This document summarizes Konrad Dziatkowski's research on magnetic anisotropy in dilute magnetic semiconductors, specifically (III,Mn)V materials. It provides an overview of ferromagnetism in (Ga,Mn)As and challenges in growing high-quality films. It also describes experiments using ferromagnetic resonance to characterize magnetic anisotropy, including polar, azimuthal, and reorientation effects. Exchange biasing of (Ga,Mn)As with MnO is shown to induce unidirectional anisotropy. The goal is to understand magnetic interactions and anisotropy in these materials for applications in spin-based electronics.

1. Magnetic anisotropy
in (III,Mn)V semiconductors: an FMR study
Konrad Dziatkowski
Division of Solid State Physics Department of Physics
Department of Physics University of Texas at Austin
University of Warsaw

2. Advisors
•Prof. Andrzej Twardowski (U. of Warsaw)
•Prof. Jacek K. Furdyna (U. of Notre Dame)
•Prof. Bernard Clerjaud (U. Pierre et Marie Curie, Paris)
Coworkers
•Dr. Marta Palczewska, Mariusz Pawłowski (Institute of Electronic
Materials Technology, Warsaw)
•Dr. Tomasz Słupiński (U. of Warsaw)
•Dr. Xinyu Liu, Zhiguo Ge, Weng Lee-Lim, Ben Fehrman (U. of Notre Dame)
•Prof. Adam Barcz (Institute of Electron Technology, Warsaw)
•Dr. Rafał Jakiela (Institute of Physics PAS, Warsaw)
Supporting institutions
•U.S. Department of State
•Foundation for Polish Science
•(polish) Ministry of Science and Higher Education

3. University of Warsaw
•established in 1816; then: about 800 of students and 40-50 of faculty
•now: about 56,000 of students and 3,000 of faculty

4. Department of Physics UW
•physics was present at UW from the very
beginning in 1816; established as
an independent department in 1969
•now: about 700 of students and about
200 of faculty
•physics of particles, nuclear physics,
optics, solid state physics, biophysics,
medical physics, relativity and gravitation,
geophysics, astronomy, ...

5. Division of Solid State Physics
•about 12 of students and about 25 of faculty
•physics of semiconductors (III-V, II-VI, oxides, DMS), superconductors,
graphene, polymers, ...
•(magneto)optics in FIR-NIR-VIS-UV, (magneto)transport, magnetometry,
hydrostatic and uniaxial pressures, electroreflectance, ...
•MOCVD, Czochralski, AMMONO (for nitrides), photolitography, Kelvin
Probe Microscopy; characterization by Hall, DLTS, SQUID, electrochemical
CV profiling, ...

6. Spintronics (spin-based electronics)
•a field of electronics involving nanoscale devices
in which the information is carried/stored with use
of the spin of an electron rather than its electric charge
antiferromagnet (AFM)
pinned ferromagnet (FM)
nonmagnetic spacer (NM)
ferromagnet (FM)
SVD - spin valve device
MTJ - magnetic tunnel junction
•magnitude of passed current is modulated by the relative
orientation of the magnetization in ferromagnetic films
P. A. Gruenberg, Rev. Mod. Phys. 80, 1531 (2008)
A. Fert, Rev. Mod. Phys. 80, 1517 (2008)

7. Dilute magnetic semiconductors
•an alloy of parent, nonmagnetic semiconductor (e.g. GaAs, CdTe)
with the atoms of magnetic elements (e.g. Mn, Co)
host semiconductor magnetic ions
•host materials
III-V: GaAs, GaP, GaN, AlAs, AlN, InAs, InN, InP, ...
II-VI: CdTe, CdSe, CdS, ZnTe, ZnS, PbTe, ...
IV: Ge, Si
•magnetic dopants:
Mn, Cr, Fe, Co, ...

