magnetic spectroscopy - ornl · 2017-03-13 · 1 0.0 0.5 1.0-0.05 780 790 800 0.00 0.05 photon...

1

0.0

0.5

1.0

780 790 800-0.05

0.00

0.05

photon energy (eV)

XA (a

rb. u

nits

)XM

LD(a

rb. u

nits

)

Fe

Co_G

aAs_

XMLD

.opj

MAGNETIC SPECTROSCOPY

+ X ray absorption, XA

+ X ray magnetic circular dichoism, XMCD

+ X ray magnetic linear dichroism, XMLD

+ X ray magnetic microscopy

+ Magnetization Dynamics

Elke Arenholz, Advanced Light Source

E. Arenholz et al., Appl. Phys. Lett. 93, 162506 (2008)

3 µm

[100]

ENiO

Co

NiO

Co

C. Boeglin et al., Nature 465, 458 (2011)

Co0.5Pd0.5

Co

Co

Co

CoO

780 790 800photon energy (eV)

XA (a

rb. u

nits

)

Co

O_C

o.op

j 0.0

0.5

1.0

780 790 800-0.5

0.0

photon energy (eV)

XA (a

rb. u

nits

)

FeCo

_GaA

s_XM

CD.o

pj

XMCD

(arb

. uni

ts)

2

X-RAY ABSORPTION – THE SIMPLEST X RAY TECHNIQUE

X-ray absorption: + Electrons excited from core shells to unoccupied valence states

through the absorption of a photon determined by energy and angular momentum conservation

Experiment/Measurement:Reduction in x ray flux transmitted through a sample.

Simplest model: One electron picture+ Photon transfers its energy and momentum to core electron + Core electron excited into unoccupied electronic state.

+ However: Not directly excited electrons also influenced by electronexcitation, i.e. hole in core shell

3

Configuration model, e.g. L edge absorption :

+ Atom is excited from ground/initial state configuration, 2p63dn

to exited/final state configuration, 2p53dn+1

+ Omission of all full subshells (spherical symmetric)

+ Takes into account correlation effects in the ground state as well as in the excited state

+ Leads to multiplet effects/structure

X-RAY ABSORPTION

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

4

Co2+

in CoOFe3+ inLaFeO3

Ni2+

in NiO

Fe Co Ni

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

XA provides + elemental specificity + sensitivity to valence

shell properties, i.e. valence state and lattice site symmetry

X-RAY ABSORPTION

5

K. Edmonds et al.,Appl. Phys. Lett. 84, 4065(2004)

SURFACE EFFECTS IN (Ga,Mn)As

+ As grown/before etch: - Multiplet structure characteristic of MnO

+ After removal of the surface layer:- Multiplet structure is less pronounced - Spectrum shifted to 0.5 eV lower photon energy.

+ Comparison with calculated spectra:- localized Mn ground state for the untreated sample - hybridized ground state after etching.

6

SENSITIVITY TO SITE SYMMETRY: Ti4+ L3,2

+ Electric dipole transitions: d0→2p53d1

+ Crystal field splitting 10Dq acting on 3d orbitals:

Octahedral symmetry: e orbitals towards ligands → higher energyt2 orbitals between ligands → lower energy

Tetragonal symmetry:e orbitals → b2 = dxy, e = dyz, dyz

t2 orbitals → b1 = dx2−y2, a1 = d3z2−r2

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

7

770 780 790 8000

2

4

6

EY_T

M.o

pj

elec

tron

yiel

d I e /

I 0

photon energy (eV)

770 780 790 8000.6

0.7

0.8

0.9

1.0

photon energy (eV)

trans

mitt

ed in

tens

ity I t /

I 0

EY_T

M.o

pj

X-RAY ABSORPTION − MEASUREMENTS

photonsabsorbed

electronsgenerated

Electron yield: + Absorbed photons create core holes that are filled predominantly by Auger electron emission+ Auger electrons create low-energy secondary electron cascade through inelastic scattering+ Emitted electrons ∝ probability of Auger electron creating ∝ absorption probability

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

8

SAMPLING DEPTH OF ELECTRON YIELD

+ Electron sample depth: 2nm in Fe, Co, Ni ⇒ 60% of the electron yield originates form the topmost 2nm

+ X ray absorption length: 500nm before the absorption edge 20nm at the L3 edge

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

9

+ Tunable photon source in the soft x ray range, 200-2000eV, i.e. undulator or bend magnet, at synchrotron.

