Calculating the Magnetic Anisotropy of Rare-Earth–Transition-Metal Ferrimagnets

Abstract

Magnetocrystalline anisotropy, the microscopic origin of permanent magnetism, is often explained in terms of ferromagnets. However, the best performing permanent magnets based on rare earths and transition metals (RE-TM) are in fact ferrimagnets, consisting of a number of magnetic sublattices. Here we show how a naive calculation of the magnetocrystalline anisotropy of the classic RE-TM ferrimagnet GdCo_{5} gives numbers that are too large at 0 K and exhibit the wrong temperature dependence. We solve this problem by introducing a first-principles approach to calculate temperature-dependent magnetization versus field (FPMVB) curves, mirroring the experiments actually used to determine the anisotropy. We pair our calculations with measurements on a recently grown single crystal of GdCo_{5}, and find excellent agreement. The FPMVB approach demonstrates a new level of sophistication in the use of first-principles calculations to understand RE-TM magnets.

Temperature-dependent magnetocrystalline anisotropy of rare earth/transition metal permanent magnets from first principles: The light RCo5 (R=Y, La-Gd) intermetallics

“…Comparing in more detail, we find agreement between experimental and calculated κ values to within a few MJm −3 for all but the lowest temperatures, where the classical statistical mechanics of DFT-DLM calculations leads to inaccuracies [37], and high temperatures, where experimentally the compounds might undergo decomposition [27]. We calculate κ 1 at room temperature for SmCo 5 to be 21.…”

“…The disordered local moment (DLM) picture accounts for this disorder within DFT [21] and, combined with the LSIC has been used successfully to calculate magnetizations, Curie temperatures and phase dia- grams of itinerant electron and RE-based magnets [22][23][24]. DFT-DLM studies of the MCA have also been performed on itinerant electron and Gd-based magnets [25][26][27], but it is important to realise that these materials are special cases, where there is no contribution to the MCA from 4f electrons interacting with their local environment (the crystal field). A first-principles, finite temperature theory which accounts for these crystal field effects (and is therefore applicable to general RE-TM magnets like Nd-Fe-B or Sm-Co) has, up to now, proven elusive.…”

“…B exch , K 1 , K 2 , M 0 Co and p are obtained using the FP-MVB procedure developed to calculate F irst-P rinciples M agnetization V s B -field curves for GdCo 5 [27]. FP-MVB fits DFT-DLM torque calculations [45] for different magnetic configurations to extract the desired quantities [27,46]. For all RE 3+ Co 5 compounds considered here, we exploit the isovalence of the RE 3+ ions and substitute the RE with Gd in the FPMVB calculations.…”

First-principles calculations of the magnetocrystalline anisotropy of the prototype 2:17 cell boundary phaseYCo1-x-yFePatrick1, Matsumoto2, Staunton3 2019Journal of Magnetism and Magnetic MaterialsSelf Cite122181View full textAdd to dashboardCite

“…Previous computational studies on YCo 5 found the LSDA to yield values of both the orbital magnetic moments and the magnetocrystalline anisotropy which are smaller than measured experimentally, but including an orbital polarization correction (OPC) [56] on the TM-d orbitals corrects this discrepancy [30][31][32]. Although the relativistic DFT-DLM calculations do allow an OPC to be included [29,57,58], in the current work we do not do so due to the large number of (Fe,Cu) compositions considered. Therefore our calculated anisotropy energies are underestimates compared to experiment.…”

Rare-earth/transition-metal magnets at finite temperature: Self-interaction-corrected relativistic density functional theory in the disordered local moment picture

“…Furthermore, the SIC has already been formulated within the KKR-CPA theory as the local selfinteraction correction (LSIC) [17]. Indeed the LSIC has been previously used in DFT-DLM calculations to study Gd [18][19][20][21]38]. However, in order to treat an arbitrary RE it is necessary to generalize the formalism.…”