... Rotter¹

Independent international Scientific Consultant, email: mcphase@icloud.com

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... Le²

Dept. Physics and Astronomy, Seoul National University, Seoul 151-742, Korea

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... Keller³

Universität Regensburg

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... Hoffmann⁴

University of Oxford, Physics Department, Clarendon Laboratory, Parks Road, Oxford, UK

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... Hoffmann⁵

Forschungszentrum Jülich, D-52425 Jülich, Germany

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... Rotter⁶

Wien, Austria

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...#tex2html_wrap_inline9852#⁷

Note that these conditions are essential and put a limit to the applicability of the theory, for example in the case of charge transfer excitations from one subsystem to the next.

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...cfze). ⁸

In addition to $\langle \mathbf J_i \rangle$ the module also returns the partition sum $z$ and the magnetic energy $u=\sum_{i=1}^{2J+1} p_{i} E_{i}$.

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.... ⁹

Note that if you use the module cfield, the choice is more unconventional:$\vec a\vert\vert y$, $\vec b\vert\vert z$ and $\vec c\vert\vert x$ Tools for rotating crystal field parameters are described in appendix I.

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... (MAXNOFMFLOOPS).¹⁰

Note two special cases:If MAXNOFMFLOOPS=1, then the mean fields are calculated from the initial values of the spin configuration and free energy is evaluated immediately without checking convergence. If MAXNOFMFLOOPS=2, then from calculated mean fields the spins are calculated and free energy is evaluated, without checking convergence. For MAXNOFMFLOOPS$>$2 free energy is only evaluated if the iteration reached the convergence limit specified by MAXSTAMF.

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... edited).¹¹

Alternatively, one may make use of the program spins.

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...Eel). ¹²

$R^{\alpha}R^{\delta}\omega_{\sigma} \epsilon_{\sigma\alpha\beta}\delta_{\beta\... ...eta}\delta_{\alpha\delta})= (\mathbf R . \mathbf \omega )^2-R^2\omega^2 \neq 0$, if $\mathbf R$ is not parallel to the rotation axis. Thus for some rotation the elastic energy will depend on rotation angle if transversal springs are introduced.

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... using ¹³

S. Bluegel, Juelich, private communication

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... first¹⁴

Note that we do not calculate all the terms in the braces in the first line of equation 4. In particular using the central field approximation the first summation produces Hydrogen-like energy levels, called configurations, which are split into terms by the second summation. What we refer to as the Coulomb interaction is only this second summation, and we shall consider the lowest energy configuration only. This configuration corresponds to the outer most electrons in ion, and is labelled $nl^\nu$, for example, $4f^1$ for Ce$^{3+}$.

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... properties¹⁵

For the case of $LS$-coupling this corresponds to ignoring the Coulomb and SO interactions, which are in this limit both much larger than the CF. For $jj$-coupling, the Coulomb interaction is treated as small and neglected, but the spin-orbit interaction is considered.

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...#tex2html_wrap_inline11898#¹⁶

Also denoted $m_J$.

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...racah49-1352¹⁷

Equation 11

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... formulae¹⁸

Except for the case of the rotation group in 3 dimensions, SO(3) (whose representations are labelled by the angular momentum quantum numbers, $L$ and $J$), where they are simply the $3j$ symbols

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...allison74¹⁹

http://cpc.cs.qub.ac.uk/cpc/cgi-bin/showversions.pl/?catid=acry

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...elliot57-509²⁰

Eqn 16 for SO, and 25-27 for CF, and reproduced in more modern notation in appendix C of [50]

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...racah49-1352²¹

Eqns 66 for the conversion of the Racah parameters to Slater integrals, 63 for the $\hat e_0$ operator, 69 for $\hat e_1$, 73-74 for $\hat e_2$, and 78, 28 and 80-87 for $\hat e_3$

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...judd88-1²²

Eqn 7-58

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... intervals²³

Depending on the Java setup on your computer, a conflict may occur between the McPhase Java programs and other Java programs, such as the Matlab GUI. If you find that no graphics windows open, and have other Java programs running in the background, try to close all other Java programs.

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...wybourne65²⁴

Note that table 6-1 and equ 6-7 are not correct in this reference.

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...#tex2html_wrap_inline13210#²⁵

Note that these conditions are essential and put a limit to the applicability of the theory, for example in the case of charge transfer excitations from one subsystem to the next [70].

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... susceptibility²⁶

the $-$ on top of $\chi$ indicates matrix notation for $\chi_{\alpha\beta}^{ss'}$

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... investigated²⁷

supplementary material - screen shot movie comparing the speed of traditional Green's function method and DMD

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... cell²⁸

In case of magnetic order. In general this will be the unit cell of the Bravais lattice in section M, which is a superlattice of the crystal lattice.

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... elements²⁹

using the appropriate expression for the matrix elements of of the scattering operator as given in [30, equ. (11.86) or (11.87b)].

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