Understanding theH−Tphase diagram of the monoaxial helimagnet

Abstract

Some unexpected features of the phase diagram of the monoaxial helimagnet in presence of an applied magnetic field perpendicular to the chiral axis are theoretically predicted. A rather general Hamiltonian with long-range Heisenberg exchange and Dzyaloshinskii-Moriya interactions is considered. The continuum limit simplifies the free energy, which contains only a few parameters which in principle are determined by the many parameters of the Hamiltonian, although in practice they may be tuned to fit the experiments. The phase diagram contains a chiral soliton lattice phase and a forced ferromagnetic phase separated by a line of phase transitions, which are of second order at low T and of first order in the vicinity of the zero-field ordering temperature, and are separated by a tricritical point. A highly nonlinear chiral soliton lattice, in which many harmonics contribute appreciably to the spatial modulation of the local magnetic moment, develops only below the tricritical temperature, and in this case, the scaling shows a logarithmic behavior similar to that at T = 0, which is a universal feature of the chiral soliton lattice. Below the tricritical temperature, the normalized soliton density curves are found to be independent of T , in agreement with the experimental results of magnetorresistance curves, while above the tricritical temperature they show a noticeable temperature dependence. The implications in the interpretation of experimental results of CrNb 3 S 6 are discussed.

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

“…A theoretical analysis at zero temperature carried out long ago 16 concluded that by increasing the field the period of the CSL increases and, eventually, as the period diverges, a phase transition takes place continuously to a forced FM (FFM) state. This prediction has been recently confirmed experimentally 19,22 and theoretically by computations at finite temperature 14 . If, on the other hand, the applied field is parallel to the DM axis, the local magnetic moment acquires a constant component along the axis and a conical helix is formed.…”

“…The parameter q 0 has dimensions of inverse length and gives the propagation vector of the helical modulation at zero field. The remaining parameters are dimensionless: µ 2 controls the continuum limit and has to be large 14 ; and γ, α, and h are proportional to the single-ion anisotropy, temperature (T ) and external magnetic field ( H), respectively. Finally, ǫ 0 is an overall constant with the dimensions of energy per unit length.…”

“…The period L 0 is independent of T , but the local magnetic moment decreases with T , and the transition to the PM state takes place at the temperature where it vanishes. The nature of the transition at T 0 is not fully understood and considerable effort is being devoted to clarify this interesting question [9][10][11][12][13][14][15] . At temperatures lower than T 0 , application of a magnetic field perpendicular to the DM axis deforms the helix and a chiral soliton lattice (CSL) appears 6,7,[16][17][18] .…”

“…The mechanisms for these two kind of transitions are qualitatively different. In the monoaxial helimagnet, the transition between the CSL and the FFM states as a perpendicular magnetic field increases at sufficiently low temperature is of nucleation type 14,16 . On the other hand, at zero field mean field theory predicts an instability type continuous transition at the ordering temperature T 0 .…”

Chiral helimagnetic state in a Kondo lattice model with the Dzyaloshinskii–Moriya interaction

“…The CHM and CSL states were observed by using the Lorentz microscopy with a transmission electron microscope and the small-angle electron diffraction [13]. Theoretically, since the pioneering work by Dzyaloshinskii [1,14], the CHM and CSL states have been studied for decades, whereas the most of them were limited to localized spin systems by omitting the degree of freedom for itinerant electrons [15,16,17,18]. Recently, the authors studied this problem by explicitly taking into account the coupling to itinerant electrons [19].…”