Publication:
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Input data and extracted results and evaluation scripts for arXiv pre-print 2303.00513,
Hidden Orders and (Anti-)Magnetoelectric Effects in Cr2O3 and α-Fe2O3
Xanthe H. Verbeek, Andrea Urru, Nicola A. Spaldin
https://doi.org/10.48550/arXiv.2303.00513
Abstract:
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We present ab initio calculations of hidden magnetoelectric multipolar order in Cr2O3 and its iron-based analogue, α-Fe2O3. First, we discuss the connection between the order of such hidden multipoles and the linear magnetoelectric effect. Next, we show the presence of hidden antiferroically-ordered magnetoelectric multipoles in both the prototypical magnetoelectric material Cr2O3, and centrosymmetric α-Fe2O3, which has the same crystal structure as Cr2O3, but a different magnetic dipolar ordering. In turn, we predict anti-magnetoelectric effects, in which local magnetic dipole moments are induced in opposite directions under the application of an external electric field, to create an additional antiferromagnetic ordering. We confirm the predicted induced moments using first-principles calculations. Our results demonstrate the existence of hidden magnetoelectric multipoles leading to local linear magnetoelectric responses even in centrosymmetric materials, where a net bulk linear magnetoelectric effect is forbidden by symmetry.
Description of uploaded tar.gz archive:
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The archive contains the data needed to run the DFT calculations described in the paper, mainly as VASP and Elk input files. To prevent multiple copies of the same file, the structure is as follows. An input file is located in the folder where it should be copied to all subdirectories. For example, the directory called 'Elk_calculations' contains a file called 'O.in', which is the one that was used for all ELK calculations. Similarly, 'VASP_calculations/Born_effective_charges' contains a file called 'KPOINTS', which was used for all calculatiions of the Born effective charges
- VASP calculations: Input and relevant output data to relax the structure, calculate the Born effective charges and determine the eigenvectors of the force constant matrix and their energies, the latter using VASP and phonopy. .hdf5 files containing the eigenvectors we were interested in and their corresponding energies, labelled by their symmetry and ascending in energy. Note that the calculation of the Born effective charges and eigenvectors of the force constant matrix were done with a different unit cell rotation and the results were rotated back in post processing.
- ELK calculations: Input and relevant output data to calculate the magnetoelectric multipoles and the magnetic canting induced by atomic displacements corresponding to different electric field strengths. .hdf5 files contain the fitted parameters for the (off-)diagonal linear and quadratic magnetoelectric responses.
- Clarification of the folder structure. The first layer contains two folders labels with the two DFT codes used, i.e VASP and ELK. Then, under each of these are the main types of calculations that were done in these code, for the VASP calculations these are:
- Structural_relaxation : contains two folders labeled with the two compounds (Cr2O3 and Fe2O3) containing the relevant input and output for relaxing the crystal structure for the given parameters
- Born_effective_charges: contains two folders labeled with the two compounds (Cr2O3 and Fe2O3), each of these contain several folders label Disp_### with ### the magnitude and sign of the displacement in angstrom. Each Disp_### folder contains 30 folders labeled Element_number_direction, for example Fe_1_x which indicates which atoms, i.e. the first Fe atom (order follows POSCAR) and in which carthesian direction it was displaced. As there are 10 atoms in each unit cell and 3 cartesian directions there are 30 folders. The magnitude of the displacement can be read from the parent folder (i.e. Disp_###). The Element_number_direction folders each contain the relevant POSCAR with the displacement and the OUTCAR where the calculated polarisation can be read. From the polarisation as a function of atomic displacement the Born effective charges can be constructed.
- Phonon_calculation: contains two folders labeled with the two compounds (Cr2O3 and Fe2O3), each of these contain the five POSCARS generated by phonopy with the command 'phonopy -d --dim="1 1 1" ', called POSCAR-00n with n = (1,2,3,4,5) and folders labelled pos_n, which contain the tar.gz zipped vasprun.xml files from an electronic relaxation where the forces were calculated for these POSCARS. These POSCARS contain specific diplacement phonopy needs to calculate the force constant matrix. The compound folders also contain a file called FORCE_SETS generated by running 'phonopy -f *vasprun.xml'. Finally there is a folder called Getting_eigenvectors_force_constant_matrix which contains the FORCE_SETS an adapted POSCAR (with all the atoms said to H), a band.conf file and band.yaml files genrated with different POSCARS. the band.yaml files were generated using 'phonopy bands.conf -p -s --dim="1 1 1"'. band_CrO.yaml and band_FeO.yaml were generated with the orginal POSCAR files of Cr2O3 and Fe2O3 and the generated phonons are the eigenvectors of the dynamical matrix (real phonons). band_Cr.yaml and band_Fe.yaml were generated with the POSCAR files adapted to have all the atoms be either Cr or Fe. This means that the generated dynamical matrix is the same as the force constant matrix (up to a constant). Similarly, band_H.yaml were generated with the POSCAR files adapted to have all the atoms be H. The phonons generated this way are not 'true' phonons, they are the eigenvectors of the force constant matrix. Finally there are .hdf5 files containing the eigenvectors we were interested in and their corresponding energies, labelled by their symmetry and ascending in energy. The energies are corrected for the mass (such that they are true eigenvalues of the force constant matrix)
For the ELK calculations the subfolders are:
- Multipoles : contains two folders labeled with the two compounds (Cr2O3 and Fe2O3) containing the relevant input and output (TMDFTUNU.OUT) for calculating the multipoles.
- Magnetic_canting: contains two folders labeled with the two compounds (Cr2O3 and Fe2O3) each containing a folder called Simulating_E_polarized_along_y which containing folders E_VperA_###, so labeled by the magnitude of the electric field E that is simulated (in Volt per Anstrom). The atomic displacement corresponding to each electric field strength are determined from the eigenevectors of the force constant matrix, their corresponding energies and the Born effective charges as explained in the paper. Each of the folders E_VperA_### conatins the elk.in file with the displacement and the main elk output file INFO.out, from which the canting of the magnetic moments can be read.
- Code versions: We used VASP 5.4.4, phonopy 1.10.4, elk 8.4.21 for the canted magnetic moment calculations and a modified elk 3.3.17 for the multipole calculations