In studies of quantum materials, Muon Spin Relaxation (MuSR) measurements can provide important information complementary to neutron scattering studies in the following aspects:
(1) Different time windows: MuSR has a sensitivity to the spin fluctuation rate ranging between 106 to 1011 [/sec], covering regions with slower fluctuations (lower energy transfers) than neutrons.
Examples: dilute alloy spin glasses , NiGa2S4 , MnSi “partial order” 
(2) MuSR can detect a very small static magnetic moment, of the size of nuclear dipolar moments even in highly disordered / random spin configurations.
Examples: time reversal symmetry breaking in Sr2RuO4 , UPt3 ; details of spin glasses 
(3) Neutron scattering Bragg peak intensity is proportional to the ordered moment S squared multiplied by the ordered volume fraction VM. MuSR can provide independent information on the local ordered moment size and VM. This feature helps detection of phase separation and first order magnetic transitions.
Examples: Mott transition systems V2O3, RENiO3 ; MnSi tuned by hydrostatic pressure ; Phase boundaries between parent AFM and SC states in unconventional superconductors 
(4) Absence of static magnetic order can be confirmed with much better accuracy by MuSR as compared to neutron scattering. MuSR’s sensitivity to slow spin fluctuations helps this.
Examples: Quantum spin liquids [8,9]; low dimensional spin systems , frustrated magnets
(5) The magnetic field penetration depth of superconductors can be determined by MuSR. The energy scales inferred from the superfluid density from MuSR can be combined with the energy scales of the magnetic resonance mode from neutron scattering
Examples: High-Tc cuprate, FeAs, heavy-fermion superconductors 
(6) MuSR can be applied to thin films with the thickness of 200 Angstroms or more, as will be discussed in a presentation of Prokscha in this meeting.
(7) MuSR can provide essential information even with polycrystalline or powder samples. The amount of specimens required is about 100 mg, which is significantly less than in neutron scattering.
Examples: Organic conductors [12,13], C60 systems 
When an unknown magnetic material is synthesized, it would be most sensible to perform MuSR first, followed by more detailed studies of spin structures and spin excitations by neutron scattering. In this presentation, I would like to point out significant merits of performing MuSR and neutron scattering on the same materials and compare and combine their results. Having the both capabilities at the same facility would lead to quite productive studies of novel magnetic / superconducting quantum systems
 Y.J. Uemura et al., Phys. Rev. B31, 546-563 (1985).
 Y. Nambu et al., PRL 115, 127202 (2015)
 Y.J. Uemura et al., Nature Physics 3 (2007) 29-35.
 G.M. Luke et al., Nature 394 (1998) 558 - 561.
 G.M. Luke et al., Phys. Rev. Lett. 71, 1466-1469 (1993).
 B.A. Frandsen et al., Nature Communications, 7 (2016) 12519.
 Y.J. Uemura, Nature Materials 8 (2009) 253-255 and references therein.
 Y.J. Uemura et al., Phys. Rev. Lett. 73, 3306-3309 (1994).
 P. Mendels et al., Phys. Rev. Lett. 98, 077204 (2002)
 K. Kojima et al., Phys. Rev. Lett. 78, 1787-1790 (1997).
 Y.J. Uemura, Phys. Rev. Materials 3 (2019) 104801, and references therein.
 L.P. Le et al., Phys. Rev. B48, 7284-7296 (1993).
 F.L. Pratt et al., Nature 471, 612-616 (2011).
 Y. Takabayashi and K. Prassides, Philos. Trans. R. Soc. A374, 20150320 (2016), and references therein.