qualitatively explains why the magnetic field $\simeq 0.5$G measured by $\mu$SR in Sr${}_2$RuO${}_4$ is far smaller than the expected intrinsic magnetic field $\simeq 50$G which is nearly the same as the lower critical field $H_{\mathrm{c}1}\simeq 50$G.

6 pages, 5 figures, submitted to J. Phys. Soc. Jpn

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