The complexity of electronic band structures in quantum materials offers new charge-neutral degrees of freedom stable for transport, a promising example being the valley (axial) degree of freedom in Weyl semimetals (WSMs). A noninvasive probe of their transport properties is possible by exploiting the frequency dependence of the magnetic noise generated in the vicinity of the material. In this Letter, we investigate the magnetic noise generically associated with diffusive transport using a systematic Langevin approach. Taking a minimal model of magnetic WSMs for demonstration, we show that thermal fluctuations of the charge current, the valley current, and the magnetic order can give rise to magnetic noise with distinctively different spectral characters, which provide a theoretical guidance to separate their contributions. Our approach is extendable to the study of magnetic noise and its spectral features arising from other transport degrees of freedom in quantum materials.

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• Fluctuations & noise
• NV centers
• Spin diffusion
• Spintronics
• Valleytronics
• Weyl semimetal
• Langevin equation