Using muons – short-lived particles like heavy, positively charged electrons – as tiny compasses inside a material. Muons from a particle accelerator arrive with their all pointing the same way, stop inside the sample and turn in whatever magnetic field they find there. When each decays, about two millionths of a second later, it fires a positron mostly along its spin, so counting the positrons shows how the spins turned. That reveals very weak or magnetism, and the field patterns inside – in bulk crystals, not in single .
As the site uses it
For time-reversal-symmetry claims, note that muon spin relaxation, Kerr and magneto-optical probes have not converged.
Spin-polarised muons stop inside a crystal and turn in the local magnetic field. Each decays within microseconds, sending a positron mostly along its spin, so the counts in detectors around the sample trace an oscillation: its frequency gives the local field, its damping how much that field varies.
A compass that reports back
A muon is an unstable relative of the electron, about two hundred times heavier, that lives 2.2 microseconds. Accelerators produce beams of positive muons with their spins aligned; implanted in a solid, each stops at a site between the atoms, behaving rather like a light proton, and its spin precesses in the local magnetic field. When it decays it emits a positron preferentially along its spin, so detectors around the sample, counting positrons from millions of muons, trace how the spins turned and how fast their alignment was lost (Blundell, 1999).
The frequency of the precession gives the size of the local field; the loss of alignment, the relaxation, gives how much that field varies from site to site and how fast it fluctuates.
Weak magnetism and superconductors
Because a muon senses the field at a point inside the crystal, μSR detects magnetism that is very weak, disordered or short-ranged, and tells static order from fluctuating spins – which is why it is used on frustrated magnets and candidate . In a superconductor in a magnetic field, the muons sample the field of the lattice; the width of that field distribution gives the penetration depth, and with it the density of superconducting electrons and clues to the symmetry of the gap.
The muons must be stopped inside the material, so μSR measures bulk crystals, mosaics of crystals or powders – the parent compounds of rather than single flakes.
The kagome debate
In the KV3Sb5, muon spin relaxation found the internal field distribution broadening just below the charge- and staying broad into the superconducting state; the increase was six times larger in a field of 8 T than in zero field, and the local susceptibility seen by the muons rose sharply at the same temperature. The authors read this as that breaks (Mielke and colleagues, 2022).
Optics disagrees. Sagnac interferometers sensitive to of 30 nanoradians found no spontaneous Kerr effect below the charge order of CsV3Sb5 at 94 K, and the authors concluded that time-reversal symmetry is very unlikely to be broken there (Saykin and colleagues, 2023). The two studies used different members of the family, and which picture holds is one of the open questions about these metals.
For specialists
Implantation of spin-polarised positive muons, which stop at interstitial sites and precess in the local field, with the spin polarisation followed through the emission of decay positrons (lifetime 2.2 µs). Zero-field μSR detects static or slowly fluctuating , including very weak, disordered and short-range magnetism; transverse-field μSR measures the field distribution of a superconductor’s vortex lattice and hence the penetration depth. In KV3Sb5 the internal field width rises just below the charge-order temperature, read as charge order breaking time-reversal symmetry, while high-resolution Kerr measurements on CsV3Sb5 see no such signal – a disagreement still open.