Micromagnetic Ordering in (Ga,Mn)As

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Micromagnetic Ordering in (Ga,Mn)As

• Kevin Edmonds
• School of Physics and Astronomy, University of
  Nottingham, Nottingham NG7 2RD, United Kingdom

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University of Nottingham Bryan Gallagher Tom
Foxon Tomas Jungwirth Richard Campion Oleg
Makarovsky Kaiyou Wang Andrew Rushforth Adam
Freeman
And also Maciej Sawicki (IFPAN Warsaw) Tomasz
Dietl (IFPAN Warsaw) Gerrit van der Laan
(Daresbury) Nicola Farley (Daresbury) Elke
Arenholz (Advanced Light Source) Julio Cesar,
Nick Brookes, Peter Bencok, Andrei Rogalev,
Fabrice Wilhelm (ESRF) Stefan Maat (Hitachi
Global Storage)
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Ohno et al JAP 91 ferromagnetic ordering in
p-type (In,Mn)As
TC 7.5K
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(Ga,Mn)As A ferromagnet with TC 173K
Jungwirth et al, Phys Rev B 72, 165204 (2005)
TC substitutional Mn concentration x
Saturation not observed up to 7 (technological
rather than fundamental limit)
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Origin of Ferromagnetism
Sandratskii PRB 69, 195203 (04) LDAU

• In narrow gap III-V magnetic semiconductors
• (Ga,In,Mn)(As,Sb)
• ferromagnetism is due to 2 properties of Mn2
  dopants
• acceptor polarized delocalized hole with mostly
  As 4p character
• d5 magnetic moment strong exchange coupling
  Jp-d to holes leads to long range Mn-Mn
  interaction

GaAs 4s,p
1 Hole / Mn
Mn 3d
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Overview

1. Magnetic anisotropy
2. X-ray magnetic circular dichroism

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Strain-induced anisotropy
Growth direction
Compressive Biaxial strain
?



(GaMn)As
D2d




GaAs(001)
Strong magnetocrystalline anisotropy favouring
in-plane magnetization
Td
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Magnetization reversal
(Ga,Mn)As/GaAs(001) with in-plane anisotropy
Welp et al, Phys Rev Lett 90, 167206 (2003)
Low T biaxial easy magnetic axes, approximately
parallel to lt100gt in-plane directions rever
sal via 900 domain walls. High T uniaxial easy
magnetic axis, parallel to either 110 or 110
in-plane direction reversal via 1800
domain walls.
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AC Susceptibility- evidence for dopant
clustering?
Hamaya et al., PRL (2005) Peak observed in AC
susceptibility from (Ga,Mn)As at the spin
reorientation transition temperature - suggestion
that the two magnetic phases are present, with
biaxial and uniaxial anisotropy respectively
TC
Temperature
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Single-domain behaviour
(Ga,Mn)As/GaAs(001), 2 Mn, p 3x1020
cm-3 Remnant magnetization after field cool at
1000 Oe Green line single domain model, M100
MS cosq Deviation from single domain only at spin
reorientation transition (SRT).
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Decreasing Hbi / Huni
Increasing Temperature
Hbi Huni Spin Reorientation
Hbi ltlt Huni Dominant uniaxial
Hbi gtgt Huni Dominant biaxial
Energy density F
Magnetization angle q
F -Hbi sin2(2q)/4 Huni sin2(q)
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Apply weak AC field...
Hext
Hext
Energy density F
Magnetization angle q
F -Hbi sin2(2q)/4 Huni sin2(q) Hext(t)
cos(q - qH)
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AC susceptibility
Peaks in AC susceptibility are dependent on the
direction of applied field wrt crystalline axes -
consistent with single-domain rotation
SRT
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Anisotropy fields
Hcubic MS3 Huniax MS
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Experiment
Calculated
Low T peak is reproduced by a simple
single-domain model ? not due to mixed
phases Wang et al., PRL 95, 217204 (2005)
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Experiment
Calculated
Include incoherent rotation ? peak
at TC is reproduced, too (occurs when driving
field gt coercive field) Wang et al., PRL 95,
217204 (2005)
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Uniaxial easy axis
p 4x1020 /cm3
p 8x1020 /cm3
90o rotation of uniaxial easy axis on
annealing due to increase in carrier density
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Hole density determines anisotropy
p-d Zener calculation
110 easy
110 hard
900 rotation of in-plane easy axis when p gt
6x1020 cm-3
Sawicki et al., Phys Rev B 71, 121302 (05)
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X-ray Magnetic Circular Dichroism(XMCD)
Excited core electrons probe unfilled states
above EF with l 1 Circular polarised x-rays
? spin-polarised emission Magnetic material
? polarised valence band ? spin-polarised
detection
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XMCD from (Ga,Mn)As
Large XMCD signal at the Mn absorption edges,
corresponding to 4.5mB per Mn atom.
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Mn L2,3 XMCD from (Ga,Mn)As
angle dependence
Edmonds et al. Phys. Rev. Lett. 96, 117207 (2006)
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Cubic anisotropy atomic property
Atomic multiplet calculation for Mn d5
tetrahedral crystal field 10Dq0.5eV
M // lt100gt M // lt111gt
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Strain effect?
Compressive Biaxial strain
Tensile Biaxial strain






(GaMn)As
(GaMn)As
D2d








(In,Ga)As
GaAs
Td
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Influence of Strain
Strain influences Mn 3d states
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Influence of carrier-density
decreasing p
Pre-edge feature is hole-density-dependent, so
must correspond to states close to Fermi level, EF
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Mn 3d local DOSfrom LDAU
From Sandratskii PRB 69, 195203 (04)
n.b. XMCD measures unoccupied states
Mn 3d
unoccupied Mn spin-up states at EF, with symmetry
of strain-split GaAs VB states
EF
atomic-like Mn 3d5 spin-down band
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As 4p polarization
As K-edge XMCD probes 1s ? 4p transitions ESRF
ID12, July 2006
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Summary

• (Ga,Mn)As shows reorientation transitions of
  magnetocrystalline anisotropy as a function of
  strain, temperature, hole density
• - AC susceptibility peak at cubic -gt uniaxial
  transition is reproduced by a simple single
  domain model (does not imply mixed phases!)
• ? Angle-dependent x-ray dichroism spectra allow
  to distinguish Mn 3d states
• cubic features weakly hybridized, atomic-like
  conduction band states
• uniaxial features states at EF, hybridized with
  valence band