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X-ray magnetic circular dichroism in and ferromagnetic materials: recent theoretical progress. Part II (Review Article)
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10.1063/1.2834255
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Affiliations:
1 Institute of Metal Physics, 36 Vernadskii St., 03142 Kiev, Ukraine
2 Max-Planck-Institut for the Physics of Complex Systems, D-01187 Dresden, Germany
a) Email: antonov@imp.kiev.ua
Low Temp. Phys. 34, 79 (2008)
/content/aip/journal/ltp/34/2/10.1063/1.2834255
http://aip.metastore.ingenta.com/content/aip/journal/ltp/34/2/10.1063/1.2834255

## Figures

FIG. 1.

Self-consistent fully relativistic spin-polarized energy band structure and total DOS (in states/(unit cell⋅eV)) calculated for with the states treated as: (1) fully localized ( in core); (2) itinerant (LSDA); and (3) partly localized .36

FIG. 2.

Partial density of states of .36 The Fermi energy is at zero.

FIG. 3.

(a) Theoretically calculated36 (dotted lines) and experimental35 (circles) isotropic absorption spectra of at the edges. The experimental spectra were measured in an external magnetic field at . (b) Experimental35 (circles) XMCD spectra of at the edges in comparison with theoretically calculated ones in the approximation without (dotted lines) and with (full lines) core-hole effect taken into account.

FIG. 4.

(a) Theoretically calculated36 (dashed line) and experimental42 (circles) isotropic absorption spectra of at the edges (the spectra are shifted towards smaller energy by ). The experimental spectra were measured on a bulklike layer deposited on a Si substrate at in the total fluorescence yield mode. The dotted lines show the theoretically calculated background spectra; the full thick lines are the sum of the theoretical XAS and background spectra. (b) Experimental42 (circles) XMCD spectra of at the edges in comparison with theoretically calculated ones in the (full lines) approximation.

FIG. 5.

(a) The experimental35 (circles) isotropic absorption spectrum of at the N edge in comparison with the calculated ones36 in the LSDA (full line) and approximations without (dashed line) and with (dotted line) the core-hole effect taken into account. The experimental spectra were measured with external magnetic field at . The dashed-dotted line shows the theoretically calculated background spectrum. (b) Experimental35 (circles) XMCD spectrum of at the Gd edge in comparison with theoretically calculated ones in the LSDA (full line) and putting the states in the core (dashed line); (c) experimental (circles) XMCD Gd spectrum in comparison with theoretically calculated in the approximation with (full line) and without (dashed line) the core-hole effect taken into account.

FIG. 6.

empty partial DOSs (in arbitrary units) for the surface layer in the 9/3 MLS (full line) and the bulk structure (dashed line)36 in comparison with the experimental XA spectrum at the N edge35 (circles).

FIG. 7.

The LSDA partial and density of states in .72

FIG. 8.

Isotropic absorption and XMCD spectra of at the uranium edges calculated in the LSDA (solid lines) and (OP) (dashed lines) approximations.72 The experimental spectra66 (circles) were measured at and at magnetic field (the spectrum is shifted by to include it in the figure). The upper panel also shows the background spectra (dashed line) due to the transitions from inner levels to the continuum of unoccupied levels.

FIG. 9.

XMCD spectra of at the uranium , , , and edges, calculated in the LSDA approximation.72 All the XMCD spectra are multiplied by a factor (the and spectra have been shifted by and , respectively, to include them in the figure).

FIG. 10.

XMCD spectra of at the Fe , , and edges in bcc Fe and Fe in , calculated in the LSDA approximation.72 The XMCD spectrum at the edge has been multiplied by a factor .

FIG. 11.

The LSDA self-consistent fully relativistic, spin-polarized energy band structure and total DOS (in states/(unit cell⋅eV)) of , , and .86

FIG. 12.

The partial density of states in calculated in the LSDA and (OP) approximations.86

FIG. 13.

Isotropic absorption and XMCD spectra of at the uranium edges calculated in the LSDA (dotted lines) and (OP) (solid lines) approximations.86 The experimental spectra71 (circles) were measured at and at a magnetic field of (the spectrum is shifted by to include it in the figure).

FIG. 14.

The XMCD spectra of and at the uranium edges calculated in the LSDA (dashed lines) and (OP) (solid lines) approximations.86 The experimental spectra for UCoAl71 (circles) were measured at a magnetic field of . The experimental data for is from Ref. 70 (the spectra are shifted by to include them in the figure).

FIG. 15.

Uranium XMCD spectrum of calculated in the ) approximation (full line) and spectra calculated with the and DOSs artificially shifted by (dashed line) and (dotted line).86

FIG. 16.

Self-consistent fully relativistic energy band structure and total DOS (in states/(unit cell⋅eV)) of calculated within the LSDA and approximations with and .116

FIG. 17.

The partial and densities of states in , , and , calculated in the LSDA and approximations.116

FIG. 18.

The partial density of states in and , calculated within the approximation.116

FIG. 19.

