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Lecture 3 continuation from Wednesday

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Dynamical Matrix -

Conduction electrons

Importance of el-ph

Matrix elements

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G. L. Zhao and B. N. Harmon, Phys. Rev. B45, 2818 (1991)

NiAl

Exp.

Thy

Confirmed by

H. Chou and S.M.Shapiro

Phys. Rev. B48, 16088

(1993)

50-50 compound

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b- phaseNi0.625 Al0.375

T = 0 KTheory

(using rigid band

approximation)

G. L. Zhao and B. N. Harmon, Phys. Rev. B45, 2818 (1992)

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Solid lines are theory, with a

fictitious temperature of 1000 K to

account for thermal and alloydisorder.

Symbols are experiment at RT, and

dashed line is experiment at 85 K.

S.M. Shapiro, Mat.Sci. Forum 56-58, 33 (1990)

and

S.M. Shapiro, B.X. Yand, G. Shirane, Y. Noda, and

L.E. Tanner, Phys. Rev. Lett. 62, 1298 (1989)

Ni0.625 Al0.375

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Xiangyang Huang, Claudia Bungaro, Vitaliy Godlevsky, and Karin M. Rabe

Phys. Rev. 65, 014108 (2001).

NiTi B2 T=0K

Unstable

phonons

Electronic

structure -

force constants

Many Phonon is Bzone are imaginary!!!(all first principlesnot a surprise perhaps, at this is for T=0)

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Problem with first principles (T=0) calculation of the bcc structure:It is unstable if the temperature effect is not included, as we saw

Can be stabilized by non-linear phonon couplings: 3 & 4 order (T=0 OK)Ye, Chen, Ho, Harmon and Lindgrd, PRL, 58, 1769 (1987)

A new way is presented above:By allowing atoms to be displaced from the (average) bcc positionsSelf-consistently calculate forces and mean-square displacementsin a 4x4x4 times larger super cell than the uinit one until convergence.Frozen glassy-like structure?This nicely illustrates the bcc problem by a direct FP calculation

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Calculated phonon spectra

T>TM

!N T=0 !N

Imaginary

Takes into account the temperature! Compare to T=0 calculations.

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Energy paths through the landscape

The Na story

Total energy calculation for structuralphase transformations

Y.Y. Ye, C.-T. Chan, K.-M. Ho and B. N. Harmon

The International Journal of Supercomputer Applications,

Volume 4, No. 3 Fall 1990, pp. 111-121.

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bcc

hcp

9R

Na - precise total energy calculations

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The bcc-hcp transition

requires

1. A shuffle of atomic planescorresponding to a T1 N-

point phonon, and

2. A shear (Bain strain) that

changes the basal plane

angle from 109.47o to 120o.

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bcc hcp

The minimum energy

path displays some

interesting physics.

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9R has slightly

lower barrier and

slightly lower totalenergy compared

to the hcp phase.

bcc

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TMS March 10, 2008

X-Ray Magnetic Circular Dichroism (XMCD)

For

Rare Earth Magnetic Materials

Toward a Quantitative Analysis

Bruce Harmon

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TMS March 10, 2008

First, a big thanks!

To

Karl Gschneidner

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TMS March 10, 2008

5dEF

RCPLCP

2p3/2

2p1/2

XRESXMCD

XRES and XMCD

L3

L2

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TMS March 10, 2008

Good Features of XMCD

for magnetism studies

1. Element specific(tune beam to core energy)

2. ~ Orbital specific(dipole selection rule)

3. No nuclear absorption(sometimes problem for neutrons)

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TMS March 10, 2008

History

Magnetic x-ray dichroism in gadolinium metal

P. Carra, B. N. Harmon, B. T. Thole, M. Altarelli, and G. A. Sawatzky

Phys. Rev. Lett. 66, 2495-2498 (1991)

L2 L3

G. Schtz, et. al., Z. Phys. B 73, 67 (1988).

THEORY

EXPERIMENTL2 L3

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TMS March 10, 2008

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TMS March 10, 2008

OrbitalXMCD SUM RULES

Spin

where X-ray circular dichroism and local magnetic fieldsP. Carra, B. T. Thole, M. Altarelli, and X. WangPhys. Rev. Lett. 70, 694-697 (1993)

X-ray circular dichroism as a probe of orbital magnetization

B. T. Thole, P. Carra, F. Sette, and G. van der LaanPhys. Rev. Lett. 68, 1943-1946 (1992)

Limitation of the Magnetic-Circular-Dichroism Spin Sum Rule for Transition Metals andImportance of the Magnetic Dipole Term

R. Wu and A. J. Freeman

Phys. Rev. Lett. 73, 1994-1997 (1994)

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TMS March 10, 2008

The Sum Rules work wonderfully for 3d-transition metals!

