## Calculation details

#### Crystal Structure Information

The structural information for the database were taken from the Crystallography Open Database (COD) [1,2,3]. The COD provides standardized cif-files which were transformed into capable input files for the Vienna ab-initio Simulation Package (VASP) by applying the Pymatgen package [3].

#### OMDB standard PBE electronic structure dataset

The electronic structure calculations are performed in the framework of the density functional theory, using a projector augmented wave method [4,5] as implemented in the Vienna Ab-initio Simulation Package - VASP. The exchange-correlation functional is approximated by the generalized gradient approximation according to Perdew, Burke and Ernzerhof [6]. The precision flag is set to "normal" and therefore the energy cut-off is given by the maximum of the specified maxima within the POTCAR files. For example, for carbon, this value is given by 400 eV. To properly describe the influence of transition metal elements, the calculations are performed spin polarized. The provided structural information are kept and no further relaxation is considered. For the integration in $$\vec{k}$$-space, a $$6\times6\times6$$ $$\Gamma$$-centred Monkhorst-Pack [7] is chosen for the self-consistent cycle. The $$\vec{k}$$-path for the band structure calculations is automatically generated by the Pymatgen package.

Please find more details in the paper 10.1371/journal.pone.0171501.

#### OMDB Magnetic Structure Dataset

In order to formulate spin Hamiltonians we have used the full-potential lin-ear muffin-tin method (FP-LMTO) software RSPt [8] to calculate Heisenberg exchange parameters. Heisenberg exchange interactions are calculated from Green functions for a reference spin structure,e.g.a ferromagnetic or collinear antiferromagnetic ordering, by means of the Liechtenstein-Katsnelson-Antropov-Gubanov (LKAG) formalism [9]. The calculations were performed using the local density approximation (LDA) for the exchange-correlation potential. The charge density and the potential inside the muffin-tin spheres are represented using an angular momentum decomposition up to lmax= 8. One energy set is used for the valence electrons. For the description of the states in the interstitial region three kinetic energy tails are used: -0.3, -2.3, and -1.5 Ryd. For the measurement of the dynamic structure factor, atomistic-spin dynamics simulations were run using the UppASD software [10], at T= 1K using a time step dt= 5·10−16s and a small Gilbert damping α= 0.0001. The correlation function was measured using a sampling step of tsamp= 5·10−15s, over a moving sampling window of twin= 5·10−11s. The corresponding frequency range for the dynamic structure factors is ω/(2π) = [0.02,0.04,...,200] THz (0.0827 meV to 827 meV)

Please find more details in the paper arXiv:1907.01817.

### References

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2. S. Gražulis, D. Chateigner, R. T. Downs, A. F. T. Yokochi, M. Quirós, L. Lutterotti, E. Manakova, J. Butkus, P. Moeck, and A. Le Bail, Journal of Applied Crystallography 42, 726 (2009).
3. S. P. Ong, W. D. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. L. Chevrier, K. A. Persson, and G. Ceder, Computational Materials Science 68, 314 (2013).
4. P. E. Blöchl, Physical Review B 50, 17953 (1994).
5. G. Kresse and D. Joubert, Physical Review B 59, 1758 (1999).
6. J. P. Perdew, K. Burke, and M. Ernzerhof, Physical Review Letters 77, 3865 (1996).
7. H. J. Monkhorst and J. D. Pack, Physical Review B 13, 5188 (1976).
8. J. M. Wills, O. Eriksson, P. Andersson, A. Delin, O. Grechnyev, and M. Alouani, Full-Potential Electronic Structure Method, Springer Series in Solid-State Sciences, Vol. 167 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2010)
9. A. Liechtenstein, M. Katsnelson, V. Antropov, andV. Gubanov, Journal of Magnetism and Magnetic Materials 67, 65 (1987)
10. “Uppsala Atomistic Spin Dynamics (UppASD) code. Available under GNU General Public license.” https://physics.uu.se/uppasd/ and https://github.com/UppASD/UppASD/.