8. Ferromagnets among (III,Mn)V
alloy Tc Ref.
(Ga,Mn)As 173 [1]
(In,Mn)As 90 [2]
(In,Ga,Mn)As 110 [3]
(Ga,Mn)N 8 [4]
[1] K. Y. Wang et al., AIP Conf. Proc. 772, 333 (2005)
[2] T. Schallenberg and H. Munekata, Appl. Phys. Lett. 89, 042507 (2006)
[3] T. Słupiński et al., Appl. Phys. Lett. 80, 1592 (2002)
[4] E. Sarigiannidou et al., Phys. Rev. B 74, 041306 (2006)
A. H. MacDonald et al., Nature Mater. 4, 195 (2005)

9. Ferromagnetism of (Ga,Mn)As
•exchange interaction between band holes and manganese ions
itinerant band holes Jpd localized electrons from
of p shell d shell of Mn ions
T. Jungwirth et al., Rev. Mod. Phys. 78, 809 (2006)
•Jpd < 0 - antiferromagnetic coupling
|Jpd| ~ 0.9 - 3.3 ... - 14 eV
•effective RKKY-like interaction between manganese ions
JMn-Mn ~ Jpd · [sin(2kF r) - 2kF r·cos(2kF r)] / (2kF r)4
2
F. Matsukura et al., Phys. Rev. B 57, R2037 (1998)
•ferromagnetic Mn-Mn coupling

10. Growth of ferromagnetic (Ga,Mn)As
•low temperature molecular beam epitaxy
formation of MnAs
substrate temperature (oC)
300
metallic (Ga,Mn)As
200 insulator
roughening
100 policrystalline
0 0.02 0.04 0.06 0.08
concentration of Mn in Ga1-xMnxAs
after: H. Ohno, J. Magn. Magn. Mater. 200, 110 (1999)
•ion implantation + pulsed layer melting
M. A. Scarpulla et al., Appl. Phys. Lett. 82, 1251 (2003)

11. Growth of ferromagnetic (Ga,Mn)As
•substitutional manganese
5
>> electronic configuration: 3d reduction of:
>> acceptor >> concentration of holes
>> magnetic moment per ion: 5mB >> magnetization
>> Curie temperature
•interstitial manganese
>> double donor (electric compensation)
>> antiferromagnetic coupling with substitutional
manganese (magnetic compensation)
•antistructural defect AsGa
>> native for LT-MBE

12. Growth of ferromagnetic (Ga,Mn)As
•TC above 300 K ?
S. Mack et al., Appl. Phys. Lett. 92, 192502 (2008) Y. J. Cho et al., J. Appl. Phys. 103, 07D132 (2008)

13. Motivation
•lack of unambiguous description (qualitative and quantitative)
for the collective excitations of spin system (ferromagnetic resonance)
in dilute ferromagnetic semiconductors
•recognition of complex magnetic anisotropy of solitude films
and multilayered structure based on (III,Mn)V, identification of various
components of the anisotropy and establishing the possibilities
for its modifications
•understanding of relations joining magnetic anisotropy
with interlayer exchange coupling in (III,Mn)V-based SVDs or MTJs
antiferromagnet (AFM)
pinned ferromagnet (FM)
nonmagnetic spacer (NM)
ferromagnet (FM)
SVD - spin valve device
MTJ - magnetic tunnel junction

14. Materials
•solitude films of (Ga,Mn)As and (In,Ga,Mn)As
AFM
•double layers MnO / (Ga,Mn)As
FM
•(Ga,Mn)As / GaAs / (Ga,Mn)As structures
NM
FM
growers: T. Słupiński (UW),
X. Liu and Z. Ge (U. of Notre Dame)
Experimental technique
•electron spin resonance (ESR) spectrometer with microwave klystron
of X-band (~ 9 GHz)
•continuous-flow helium cryostat, T = 4 - 300 K
•electromagnet up to 1.4 T

15. Ferromagnetic resonance (FMR)
long range
ferromagnetic order + resonance transitions between
Zeeman-splitted spin states
•ground state: saturation
•resonance: collective excitation
energy
of the entire spin system hw
saturation
•uniform mode of FMR: coherent
magnetic field
behavior (”precession”) of all spins
w = g×mB×Hrez / h
•non-uniform modes (spin waves): P
non-trivial spatial dependence of the
dP/dH
local phase of excitation magnetic field

16. Anisotropy of FMR
(arb. units)
anisotropy of FMR ferromagnetic
resonance
ß ß ß dirt in cryostat
anisotropic magnetic
properties Hres
magnetization [001] magnetic field,
easy axis
q polar angle
H
minimum of
the resonance field
j
[100] [010]
azimuthal angle

