Control of magnetic anisotropy in (Ga,Mn)As by lithography-induced strain relaxation

0.39 MB·English

by  J. Wenisch

Control of magnetic anisotropy in (Ga,Mn)As by lithography-induced strain relaxation
J. Wenisch, C. Gould, L. Ebel, J. Storz, K. Pappert, M.J. Schmidt,
C. Kumpf, G. Schmidt, K. Brunner, and L.W. Molenkamp
Physikalisches Institut, Universit¨at Wu¨rzburg, Am Hubland, D-97074 Wu¨rzburg, Germany
7 (Dated: February 4, 2008)
0
0 Weobtaincontrolofmagneticanisotropyinepitaxial(Ga,Mn)Asbyanisotropicstrainrelaxation
2 in patterned structures. The strain in the structures is characterized using sophisticated X-ray
techniques. The magnetic anisotropy before patterning of the layer, which shows biaxial easy axes
n
along [100] and [010], is replaced by a hard axis in the direction of large elastic strain relaxation
a
J andauniaxialeasy axisin thedirection wherepseudomorphicconditions areretained. This strong
anisotropycan notbeexplainedbyshapeanisotropyandisattributedsolely tolattice strainrelax-
9
ation. Upon increasing theuniaxialstrain anisotropy in the(Ga,Mn)As stripes, wealso observean
1
increase in magnetic anisotropy.

