This repository contains data from "Energy-gap driven low-temperature magnetic and transport properties in Cr1/3MS2 (M = Nb, Ta)", and the associated Supplemental Material.
The data is grouped by Figure and includes the data plotted in the figure, and, where possible, the raw data used to generate it. An explanation of each dataset is provided.
In addition to these data, raw data measured at ISIS Neutron and Muon Source can be obtained from the following DOI:
    - https://doi.org/10.5286/ISIS.E.RB2010327

If there are issues with this repository, or to get in touch about the paper, please email tom.lancaster@durham.ac.uk.


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***** Main paper *****
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*** Figure 1 ***

This figure shows the density of states from Density Functional Theory (DFT) calculations of Cr1/3NbS2 and Cr1/3TaS2.

Files provided:
    - CrNbS.pdos.[atom].[orbital].dat: The contribution to the density of states of Cr1/3NbS2 shown in Fig. 1(a), separated by atomic species ([atom]), and atomic orbitals ([orbital]). Columns are labelled.
    - CrTaS.pdos.[atom].[orbital].dat: As CrNbS.pdos.[atom].[orbital].dat, but for Cr1/3TaS2, Fig. 1(b).
    - [material].param: Some example CASTEP param files which could be used to recreate our analysis in new calculations. One file per material ([CrNbS] = Cr1/3NbS2, [CrTaS] = Cr1/3TaS2).


*** Figure 2 ***

This figure shows some of the experimentally measurable quantities calculated from the DFT calculations.

Files provided:
    - CrNbS_SvsT.dat: The calculated Seebeck coefficient of Cr1/3NbS2 plotted as a solid line in Fig. 2(a). Columns are labelled.
    - CrNbS_SvsT_scaled.dat: As above, but scaled to generate the dashed line in Fig. 2(a).
    - CrTaS_SvsT: The calculated Seebeck coefficient of Cr1/3TaS2 plotted in Fig. 2(b). Columns are labelled, where the offset on the Fermi Energy is indicated.
    - CrNbS_integrate_[atom]_[orbital].dat: The contribution to the magnetic moment of Cr1/3NbS2 shown in Fig. 2(c), separated by atomic species ([atom]), and atomic orbitals ([orbital]). For the "Total" line, all files are added. In each file, the first column is the temperature, and the second is the magnetic moment.
    - CrTaS_integrate_[atom]_[orbital].dat: As above, but for Cr1/3TaS2. These data are plotted in Fig. 2(d).
    - CrNbS_muonfield.txt: The calculated field at the muon site in Cr1/3NbS2, shown by a black line in Fig. 2(e). Columns are labelled.
    - CrNbS_Cr_muonfield.txt: The calculated field at the muon site in Cr1/3NbS2 when considering the moment on Cr atoms only, as shown by a red line in Fig. 2(e). Columns are labelled.
    - CrTaS_muonfield.txt: As CrNbS_muonfield.txt, but for Cr1/3TaS2. Plotted as a black line in Fig. 2(f).
    - CrTaS_Cr_muonfield.txt: As CrNbS_Cr_muonfield.txt, but for Cr1/3TaS2. Plotted as a red line in Fig. 2(f).
    
Notes:
    - The experimental data in Fig. 2(a) is taken from Ghimire et al., Phys. Rev. B 87, 104403 (2013).
    - In Figs. 2(c-d) the data has been plotted such that it passes through the origin. This was achieved by subtracting the 1 K magnetic moment from the data in the included files.
    - The experimental data in Fig. 2(e) is taken from Braam et al., Phys. Rev. B 91, 144407 (2015).
    - The marked offsets in Fig. 2(e-f) have not been applied to the data files provided (which represent the direct experimental output). To reproduce the figure exactly, these offsets would need to be performed by way of a simple subtraction of the indicated amount.


*** Figure 3 ***

This figure shows experimentally measured ac suscpetibility results for Cr1/3NbS2 and Cr1/3TaS2.

