Karel Výborný, Jan Zemen, Kamil Olejník, Petr Vašek, Miroslav Cukr, Vít Novák, Andrew...
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Karel Výborný, Jan Zemen, Kamil Olejník, Petr Vašek, Miroslav Cukr, Vít Novák, Andrew Rushforth, R.P.Campion, C.T. Foxon, B.L. Gallagher, Tomáš Jungwirth Fyzikální ústav AV ČR, Cukrovarnická 10, Praha 6, CZ-16253 School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK internal structure magnetotransport anisotropy (AMR) Conclusion • a recipe how to extract anisotr • classification of anisotropy us (normal/cubic/monocli • microscopic calculation of the anisotropy parameters • in agreement with (different) e normal AMR < 0, • sign switch AMRip vs. AMRop due to growth strain Acknowledgements: LC510 (Center for fund. res.), NA Intro In an isotropic material, the sheet resistance does not depend on current direction and transversal resistance is zero. In a ferromagnet, (for instance diluted magnetic semiconductors) a special direction is given by the magnetization, the symmetry is lowered and both resistances become a function of the current direction. This effect, called magnetotransport anisotropy is further promoted by the particular symmetry of the crystalline environment: e.g. cubic in GaAs. Experimental Model calculations Phenomenology Modelling the effect of strain Isotropic • : angle between M and I the only param. • = polycrystalline (random psi, constant phi) • • 2 || cos ) ( xx Cubic any angles: (M), (I) • two angles: , , while • : magnetization to [100] • : current to [100] Cubic – inplane configuration • • for current I along ( ), voltage U along ( ): Most general AMR (Cubic material): • • Fourier expansion of U and V • • Keeping only the lowest terms: ´Magnetocrystalline anisotropy´ Isotropic vs. cubic Normal AMR: =NOR Cubic AMR: =CUB Uniaxial (in the plane) vs. • • (this is if I ||[100]) Uniaxial AMR: = UNI Six-band model GaAs within k.p approximation + SO interaction Mn moments: mean field, Kohn-Luttinger Hamiltonian Linear transport: Boltzmann equation equilibrium distribution shifted by relaxation time: , Fermi golden rule Transversal AMR ( ) Longitudinal AMR ( ) Transversal AMR ( ) Longitudinal AMR ( ) • NOR = -3.6% • CUB = 0.79% • UNI = 0.25% • 3.5% Mn, 50 nm film, measured at 4 K and inplane B = 1.3 T Inferred AMR: • negative normal AMR (contrary to metals) • uniaxial anisotr. present • NOR = -6.0% • CUB = 1.5% • UNI not calc. Microscopic mechanism: • mostly due to the minority hh band • Fermi surf./vel. change only little • relaxation times strongly anisotropic • 3.5% Mn, bulk, no strain, saturated Mn moments, in-plane geomet • 2.0% Mn, saturated Mn moments • biaxial strain (substrate – GaMnAs lattice mismatch) • current along [100] • w/o strain [010] = [001] • strain lifts the degeneracy • tensile/compressive – different sign of AMRip-AMRop • in agreement with exp. (Matsukura et al., Phys. E ’04) Relaxation times: • 5% Mn, 25 nm film, measured at 4 K and inplane B = 1.0 T • NOR = -3.0% • CUB = 0.36% • UNI = 0.54% 2 sin 2 sin 2 1 2 cos 2 cos 2 1 1 2 0 v u xx 2 sin 2 cos 2 1 2 cos 2 sin 2 1 1 2 v u xy cos sin ) ( || xy ) ( k 3 2 1 , , 3 2 1 , , xy xy xx xx 3 2 1 , , 3 2 1 , , j E j i j i ij I U R , / 2 1 2 2 2 2 1 2 2 2 2 2 1 2 1 )] ( ) ( [ ) ( ) ( 1 V V U U xx ] ) ( ) ( [ ) ( ) ( 2 2 2 2 2 1 2 2 1 1 2 2 2 2 1 2 1 1 V V U U xy 1 2 1 ) ( v V 4 1 4 2 1 2 1 2 1 ) ( u u u U 4 sin 2 sin 4 cos 2 cos 1 / 1 1 2 4 1 1 1 2 1 1 2 4 1 1 u v u u v u u v u u xx 2 1 u v 2 1 1 2 12 2 1 12 2 2 2 1 22 2 1 1 2 22 )] , ( ) , ( [ ) , ( ) , ( w w w w xx 2 1 u v 1 1 2 / ) ( u v u 1 2 1 / ) ( u u v xx 2 1 4 2 1 2 1 2 1 22 ) , ( u u u w 1 4 / u u )) ( ( k v E e k ) / )( / 1 ( ) ( i i k E k v ) ( )) ( ( ) ( ) 2 ( 2 3 3 k v E f k v E e k k d e j i k i I i I i i I pd MF R r s S J H , ) (
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Transcript of Karel Výborný, Jan Zemen, Kamil Olejník, Petr Vašek, Miroslav Cukr, Vít Novák, Andrew...