But they do not work for Rare Earth materials!

Why?

(Atomic model assumptions breakdown!)

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TMS March 10, 2008

2p position

4pr2R2(r) 5d

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TMS March 10, 2008

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TMS March 10, 2008

Solid State Effects

5d spin up wave function is contracted by4f-5d exchange interaction

Spin up Radial Matrix Elements (ME) are largerthan spin down

Energy dependent ME

Top of

d-bands

EF

4f

up2pdown

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TMS March 10, 2008

Trend of Exchange and S-O Energyof Heavy Rare-Earth 5d States

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TMS March 10, 2008

0

2

4

6

8

10

RNi2Ge

2

Theory - hcp

LIII

/LII

Tb Dy Ho Er TmGd

Experiment RNi2Ge

2

Theory - HCP

BRANCHINGR

ATIO

No-Spin Orbit

6

Branching Ratio L3/L2

Experiment vs. Theory

J. W. Kim, Y. Lee, D. Wermeille, B. Sieve, L. Tan, S.L. Budko, S. Law, P. C. Canfield, B. N. Harmon,and A. I. GoldmanPhys. Rev. B 72, 064403 (2005)

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TMS March 10, 2008

(Low T) Orthorhombic Monoclinic (High T)

Thebreaking of Ge(Si) bonds is responsible for loss of magnetism

Gd5Si2Ge2

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TMS March 10, 2008

Gd5Si2Ge2 : XMCD

* XMCD data at the Ge K and Gd L3 edges.* XMCD signal of Ge K-edge indicates that the Ge 4p states carry

magnetic polarization.

D. Haskel et al. PRL 98 247205 (2007)

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TMS March 10, 2008

Ge2

Gd

Si

Ge1

Orthorhombic Monoclinic

ba

Gd5Si2Ge2:spin density contours

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TMS March 10, 2008

The Er2

Fe17

Story

J. Chaboy, H. Maruyama, N. Kawamura, and M. Suzuki

Phys. Rev. B 69, 014427 (2004)

The Er2Fe17N2.4XMCDspectra were

taken at roomtemperature and at

50K. Large spectralchanges, and

quadrupole features

observed.

Er L3 edge

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TMS March 10, 2008

The Er2Fe17 StoryJ. Chaboy, H. Maruyama, N. Kawamura, and M. Suzuki

Phys. Rev. B 69, 014427 (2004)

The Er L2 spectra

changes sign with

temperature!

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TMS March 10, 2008

Calculated L3 for Er2Fe17Yongbin Lee

with E2 contribution added

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TMS March 10, 2008

Calculated L2 for Er2Fe17

with E2 contribution added

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TMS March 10, 2008

Goldman et. al. L3

Experiment

Yongbin

TheoryEr L3 edge normalized to peak

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

-15 -10 -5 0 5 10 15 20

Energy (eV)

NormalizedDic

hroism(

topeak)

T=300K

T=200K

T=125K

T=75K

Experiment

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TMS March 10, 2008

Goldman et. al. L2

Experiment

Yongbin

Er L2 edge peak normalized

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

-10 -5 0 5 10 15 20

Energy (eV)

NormalizedDichroism(

toPeak)

T=300K

T=200K

T=125K

T=75K

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TMS March 10, 2008

The qualitative agreement leaves

little doubt the physics is correct,but the quantitative agreement is

poor!

New results indicate enhanced

orbital polarization on Er and also

possibly on Fe can account for all

the differences.

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TMS March 10, 2008

Thank You

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TMS March 10, 2008

K. Takeda et al.,

J. Alloys Compd. 281, 50 (1998)