Spiral spin-liquid and the emergence of a vortex-like state in MnSc${}_2$S${}_4$

Abstract

Spirals and helices are common motifs of long-range order in magnetic solids, and they may also be organized into more complex emergent structures such as magnetic skyrmions and vortices. A new type of spiral state, the spiral spin-liquid, in which spins fluctuate collectively as spirals, has recently been predicted to exist. Here, using neutron scattering techniques, we experimentally prove the existence of a spiral spin-liquid in MnSc${}_2$S${}_4$ by directly observing the 'spiral surface' - a continuous surface of spiral propagation vectors in reciprocal space. We elucidate the multi-step ordering behavior of the spiral spin-liquid, and discover a vortex-like triple-q phase on application of a magnetic field. Our results prove the effectiveness of the $J_1$-$J_2$ Hamiltonian on the diamond lattice as a model for the spiral spin-liquid state in MnSc${}_2$S${}_4$, and also demonstrate a new way to realize a magnetic vortex lattice.

10 pages, 11 figures

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• Evolution of Magnetic and Orbital Properties in the Magnetically-Diluted A-Site Spinel Cu${}_{1-x}$Zn${}_x$Rh${}_2$O${}_4$
• Realising square and diamond lattice $S=1/2$ Heisenberg antiferromagnet models in the $\alpha$ and $\beta$ phases of the coordination framework, KTi(C${}_2$O${}_4$)${}_2\cdot$\textit{x}H${}_2$O
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