  Exotic quantum phases in low dimensional frustrated quantum magnets emerge
due to strong quantum fluctuations and competing spin exchanges. Two legged
skewed spin ladders with periodically missing rung bonds and periodically
placed slanted rung bonds are particularly interesting from this stand point.
Here, we study ground state (gs) properties of a spin- 1/2 Heisenberg model on
3/4, 3/5 and 5/5 skewed ladders in the presence of an axial magnetic field, B,
using exact diagonalization and the density matrix renormalization group
method. We note the existence of plateaus at m = 1/3 and 2/3 for 3/4 skewed
ladder, at m = 1/4, 1/2, and 3/4 for 3/5 skewed ladder, and at m = 0, 1/3, and
2/3 for 5/5 skewed ladder. The plateau state is always a gapped state and it
depends on the gap in the system. Surprisingly, the 3/4 and 5/5 skewed ladders
show interesting quadrupolar or n-type spin nematic phases below the 1/3rd
plateau, i.e, at very low magnetic fields. These two systems are unique as they
host both a plateau and a quadrupolar phase at low magnetic fields. The linear
variation of pitch angle of the spin with magnetization and behavior of binding
energy of magnon pairs as function of magnetic field are also studied in both
the systems.