Files provided:
    - CrNbS_[freq]Hz.txt: The plotted phase offsets for Cr1/3NbS2 shown in Fig. 3(a). One file per frequency ([freq]). Columns are labelled.
    - CrTaS_[freq]Hz.txt: As above, but for Cr1/3TaS2, Fig. 3(b).
    - CrNbS_arrhenius.txt: The data for the Arrhenius plot in Fig. 3(c). Columns are labelled.
    - CrTaS_arrhenius.txt: As above, but for Cr1/3TaS2, Fig. 3(d).
    
Notes:
    - The red lines in Figs. 3(c-d) are straight line fits and are detailed in the text. There is no accompanying data.


*** Figure 4 ***

This figure shows muon-spin spectrscopy (muSR) results.

Files provided:
    - 15K_20Oe.dat: The data and fit shown in the inset of Fig. 4(a). Columns are labelled.
    - 20Oe_A0.dat: The initial assymetry shown in Fig. 2(a). Columns are labelled.
    - [field]Oe_fits.dat: The fitted parameters shown in Figs. 4(b-d). One file per applied field ([field]). Columns are labelled.
    - 20K_20Oe.dat: The data and fit shown in the inset of Fig. 4(e). Columns are labelled.
    - TF[field]Oe.dat: The fitted parameters shown in Figs. 4(e-f). One file per applied field ([field]). Columns are labelled.

Notes:
    - The solid line in Fig. 4(c) is a guide to the eye and has no associated data.


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***** Supplemental Material *****
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*** Figure S1 ***

This figure shows the bandstructures from DFT calculations of Cr1/3NbS2 and Cr1/3TaS2.

Files provided:
    - [material].bands: The CASTEP output .bands file which can be used to generate the bandstructures shown in Fig. S1. One file per material ([CrNbS] = Cr1/3NbS2, [CrTaS] = Cr1/3TaS2).


*** Figure S2 ***

This figure shows the Hall coefficient calculated from from DFT calculations of Cr1/3NbS2 and Cr1/3TaS2.

Files provided:
    - [material]_Hall.dat: The data plotted in Fig. S2. One file per material ([CrNbS] = Cr1/3NbS2, [CrTaS] = Cr1/3TaS2). Columns are labelled.


*** Figure S3 ***

This figure shows the electron orbitals from DFT calculations of Cr1/3NbS2 and Cr1/3TaS2. The files needed to generate these plots are too large to easily store, but can be generated from calculations based off those set up by the .param files include in Fig. 1.


*** Figure S4 ***

This figure shows the Fermi surfaces from DFT calculations of Cr1/3NbS2 and Cr1/3TaS2. The output can be generated by combining the below files with the .bands file provided as part of Fig. S1.

Files provided:
    - [material]-out.cell: The CASTEP output .cell file, giving the geometry of the crystal. One file per material ([CrNbS] = Cr1/3NbS2, [CrTaS] = Cr1/3TaS2).


*** Figure S5 ***

This figure shows the bandstructures from DFT calculations of Cr1/3NbS2 and Cr1/3TaS2.

Files provided:
    - [material].dos.dat: The density of states in the absence of spin-orbit coupling, as plotted in Fig. S5. One file per material ([CrNbS] = Cr1/3NbS2, [CrTaS] = Cr1/3TaS2).
    - [material].soc.dat: The density of states with the inclusion of spin-orbit coupling, as plotted in Fig. S5. One file per material ([CrNbS] = Cr1/3NbS2, [CrTaS] = Cr1/3TaS2).
    - [material].bands: The CASTEP output .bands file from calculations without spin-orbit coupling, which can be used to generate the bandstructures shown in Fig. S5. One file per material ([CrNbS] = Cr1/3NbS2, [CrTaS] = Cr1/3TaS2).
    - [material]_SOC.bands: The CASTEP output .bands file from calculations with spin-orbit coupling, which can be used to generate the bandstructures shown in Fig. S5. One file per material ([CrNbS] = Cr1/3NbS2, [CrTaS] = Cr1/3TaS2).


