Interplay of Anisotropy, Dzyaloshinskii Moriya Interaction and Symmetry breaking Fields in a 2D XY Ferromagnet

Abstract

A two dimensional ferromagnetic XY model with its bound vortex-antivortex dominated quasi long range ordered phase at low temperatures is a long standing as well as well studied problem of interest in the field of condensed matter. We conduct a detailed Monte Carlo study of such model with rather unexplored extensions where additional anisotropic exchange coupling and Dzyaloshinskii-Moriya interactions (DMI) together affect the Kosterlitz-Thoulass (KT) transition in presence/absence of symmetry breaking fields. Without DMI, the exchange term promotes collinear (ferromagnetic) order, whereas the DMI term induces spin cantings. By tuning anisotropy upto Ising limit, we document energy, specific-heat, magnetizations as well as helicity modulus and vortex densities for different tempeatures and DMI strength. We also compute the 2nd moment of correlation lengths in order to probe the spatial correlation of the spins. Furthermore, the effect of U(1) symmetry breaking 4-fold and 8-fold symmetric h4 and h8 fields are explored which shows how the double-peaked specific heat profiles changes in presence of DMI. Overall, our findings append many important updates in the low temperature phases of a topological XY ferromagnet when additional DMI and isotropy-breaking exchange and/or field terms are considered and thus providing a practical blueprint for suitably engineering topological spin systems.

Figures (8)

• Figure 1: (Color online)(a) Specific heat $C_V$ annd (b) spin stiffness $\rho_S$ as a function of inverse temperature $J\beta$ for different lattice sizes. The intersecting line in (b) corresponds to $\rho_S=\frac{2}{\pi}T$.
• Figure 2: (Color online)(a) Specific heat $C_V$, (b) Energy per spin $<E>/N$ and (c) spin stiffness $\rho_S$ vs inverse temperature $J\beta$ for various $\Gamma$'s.
• Figure 3: (Color online)Specific heat $C_V$ as a function of inverse temperature $J\beta$ for different DMI strength $d=0.2,1.0,1.4$ in the 2D isotropic XY ferromagnet. Inset shows Phase Diagram for QLRO-DO phase.
• Figure 4: (Color online)Variations of typical spin configurations in terms of $\partial_x\theta$ for $(d,~\Gamma)~=$ (0,0) at (a) $T=0.2$, (b) $5.6$ (in units of $J/k_B$) respectively while typical spin configurations $(\theta)$ at $T=0.2$ for $(d,~\Gamma)~=$ (c) (1,0) and (d) (0,0.4) respectively.
• Figure 5: (Color online)(a) Specific heat $C_V$ as a function of inverse temperature $J\beta$ for $d=1.0$ and different $\Gamma$. (b), (c) Phase diagrams based on $C_V$ peak positions for $d = 0$ and 1 respectively.