Light Matter Interactions (II) Light Matter Interactions (II) - PowerPoint PPT Presentation

Light – Matter Interactions (II) Light – Matter Interactions (II) Peter Oppeneer Department of Physics and Astronomy Uppsala University, S-751 20 Uppsala, Sweden 1

Outline – Lecture II – Light-magnetism interaction  Phenomenology of magnetic spectroscopies  Electronic structure theory, linear-response theory  Theory/understanding of magnetic spectroscopies • Optical regime • Ultraviolet and soft X-ray regime 2

In the beginning … First observation of magneto-optics Magneto-optical Faraday effect (1845)  Observation of interaction light-magnetism enormous impact on development of science! Faraday effect E q F (- M ) = - q F ( M ) Michael Faraday q F ( M ) ~ lin. M (1791 – 1868) 3

Magneto-optical Kerr effect Kerr (1876) Kerr (1878) Zeeman (1896) pol. analysis pol. analysis intensity measurement  r r b      tan K  a r r   Rotation of the polarization plane & ellipticity: Completely a magnetic effect! One of the best tools in magnetism research! 4

Magneto-optical Voigt effect Voigt effect (1899) ^ q V 45 o Woldemar Voigt (1850 – 1919) Very different from Faraday effect; Voigt effect is “ quadratic ” (even) in M Voigt effect Kerr effect Imaging of magnetic domains using Voigt and Kerr effect in reflection (Courtesy R. Schäfer) 5

Magnetic circular and linear dichroism M E || E  E ^ MCD  ( I   I  )/( I   I  ) MLD  ( I ||  I ^ )/( I ||  I ^ ) Magnetic Circular Dichroism Magnetic Linear Dichroism ”odd in M” ”even in M” 6

Development of light-magnetic material interaction Inv. Faraday effect Electron MCD Ultrafast magn.switching Non-linear magneto-optics Spin Hall effect XMLD XMCD, XRMS Vector magnetometry Domain imaging MO Kerr loops Magn. circ. dichroism Zeeman effect Voigt effect Kerr effect Faraday effect (1845) 7

Recent Examples of Light – Magnetism Interactions Observation of the spin Hall effect Kato, Myers, Gossard & Awschalom, Science 306 , 1910 (2004) Spin Hall effect Kerr rotation image Dyakonov & Perel, JETP Lett. Reflection 13 , 467 (1971) image Material: non-magnetic n-GaAs [110] MO Kerr rotation detection ~ 10 -5 deg. 8

Spin Hall effect in heavy metals Gives rise to spin-orbit torque Direct observation of SHE in pure heavy-metal difficult because of short spin lifetime and spin diffusion length Miron et al, Nature 476 , 189 (2011) Liu et al, Science 336 , 555 (2012) J c MOKE detection could be possible due to penetration depth 9

Experimental direct observation of spin Hall effect Pt j =10 7 A/cm 2 SH (exp)  1880 [ W cm ]  1 s xz SH ( th )  1890 [ W cm ]  1 s xz Excellent agreement with experiment Stamm, Murer, Berritta, Feng, Gabureac, Oppeneer Estimated l s =11.4 ± 2 nm for pure Pt & Gambardella, PRL 119 , 087203 (2017)  Accurate MOKE measurements of SH conductivity in heavy metals feasible with nrad sensitivity 10

Optically induced magnetization Due to nonlinear “opto-magnetic” effect, the inverse Faraday effect: Induces magnetization  M Could potentially lead to a fast, optically driven magnetization reversal Kimel et al, Nature 435 , 655 (2005) 11

All-optical writing of magnetic domains GdFeCo FePt Stanciu et al, PRL 99 , 047601 (2007 ) Lambert et al, Science 345 , 1337 (2014)  Due to inverse Faraday effect?  Background all-optical magn. recording  Erasing & writing with fs-laser pulses  Approx. 10 3 times faster recording? (symposium Th. Rasing, A. Kirilyuk) 12

Ultrafast magnetism Measurement of ultrafast magnetic response with time-resolved magneto-optics x t t M ( ), n ( ) z y Ni q t  t ( , M ) , R ( ) fs laser pulse K t s E e p fs laser pulse (pump) Hofherr et al, PRB 96 , Beaurepaire, Merle, Danois, 100403R (2017) Bigot, PRL 76 , 4250 (1996)  Magnetization decay  Very fast decay in <250 fs ~40 fs 13

