Pseudo-Goldstone magnons in the frustrated S=3/2 Heisenberg helimagnet ZnCr2Se4 with a pyrochlore magnetic sublattice

TL;DR

This study investigates low-energy magnetic excitations in the frustrated S=3/2 Heisenberg helimagnet ZnCr2Se4, revealing pseudo-Goldstone magnons with small energy gaps, supported by neutron spectroscopy and theoretical calculations.

Contribution

It uncovers the existence of pseudo-Goldstone magnons with finite gaps in a cubic spinel helimagnet, highlighting their universal presence and implications for studying magnon interactions.

Findings

Identification of soft helimagnon modes with ~0.17 meV gap

Observation of pseudo-Goldstone magnons emerging from orthogonal wave vectors

Support for the universality of these excitations in symmetric helimagnets

Abstract

Low-energy spin excitations in any long-range ordered magnetic system in the absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating from the ordering wave vectors. In helimagnets, these modes hybridize into the so-called helimagnon excitations. Here we employ neutron spectroscopy supported by theoretical calculations to investigate the magnetic excitation spectrum of the isotropic Heisenberg helimagnet ZnCr2Se4 with a cubic spinel structure, in which spin-3/2 magnetic Cr3+ ions are arranged in a geometrically frustrated pyrochlore sublattice. Apart from the conventional Goldstone mode emanating from the (0 0 q) ordering vector, low-energy magnetic excitations in the single-domain proper-screw spiral phase show soft helimagnon modes with a small energy gap of ~0.17 meV, emerging from two orthogonal wave vectors (q 0 0) and (0 q 0) where no magnetic Bragg peaks are present. We term them pseudo-Goldstone magnons, as they appear gapless within linear spin-wave theory and only acquire a finite gap due to higher-order quantum-fluctuation corrections. Our results are likely universal for a broad class of symmetric helimagnets, opening up a new way of studying weak magnon-magnon interactions with accessible spectroscopic methods.

Figures

Tables

Table 1. Table 1.:  Ratios of the exchange constants in different chromium spinels after Ref.  7 , taken for a moderate effective Coulomb repulsion U = 2 𝑈 2 U=2  eV. For each compound, its experimentally measured ground state is also given: antiferromagnetic (AFM), ferromagnetic (FM), or proper-screw spin spiral. The bottom row shows experimental values for ZnCr 2 Se 4 estimated from our INS data in Section II.B of this work .

Compound	$J_2/\left|J_1\right|$	$J_3/\left|J_1\right|$	$J_4/\left|J_1\right|$	ground state	Refs.
HgCr2O4	0.1714	0.471	0	AFM	Matsuda et al. (2007)
ZnCr2S4	0.0395	0.198	–0.014	$\left(00q\right)$ spiral	Yokaichiya et al. (2009)
CdCr2S4	0.0065	0.116	–0.015	FM	Menyuk et al. (1966)
HgCr2S4	0.0222	0.111	–0.013	$\left(00q\right)$ spiral	Hastings and Corliss (1968); Tsurkan et al. (2006)
ZnCr2Se4	0.0102	0.169	–0.018	$\left(00q\right)$ spiral	Plumier (1966); Cameron et al. (2016)
CdCr2Se4	–0.0071	0.101	–0.013	FM	Menyuk et al. (1966)
HgCr2Se4	–0.0014	0.109	–0.013	FM	Wojtowicz (1969)
Experimental values:
ZnCr2Se4	0.0118	0.170	–0.014	[this work]

Equations

$$H=\sum _{ij}{J}_{ij}{\mathbf{S}}_i\cdot {\mathbf{S}}_j,\text{vspace}-4pt$$

$$H=\frac{1}{4}\sum _{i=1}^4\sum _{n=1}^4\sum _{j=1}^{z_n}{J}_n{\mathbf{S}}_i\cdot {\mathbf{S}}_j,$$

$$J_1+J_2+4J_4+4(J_2+2J_3)\cos (\gamma )+6J_4\cos (2\gamma )=0.$$

$$J_1$$

$$J_3^{\prime }$$

$$H=J_1\sum _{⟨i,j⟩}{\mathbf{S}}_i{\mathbf{S}}_j+J_2\sum _{⟨⟨i,j⟩⟩}{\mathbf{S}}_i{\mathbf{S}}_j+J_4\sum _{⟨⟨⟨⟨i,j⟩⟩⟩⟩}{\mathbf{S}}_i{\mathbf{S}}_j,$$

$${\tilde{\omega }}_{\mathbf{q}}+\mathrm{i}{}_{\mathbf{q}}={}_{\mathbf{q}}+{}_{\mathbf{q}}^{(4)}+{}_{11}(\omega ,\mathbf{q}).$$