]
l PACSnumbers: 75.50.Pp,75.30.Gw
l
a
h
- The (Ga,Mn)As materialsystemhasbeen the focus of relationshipbetweenthe structuralandmagneticbehav-
s
e manystudiesoverthelastyears. Astheunderstandingof ior observed in our samples.
m its complex transportandmagnetic propertiesincreases, The samples are grown in a dedicated III-V MBE
. thefocusofinterestshiftsfrombasicresearchtowardsits chamber with effusion cells for Ga, In, Mn, and a valved
t
a application in devices. For this, it is necessary to under- As4 cell. A 200nm thick high-quality GaAs buffer is de-
m stand how different parameters influence the ferromag- posited at T =620 ◦C, on an epi-ready semi-insulating
S
- netic material in structures at the device level. In this (001)GaAssubstrate,toimprovesurfaceandlayerqual-
d
letter we present a systematic study of the role of strain ity. Duringa growthinterruption,the temperatureis re-
n ◦
relaxation as the dominating factor contributing to the ducedto270 C.Atthistemperature,a(Ga,Mn)Aslayer
o
c magnetic anisotropy in (Ga,Mn)As nanostructures. A of70 nmthickness is depositedata rate of0.86˚A/s and
[ (Ga,Mn)As layer grown epitaxially on a GaAs substrate a beam equivalent pressure of As /Ga = 25. The Mn
4
is subject to compressive strain in the plane of the sam- content is determined by HRXRD to be ∼2.5% [5]. For
1
v pleandtypicallyexhibitsbiaxialin-planeeasyaxesalong one sample an additional 80 nm thick (In,Ga)As layer
◦
9 [100]and[010],attemperaturesaround4K[1,2]. Inear- with 7.4% In was grown at 500 C prior to (Ga,Mn)As
7 lier studies, control of the magnetic anisotropy has been deposition.
4
achieved by modifying the strain in the layer. Tensile
1
strain can be imposed on the (Ga,Mn)As by growing it
0
7 on a thick, plastically relaxed (In,Ga)As buffer with a
0 larger lattice parameter, and results in an out-of-plane
/ easy axis [3, 4].
t
a
m Here, we follow an alternative approach in modifying
- the lattice strainof(Ga,Mn)As onGaAs by lithography,
d
whichallowsustolocallycontrolthemagneticanisotropy
n
ofthematerial. Bystructuringafullypseudomorphic70
o FIG. 1: (color online) (a) SEM picture of the sample surface
c nm (Ga,Mn)As layer into thin, elongated stripes, we al- after patterning. (b) Simulation of the lattice displacement
: lowanisotropic,elasticstrainrelaxationperpendicularto (100 times exaggerated) after strain relaxation in a cross-
v
i the long axis of the stripe. To increase the strain in the section of a 200 nm wide stripe.
X
structurecomparedtothecaseof(Ga,Mn)AsonGaAs,a
r second sample is processedwhich includes a highly com- After growth, electron beam lithography and chemi-
a
pressively strained layer acting as an extra stressor to cally assisted ion beam etching are used to pattern both
the overlying (Ga,Mn)As layer. The uniaxial strain re- samplesintothestructureshowninFig.1a. Atotalarea
laxation in the structures is investigated by grazing in- of4 x 4 mm is coveredby arraysof stripes,eachindivid-
cidence X-ray diffraction (GIXRD) and high-resolution ual stripe measuring nominally 200 nm x 100 µm with a
X-ray diffraction (HRXRD). To determine the influence separating distance of 200 nm. The etch depth is about
ofpatterningonthemagneticanisotropy,aseriesofmag- 200nm,thuswellintotheGaAsbufferlayer. Thestripes
netometricandmagnetotransportstudiesareperformed. are aligned along the [100] crystal direction.
We also present finite-element simulations of anisotropic To optimize the stripe dimensions, the relaxation of
strainrelaxationand k·p calculations which confirm the the stripes has been modeled by finite element simula-
2
tionspriortosamplepreparation. The simulationmakes
use of elasticity theory to describe the strain and dis-
placements in the stripe structure by minimizing strain
energy. A typical resulting cross-sectionof a stripe after
relaxationis displayed in Fig. 1b. Simulations for varied
stripedimensionsatafixedmaterialcompositionsuggest
that a spatially rather homogeneouselastic relaxationof
the (Ga,Mn)As stripe core is reached for stripe widths
below about 500 nm, while inhomogeneous strain relax-
ation, concentrated primarily at the edges of the stripe,
is observed for wider structures. The etch depth also
plays a critical role in degree and homogeneity of strain
relaxation. As the substrate pillar height is reduced, the
relaxinglayerismorerestrictedatthelowerinterfacere-
sulting in reduced relaxationand a strain gradientalong
the [001] direction.
The strain relaxation in the (Ga,Mn)As stripes is
determined from GIXRD reciprocal space mapping
in the vicinity of the (333) Bragg reflection. The
GIXRD experiments were performed at beamline BW2
of the Hamburger Synchrotronstrahlungslabor (HASY-
LAB). Due to the small lattice mismatch between GaAs
and (Ga,Mn)As of f = 0.15 · 10−3, the Bragg reflec-
tions of both materials lie very close to each other. If
the (Ga,Mn)As stripes were purely pseudomorphically
strained, the difference between both reflections would
be only ∆l = 0.0033 r.l.u. (reciprocal lattice units), a
value which can hardly be resolved with our experimen-
tal setup. However, since the thickness of the layer is
only about70nm, the (Ga,Mn)As (333)reflectionis sig-
nificantly broadened in l-direction. Therefore, by map-
ping the reciprocal space close to but not precisely at
the l-position of the GaAs bulk-peak one is mainly sen-
sitive to the (Ga,Mn)As stripes. This measurement, a
h-k-map at l = 2.98, is shown in Fig. 2a, and a simi-
lar map through the GaAs bulk-peak in Fig. 2b. The
latter is a bulk-sensitive measurement and shows a peak
located at (333) providing a coordinate system of the
lattice units. In the stripes-sensitive measurement, one
can clearly observe (Fig. 2a) a shift of the peak towards FIG.2: (coloronline)Reciprocalspaceh-k-mapsinthevicin-
smaller values in k. This shift indicates the relaxationof ityofthe(333) Bragg reflection at (a)astripes-sensitiveand
the (Ga,Mn)As structure in [010] direction, whereas in (b) a bulk-sensitive position. In (c) the corresponding k-line
[100] direction no relaxation takes place (no peak shift scans(horizontalscansthroughthemaximumof(a)and(b))
and best fittingVoigt-profiles are shown, see text.
visible in h-direction). The different widths of the peaks
in h- and k-direction are due to the different lateral di-
mensions of the stripes.
pseudomorphicallystrainedinthe[100]-butshowalarge
In order to quantify the shift, we fit the measured
degree of strain relaxation in the [010]-direction.
peaks to Voigt-profiles. Fig. 2c shows the central line
scan through the peaks of both reciprocal space maps For magnetic characterization, a superconducting
(opencirclesinthefigure). Eachcurveisfitwiththesum quantum interference device (SQUID) is used to mea-
of two Voigt-peaks (thick solid lines), one fixed at h=3 sure magnetization behavior along selected directions in
representingthebulk-contribution,theotherwithavari- the parent and patterned layers. The results are shown
able position. All four individual peaks are also shown in Fig. 3.
asthinlines. Bythisprocedureweobtainavalueforthe The parent layer (inset of Fig. 3) exhibits the well
strainin [010]directionof ǫ =(a −a )/a = known biaxial anisotropy at 4 K with easy axes along
[010] meas nat nat
−2.8·10−4. Weconcludethatthe(Ga,Mn)Asstripesare the[100]and[010]crystaldirectionsandhardaxesalong
3

