Fully Relativistic Full-Potential Calculations of Magnetic Moments in Uranium Monochalcogenides with the Dirac Current
Summary (2 min read)
- For more than a half century, the properties of actinide compounds have been studied both experimentally and theoretically.
- 14) That is, if the current density is obtained, one can calculate the magnetic moments by integrating the cross product between the posi- tion vector and the current density.
- To their knowledge, the cal- culation of the magnetic moments in UX as well as other actinide compounds with the Dirac current has not been reported so far.
- 24) On the other hand, even if the authors restrict ourselves within SDFT, it seems important to compare Morb calculated using the two different methods, i.e., 2/12 the conventional method and the method with the Dirac current; since all the calculations of Morb in UX reported so far have been performed within SDFT, the restriction within SDFT at this stage may be useful for unambiguous comparison and also for step-by-step progress.
- 25) With the two methods, whose basis sets are distinctly different from each other, the authors can examine the reliability of the results with respect to the quality of basis sets.
2. Method of Calculations
- (3) In the Dirac Hamiltonian in the left-hand side of eq. (1), c and m denote the speed of light and the rest mass of an electron, respectively, and the rest energy of an electron,mc2, is subtracted.
- (11) Also, using the Dirac current associated with the ath atom, ja(r) = wa(r)j(r), the authors calculate the atomic total magnetic moment, M tota : M tota = 1 2c ∫ r × ja(r) dr .
- Here, it may be worth mentioning again that j(r) consists of not only the orbital contribution but also the spin contribution.
- It is important to note that eq. (15) is applicable only if the authors can evaluate lχq(r) definitely; for example, it is impossible to calculate Morb with eq. (15) if the basis set includes plane waves.
- These experimental lattice constants were used in their calculations.
3. Results and discussion
- In the first and second rows for each material, the authors show the magnetic moments obtained in this work using the FFLCAO and FFMB calculations with eqs. (11)-(13), respectively.
- With the above classification in mind, the most definite comparison of the results of this work can be made with those of their previous FFLCAO study and with those of the ASW study.
- It is also found that M totU+X calculated with eqs. (11)-(13) is 0.95, 1.16, 1.47 µB for US, USe, and UTe, respectively.
- It is then found that, considering the differences in the employed methodologies, MorbU , M spin U , and M tot U obtained in both the FPLMTO and RLMTO studies are in acceptable agreement with MorbU+X , M spinU+X , and M tot U+X obtained in their previous FFLCAO study and also with those obtained in the ASW study; this indicates again that MorbU+X and M tot U+X calculated with eq. (15) are smaller by nearly 0.4 µB than those calculated using the method with the Dirac current.
- The authors now consider the calculated magnetic moments of the X atom.
- The authors have studied Morb, M spin, and M tot in UX using the FFLCAO and FFMB methods.
- In particular,Morb are calculated with the Dirac current.
- This work; fully relativistic full-potential LCAO calculations.
- G) Ref. 8; relativistic linear muffin-tin-orbital calculations using a second variational method.
- H) Ref. 9; fully relativistic linearized-augmented-plane-wave calculations.
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