We present theoretical results for Josephson spin current through Tomonaga Luttinger liquid (TLL), where a magnetic field violates spin-charge separation. Phase dependence of spin current is calculated using functional bosonization procedure. In the presence of electron-electron interactions in TLL, the effect of Zeeman splitting is found to become relevant in Josephson effect. We show that finite Josephson spin currents can flow due to the spin-imbalance effect induced by interactions especially at low temperatures.
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