*** Figure S6 ***

This figure shows the calculated muon-stopping site, as discussed in the paper. There is no associated data.


*** Figure S7 ***

This figure shows magnetisation and ac suscpetibility measurements of Cr1/3NbS2 and Cr1/3TaS2 as a function of temperature.

Files provided:
    - CrNbS_[field]Oe.dc.ndat: The magnetisation of Cr1/3NbS2 plotted in Fig. S7(a). One file per field ([field]). The columns are labelled.
    - CrNbS_ac_[field]Oe_79Hz.dat: The ac suscpetibility data of Cr1/3NbS2 plotted in Fig. S7(b-c). One file per field ([field]). The columns are Temperature, chi', chi''.
    - CrTaS_[field]Oe.dc.dat: As CrNbS_[field]Oe.dc.ndat, but for Cr1/3TaS2, Fig. S7(d).
    - CrTaS_ac_[field]Oe_79Hz.dat: As CrNbS_ac_[field]Oe_79Hz.dat, but for Cr1/3TaS2, Fig. S7(e-f).

Notes:
    - Data in the presented figure has been normalised, taking into account the sample mass.


*** Figure S8 ***

This figure shows magnetisation and ac suscpetibility measurements of Cr1/3NbS2 and Cr1/3TaS2 as function of applied field.

Files provided:
    - CrNbS_[temp]K.dc.ndat: The magnetisation of Cr1/3NbS2 plotted in Fig. S8(a). One file per temperature ([temp]). The columns are labelled.
    - CrNbS_ac_[temp]K_79Hz.dat: The ac suscpetibility data of Cr1/3NbS2 plotted in Fig. S8(b-c). One file per temperature ([temp]). The columns are Field, chi', chi''.
    - CrTaS_[temp]K.dc.dat: As CrNbS_[temp]K.dc.ndat, but for Cr1/3TaS2, Fig. S8(d).
    - CrTaS_ac_[temp]K_79Hz.dat: As CrNbS_ac_[temp]K_79Hz.dat, but for Cr1/3TaS2, Fig. S8(e-f).

Notes:
    - Data in the presented figure has been normalised, taking into account the sample mass.


*** Figure S9 ***

The figure shows the proposed magnetic phase diagrams of Cr1/3NbS2 and Cr1/3TaS2, as well as cartoons of the mangetic states. The figures are illustrative, hence there is no associated data.


*** Figure S10 ***

This figure shows example longitudinal field (LF) muSR measurements of Cr1/3NbS2 and Cr1/3TaS2, and their associated fits.

Files provided:
    - CrNbS_[temp]K_20Oe.dat: The data and fits shown for Cr1/3NbS2 in Fig. S10(a). One file per temperature ([temp]). Columns are labelled.
    - CrTaS_[temp]K_15Oe.dat: As CrNbS_[temp]K_20Oe.dat, but for Cr1/3TaS2, Fig. S10(b).


*** Figure S11 ***

This figure provides additional fitting parameters for LF muSR measurements of Cr1/3NbS2. These parameters are in the files provided for Figure 4.


*** Figure S12 ***

This figure provides additional fitting parameters for LF muSR measurements of Cr1/3NbS2.

Files provided:
    - 100Oe_fits.dat: The fitted parameters shown in Fig. S12. Columns are labelled.


*** Figure S13 ***

This figure provides fitting parameters for TF muSR measurements of Cr1/3TaS2.

Files provided:
    - 15Oe.txt: The fitted parameters shown in Fig. S13. Columns are labelled.


*** Figure S14 ***

This figure provides additional fitting parameters for TF muSR measurements of Cr1/3TaS2. These parameters are in the files provided for Figure 4.