+ Beamlines/Monochromators provide photons withwell defined characteristics: - tunable energy/wavelength - fixed polarization: (variable) linear, circular, elliptical, …

Advanced Light Source

BL6.3.1

PHOTON SOURCES AND MONOCHROMATORS

10

+ Endstations provide well defined sample environments for the interaction with photons:- precisely defined experimental geometries - sample temperature- external magnetic and electric fields…

ENDSTATIONS

2cm 2T magnet atALS BL6.3.1

11

2cmVector magnet at ALS BL4.0.2

H

H1 H2H3 H4

+ Magnetic fields in arbitrary directions obtained through superposition of fields generated by 4 dipole pairs in octahedral configuration.

bias mesh

azimuthal rotation

sample

ENDSTATIONS

12

+ Magnetic moments in Fe, Co, Ni are well described by the Stoner model:d-bands containing up and down spins shifted relative to each other by “exchange splitting”

+ Spin- up and spin-down bands filled according to Fermi statistics.

+ Magnetic moment |m| determined the difference in number of electrons in majority and minority bands

empty states,“holes”

exchange splitting

3d shell

spin-upspin-down

empty states,“holes”

)n(nμ |m| mine

majeB −=

STONER MODEL FOR FERROMAGNETIC TRANSITION METALS

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

13

Photoelectrons excited from 2p3/2, 2p1/2 to 3d states

First step:+ Excitation of electron from 2p states by absorption of circularly

polarized x rays. + Note: Dipole operator does not act on the spin and

⇒ No spin flips during excitation.+ Conservation of angular momentum ⇒ transfer of angular momentum (±ħ) from photon to electron

+ Spin-orbit coupling: Angular momentum of photon transferredin part to electron spin

⇒ Excited photoelectrons are spin polarized

Second step:+ Unequal spin-up and spin-down populations

determines spin or orbital momentum of possible excitations

TWO-STEP MODEL OF XMCD

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

14

TWO-STEP MODEL OF XMCD

Magnitude of the dichroismeffect depends on

+ degree of circular photon polarization, Pcirc

+ angle θ between photon angular momentum, Lph and magnetic moment, m

+ expectation value of 3dmagnetic moment

IXMCD ∝ Pcirc ⟨m⟩ cos θ

+ XMCD allows studying ferri-and ferromagnets.

IXMCD = I↑↓ − I↑↑

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

0.0

0.5

1.0

770 780 790 800

-0.4

-0.2

0.0

photon energy (eV)

XA (a

rb. u

nits

)

FeCo

_GaA

s_XM

CD.o

pj

XMCD

(arb

. uni

ts)

L3 L2

Co

15

TWO-STEP MODEL OF XMCD

+ 2p3/2 and 2p1/2 have opposite spin orbit coupling (l+s, l −s) ⇒ Spin polarization and

XMCD have opposite sign at two edges

+ Spin polarization opposite for x rays with opposite helicity, i.e. photon spin, ±ħ ⇒ XMCD reverses sign with

polarization

+ Reversing the x ray polarization is equivalent to reversing magnetization/spin direction

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

0.0

0.5

1.0

770 780 790 800

-0.4

-0.2

0.0

photon energy (eV)

XA (a

rb. u

nits

)

FeCo

_GaA

s_XM

CD.o

pj

XMCD

(arb

. uni

ts)

L3 L2

Co

16

0.0

0.5

1.0

700 710 720 730 780 790 800

-0.2

0.0

XA (a

rb. u

nits

)

photon energy (eV)

XMCD

(arb

. uni

ts)

Co

Fe2O

4.op

j

L3 Fe Co

L2

L3

L2

CoFe2O4

Fe2+,Oh

Fe3+, Oh

Fe3+, Td

Co2+

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

H

circularlypolarized

+ XMCD provides magnetic information resolving elements Fe, Co, …valence states: Fe2+, Fe3+, …lattice sites: octahedral, Oh, tetrahedral, Td, …

