  In the standard model (SM), lepton flavor violating (LFV) Higgs decay is
absent at renormalizable level and thus it is a good probe to new physics. In
this article we study a type of new physics that could lead to large LFV Higgs
decay, i.e., a lepton-flavored dark matter (DM) model which is specified by a
Majorana DM and scalar lepton mediators. Different from other similar models
with similar setup, we introduce both left-handed and right-handed scalar
leptons. They allow large LFV Higgs decay and thus may explain the tentative
Br$(h\ra\tau\mu)\sim1\%$ experimental results from the LHC. In particular, we
find that the stringent bound from $\tau\ra\mu\gamma$ can be naturally evaded.
One reason, among others, is a large chirality violation in the mediator
sector. Aspects of relic density and especially radiative direct detection of
the leptonic DM are also investigated, stressing the difference from previous
lepton-flavored DM models.
