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The effects of $\bar\Lambda\bar\Lambda\omega$-tensor coupling on the spinsymmetry of $\bar{\Lambda}$ spectra in $\bar{\Lambda}$-nucleus systems havebeen studied with the relativistic mean-field theory. Taking$^{12}$C+$\bar{\Lambda}$ as an example, it is found that the tensor couplingenlarges the spin-orbit splittings of $\bar\Lambda$ by an order of magnitudealthough its effects on the wave functions of $\bar{\Lambda}$ are negligible.Similar conclusions has been observed in $\bar{\Lambda}$-nucleus of differentmass regions, including $^{16}$O+$\bar{\Lambda}$, $^{40}$Ca+$\bar{\Lambda}$ and$^{208}$Pb+$\bar{\Lambda}$. It indicates that the spin symmetry inanti-lambda-nucleus systems is still good irrespective of the tensor coupling.

Tensor coupling effects on spin symmetry in anti-Lambda spectrum of hypernuclei