Crystallographic anisotropy and distortions in helicoidal magnetic structure
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SORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
Crystallographic Anisotropy and Distortions in Helicoidal Magnetic Structure E. V. Rosenfeld Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620041 Russia email: [email protected] Received July 28, 2009
Abstract—The appearance and development of aperiodic distortions in a helicoidal, layered magnetic struc ture with increasing crystallographic magnetic anisotropy in the magnetization rotation plane have been the oretically studied. A simple phase diagram for this system is proposed. It is established that, at a weak anisot ropy, the spiral splits into regions of various lengths with an approximately uniform rotation of the magneti zation in each region and a deviation from uniformity at the boundaries; the stronger the anisotropy, the shorter the regions and the greater the deviations. In the limit of high anisotropy, the minimum energy of the system corresponds (depending on the ratio of interlayer exchange integrals J1 and J2) to either a spiral with constant angular pitch (a multiple of the angle between easy axes) or a double antiferromagnetic structure with a fourlayer period. In the case of sixthorder anisotropy with J 1 = –J2, the energies of phases with dif ferent periods (four and six layers for J1 > 0; four and three layers for J1 < 0) coincide and the excess boundary energy vanishes. In the case of a fourth and secondorder anisotropy, the analogous anomalies appear at J 1 = –2J2. As a result, the magnetic structure at these points becomes unstable and the phase diagram exhibits the corresponding singularities. DOI: 10.1134/S1063776110090141
1. INTRODUCTION This investigation is devoted to distortions that appear and develop in a helicoidal layered magnetic structure in response to an increase in crystallographic anisotropy in the magnetization rotation plane. This problem was studied extensively in a continuum approximation for about 25 years after the appearance of an original work by Dzyaloshinskii [1]. For an exhaustive review of these investigations, which were related mostly to an analysis of the Ginzburg–Landau functionals of various types, see, e.g., [2] and the ref erences therein. The present study makes an allow ance from the very beginning for the discrete character of a layered magnetic structure and traces variation of the magnetization rotation angle Φ on the passage from one layer to another (i.e., at a step equal to the spiral pitch) in the cases of both low and high anisot ropy. Special attention is devoted to an analysis of the properties of a double antiferromagnetic structure with a fourlayer period, which coincides with a 1/4 phase according to the ANNNI model [3] and is related to two curious effects. First, a hexagonal crystal with this structure features magnetic scattering (e.g., of neutrons) with a wave vector of q = 1/4. Second, this structure makes the degeneracy of the ground state and the appearance of a domain structure in the spiral both possible, which can be of intere
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