Anisotropic magnetoresistance effects in ferromagnetic semiconductor and metal devices Tomas Jungwirth University of Nottingham Bryan Gallagher, Tom Foxon, Richard Campion, Kevin Edmonds, Andrew Rushforth, Chris King et al. Hitachi Labs., UK & Japan University of Texas and Texas A&M Jorg Wunderlich, Byong-Guk Park, Andrew Irvine, Allan MacDonald, Jairo Sinova David Williams, Akira, Sugawara, et al. Institute of Physics ASCR Alexander Shick, Jan Mašek, Josef Kudrnovský, František Máca, Karel Výborný, Jan Zemen, Vít Novák, Kamil Olejník, et al. University of Wuerzburg Polish Academy of Sciences Tohoku University Laurens Molenkamp, Charles Gould Tomasz Dietl, et al. Hideo Ohno, et al.

Outline 1. Intro - basic micromagnetics in DMSs 2. DMS materials science 3. AMR effects in DMSs and metals – devices and physics

(Ga,Mn)As: an archetypical dilute moment FM semiconductor Mn-d-like local moments As-p-like holes Mn Ga As Mn SW-transf.  J pd S Mn. s hole Dilute Mn-doped SC: sensitive to doping; 100  smaller M s than in conventional metal FMs Mn-Mn coupling mediated by holes in SO-coupled SC valence bands: sensitive to gating, comparable magnetocrystalline anisotropy energy and stiffness to metal FMs For not too strong p-d hybridization: kinetic-exchange (J pd ) & host SC bands provides simple yet often semiquantitative description

MF-like M(T); square hysteresis loops 1 mm500 nm 8 K 22 K Macro (100’s  m) domains; nm domain walls (~  A/K) reflecting combined T-dependent uniaxial and cubic anisotropies

One  m Strain controlled micromagnetics and current induced DW dynamics  tunable 100x smaller critical currents than in metals Huge hysteretic MR tunable by gate due to CBAMR  spintronic transistor … plus weak dipolar crosslinks  prospect for dense integration of magnetic microelements

Outline 1. Intro - basic micromagnetics in DMSs 2. DMS materials science 3. AMR effects in DMSs and metals – devices and physics

Magnetism in systems with coupled dilute moments and delocalized band electrons (Ga,Mn)As coupling strength / Fermi energy band-electron density / local-moment density

VB-CB VB-IB Mn-acceptor level (IB) Short-range ~ M. s potential - additional Mn-hole binding - ferromagnetism - scattering GaAs:Mn extrinsic semiconductor GaAs VB GaMnAs disordered VB   2.2x10 20 cm -3

MIT in GaAs:Mn at order of magnitude higher doping than quoted in text books

MIT in p-type GaAs: - shallow acc. (30meV) ~ cm -3 - Mn (110meV) ~10 20 cm -3 Mobilities: x larger in GaAs:C - similar in GaAs:Mg or InAs:Mn > 2% Mn: metallic but strongly disordered Model: SO-coupled, exch.-split Bloch VB & disorder - conveniently simple and increasingly meaningful as metallicity increases - no better than semi-quantitative   Mn spacing

Covalent SCs do not like doping  self-compensation by interstitial Mn Interstitial Mn Int is detrimental to magnetic order charge and moment compensation defect Mn sub Mn Int Mn sub As Ga Mn Int + - Can be annealed out T c 95K in as-grown (9% Mn) to 173 in annealed (6% Mn sub ) but Mn Ga < nominal Mn theory & exp. Mn Ga solubility limit

d4d4 d Weak hybrid. Delocalized holes long-range coupl. Strong hybrid. Impurity-band holes short-range coupl. d 5  d 4 no holes InSb, InAs, GaAs GaN GaP, AlAs d5d5 Search for optimal III-V host: optimal combination of hole delocalization, p-d coupling strength, low self-compensation

I-II-Mn-V ferromgantic semiconductors III = I + II  Ga = Li + Zn GaAs and LiZnAs are twin semiconductors Prediction that Mn-doped are also twin ferromagnetic semiconductors No limit for Mn-Zn (II-II) substitution Independent carrier doping by Li-Zn stoichiometry adjustment

Outline 1. Intro - basic micromagnetics in DMSs 2. DMS materials science 3. AMR effects in DMSs and metals – devices and physics

M || Anisotropic, SO-coupled, exchange-split hole bands Chemical potential  CBAMR Tunneling DOS  TAMR M M I I Impurity scattering rates  AMR

& electric & magnetic control of Coulomb blockade oscillations Coulomb blockade AMR – anisotropic chemical potential SourceDrain Gate VGVG VDVD Q [ 010 ]  M [ 110 ] [ 100 ] [ 110 ] [ 010 ] 

CBAMR if change of |  (M)| ~ e 2 /2C CBAMR if change of |  (M)| ~ e 2 /2C  In our (Ga,Mn)As ~ meV (~ 10 Kelvin)In our (Ga,Mn)As ~ meV (~ 10 Kelvin) In room-T ferromagnet change of |  (M)|~100KIn room-T ferromagnet change of |  (M)|~100K Room-T conventional SET (e 2 /2C  >300K) possible Worth trying to look for CBAMR in SO-coupled room-T c metal FMs

Tunneling AMR – anisotropic TDOS TAMR in GaMnAs GaMnAs Au AlOx Au Resistance Magnetisation in plane M perp. M in-plane ~ 1-10% in metallic GaMnAs Huge when approaching MIT in GaMnAs Anisotropc tunneling amplitudes

TAMR in metals theory experiment

Anisotropic magnetoresistance THEORY EXPERIMENT Semiquantitative numerical understanding in GaMnAs

SO & polarized scatterers Qualitative physical (analytical) picture anisotropic scattering