Influence of longitudinal spin fluctuations on the phase transition features in chiral magnets

Using the classical Monte Carlo calculations, we investigate the effects of longitudinal spin fluctuations on the helimagnetic transition in a Heisenberg magnet with the Dzyaloshinskii-Moriya interaction. We use variable spin amplitudes in the framework of the spin-lattice Hamiltonian. It is this kind of fluctuations that naturally occur in an itinerant system. We show that the basic features of the helical phase transition are not changed much by the longitudinal spin fluctuations though the transition temperature $T_c$ and the fluctuation hump seen in specific heat at $T>T_c$ is significantly affected. We report thermodynamic and structural effects of these fluctuations. By increasing the system size in the Monte Carlo modeling, we are able to reproduce the ring shape scattering intensity above the helimagnetic transition temperature $T_c$, which transforms into the spiral spots seen below $T_c$ in the neutron scattering experiments.

Figure 1

Temperature dependence of the specific heat $C\left(T\right)$ for different values of the DM interaction $D=0.4$ (a), 0.75 (b), and 1.1 (c) and spin amplitude fluctuation $dS$. (Inset) The corresponding dependencies of the magnetic susceptibility $\chi \left(T\right)$.

Figure 2

(a) Specific heat obtained by differentiation of energy (curve 1) and from the fluctuation of energy (curve 2). (b) The specific heat for different system sizes, $L=30$ (curves with markers) and $L=60$ (presented by thick curves 1, 2, and 3 in limited temperature intervals).

Figure 3

[(a) and (b)] Energy distribution function $P\left(E\right)$ at $T_c$ for different values of $D$ and $dS$. Curves 1 and 2 in (a) correspond to the two different MC updates used for generation of new spin configurations.

Figure 4

Spin configuration $\langle {\mathbf{S}}_i\rangle$ in an $xy$ plane (left) and a profile $I^{*}$ of the Bragg intensity projected onto the $(q_x,q_y)$ plane (right) for $dS=0.0,D=1.1$ (a), and $D=0.75$ (b). Spins with positive $S_z$ are marked as red and negative $S_z$ as blue.

Figure 5

Spin configuration $\langle {\mathbf{S}}_i\rangle$ and projected Bragg intensity profile $I^{*}$ for $dS=1.0,D=1.1$ (a) and $D=0.75$ (b). Designations are the same as in Fig. 4.

Figure 6

Spin configuration $\langle {\mathbf{S}}_i\rangle$ in an $xy$ plane (left) and cuts of Bragg intensity $I\left(\mathbf{q}\right)$ by planes $q_x=0$ (upper right) and $q_z=0$ (lower right) for $D=1.1,dS=0.0$.

Figure 7

The same as in Fig. 6 for $dS=1.0$.