Karel Výborný, Jan Zemen, Kamil Olejník, Petr Vašek, Miroslav Cukr, Vít Novák, Andrew Rushforth, R.P.Campion, C.T. Foxon, B.L. Gallagher, Tomáš Jungwirth
Fyzikální ústav AV ČR, Cukrovarnická 10, Praha 6, CZ-16253School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
internal structuremagnetotransportanisotropy (AMR)
Conclusion• a recipe how to extract anisotropy params.• classification of anisotropy using these: (normal/cubic/monoclinic symmetry)• microscopic calculation of the anisotropy parameters• in agreement with (different) experiments: normal AMR < 0, • sign switch AMRip vs. AMRop due to growth strain
Acknowledgements:LC510 (Center for fund. res.), NANOSPIN
Conclusion• a recipe how to extract anisotropy params.• classification of anisotropy using these: (normal/cubic/monoclinic symmetry)• microscopic calculation of the anisotropy parameters• in agreement with (different) experiments: normal AMR < 0, • sign switch AMRip vs. AMRop due to growth strain
Acknowledgements:LC510 (Center for fund. res.), NANOSPIN
IntroIn an isotropic material, the sheet resistance does not depend on current direction andtransversal resistance is zero. In a ferromagnet,(for instance diluted magnetic semiconductors)a special direction is given by the magnetization,the symmetry is lowered and both resistancesbecome a function of the current direction. This effect, called magnetotransport anisotropyis further promoted by the particular symmetryof the crystalline environment: e.g. cubic in GaAs.
IntroIn an isotropic material, the sheet resistance does not depend on current direction andtransversal resistance is zero. In a ferromagnet,(for instance diluted magnetic semiconductors)a special direction is given by the magnetization,the symmetry is lowered and both resistancesbecome a function of the current direction. This effect, called magnetotransport anisotropyis further promoted by the particular symmetryof the crystalline environment: e.g. cubic in GaAs.
Experimental
Model calculations
Phenomenology
Modelling the effect of strain
Isotropic• : angle between M and I the only param.• = polycrystalline (random psi, constant phi)• •
2|| cos)( xx
Cubic
• many angles: (M), (I)• •
• two angles: , , while • : magnetization to [100]• : current to [100]
Cubic – inplane configuration
• • for current I along ( ), voltage U along ( ):
Most general AMR (Cubic material): • •
Fourier expansion of U and V• •
Keeping only the lowest terms:
´Magnetocrystalline anisotropy´ Isotropic vs. cubic
Normal AMR: =NORCubic AMR: =CUB
Uniaxial (in the plane)
vs.
•
• (this is if I ||[100])
Uniaxial AMR: = UNI
Six-band model
• GaAs within k.p approximation + SO interaction• Mn moments: mean field, • Kohn-Luttinger Hamiltonian
Linear transport: Boltzmann equation
• equilibrium distribution shifted by •
• • relaxation time: , Fermi golden rule
Transversal AMR ( ) Longitudinal AMR ( )
Transversal AMR ( ) Longitudinal AMR ( )
• NOR = -3.6%• CUB = 0.79%• UNI = 0.25%
• 3.5% Mn, 50 nm film, measured at 4 K and inplane B = 1.3 T
Inferred AMR:
• negative normal AMR (contrary to metals) • uniaxial anisotr. present
• NOR = -6.0%• CUB = 1.5%• UNI not calc.
Microscopic mechanism:• mostly due to the minority hh band• Fermi surf./vel. change only little• relaxation times strongly anisotropic
• 3.5% Mn, bulk, no strain, saturated Mn moments, in-plane geometry
• 2.0% Mn, saturated Mn moments• biaxial strain (substrate – GaMnAs lattice mismatch)
• current along [100]• w/o strain [010] = [001]• strain lifts the degeneracy• tensile/compressive – different sign of AMRip-AMRop
• in agreement with exp. (Matsukura et al., Phys. E ’04)
Relaxation times:
• 5% Mn, 25 nm film, measured at 4 K and inplane B = 1.0 T
• NOR = -3.0%• CUB = 0.36%• UNI = 0.54%
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