This is a description of the data contained in the included files:

*Fig 1*

NiI2.cif - NiI2 cif file

NiI2_muon.cif - muonated NiI2 cif file with all muon sites obtained for the rhombohedral phase (These sites are all used in the calculation of a simulated muSR spectrum as described in the text). Muons are labelled as hydrogen atoms, H:mu1 is the site used in Figure 1

NiI2_muon_field.dat - Dipole field distribution for single muon site

*Fig 2*

main.dat - panels (a) and (b) of Figure 2. Columns are as follows: Temperature, lambda_1, lambda_1 error, nu_1, nu_1 error

inset.dat - the inset (c) of Figure 2. Columns are as follows: Time, asymmetry, asymmetry error, fitted asymmetry

*Fig 3*

main.dat - panels (a) and (b) of Figure 3. Columns are as follows: Temperature, lambda_4, lambda_4 error, A_0, A_0 error

inset.dat - the TF baseline in the inset of Figure 3. Columns are as follows: Temperature, A_4, A_4 error

*SI*

SI_1.dat - Figure 1 of the SI. Columns are as follows: Temperature, A_6, A_6 error, A_7, A_7 error, lambda_7, lambda_7 error

SI_2_10K - 10 K panel of Figure 2 of the SI. Columns are as follows: Time, asymmetry, asymmetry error, fitted asymmetry

SI_2_60K - 60 K panel of Figure	2 of the SI. Columns are as follows: Time, asymmetry, asymmetry error, fitted asymmetry

