  We present studies of thermal entanglement of a three-spin system in
triangular symmetry. Spin correlations are described within an effective
Heisenberg Hamiltonian, derived from the Hubbard Hamiltonian, with
super-exchange couplings modulated by an effective electric field. Additionally
a homogenous magnetic field is applied to completely break the degeneracy of
the system. We show that entanglement is generated in the subspace of doublet
states with different pairwise spin correlations for the ground and excited
states. At low temperatures thermal mixing between the doublets with the same
spin destroys entanglement, however one can observe its restoration at higher
temperatures due to the mixing of the states with an opposite spin orientation
or with quadruplets (unentangled states) always destroys entanglement. Pairwise
entanglement is quantified using concurrence for which analytical formulae are
derived in various thermal mixing scenarios. The electric field plays a
specific role -- it breaks the symmetry of the system and changes spin
correlations. Rotating the electric field can create maximally entangled qubit
pairs together with a separate spin (monogamy) that survives in a relatively
wide temperature range providing robust pairwise entanglement generation at
elevated temperatures.
