Lecture 3 … continuation from Wednesday

Dynamical Matrix -

Conduction electrons

Importance of el-ph

Matrix elements

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

b - phase Ni0.625 Al0.375

T = 0 K

Theory (using rigid band approximation)

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

Solid lines are theory, with a fictitious temperature of 1000 K to account for thermal and alloy disorder.

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

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 principles…not a surprise perhaps, at this is for T=0)

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 Lindgård, PRL, 58, 1769 (1987)

A new way is presented above: By allowing atoms to be displaced from the (average) bcc positions Self-consistently calculate forces and mean-square displacements in 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

Calculated phonon spectra

T>TM !N T=0 !N

Imaginary

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

Energy paths through the landscape

The Na story

Total energy calculation for structural phase 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.

bcc

hcp

9R

Na - precise total energy calculations

The bcc-hcp transition requires

1.  A shuffle of atomic planes corresponding to a T1 N-point phonon, and

2. A shear (Bain strain) that changes the basal plane angle from 109.47o to 120o.

bcc hcp

The minimum energy path displays some interesting physics.

9R has slightly lower barrier and slightly lower total energy compared to the hcp phase.

bcc

TMS March 10, 2008

X-Ray Magnetic Circular Dichroism (XMCD)

For

Rare Earth Magnetic Materials

Toward a Quantitative Analysis

Bruce Harmon

TMS March 10, 2008

First, a big thanks! To

Karl Gschneidner

TMS March 10, 2008

5d EF

RCP LCP

2p3/2

2p1/2

XRES XMCD

XRES and XMCD

L3

L2

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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)

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

THEORY

EXPERIMENT L2 L3

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Orbital

XMCD SUM RULES

Spin

whereX-ray circular dichroism and local magnetic fields P. Carra, B. T. Thole, M. Altarelli, and X. Wang Phys. 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 Laan Phys. Rev. Lett. 68, 1943-1946 (1992)

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

R. Wu and A. J. Freeman Phys. Rev. Lett. 73, 1994-1997 (1994)

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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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2p position

4pr2R2(r) 5d

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Solid State Effects

•  5d spin up wave function is contracted by 4f-5d exchange interaction

•  Spin up Radial Matrix Elements (ME) are larger than spin down

•  Energy dependent ME

Top of d-bands

EF

4f

up2pdown

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

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0

2

4

6

8

10

RNi2Ge2 Theory - hcp

LIII/LII

Tb Dy Ho Er TmGd

Experiment – RNi2Ge2

Theory - HCP

BR

AN

CH

ING

RAT

IO

No-Spin Orbit

6

Branching Ratio L3/L2 Experiment vs. Theory

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

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(Low T) Orthorhombic Monoclinic (High T)

The breaking of Ge(Si) bonds is responsible for loss of magnetism

Gd5Si2Ge2

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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)

TMS March 10, 2008

Ge2

Gd Si

Ge1

Orthorhombic Monoclinic

b a

Gd5Si2Ge2:spin density contours

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The Er2Fe17 Story

J. Chaboy, H. Maruyama, N. Kawamura, and M. Suzuki Phys. Rev. B 69, 014427 (2004)

The Er2Fe17N2.4 XMCD spectra were taken at room temperature and at 50K. Large spectral changes, and quadrupole features observed.

Er L3 edge

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The Er2Fe17 Story J. 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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Calculated L3 for Er2Fe17 Yongbin Lee

with E2 contribution added

TMS March 10, 2008

Calculated L2 for Er2Fe17

with E2 contribution added

TMS March 10, 2008

Goldman et. al. L3

Experiment

Yongbin

Theory Er 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)

No

rmal

ized

Dic

hro

ism

(to

pea

k)

T=300KT=200KT=125KT=75K

Experiment

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)

Nor

mal

ized

Dic

hroi

sm (t

o P

eak)

T=300KT=200KT=125KT=75K

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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.

TMS March 10, 2008

Thank You

TMS March 10, 2008

K. Takeda et al., J. Alloys Compd. 281, 50 (1998)