X RAY MAGNETIC CIRCULAR DICHROISM (XMCD)

17

P. Morrall et al.,Phys. Rev. B 67, 214408 (2003)The Department of Geology and Geophysics,

University of Wisconsin-Madison

+ Geobacter sulfurreducens bacteria form magnetite via extracellular reduction of amorphous Fe(III)-bearing minerals

V. Cocker et al., Eur. J. Mineral. 19, 707–716 (2007)

CHARACTERISTICS OF MAGNETIC BIONANOSPINELS

18

Magnetite and Co ferrites produced from Co(II) containing Fe(III)-oxyhydroxides using metal-reducing bacterium (Geobacter sulfurreducens)+ Up to 23at% Co2+ incorporated

(compared to 1at% using magnetotactic bacteria)

+ Co2+ in Fe2+ Oh sites+ 10fold increase in magnetic anisotropy

Fe3O4

Co-ferrite-1 6 at% Co

Co-ferrite-2 23 at% Co

XMCD

photon energy (eV)

710 720 730 710 720 730

expt.sim.

−2 0 +2

M (e

mu

g−1 ) −60

0

+60

H (T)V. Cocker et al., Eur. J. Mineral. 19, 707–716 (2007)

CHARACTERISTICS OF MAGNETIC BIONANOSPINELS

19

+ Comparing XMCD spectra with model compounds and/or theoretical multiplet calculations allows

⇒ Identifying the contributions to the magnetic phase of a system.

XMC

D (a

rb. u

nits

)XA

(arb

. uni

ts)

J.-Y. Kim et al., Phys. Rev. Lett. 90, 017401 (2003)

XA, X

MCD

Co metal

XA

XA

XMCD

XMCD

photon energy (eV)

Co2+ in CoFe2O4

780 790 800

0

0

XA, X

MCD

Co_C

o2+.

opj

Co-DOPED TiO2

20

CuCoCuCo

…

+ The element-specificity makes XMCD measurements an ideal tool to determine induced moments at interfaces between magnetic and non-magnetic elements.

INDUCED MOMENTS AT Co/Cu INTERFACES

M. G. Samant et al.,Phys. Rev. Lett. 72, 1112 (1994)

21

1.0

1.5

2.0

2.5

Co L3,2

Mn L3,2

XMCD

(%)

XA(a

rb. u

nits

)

630 640 650 660 770 780 790 800 810

-5

0

photon energy (eV)

-0.2

0.0

20 Å Co / 200 Å Ir20Mn80

+ The weak Mn XMCD signal indicates uncompensated Mn at the Co/IrMn interface.

+ The same sign of XMCD signal for Co and Mn and indicates parallel coupling.

+ The nominal thickness of uncompensated interface moments is (0.5±0.1)ML for Co/Ir20Mn80.

IrMn

Co

ANTIFERROMAGNET/FERROMAGNETIC INTERFACES

22

MAGNETISM AT FERROMAGNET/SUPERCONDUCTOR INTERFACES

J. Chakhalian et al.,Nature Phys. 2, 244 (2006)

+ LCMO : significant Mn L3,2 XMCD at T = 30K ferromagnetic transition ~180 K

+ YBCO: Weak Cu L3,2 XMCD⇔ net ferromagnetic polarization on Cu

i.e. presence of uncompensated induced magneticmoment in the YBCO layer close to LCMO interface.

+ opposite sign of Cu and Mn XMCD ⇔ antiparallel orientation of Cu and Mn moments

23

640 650 660 710 720 730

0.0

0.5

1.0

XMCD

(arb

. uni

ts)

XA

(arb

. uni

ts)

photon energy (eV)

Mn

Fe

x20

0 100 200 3000.0

0.1

0.2

temperature (K)

XMCD

(arb

. uni

ts)

Fe Mn

+ La0.7Sr0.3MnO3 : significant Mn L3,2 XMCD at T = 10K ferromagnetic transition ~300 K

+ BiFeO3: Weak Fe L3,2 XMCD⇔ net ferromagnetic polarization on Fe

i.e. presence of uncompensated induced magneticmoment in the BiFeO3 layer close to La0.7Sr0.3MnO3

interface.