Full text

magnetic frustration, spin waves, helimagnets, spinels, pyrochlore lattice, Heisenberg model, neutron scattering

I Introduction

I.1 Classical Heisenberg model on the pyrochlore lattice

The Heisenberg model on the pyrochlore lattice attracts a lot of interest as various spin models on this lattice give rise to the simplest three-dimensional frustrated spin systems. Even for classical spins, this model hosts a wide range of different ground states. Considering only the antiferromagnetic nearest-neighbor (NN) interactions results in a classical spin liquid Moessner and Chalker (1998), exhibiting no long-range magnetic order down to zero temperature. This is explained by strong geometric frustration that leads to a highly degenerate classical ground state. However, inclusion of further-neighbor interactions relieves this frustration and stabilizes various ordered ground states, among them ferromagnetism, single- or multi-$\mathbf{q}$ spin spirals, nematic order, and other exotic phases Reimers et al. (1991); Lapa and Henley ; Takata et al. ; Okubo et al. (2011); Conlon and Chalker (2010).

Chromium spinels provide great opportunities to investigate magnetic interactions between classical spins on the structurally ideal pyrochlore lattice. These compounds have the general formula $A$Cr${}_{\text{2}}X_{\text{4}}$, where $A$ and $X$ are non-magnetic ions and Cr${}^{\text{3+}}$ is the magnetic cation in the $3d^{3}$ configuration Yaresko (2008). Its magnetic sublattice has the pyrochlore structure with spins $S=3/2$ at the Cr sites. Using the classical Heisenberg model,

[TABLE]

is justified by the negligibly small magneto-crystalline anisotropy Siratori (1971); Zhang et al. (2016); Aoyama and Kawamura (2016). Thus we consider throughout the paper $J_{ij}\equiv J_{n}$ if sites $i$ and $j$ are $n^{\rm th}$ neighbors [see Fig. I.1 (a)]. Depending on the chemical composition, chromium spinels exhibit different mechanisms of frustration, such as geometric frustration that occurs if dominant NN interactions are antiferromagnetic, or bond frustration which originates from competition between ferromagnetic NN and antiferromagnetic further-neighbor exchange.

To estimate the range and relative strengths of coupling constants $J_{n}$ in chromium spinels, Yaresko Yaresko (2008) performed ab initio calculations to extract exchange parameters up to the fourth nearest neighbor for various compounds of this family. Calculations showed that the NN interaction $J_{1}$ changes gradually from antiferromagnetic in some oxides to ferromagnetic in sulfides and selenides, while the next-nearest-neighbor (NNN) interaction $J_{2}$ is noticeably weaker than the antiferromagnetic $J_{3}$ exchange parameter (see Table I.2). For the HgCr2O4 system, $J_{1}$ can be even weaker than $J_{2}$ (or comparable, depending on the effective Coulomb repulsion $U$), so that the third-nearest-neighbor interaction $J_{3}$ may become dominant. Therefore, the existing theoretical phase diagram restricted to only NN and NNN interactions Lapa and Henley appears insufficient for a realistic description of these materials. The importance of the two $3^{\text{rd}}$-nearest-neighbor exchange paths on the pyrochlore lattice has been also emphasized for the spin-$\frac{1}{2}$ molybdate Heisenberg antiferromagnet Lu2Mo2O5N2 Clark et al. (2014), where $J_{3}^{\prime}$ and $J_{3}^{\prime\prime}$ have opposite signs and dominate over $J_{2}$. It was recently conjectured that this may lead to an unusual “gearwheel” type of a quantum spin liquid Iqbal et al. .