Fig. 5: Anomalous long-distance spin transport in GGG.

a \(|{V}_{2\omega }|\) versus channel length d for normal and anomalous spin transport states. Anomalous GGG (marked as an-GGG): blue circles, \(B=3{{\rm{T}}}\), \({I}_{{in}}=200\, \mu {{\mathrm{A}}}\), T = 2 K; normal GGG (marked as n-GGG): purple triangles, \(B=3{{\rm{T}}}\), \({I}_{{in}}=100\, \mu {{\mathrm{A}}}\), T = 5 K; red squares, \(B=14{{\rm{T}}}\), \({I}_{{in}}=100\, \mu {{\mathrm{A}}}\), T = 2 K; MnPS₃: yellow triangles, \(B=4{{\rm{T}}}\), \({I}_{{in}}=100\, \mu {{\mathrm{A}}}\), T = 2 K. Every data point is extracted by a cosine fit from a magnetic field angle-dependent measurement, with error bar represented the standard error of fit. The yellow solid line is a fit to the 1D magnon diffusion model⁵ while other solid lines are fits to the 2D diffusion model due to larger sample thickness¹¹. b Comparison of our work and the reported maximum transport distances of thermal excited magnons in the literature^5,6,44,45, grouped in magnetically ordered region (blue part), and magnetically frustrated region (red part).