Lecture 3 continuation from Wednesday

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1 Lecture 3 continuation from Wednesday

2 Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements

3 NiAl compound Confirmed by H. Chou and S.M.Shapiro Phys. Rev. B48, (1993) Exp. G. L. Zhao and B. N. Harmon, Phys. Rev. B45, 2818 (1991) Thy

4 - phase Ni Al T = 0 K Theory (using rigid band approximation) G. L. Zhao and B. N. Harmon, Phys. Rev. B45, 2818 (1992)

5 Ni Al 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)

6 Many Phonon is Bzone are imaginary!!! (all first principles not a surprise perhaps, at this is for T=0) NiTi B2 T=0K Electronic structure - force constants Unstable phonons Xiangyang Huang, Claudia Bungaro, Vitaliy Godlevsky, and Karin M. Rabe Phys. Rev. 65, (2001).

7 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

8 Takes into account the temperature! Compare to T=0 calculations. Calculated phonon spectra Imaginary T>T M! N T=0! N

9 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

10 Na - precise total energy calculations bcc hcp 9R

11 The bcc-hcp transition requires 1. A shuffle of atomic planes corresponding to a T 1 N- point phonon, and 2. A shear (Bain strain) that changes the basal plane angle from o to 120 o.

12 The minimum energy path displays some interesting physics. bcc hcp

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

14 X-Ray Magnetic Circular Dichroism (XMCD) For Rare Earth Magnetic Materials Toward a Quantitative Analysis Bruce Harmon

15 First, a big thanks! To Karl Gschneidner

16 XRES and XMCD E F 5d XRES XMCD LCP 2p 3/2 L 3 RCP 2p 1/2 L 2

17 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)

18 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, (1991) THEORY L 2 L 3 L 2 EXPERIMENT L 3 G. Schütz, et. al., Z. Phys. B 73, 67 (1988).

20 XMCD SUM RULES Orbital 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, (1992) Spin where X-ray circular dichroism and local magnetic fields P. Carra, B. T. Thole, M. Altarelli, and X. Wang Phys. Rev. Lett. 70, (1993) 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)

21 The Sum Rules work wonderfully for 3dtransition metals! But they do not work for Rare Earth materials! Why? (Atomic model assumptions breakdown!)

22 4 r 2 R 2 (r) 5d 2p position

24 Solid State Effects 4f 5d spin up wave function is contracted by 4f-5d exchange interaction 2p down up Spin up Radial Matrix Elements (ME) are larger than spin down Energy dependent ME E F Top of d-bands

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

26 Branching Ratio L 3 /L 2 Experiment vs. Theory BRANCHING RATIO 10 8 LIII /LII Gd RNi 2 Ge 2 Theory - hcp Experiment RNi 2 Ge 2 Theory - HCP No-Spin Orbit Tb Dy Ho Er Tm 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, (2005)

27 Gd 5 Si 2 Ge 2 (Low T) Orthorhombic Monoclinic (High T) The breaking of Ge(Si) bonds is responsible for loss of magnetism

28 Gd 5 Si 2 Ge 2 : XMCD D. Haskel et al. PRL (2007) * XMCD data at the Ge K and Gd L 3 edges. * XMCD signal of Ge K-edge indicates that the Ge 4p states carry magnetic polarization.

29 Gd 5 Si 2 Ge 2 :spin density contours Orthorhombic Monoclinic b a Ge 2 Gd Si Ge 1

30 The Er 2 Fe 17 Story J. Chaboy, H. Maruyama, N. Kawamura, and M. Suzuki Phys. Rev. B 69, (2004) Er L 3 edge The Er 2 Fe 17 N 2.4 XMCD spectra were taken at room temperature and at 50K. Large spectral changes, and quadrupole features observed.

31 The Er 2 Fe 17 Story J. Chaboy, H. Maruyama, N. Kawamura, and M. Suzuki Phys. Rev. B 69, (2004) The Er L 2 spectra changes sign with temperature!

32 Calculated L 3 for Er 2 Fe 17 Yongbin Lee with E 2 contribution added

33 Calculated L 2 for Er 2 Fe 17 with E 2 contribution added

34 0.04 Experiment Er L3 edge normalized to peak Experiment Theory Normalized Dichroism (to peak) T=300K T=200K T=125K T=75K Energy (ev) Goldman et. al. L 3 Yongbin

35 Experiment Er L2 edge peak normalized Normalized Dichroism (to Peak) T=300K T=200K T=125K T=75K Energy (ev) Goldman et. al. L 2 Yongbin

36 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.

37 Thank You

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

X-ray Magnetic Circular and Linear Dichroism (XMCD, XMLD) and X-ray Magnetic Imaging (PEEM,...)

X-ray Magnetic Circular and Linear Dichroism (XMCD, XMLD) and X-ray Magnetic Imaging (PEEM,...) Jan Vogel Institut Néel (CNRS, UJF), Nanoscience Department Grenoble, France - X-ray (Magnetic) Circular