17. Polar anisotropy
[001]
(degrees)
(degrees)
polar
q
angle
H
polar angle,
(Ga,Mn)As
polar angle,
200 nm
bufor GaAs
220 nm
GaAs (001)
magnetic field,
SL-A1
magnetic field,
magnetic field markers
spin wave resonance FMR line
K. Dziatkowski et al., Phys. Rev. B 70, 115202 (2004)
•both for (Ga,Mn)As/GaAs and (In,Ga,Mn)As/(In,Ga)As/InP
the magnetization easy axis is confined in the growth plane

18. Magnetic interactions vs anisotropy
dipol-dipol
interaction Þ shape
anisotropy in epitaxial (III,Mn)V
the crystalline anisotropy
dominates over
exchange
interaction Þ crystalline
anisotropy
shape anisotropy
compressive tensile
strain strain X. Liu et al., Phys. Rev. B 67, 205204 (2003)
W. L. Lim et al., Phys. Rev. B 74, 045303 (2006)
K. Dziatkowski et al., Phys. Rev. B 70, 115202 (2004)

19. Model of FMR
•Laudau-Lifschitz equation: dM / dt = g M ´ H
•small deviations of M from equilibrium
•harmonic solutions
(wres / g)2 = ( Fqq × Fjj - Fqj ) / (M2sin2q)
2
q, j - polar and azimuthal angle of M at equilibrium
F = FZeeman + Fshape + Fcrystal
•Hres(jH), qH = p/2
Þ
parametrized by
•Hres(qH), jH = p/4
H4II, H4^, H2II, H2^, geff
•Hres(qH), jH = -p/4
J. Smit and H. G. Beljers, Phillips Res. Rep. 10, 113 (1955)
M. Farle, Rep. Prog. Phys. 61, 755 (1998)

20. Polar anisotropy
fitting of the model to the experimental data
(degrees)
(degrees)
polar angle,
polar angle,
magnetic field, magnetic field,
magnetic field markers
spin wave resonance FMR line
polar angle, (degrees)

21. Azimuthal anisotropy
model
(arb. units)
resonance field,
resonance field,
resonance field,
azimuthal angle, (degrees) azimuthal angle, (degrees) azimuthal angle, (degrees)
(In,Ga,Mn)As
FCT lattice Þ biaxial anisotropy H 50 nm
Þ four-fold symmetry (90o rotation) [100] j (In,Ga)As
100 nm
? ? ? Þ uniaxial anisotropy azimuthal
InP (001)
Þ two-fold symmetry (180o rotation) angle
SL-B2
U. Welp et al., specific reconstruction of (001) GaAs
Appl. Phys. Lett. 85, 260 (2004) surface promoting correlated arrangements
M. Sawicki et al.,
of manganese ions along [110] or [1-10]
Phys. Rev. B 71, 121302 (2005)

22. Reorientation of the easy axis of magnetization
temperature-induced
reorientation of the easy axis
of magnetization
resonance field,
?
different dependence of biaxial
azimuthal angle, (degrees)
and uniaxial anisotropy constants
on magnetization 4.5
Resonance Magnetic Field (kOe)
[001]
K.-Y. Wang et al., Phys. Rev. Lett. 95, 217204 (2005)
[110]
two magnetic phases with different 3.0
g=2
anisotropies and different critical [110]
temperatures [100]
TC
K. Hamaya et al., Phys. Rev.Lett. 94, 147203 (2005) 1.5
0 20 40 60 80
Temperature (K)

23. Other magnetic anisotropies in (III,Mn)V
resonance field,
polar angle, (degrees) vicinal angle,
vicinal GaAs substrate [001]
ß
anisotropy dependent on the orientation Hrf
Hdc
of (dynamic) microwave magnetic field
speculation !! ß
nonlinear response of (Ga,Mn)As [110]
on rf magnetic excitation [110]

24. Exchange bias - discovery and basic idea
W. H. Meiklejohn and C. P. Bean, •due to interfacial exchange interaction an
Phys. Rev. 102, 1413 (1956)
antiferromagnet - which is unaffected by the
magnetic field reversal - acts on a ferromagnet
as a source of gain or loss of magnetic energy
•under field cooling (FC) conditions:
the hysteresis loop is shifted out of
H = 0 position due to exchange
coupling between antiferromagnetic
CoO and ferromagnetic Co J. Nogues and I. K. Schuller,
J. Magn. Magn. Mater. 192, 203 (1999)