+ opposite sign of Fe and Mn XMCD ⇔ antiparallel orientation of Fe and Mn moments

+ Transition temperature of the magnetic phase in BiFeO3 significantly lower than La0.7Sr0.3MnO3

T = 10K

La0.7Sr0.3MnO3 / BiFeO3 INTERFACE

P. Yu et al., Phys. Rev. Lett. 105, 027201 (2010)

24

1.01.52.02.5

×3

( )

H=+0.2 TH=−0.2 T

inte

nsity

(arb

. uni

ts)

700 750 800 850-10-505

asym

. (%

)

photon energy (eV)

ELEMENT-SPECIFIC MAGNETIZATION REVERSAL

-2000 -1000 0 1000 2000-10

-5

0

5

10

XM

CD (%

)

field (G)

NiFeCo

Fe

Co

Ni

5 ML Co

8,10 ML Fe

18 ML Ni

-400 -200 0 200 400-10

-5

0

5

10

XMCD

(%)

field (Oe)

NiFeCo

+ Monitoring the field dependence of the XMCD signal

⇒ Detailed information on magnetization reversal in complexmagnetic hetero-structures

8 ML Fe 10 ML Fe

25

A < 0

B > 0

+ Theoretically derived sum rules correlate the XMCD spectra with the spin and orbital moment providing a unique tool for studying magnetic materials.

mS = µB⟨–A + 2B⟩ / C mL = –2µB⟨A + B⟩ / 3CNh = ⟨ IL3 + IL2 ⟩/C

SUM RULES

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

26

morb

mspin

2q9p – 6q=

C.T. Chen et al., Phys. Rev. Lett. 75, 152(1995)

+ Separation of spin and orbital moments requires very high quality data.

morb = – –––––––––––4q (10 – n3d)

3r

mspin = – –––––––––––––––––(6p – 4q) (10 – n3d)

r

SUM RULES

27

+ Strong variation of orbital and spin magnetic moment observable as change in L3 and L2 in the XMCD spectrum.

+ Co atoms and nanoparticles on Pt have enhanced orbital moments up to 1.1 µB

P. Gambardella et al.,Science 300, 1130 (2003)

ORBITAL MOMENT OF Co NANOPARTICLES

28

L2mS and mL

only mL

XMCD

photon energy

only mS

L3

+ Spin and orbital moment only systems have distinct XMCD spectra:

mS = µB⟨–A + 2B⟩ / C = 0 for A = 2B

mL = –2µB⟨A + B⟩ / 3C = 0 for A = –B

A < 0

B > 0

SUM RULES

29

+ Linear dichroism: difference in x-ray absorption for different polarization direction relative to crystalline and/or spin axis.

+ Linear dichroism is due to the anisotropic charge distribution about the absorbing atom caused by bonding and/or magnetic order.

+ “Search Light Effect”: X ray absorption of linear polarized x rays proportional to density of empty valence states in direction of electric field vector E.

Cu

O

photon energy (eV)920 940 960

La1.85Sr0.15CuO4

L2

Cu

XA (a

rb. u

nits

)

L3

C. T. Chen et al. PRL 68, 2543 (1992)

X-RAY LINEAR DICHROISM

E

30

Pb2+ O2− Ti4+, Zr4+

+

−

ferroelectric polarization

+ Spontaneous electric polarizationdue to off-center shift of Ti4+, Zr4+ ;associated with tetragonal distortion ⇔ linear dichroism

+ Reversing the polarization changes XA ⇔ Change in tetragonal distortion

0.0

0.5

1.0

455 460 465 470

-0.05

0.00

XA(a

rb. u

nits

)

diffe

renc

e (a

rb. u

nits

)

// //

0.0

0.5

1.0

XA(a

rb. u

nits

)

-0.2

0.0

0.2

photon energy (eV)

diffe

renc

e (a

rb. u

nits

)

////

////

STRUCTURAL CHANGES IN PbZr0.2Ti0.8O3

as grown

reversed

31

→

0.0

0.5

1.0

XMLD

(arb

. uni

ts)

XA (a

rb. u

nits

)-0.02

0.00

0.02

photon energy (eV)

700 710 720 730 780 790 800

//

//

//

+ IXMLD = I|| − I⊥ ∝ ⟨m 2 ⟩, ⟨m 2⟩ = expectation value of the square of the atomic magnetic moment

+ XMLD allows investigating ferri- and ferromagnets as well as antiferromagnets.

