Magnetic spiral order in the square-lattice spin system (CuBr)Sr₂Nb₃O₁₀

Highlights

• Strongly frustrated $J_1-J_2-J_3$ Heisenberg model can be used to describe quasi-two-dimensional compounds with helicoidal spin order, when the Dzyaloshinsky-Moria interaction is inconsistent.

• We demonstrate that the magnetic and thermodynamic properties of the quasi-two-dimensional square-lattice compound (CuBr)Sr₂Nb₃O₁₀ can be interpreted within quantum $J_1-J_2-J_3$ Heisenberg model.

• This work will help researchers in theoretical describing a rich variety of experimental compounds with helicoidal spin order, where inversion symmetry is preserved.

Abstract

We address quantum spin helical states in the strongly frustrated Heisenberg model. Contrary to conventional Dzyaloshinskii–Moriya approach we show that such states appear without central symmetry breaking. As an example, we demonstrate that the magnetic and thermodynamic properties of the quasi-two-dimensional square-lattice compound (CuBr)Sr₂Nb₃O₁₀ can be interpreted within 2D $S=1∕2$ $J_1-J_2-J_3$ Heisenberg model. In this compound neutron experiment indicates helical spin order while central symmetry does hold.

Introduction

Helical (spiral) spin states constitute a topical and intriguing field of magnetism being the subject of intense research last years. Most of the investigations consider the helical state caused by the Dzyaloshinskii–Moriya interaction (DMI) [1], [2].

The DMI is widely used mechanism for theoretical description of neutron scattering experimental data for complex spin structures [3], [4], [5]. The DMI can induce helical or cycloidal magnetic structure with a determined chirality such as skyrmion with exotic thermodynamic properties [6], [7], [8]. In addition, the DMI plays a key role in the ground-state phase diagram of a spin-1 Heisenberg–Ising alternating chains and appearance of the Haldane phase in such systems [9].

It is however noteworthy that DMI approach presumes broken inversion symmetry. Basically, there exists alternative way to get helical states that does not require inversion symmetry breaking. It appears to be strongly frustrated Heisenberg model [10], [11], [12]. In particular, in two dimensions for the square lattice helices emerge when exchange interaction on three nearest coordination spheres are considered.

Hereinafter we address quasi-two-dimensional compound with stacked square lattice magnetic planes $\left(\mathrm{CuBr}\right){\mathrm{Sr}}_2{\mathrm{Nb}}_3{\mathrm{O}}_{10}$. Neutron scattering experiment [13], [14] indicates helical spin order in this substance, while DMI-based explanation is unacceptable (inversion symmetry is preserved). This dyad brings forth the assumption to describe the magnetic order via $J_1-J_2-J_3$ Heisenberg model [13], [14].

In the present communication we verify the mentioned assumption, we show that the experimental properties of the layered compound $\left(\mathrm{CuBr}\right){\mathrm{Sr}}_2{\mathrm{Nb}}_3{\mathrm{O}}_{10}$ [13], [14], [15] are well reproduced within the limits of quantum $S=1∕2J_1-J_2-J_3$ Heisenberg model on the square lattice.

Our consideration is strictly two-dimensional, hence at nonzero temperature long-range order is impossible due to Mermin–Wagner theorem. So we address spin-liquid state, in particular with helicoidal structure of short-range order. This approach leads to adequate description of both neutron scattering experiment and thermodynamic properties. At the very end we propose the possible way of experimental verification of the approach adequacy by the analysis of spin excitation spectrum.

The rest of the paper is organized as follows. In Section 2 we introduce the model and briefly discuss the adopted method. In Section 3 the theoretical conclusions are presented and discussed with respect to the neutron diffraction, susceptibility and specific heat experimental data for the square-lattice quasi-two-dimensional $\left(\mathrm{CuBr}\right){\mathrm{Sr}}_2{\mathrm{Nb}}_3{\mathrm{O}}_{10}$. To the end, in Section 4 the results obtained are summarized.