CCP9 - Computational Electronic Structure of Condensed Matter

Magnetism

Recent work

Recently, multiple scattering methods, for solving selfconsistent the Schrodinger equation for electrons in periodic solids, such as the Korringa-Kohn-Rostoker (KKR) [1,2] and linear muffin tin orbital (LMTO) method have undergone a remarkable revolution. In short, the problem has been reformulated in terms of scattering from a reference system[3], which is not free space, and the freedom of choice offered by the arbitrariness of the reference system was exploited to make the structure constants of the theory short ranged[4-7].

One of the more spectacular consequences of this screening transformation is that it rendered the calculation of the electronic structure of semi-infinite systems, such as a crystal with a surface, tractable [6]. Another problem of importance which can now be attacked is the calculation of electronic structure in the presence of magnetic domain walls so called Bloch walls.

A ferromagnet as for example iron has non zero local magnetic moments which tend to be aligned parallel to each other. When, however, all the moments were parallel a strong magnetic field would result which is energetically unfavourable. Therefore, in the thermodynamic ground state, the magnet will consist of a large number of magnetic domains such that the moments inside each domain are aligned but different domains may have different directions of magnetization such that the average magnetic moment of the whole magnet is zero. The interfaces between magnetic domains are called Bloch walls. They determine the magnetic morphology of the sample. They play an important role in the technologically important process of magnetic reorientation under external magnetic fields and they influence all transport properties. Much is known about Bloch walls on the basis of Ginzburg-Landau theory or spin only Hamiltonians. But these approaches suffer from uncertainties concerning the parameters involved. The screening transformation now allows for the first time to treat Bloch walls as being built up from the spin of mobile electrons moving in a lattice potential. This not only yields a parameter free description of Bloch wall properties but also yields the electronic structure in the presence of Bloch walls. Thus opening up the possibility of tackling the problem of electronic scattering from Bloch walls or the interaction of Bloch walls with defects or impurities.

The first half of the projects time has been dedicated to investigations of the screening procedure itself. We have studied a one dimensional chain of potential wells with screened KKR as well as screened LMTO. The reduction to one spatial dimension reduces the numerical difficulties without changing the conceptual features of the calculations. Thus the one dimensional model is an ideal tool for investigating the screening procedure. The main -quite technical- results of this work are contained in three published papers [8-10].

The second part is concerned with the application of the screening method to the Bloch wall calculation. The computational problems involved in this project are considerable. One reason is the size of systems under consideration: the thickness of a Bloch wall may well exceed several hundred atomic layers.

We have chosen to use the KKR code written by L. Szunyogh and B. Ujfalussy[6]. This code already displays the main features needed. It uses the screening method, is adopted to layered systems, it is relativistic and allows for spin-polarization. However, modifications have been necessary in order to deal with systems as big as Bloch walls are. An important breakthrough has been the use of symmetry inherent in a Bloch Wall. The exploitation of this symmetry has reduced demand for CPU time and working space by a factor of two which proved to be essential. Another important step has been the parallelization of the program. The code is now running successfully on the Daresbury SP2 and on the new T3E in Manchester.

We have performed calculations for bcc iron. We have calculated the Bloch wall energy as a function of the Bloch wall thickness for walls up to 430 lattice parameters thick (860 atomic layers). This curve shows a minimum at just above 400 atomic layers indicating that our calculations are able to reflect properly the two competing energy contributions namely the exchange energy which gets smaller and the anisotropy energy which gets bigger with increasing wall width. Thus, as envisaged in the original application, we have, for the first time, crossed the scale gap from the microscopic to the mesoscopic. As is well known the anisotropy energy for iron is underestimated in band structure calculations by about a factor of two and our calculations are no exception to this. This together with the fact that we allow the magnetization to turn only by the same amount from layer to layer explains that the minimum in our energy curve is located at a thickness which is about twice that given in the literature for the Bloch wall thickness.

Our latest result is the fully selfconsistant calculation of the electronic structure of a 60 layer Bloch wall in bcc iron. The results show a slight decrease of the magnetic moment throughout the whole wall but largest near the center (of the order 1 in 10-4). We have also calculated the layer resolved local density of states for this 60 layer Bloch wall. These results will be published in a forthcoming paper[11].

References

  1. J. Korringa, Physica, XIII 392, (1947).
  2. W. Kohn and N. Rostoker, Phys. Rev., 94 1111, (1954).
  3. Lodder and P.J. Braspenning, Phys. Rev. B 49 10215, (1994).
  4. O.K. Andersen and O. Jepsen, Phys. Rev. Letters, 53 2571, (1984).
  5. O.K. Andersen, A.V. Postnikov, and S. Yu Savrasov, In W.H. Butler, P.H. Dederichs, A. Gonis, and R.L. Weaver, editors, Applications of Multiple Scattering Theory to Materials Science, MRS Symposia Proceedings, volume 253, page 37, Pittsburgh, (1992) Materials Research Society.
  6. L. Szunyogh, B. Ujfalussy, P. Weinberger and J. Kollar, Phys. Rev. B 49 2721, (1994).
  7. R. Zeller, P.H. Dederichs, B. Ujfalussy, L. Szunyogh, and P. Weinberger. Phys. Rev. B 52 8807, (1995).
  8. J. Schwitalla and B.L. Gyorffy. J. Phys.: Condens. Matter, 10 10955, (1998).
  9. J. Schwitalla and B.L. Gyorffy. Phil. Mag. B 78 441, (1998).
  10. J. Schwitalla and B.L. Gyorffy. J. Phys.: Condens. Matter, 11 7125, (1999). 11. J. Schwitalla, B.L. Gyorffy and L. Szunyogh, to be published.

Collaborations

CCP9's Magnetism project has members in the Universities of Bristol, Warwick, Keele, Bath, Sheffield and Daresbury. They organize regularly small workshops (see Appendix 3). In 1999 they organised two KKR miniworkshops. This project is the UK partner in two EU Networks coordinated by Walter Temmerman: the TMR Network on "Interface Magnetism" and the RTN on "Computational Magnetoelectronics". Reports on the activities of this TMR Network can be found in the Ψk Newletters. This project needs mostly funding to organise KKR mini-workshops, attendance at EU workshops hosted in the UK and collaborative visits between Bristol, Warwick, Keele, Bath, Sheffield and Daresbury.

In addition to adopting the Szunyogh and Ujfalussy code to the problem of Bloch Walls Dr. Schwitalla was also instrumental in establishing it in Dr. Stauntons group at Warwick where it is now used as a basis for studying the Disordered Local Moment (paramagnetic) state in ultrathin Fe films.