25. Exchange biasing of (Ga,Mn)As with MnO
40 400
(a) (b)
HC
HC & HEB (Oe)
M (emu/cm )
3
20 300
HEB
0 200
15 nm
-20 30 nm 100
60 nm
-40 0
-1.0 -0.5 0.0 0.5 1.0 0 20 40 60 80
H (kOe) dFM (nm)
K. Dziatkowski et al., Appl. Phys. Lett. 88, 142513 (2006)
•proximity phenomenon
•exchange bias in MnO/(Ga,Mn)As reveals no training effect
for the alternating magnetic fields up to 9 kOe

26. Unidirectional anisotropy
MnO
15 nm
FMR line
(Ga,Mn)As
(arb. units)
15 - 60 nm
dirt in
bufor GaAs
cryostat ESR line 164 nm
GaAs (001)
FMR signal,
unidirectional anisotropy,
magnetic field,
interfacial exchange
interaction MnO«(Ga,Mn)As
ß
thickness of (Ga,Mn)As,
unidirectional anisotropy, breaking
O
of 180 -rotation symmetry K. Dziatkowski et al., Acta Phys. Polon. A 110, 319 (2006)

27. Unidirectional anisotropy
anisotropy field,
resonance field,
unidirectional
temperature, temperature,
•nonmonotonic temperature dependence of unidirectional anisotropy
field Ü interplay between bi- and uniaxial magnetic anisotropies
•interfacial exchange coupling in MnO/(Ga,Mn)As relatively robust
with respect to temperature

28. Fully coupled (Ga,Mn)As / GaAs / (Ga,Mn)As
(Ga,Mn)As
9 nm
GaAs
3 - 12 nm
(arb. units)
(Ga,Mn)As
14 nm
bufor GaAs
137 nm
GaAs (001)
FMR signal,
•for 3nm-thin GaAs spacer the observed
anisotropy resembles that observed for
a single FM layer
magnetic field, •diffusion of manganse from (Ga,Mn)As
K. Dziatkowski et al., Acta Phys. Polon. A 112, 227 (2007) into GaAs and the effective thinning
of GaAs spacer is a likely cause

29. Fully coupled (Ga,Mn)As / GaAs / (Ga,Mn)As
(Ga,Mn)As
9 nm
GaAs
3 - 12 nm
resonance field,
resonance field,
(Ga,Mn)As
14 nm
bufor GaAs
137 nm
GaAs (001)
polar angle, (degrees) polar angle, (degrees)
uniform mode of FMR
spin wave mode
•other authors point out the possible redistribution of the hole wave
function resulting in the electronic coupling of two (Ga,Mn)As layers
Z. Ge et al., Appl. Phys. Lett. 91, 152109 (2007)

30. Acoustic and optic modes of FMR
acoustic Hrf optic
mode mode
H
(arb. units)
dirt in •for GaAs spacer of ³ 6nm thickness: two FMR
cryostat
FMR signal,
lines corresponding to different collective
(magnetic) excitations of the entire sample
FMR lines
magnetic field,

31. Interlayer exchange coupling vs anisotropy
|JIEC| ~ 10 erg/cm
optic mode –4 2
(weak)
resonance field,
separation of modes,
acoustic mode
(strong)
acoustic mode
(strong)
optic mode
(weak)
GaAs spacer thickness, GaAs spacer thickness,
•separation and ordering of two FMR lines depend
on the quantitative balance of magnetocrystalline
anisotropy energy and interlayer exchange coupling

32. Summary
•unambiguous qualitative and quantitative description for the anisotropic
FMR in (III,Mn)V semiconductors
•peculiarities of magnetic anisotropy in solitude layers and heterostructures
made of (III,Mn)V, identification of various components of magnetic anisotropy
(biaxial, uniaxial, demagnetization, step-induced, dynamic, unidirectional, ...)
•dominating role of crystalline anisotropy
•reorientation of the magnetization easy axis promoted by an interplay
between bi- and uniaxial (magneto)crystalline anisotropies
•robust proximity effects - exchange bias and unidirectional anisotropy -
in the exchange coupled MnO/(Ga,Mn)As system
•influence of bi- and uniaxial anisotropies competition on unidirectional
anisotropy
•full coupling or acoustic/optic modes of FMR in (Ga,Mn)As/GaAs/(Ga,Mn)As
•quantitative relation joining magnetic anisotropy with interlayer
exchange coupling in (Ga,Mn)As-based FM/NM/FM trilayers