Publication:
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Input data and extracted results for arXiv pre-print 2405.10675,
Non-relativistic ferromagnetotriakontadipolar order and spin splitting in hematite
X. H. Verbeek, D. Voderholzer, S. Schären, Y. Gachnang, N. A. Spaldin, S. Bhowal
https://doi.org/10.48550/arXiv.2405.10675

Abstract:
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We show that hematite, $\alpha$-Fe$_2$O$_3$, below its Morin transition, has a ferroic ordering of rank-5 magnetic triakontadipoles on the Fe ions. In the absence of spin-orbit coupling, these are the lowest-order ferroically aligned magnetic multipoles, and they give rise to the $g$-wave non-relativistic spin splitting in hematite. We find that the ferroically ordered magnetic triakontadipoles result from the simultaneous antiferroic ordering of the charge hexadecapoles and the magnetic dipoles, providing a route to manipulating the magnitude and the sign of the magnetic triakontadipoles as well as the spin splitting. Furthermore, we find that both the ferroic ordering of the magnetic triakontadipoles and many of the spin-split features persist in the weak ferromagnetic phase above the Morin transition temperature.  
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Description of uploaded tar.gz archive:
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The archive contains the data needed to run the DFT calculations in VASP described in the paper. The necessary input files are given in each, as well as some of the OUTPUT files (OUTCAR, OSZICAR, DOSCAR). For multipole calculations, there is an additional output file called TENSMOM.R1.OUT, which contains the multipole elements obtained from the density matrix. Each multipole element is labeled using the w^kpr_t formalism described in the paper. 

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- Clarification of the folder structure of VASP calculations: 
               -The first layer contains three folders labeled with the Fe2O3 phase: low temperature, high temperature, or the artificial high symmetry structure described in the paper. 
               -Then, under each of these are the 2 choices for Hubbard U and J (U 5.5, J 0.5  or U 1.0, J 0.5)
               -The layer beneath contains the different domains: domain_1(AFM ordering +--+), domain_2(AFM ordering -++-), and with_Cr2O3_ordering(+-+-) for the low-temperature phase, just domain 1 for the artificial high symmetry phase, and constrained_canting_AFMy, constrained_canting_AFMy_FMx for the high-temperature phase 
               -Subsequently, there are the folders labeling the different constrained multipoles. They are labeled by shift_### or col_shift, where ### = (change in charge hexadecapole in units of |e|)/2 e.g. -02 means a change in magnitude of -0.4 |e| in the magnitude of the charge hexadecapole. The relevant charge hexadecapoles are w^404_3 for the low-temperature phase and w^404_3 for the artificial high-symmetry structure, as described in the paper.
               -Finally, there are 2 folders, one called 'relaxation', which contains in and output files for an electronic relaxation, and one called 'bandstructure_###', which contains a bandstructure calculation, with ### indicating the path in reciprocal space.

- Code versions: We used VASP 5.4.4