The XMCD spectra of , , and at the uranium edges calculated within the LSDA (dashed lines), LSDA + U(OP) (dotted lines), and (solid lines) approximations.116 The experimental spectra of US71 (circles) were measured at a magnetic field of (the spectra are shifted by to include them in the figure).

FIG. 20.

The self-consistent fully relativistic, spin-polarized energy band structure and total DOS (in states/(unit cell⋅eV)) of calculated in the LSDA and approximations.140

FIG. 21.

The partial density of states in and , calculated in the approximation.

FIG. 22.

The model representation of the (a) and (b) XMCD of for two solutions with occupied states (full lines) and (dashed lines): (a) presents the partial densities of states ; (b) (full line) and (dashed lines)140 (see the explanation in the text).

FIG. 23.

The XMCD spectra of and at the uranium edges, calculated in the LSDA, (OP), and approximations.140 The experimental spectra for 65 (circles) were measured in a magnetic field of at (the spectra are shifted by to include them in the figure).

FIG. 24.

The self-consistent fully relativistic, spin-polarized energy band structure and total DOS (in states/(unit cell⋅eV)) of calculated in the LSDA and approximations.140

FIG. 25.

The partial density of states in calculated in the LSDA approximation140 (the partial DOS has been multiplied by a factor of 3 for clarity).

FIG. 26.

Isotopic absorption and XMCD spectra of at the uranium edges calculated in the LSDA (dashed lines) and (full lines) approximations.140 The experimental spectra69 (circles) were measured at and in a magnetic field of (the spectra are shifted by to include them in the figure).

FIG. 27.

The self-consistent fully relativistic, spin-polarized energy band structure and total DOS (in states/(unit cell⋅eV)) of and , calculated in the LSDA approximation.140

FIG. 28.

The partial density of states in .140

FIG. 29.

The XMCD spectra of and at the uranium edges calculated in LSDA and approximations.140 The experimental spectra69 for were measured in a magnetic field of and . The experimental data for the XMCD spectrum of is from Ref. 68 (the spectra are shifted by to include them in the figure).

FIG. 30.

Crystal structure of .

FIG. 31.

The energy band structure and total density of states (in states/(unit cell⋅eV)) in , calculated in the LSDA and approximations.140

FIG. 32.

The -projected and total density of states in , calculated in the LSDA and approximations.140

FIG. 33.

Comparison of the calculated partial DOS in the LSDA (dotted line) and approximations with the experimental BIS spectrum (circles) of .184 The dashed line shows the DOS calculated with the nonspherical correction to the Coulomb matrix elements, whereas the full line is calculated with averaged and .140

FIG. 34.

Isotropic absorption and XMCD spectra of at the uranium edges, calculated in the LSDA (dotted lines), and approximations. The dashed line presents XMCD spectra calculated with nonspherical corrections to Coulomb matrix elements, whereas the full line results are calculated with averaged and .140 The experimental spectra65 (circles) were measured at and in a magnetic field of (the spectrum is shifted by to include it in the figure).

FIG. 35.

(a) Theoretically calculated193 (dashed line) and experimental191 (circles) isotropic absorption spectra of at the edges. The experimental spectra were measured with external magnetic field at . The dotted lines show the theoretically calculated background spectra; the full thick lines are the sum of the theoretical XAS and background spectra. (b) The experimental191 (circles) XMCD spectra of at the edges in comparison with theoretically calculated ones in the LSDA (dotted lines) and (full lines) approximations.

FIG. 36.

(a) Theoretically calculated193 (dashed line) and experimental191 (circles) isotropic absorption spectra of at the U N 3 edge. The dotted lines show the theoretically calculated background spectrum; the full thick line is the sum of the theoretical XAS and background spectrum. (b) Experimental191 (circles) XMCD spectrum of at the edge in comparison with theoretically calculated ones in the approximations (full line).

FIG. 37.

(a) Theoretically calculated193 XMCD spectra of at the and Ge edges at different Ge sites; (b) experimental191 (circles) XMCD spectra of at the Ge and edges in comparison with the theoretically calculated one in the approximation (full line).

FIG. 38.

(a) Theoretically calculated193 XMCD spectra of at the edge at different Ge sites; (b) theoretically calculated XMCD spectrum of at the Ge edge in the approximation (full line) in comparison with the experimental one192 (circles). The experimental spectrum was measured at in an external magnetic field applied along the axis.

## Tables

Table I.

The dipole allowed transitions from core levels to the unoccupied valence states for left- and right- polarized x rays.

Table II.

The dipole allowed transitions from core levels to the unoccupied valence states for left- and right- polarized x rays.

Table III.

The experimental and calculated spin , orbital , and total magnetic moments at the uranium site (in ) for , , and .

Table IV.

The experimental and calculated spin , orbital , and total magnetic moments at the uranium site (in ) for , , and .116

Table V.

The experimental and calculated spin , orbital , and total magnetic moments at the uranium site (in ) for and . The magnetic moments are calculated for the easy magnetic axes, namely, the hexagonal plane in and the axis in .140

/content/aip/journal/ltp/34/2/10.1063/1.2834255
2008-02-01
2014-04-18

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