Magnetic excitations are revealed in the parent compounds of intercalated ternary iron selenide superconductors with one-quarter Fe vacancies.

The newly discovered intercalated ternary iron selenide superconductors AyFexSe2 (A = K, Tl) show rich phase diagrams and many unusual physical properties that have not been found in other iron-based superconductors. These properties reveal the close relationship between unconventional superconductivity and antiferromagnetism and have triggered a surge of interest. In order to fully understand the magnetism in the compound AFe1.5Se2, in J. Phys.: Condens. Matter 25 036004 we have studied the magnetic excitations and spin dynamical structure factors.

The stable structures of AyFexSe2 contain Fe vacancies ordered in either a √5 × √5 or a 4 × 2 superstructure due to the balance required in chemical valences. The superstructures correspond to A0.8Fe1.6Se2 (√5 × √5, with one-fifth Fe vacancies) or AFe1.5Se2 (4 × 2, with one-quarter Fe vacancies). For AFe1.5Se2, the theoretical calculations predicted that its ground state is a 4 × 2 collinear antiferromagnetic semiconducting state with six spins per magnetic unit cell. These predictions have recently been confirmed and further shown to be the parent compound of superconductors AyFexSe2 by the neutron diffraction experiment.

To describe the magnetism in the compound AFe1.5Se2, an effective spin Heisenberg model was adopted. For a spin Heisenberg model with a long-range magnetic order in its ground state, the linearized spin wave theory with the Holstein-Primakoff transformation is a standard approach to obtain the spin wave excitations and other dynamical properties. However, for a complex magnetic order with more than two spins per unit cell, it is still a severely challenging task to analytically solve the spin wave excitations.

In J. Phys.: Condens. Matter 25 036004, rather than constructing a Bogoliubov transformation as conventionally, we illustrated an alternative method, which is able to analytically solve spin wave excitations for the cases of multi-spin unit cells. The method employs the equation of motion to construct a secular equation, i.e. an algebraic equation. An algebraic equation can be analytically solved up to the fourth power, which corresponds to an antiferromagnetic order with eight spins per unit cell. By using this method, we found that there is one acoustic branch (gapless Goldstone mode) and two gapful optical branches of spin wave excitations with each in double degeneracy (top figure) in AFe1.5Se2. The constant-energy cuts of the spin dynamical structure factor were calculated for different excitation energies, ranging from 20 meV to 120 meV (bottom figure). Through further computing the antiferromagnetic quantum fluctuation, the Fe spin was found to be S = 3/2.