Phenomenological theory of magnetic 90$^{\circ}$ helical state

Abstract

We explore a phenomenological phase diagram for the magnetic helical state with 90 • turn angle between neighboring spins in external magnetic field. Such state is formed by the Eu spin layers in the superconducting iron arsenide RbEuFe4As4. The peculiarity of this spin configuration is that it is not realized in the standard Heisenberg model with biliniear exchange interactions. A minimum model allowing for such state requires the biquadratic nearest-neighbor interaction term. In addition, in tetragonal materials the 90 • helix state may be stabilized by the in-plane four-fold anisotropy term, which also fixes helix orientation with respect to crystal lattice. A key feature characterizing the behavior in the magnetic field is the metamagnetic transition to the double-periodic state with the moment angles (α, α, −α, −α) with respect to the field for the four subsequent spins. The transition field to this state from the deformed helix is determined by the strength of biquadratic interaction. When this interaction is weak the double-periodic state occupies a wide field range. The transition is second order for small biquadratic coupling and becomes first order when this coupling exceeds the critical value. In addition, when the magnetic field is applied along one of four the equilibrium moment directions, the deformed helix state experience the first-order rotation transition at the field determined by the four-fold anisotropy.