Incommensurate-commensurate transitions in the monoaxial chiral helimagnet driven by the magnetic field

Abstract

The zero-temperature phase diagram of the monoaxial chiral helimagnet in the magnetic-field plane formed by the components parallel and perpendicular to the helical axis is thoroughly analyzed. The nature of the transition to the commensurate state depends on the angle between the field and the helical axis. For field directions close to the directions parallel or perpendicular to the helical axis the transition is continuous, while for intermediate angles the transition is discontinuous and the incommensurate and commensurate states coexist on the transition line. The continuous and discontinuous transition lines are separated by two tricritical points with specific singular behavior. The location of the continuous and discontinuous lines and of the tricritical points depend strongly on the easy-plane anisotropy, the effect of which is analyzed. For high anisotropy the conical approximation locates the transition line very accurately, although it does not predict the continuous transitions and the tricritical behavior. It is shown that for high anisotropy, as in CrNb 3 S 6 , the form of the transition line is universal, that is, independent of the sample, and obeys a simple equation. The position of the tricritical points, which is not universal, is theoretically estimated for a sample of CrNb 3 S 6 .

Stability of skyrmion textures and the role of thermal fluctuations in cubic helimagnets: A new intermediate phase at low temperature

“…[9], by the thermal fluctuations, analogously to what happens in the CH case. The conical helicoid has always higher free energy, at tree as well as at 1-loop level, than the CH.…”

“…If the propagation direction is alonĝ z and the magnetic field has components alongx andẑ, the conical helicoid is described by two functions, θ (z) and ψ(z), that were obtained in Refs. [9,11,12]. It is characterized by two parameters, the angle α and the period L. The CH is recovered in the α → 0 limit, while in the limiting case of h z = 0 we have θ = 0 and cos(ψ/2) = sn( √ h x q 0 z/κ), where sn(x) is the Jacobian elliptic function and κ is the ellipticity modulus [13].…”

“…The next two sections are devoted to describe the model and the saddle point expansion used to solve it. Then, the stability and the free energy including thermal fluctuations at Gaussian level are analyzed for the four known stationary points: the FM state, the conical helix (CH), the conical helicoid [9], and the SKL, which is treated in the circular cell approximation [5]. To conclude, the resulting phase diagram is analyzed and a brief discussion of the results is given.…”

Nucleation, instability, and discontinuous phase transitions in monoaxial helimagnets with oblique fields

“…2, respectively. The value γ = 2.58 has been chosen so that the critical parallel field of CrNb 3 S 6 at relatively low T is reproduced 24 . Let us discuss first the general case with non vanishing anisotropy.…”

“…Recently, the zero temperature phase diagram of the monoaxial helimagnet has been theoretically analized for oblique magnetic fields 24 , which are neither perpendicular nor parallel to the DM axis. It has been found that in the thermodynamic space formed by the parallel and perpendicular components of the magnetic field two separated continuous transition lines appear.…”