+ XMLD spectral shape and angular dependence are determined by magnetic order and lattice symmetry.

L3

Fe Co

L3L2

Isotropic d electron charge density⇒ No polarization dependence

magnetically alignedSpin-orbit coupling distorts

charge density⇒ polarization dependence

CoFe2O4

L2

θ = 0°

S→

θ = 45°H

H

X-RAY MAGNETIC LINEAR DICHROISM

L[001]

32

770 780 790 850 860 870

0.0

0.5

1.0L3

L2

L2Ni

Co

CoNi

O_6

.3.1

.opj

XM

CD, X

A (a

rb. u

nits

)

photon energy (eV)

Co/NiO

x50

L3

A. Scholl et al.,Phys. Rev. Lett. 92, 247201 (2004)

Co

NiO

1

2

868 870 872

-0.2

0.0

photon energy (eV)

XMLD

(arb

. uni

ts)

NiO

Co/NiO

XA(a

rb. u

nits

)

0.0 0.2 0.4 0.6

0.9

1.0

1.1

1.2

Ni L

2 rat

io

applied field (T)

E⊥H E||H

0o

10o

20o

30o

40o

50o

wall angle

H

-0.5 0.0 0.5

-10

0

10

Co X

MCD

(arb

. uni

ts)

field (T)

NiOCo

HH

PLANAR DOMAIN WALL NEAR Co/NiO INTERFACES

33

LSFO

640 650-0.2

0.0

0.0

0.5

1.0

XA (a

rb. u

nits

)

photon energy (eV)

XMCD

(arb

. uni

ts)

0.0

0.5

1.0

710 720-0.2

0.0

0.2

XA (a

rb. u

nits

)

expt. calc.

photon energy (eV)

XMLD

(arb

. uni

ts)

0.0

0.5

1.0

710 720-0.1

0.0

0.1

XA (a

rb. u

nits

)

XMLD

(arb

. uni

ts)

photon energy (eV)

MAGNETIC COUPLING AT La0.7Sr0.3MnO3/La0.7Sr0.3FeO3 INTERFACES

HMn XMCD

Fe XMLD

H

⇒ Perpendicular coupling at LSMO/LSFO interface

LSMO

La0.7Sr0.3MnO3 (LSMO)ferromagnet

La0.7Sr0.3FeO3 (LSFO)antiferromagnet

H

0.0

0.5

1.0

0.0

0.5

1.0

0 100 200 300 4000.0

0.5

1.0

Fe L3,2 XM

LD (arb. units)

Mn

L 3,2 X

MCD

(a

rb. u

nits

)Fe

L3,

2 XM

LD

(arb

. uni

ts)

temperature (K)

34

MAGNETIC MICROSCOPY

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

Magnetism

35

MAGNETIC MICROSCOPY

10-50 nm spatial resolutionJ. Stöhr, H.C. Siegmann,Magnetism (Springer)

36

i070

725_

046_

047_

div.

jpg

A / B

A − B

IMAGING FERROMAGNETIC DOMAINS USING XMCD

i070

725_

049_

050_

div.

jpg

2µm

A / B A − B

A

i070

725_

046.

jpg

B

i070

725_

050.

jpg

left circ. right circ.

780 790 800

0.0

0.5

1.0Co/NiO(001)

photon energy (eV)

XMCD

, XA

(arb

. uni

ts)

0707

27_C

o_XM

CD.o

pj

+ Images taken with left and right circularly polarized x-rays at photon energies with XMCD, i.e. Co L3 edge, provide magnetic contrast and domain images.

37

850 860 870 8800.0

0.2

0.4

0.6

0.8

1.0

photon energy (eV)

XA (a

rb. u

nits

)

Co/NiO(001)

B

AB

A − BA / B

2µm

A

IMAGING ANTIFERROMAGNETIC DOMAINS USING XMLD

E in plane

5 µm

+ Images taken with linearly polarized x-rays at photon energies with XMLD, i.e. Ni L2 edge, provide magnetic contrast and domain images.

