Analysis on the stability of Josephson vortices at tricrystal boundaries: A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>3</mml:mn><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>∕</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>-flux case

We consider Josephson vortices at tricrystal boundaries. We discuss the specific case of a tricrystal boundary with a $\ensuremath{\pi}$ junction as one of the three arms. It is recently shown that the static system admits an $(n+1∕2){\ensuremath{\phi}}_{0}$ flux, $n=0,1,2$ [Phys. Rev. B 61, 9122 (2000)]. Here we present an analysis to calculate the linear stability of the admitted states. In particular, we calculate the stability of a $3{\ensuremath{\phi}}_{0}∕2$ flux. This state is of interest, since energetically this state is preferable for some combinations of Josephson lengths, but we show that in general it is linearly unstable. Finally, we propose a system that can have a stable $(n+1∕2){\ensuremath{\phi}}_{0}$ state.

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