Dimensional change of quadrupole orders in pseudospin-$\frac{1}{2}$ pyrochlore magnets under [111] field

Abstract

We have studied long range orders of electric quadrupole moments described by an effective pseudospin-$\frac{1}{2}$ Hamiltonian representing pyrochlore magnets with non-Kramers ions under [111] magnetic field, in relevance to Tb${}_2$Ti${}_2$O${}_7$. Order parameters and phase transitions of this frustrated system are investigated using classical Monte-Carlo simulations. In zero field, the model undergoes a first-order phase transition from a paramagnetic state to an ordered state with an antiparallel arrangement of pseudospins. This pseudospin order is characterized by the wavevector $\mathbf{k}=0$ and is selected by an energetic or an order-by-disorder mechanism from degenerate $\mathbf{k}=(h,h,h)$ mean-field orders. Under [111] magnetic field this three-dimensional quadrupole order is transformed to a quasi two-dimensional quadrupole order on each kagomé lattice separated by field-induced ferromagnetic triangular lattices. We discuss implication of the simulation results with respect to experimental data of Tb${}_2$Ti${}_2$O${}_7$.

11 pages, 10 figures; Fig. 1 and Eqs. (A1), (A2), (A3) are corrected (v3)