38

Co XMCD

Ni XMLD

probing out-of-planeprobing in-plane

5 µm

5 µm5 µm

x rays

+ Taking into account the geometry dependence of the Ni XMLD signal⇒ perpendicular coupling of Co and NiO

moments at the interface.

MAGNETIC COUPLING AT Co/NiO INTERFACE

39

+ First direct observation of vortex state in antiferromagnetic CoO and NiO disks in Fe/CoO and Fe/NiO bilayers using XMCD and XMLD.

+ Two types of AFM vortices:- conventional curling vortex

as in ferromagnets- divergent vortex,

forbidden in ferromagnets- thickness dependence of magnetic

interface coupling

J. Wu et al., Nature Phys. 7, 303 (2011)

divergent vortexconventional curling vortex

OBSERVATION OF ANTIFERROMAGNETIC VORTICES

40

τel-sp τlat-sp

τel-lat

ULTRAFAST MAGNETISM

Spin-lattice relaxation time

Electron-phonon relaxation time

Electron-spinrelaxation time

+ Energy reservoirs in a ferromagnetic metal

+ Deposition of energy in one reservoir

⇒ Non-equilibrium distribution and subsequent relation through energy and angular momentum exchange

J. Stöhr, H.C. Siegmann,Magnetism (Springer)

41

+ 256-320 bunches for 500mA beam current+ Possibility of one or two 5mA "camshaft"

bunches in filling gaps+ Bunch spacing:

multibunch mode: 2 nstwo-bunch mode: 328 ns

+ Pulse length 70ps

ALS TIME STRUCTURE

bunch spacing

Pulse length 70 ps

camshaft

+ <300 fs x ray pulses though “laser bunch-slicing technique”

42

C. Boeglin, et al., Nature 465, 458 (2010)

+ Orbital (L) and spin (S) magnetic moments can change with total angular momentum is conserved.

+ Efficient transfer between L and S through spin–orbit interaction in solids

+ Transfer between L and S occurs on fs timescales.

+ Co0.5Pt0.5 with perpendicularmagnetic anisotropy

+ 60 fs optical laser pulses change magnetization

+ Dynamics probed with XMCD using 120fs x-ray pulses

+ Linear relation connects Co L3 and L2 XMCD with Lz and Sz using sum rules

Co0.5Pt0.5

ULTRAFAST DYNAMICS OF SPIN AND ORBITAL MOMENTS

43

ULTRAFAST DYNAMICS OF SPIN AND ORBITAL MOMENTS

+ Characteristic thermalization:Faster decrease of orbital moment

+ Theory: Orbital magnetic moment strongly correlated with magnetocrystalline anisotropy

+ Reduction in orbital moment ⇔ Reduction in magnetocrystalline anisotropy

+ Typically observed at elevated temperatures in static measurements as well

+ Further studies needed

C. Boeglin, et al., Nature 465, 458 (2010)

44

0.0

0.5

1.0

780 790 800-0.05

0.00

0.05

photon energy (eV)

XA (a

rb. u

nits

)XM

LD(a

rb. u

nits

)

Fe

Co_G

aAs_

XMLD

.opj

MAGNETIC SPECTROSCOPY

+ X ray absorption

+ X ray magnetic circular dichoism, XMCD

+ X ray magnetic linear dichroism, XMLD

+ X ray magnetic microscopy

+ Magnetization Dynamics

E. Arenholz et al., Appl. Phys. Lett. 93, 162506 (2008)

3 µm

[100]

ENiO

Co

NiO

Co

C. Boeglin et al., Nature 465, 458 (2011)

Co0.5Pd0.5

Co

Co

Co

CoO

780 790 800photon energy (eV)

XA (a

rb. u

nits

)

Co

O_C

o.op

j 0.0

0.5

1.0

780 790 800-0.5

0.0

photon energy (eV)

XA (a

rb. u

nits

)

FeCo

_GaA

s_XM

CD.o

pj

XMCD

(arb

. uni

ts)

45

J. Stöhr, H.C. SiegmannMagnetism− From Fundamentals to Nanoscale DynamicsSpringer

D. AttwoodSoft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications

REFERENCES AND FURTHER READING