Theoretical description of light – magnetism interaction Use 2 nd level: Combination of Maxwell-Fresnel theory and ab initio quantum theory Fresnel equation for modes in material: Geometry & materials ´ boundary     r   i r r E E      ss sp  s   s conditions:       r i r r E E       ps pp p p q  q r E n cos n cos    s r i i t t E s ss q  q i E n cos n cos s i i t t q q a t E 2 n cos   s t i i E p ss b q  q i E n cos n cos s i i t t Polarization analysis or intensity measurement And: ab initio theory for calculation of  ( w ) 14

Dependence of the dielectric tensor on fields         w ( k , , B , E ) The dielectric tensor depends on external fields    ( 1 ) Use a Taylor expansion for effects to lowest order:     w  ( k , B , E , )         O ( k ) O ( B ) O ( E ) O ( B E ) O ( B B ) O ( E E )  0 i j i j i j All the (linear) phenomena can be described, using the Fresnel formalism 15

Magnetic effects in Fresnel equations Typical  tensor: Onsager relations  Magnetic parity     0   w    w ( H , ) ( H , )  odd   ^ xy  xy xy       0 ^ yx   w    w ( H , ) ( H , )    even    0 0   || Magn. effects probe always ~ M or ~ M 2 (to lowest order) Examples:    w d    2 w d  xy Re MCD Odd in M; MLD      xy even   Im   ^ 2 c n ||    2 cn     ^    0   2 M     16

Magneto-optical Kerr and Faraday effects polar Kerr effect, normal incidence Faraday effect, normal incidence     2 n i Assume    s  s Use or  xx xy xy xx xy xx s w  s w  ( ) ( ) 2 d q    xy q    xy i i F F K K   s w s   s w 1 / 2 1 / 2 c ( 1 4 i / ) ( 1 4 i / ) xx xx xx 17

Classification of magnetic spectroscopies Linear (odd) in M spectroscopies: Classification criteria: Polarization Intensity analysis 1. Magnetic parity 2. Transmission or Transmission Faraday MCD L C reflection 3. Polarization or C P-MOKE T-MOKE Reflection intensity L-MOKE L L RMS 4. Linearly or circ. polarized light 2 quantities 1 quant. Suitable for (element-selective) study of ferro-, ferrimagnets 18

Even-in- M magnetic spectroscopies Quadratic (even) in M spectroscopies: Polarization Intensity analysis Transmission Voigt MLD L L birefringence Reflection R-MLD L L R-Voigt 2 quantities 1 quant. Suitable for (element-selective) study of antiferromagnets (and ferromagnets as well) 19

Linear-response theory Lifetime broadening, 1/ t ~ 0.4 eV  2 2 4 e   w     w  w x x Im[ ( )] Re{ } ( ) xx n ' n nn ' nn ' w 2 2 m V  n n ' un . occ .  2 2 4 e   w     w  w x y Re[ ( )] Im{ } ( ) xy n ' n nn ' nn ' w 2 2 m V  n n ' (for 1/ t -> 0) un . occ . Lifetime broadening happens and needs to be taken into account 20

Lifetime broadening – linear magneto-optics calc. Optical frequencies: lifetime G1/t ≈ 0.03 Ry Oppeneer, Handbook of Magnetic Materials, Vol. 13 (2001) 21

Origin of magneto-optical effects Effective Kohn-Sham Hamiltonian: Exchange field      2     ˆ  ˆ ˆ ˆ       s    s H V ( r ) V ( r ) 1 B ( r )    e , N 0 xc 2 m   Spin-orbit coupling Spin-density (2x2):           n ( r ) n ( r ) n ( r )    s n ( r ) { n ( r ) 1 m ( r ) } / 2        0    m ( r ) n ( r ) n ( r ) B   Vary the two magnetic interactions (exchange & spin-orbit) to deduce how magnetic spectra depend on these. 22

Effect of SOI and exchange interaction    2 e  1 dV      s    Full form of SOI:   H SO L ( L S ) 2 2 4 m c  r dr  Ni (small relativistic effect) Exchange splitting, 1 – 2 eV (3d atom) Spin-orbit splitting ~20 meV    ex SOC 1 eV Spin-orbit coupling breaks crystal symmetry 23

Leading order quantity: spin-orbit coupling Leading quantity determining the valence band MO effect is spin-orbit coupling   L.S)  Kerr and Faraday effect scale linear in the SOC, not in the exc.-splitting! Scaling of SOI Scaling of exc.int. Ni 24

What about the X-ray regime ? w   w    i / c ( n z ) i t X-ray magnetic circular dichroism E ( z , t ) ( e i e ) e   x y Co XMCD Understand origin of and perform ab initio calculations for XMCD & XMLD at L-edges 25