Magnetic anisotropy and conical phase transition in monoaxial chiral magnets

Magnetic anisotropies in chiral spin systems can affect dramatically the allowed stable magnetic configurations. Using a Green's function approach, we examine the role of fluctuations in determining boundaries between allowed states in a monoaxial chiral magnet. The effects of uniaxial anisotropy are found to be most pronounced near the point separating the helicoidal, ferromagnetic, and paramagnetic phases. The cone state, which can appear when an external magnetic field is applied, is particularly strongly affected near the boundary with the paramagnetic phase. A metastable region is found, indicating the appearance of a fluctuation-induced phase transition. This metastable region arises from off-diagonal elements in the Green's functions, and can exist even without anisotropy.

Figure 1

Sketches of the three magnetic states: HM, FM, and conical. The top image describes the directions of spins $\left\{{\overrightarrow{\stackrel{̃}{S}}}_i\right\}$ in the original frame, which have the cone angle ${\theta }_0$ defined by the angle between ${\overrightarrow{\stackrel{̃}{S}}}_i$ and $z$ axis of the original frame. (a) The helicoidal (HM) state is described by ${\theta }_0=\pi /2$, (c) the ferromagnetic (FM) state by ${\theta }_0=0$, and (b) otherwise we call the state conical.

Figure 2

Left: Zero magnetic field phase diagram using (a) the mean field approximation and (b) the Green's function method. Fluctuations included in the Green's function method create a region near the HM-FM phase boundary where the HM and FM states have different energies and are either stable or metastable. The region is very narrow and cannot be discerned visually in this plot. Middle: Threshold field for a continuous transition using (c) the mean field approximation and (d) the Green's function method. The blue dashed lines correspond to the boundary shown in (a) and (b). In the Green's function method, there is a shaded region where multiple solutions exist. Right: Magnetic field dependence of the FM resonance frequency $E_Q$ and the cone angle ${\theta }_0$ for $K/J_{\parallel }=0.005$. (e) is for $T/J_{\parallel }=2.4$ outside the shaded region of (d), and (f) for 2.64 in the shaded region. In the top panel, there is always a single solution to the self-consistent equation for all values of the magnetic field. In the lower panel, there are two solutions for some magnetic field values. In experiment this would appear as a discontinuous change, or “gap.” We use $J_{\perp }/J_{\parallel }=1$ and $D/J_{\parallel }=0.1$ for (a)–(f).