Magnetic structure and magnetization of helical antiferromagnets in high magnetic fields perpendicular to the helix axis at zero temperature

The zero-temperature angles of magnetic moments in a helix or sinusoidal fan confined to the xy plane, with respect to an in-plane magnetic field H-x applied perpendicular to the z axis of a helix or fan, are calculated for commensurate helices and fans with field-independent turn angles kd between moments in adjacent layers of the helix or fan using the classical J(0)-J(1)-J(2) Heisenberg model. For 0 < kd < 4 pi/9, first-order transitions from helix to a fan structure occur at fields H-t as previously inferred, where the fan is found to be approximately sinusoidal. However, for 4p/9 <= kd <= pi, different behaviors are found depending on the value of kd and these properties vary nonmonotonically with kd. In this kd range, the change from helix to fanlike structure is usually a crossover with no phase transition between them, although first-order transitions are found for kd = 3 pi/5 and 8 pi/11 and a second-order transition for kd = 3 pi/4. At a critical field H-c, the fan or fanlike structures exhibit a second-order transition to the paramagnetic state. The H-c for a helix undergoing a field-induced change to a fan or fanlike structure is found to be the same as for a sinusoidal fan with the same kd and interlayer interactions. Analytical expressions for H-c versus kd are presented. We also calculated the average x-axis moment per spin mu(xave) versus H-x for helices and fans with crossovers and phase transitions between them. When smooth helix to fanlike crossovers occur in the range 4p/9 <= kd <= pi, mu(xave) exhibits an S-shape behavior with increasing H-x. This predicted behavior is consistent with mu(xave)(H-x) data previously reported by Sangeetha et al. [Phys. Rev. B 94, 014422 (2016)] for single-crystal EuCo2P2 possessing a helix ground state with kd approximate to 0.85 pi. The low-field magnetic susceptibility and the ratio H-t/H-c are calculated analytically or numerically versus kd for helices, and are shown to approach the respective known limits for kd -> 0.