The relationship between interlayer spacing and magnetic ordering in gadolinium

Abstract

We report on the application of the local spin-density approximation (LSDA) and the generalized gradient approximation of Perdew, Burke and Ernzerhof (PBE) within the linear muffintin orbital method in both the atomic sphere approximation (LMTO-ASA) and in the full-potential (FP-LMTO) method to the description of the magnetic coupling within bulk Gd. Using the LMTO-ASA approach to the band-structure problem it is found that, at the experimental lattice parameters, the PBE approximation predicts the experimentally observed ferromagnetic (FM) ground state whereas the LSDA does not. Moreover the nature of the magnetic coupling between successive layers is found to be dependent on the interlayer separation-in particular a reduction of the interlayer spacing will lead to an increased tendency towards FM coupling between successive layers and, conversely, increase of the interlayer spacing will lead to antiferromagnetic (AFM) coupling between layers being energetically favourable. A similar interdependence between the interlayer spacing and the magnetic coupling is also observed from calculations using the FP-LMTO method. These observations are used to analyse the nature of the magnetic coupling of the Gd(0001) surface to the underlying FM bulk.

Magnetism and electronic structure of hcp Gd and the Gd(0001) surface

“…Comparing the results of the 4f-band model, the total moment per atom is in excellent agreement with other recent results (e.g. [11,40]) and also with the experimental value of 7.63 µ B . However, the 4f-core model yields a slightly larger value, which has already been observed by other authors (e.g.…”

Structural, electronic and magnetic properties of Gd investigated by DFT+Umethods: bulk, clean and H-covered (0001) surfaces

“…Heinemann and Temmerman [11,12] found that the LSDA favours antiferromagnetic over ferromagnetic order when the 4f electrons are treated as valence band states, in contradiction to experiment. This was confirmed in a number of subsequent studies [6,[13][14][15][16]. The application of gradient corrections, as proposed by Langreth, Mehl and Hu [17,18], to the exchange-correlation functional led to the prediction of the correct ferromagnetic ground state in linearized muffin tin orbital (LMTO) calculations employing the atomic sphere approximation (ASA) [11].…”

“…We reproduce the well-documented (incorrect) favouring of the AFM ground state in our PBE calculations, with the 4f electrons treated as band states. Jenkins et al [14] similarly found that the PBE functional favours the AFM ground state in their FP-LMTO calculations in which the 4f electrons were treated as itinerant band states, although they obtained the correct FM ground state when using the LMTO-ASA method instead. We note that in our calculations, the c/a ratio is relaxed at each volume to obtain the total energy curves in figure 2, whereas Jenkins et al [14] performed their calculations with c/a fixed at the experimental value of 1.597.…”

“…Jenkins et al [14] similarly found that the PBE functional favours the AFM ground state in their FP-LMTO calculations in which the 4f electrons were treated as itinerant band states, although they obtained the correct FM ground state when using the LMTO-ASA method instead. We note that in our calculations, the c/a ratio is relaxed at each volume to obtain the total energy curves in figure 2, whereas Jenkins et al [14] performed their calculations with c/a fixed at the experimental value of 1.597. Both Eriksson et al [13] and Kurz et al [6] observed that the application of the GGA in the form of the PW91 functional only succeeds in reversing the favouring of the AFM state when the 4f electrons are treated as core rather than band states.…”

“…The application of gradient corrections, as proposed by Langreth, Mehl and Hu [17,18], to the exchange-correlation functional led to the prediction of the correct ferromagnetic ground state in linearized muffin tin orbital (LMTO) calculations employing the atomic sphere approximation (ASA) [11]. Although Jenkins et al [14] obtained the same result using the LMTO-ASA approach with both the generalized gradient approximations (GGA) of Perdew and Wang (PW91) [19] and of Perdew, Burke and Ernzerhof (PBE) [20], they found that the antiferromagnetic state was once again favoured when a full-potential (FP)-LMTO method was used instead. This result was consistent with previous FP-LMTO calculations [13] and subsequent full-potential linearized augmented-plane wave (FLAPW) calculations [6] using the PW91 functional when treating the 4f electrons as valence band states.…”