3
u) 20
m 10
e2
6 0
-0 -10
nt (11 -2-0200-100 0 100 200
e
m0
o
M
c
eti-1
n [ ]
Mag-2 [010100]
-3
-200 -150 -100 -50 0 50 100 150 200
Field (mT)
FIG. 3: (color online) SQUIDmagnetization data at 4 K for FIG. 4: (color online) Reciprocal space maps of the (206)
the parent layer (inset) and the patterned layer with stripes Bragg reflection with incident X-rays (a) perpendicular and
aligned along [100]. (b)paralleltothestripeaxis. Thesolidredlineindicatesthe
triangle of relaxation for this special case of uniaxial relax-
ation.
[1¯10] and [110]. The two easy axes are both plotted
but not distinguishable in the inset. Fig. 3 shows the
anisotropy after patterning. Along the [010] direction, stripe structure. To distinguish between the lattice con-
the magnetic moment atzero field dropsby ∼90%com- stants along the long axis of the stripes ([100] direction)
pared to the [100] direction. This previously easy axis is andperpendiculartothestripes([010]direction),twore-
nowclearlyaveryhardmagnetizationaxis. Theremain- ciprocalspace maps (RSM) of the (206)Braggreflection
ing easy axis along [100] also reflects this change by an were taken with the incident X-ray beam perpendicular
increase in coercive field from 4 mT in the parent layer (Fig. 4a) and parallel (Fig. 4b) to the stripe axis. In
to 43 mT in the patterned layer. This effect is caused thefirstcase,the(In,Ga)Aslayerpeakmaximumclearly
by the increasedenergy necessaryto rotatethe magneti- indicates a largerlateralandsmaller verticallattice con-
zation through the now hard [010] axis during magneti- stantthanexpectedforafullypseudomorphiclayer(bot-
zation reversal. Thus, the presented results show a clear tomtipoftherelaxationtriangle). The(Ga,Mn)Aslayer
modificationofthemagneticanisotropyofnanopatterned is expected to have a similar lateral lattice constant and
(Ga,Mn)As/GaAs stripes. therefore lateral peak coordinate in the RSM to the un-
The observed strong anisotropy can not be explained derlying (In,Ga)As. Hence, the bulge in the substrate
by shape anisotropy. As-grown (Ga,Mn)As shows peak at (1.992, 5.988) and (2.000, 5.986) in Fig. 4a and
mainly biaxialcrystalline magneticanisotropy(K ∼ Fig. 4b, respectively, is attributed to the (Ga,Mn)As
cryst
3000 J/m3), which dominates the magnetic reversal be- layer. Because of the peak location, we conclude that
havior. Calculating the uniaxial term stemming from tensile strain(ǫ=2.2·10−3)has beeninducedbythe re-
the shape anisotropy produced by our geometry (fer- laxed (In,Ga)As layer. With incident X-rays along [100]
romagnetic prism [8]) leads to K ∼ 280 J/m3, (Fig. 4b), both layer peaks are located directly below
shape
much smaller than the crystalline anisotropy contribu- the substrate peak, but shifted to smaller verticallattice
tion. Thus we attribute the observed emergence of constant (due to Poissoneffect) compared to the biaxial
the dominant uniaxial anisotropy in our samples to the pseudomorphic case. The position of the peaks in both
anisotropic strain relaxation which, as we show in the maps can be explained unambiguously by a large uniax-
k·p modeling below, contributes an additional term in ial strain relaxation in the [010] crystal direction while
themagnetostaticsenergyequation,withenoughimpact retaining fully pseudomorphic conditions along the [100]
to overcome the otherwise dominant biaxial anisotropy. direction.
Itispossibletofurtherincreasethestrengthoftheim- This sample shows a very similar behavior in SQUID
posed uniaxial anisotropy by increasing the strain in the comparedto the pure (Ga,Mn)As sample, with the well-
parentlayer. Forthisweusean(In,Ga)Aslayerwithcon- known biaxial easy-axes in the parent layer, as well as
siderablylargerlatticemismatchoff =0.53·10−3tothe theemergenceofthestronguniaxialanisotropyafterpat-
substrate, deposited prior to the (Ga,Mn)As layer with terning.
f =0.15·10−3. Thislayer,whichisgrowntoathickness That the imposed uniaxial anisotropy in the sample
close to but below the critical value for plastic strain re- containing the (In,Ga)As layer stressor is even stronger,
laxation, acts as a stressor to the overlying (Ga,Mn)As can be inferred from magnetoresistance measurements.
layer. InFig.4wepresentHRXRDdataofthepatterned In(Ga,Mn)As,whichisinherentlyhighlyp-dopedbyMn,
4
Angle between M and the crystalline [100] axis
1.62 90(cid:176) 0˚ 45˚ 90˚ 135˚ 180˚
y)
Ω)k 1.60 -40R 4
(e 1.58 e (1 3
stanc 1.56 0(cid:176) er hol
esi 2.40 90(cid:176) y p 2
R g
er
2.36 n 1
e
n
a
2.32 e
0(cid:176) M 0
[100] [110] [010] [ -110] [ -100]
-200 -150 -100 -50 0 50 100 150 200
Magnetization Direction
Magnetic Field (mT)
FIG. 5: (color online) Magnetoresistance scans of FIG. 6: (color online) Mean energy per valence band hole of
(Ga,Mn)As/GaAs (top) and (Ga,Mn)As/(In,Ga)As/GaAs a(Ga,Mn)Aslayerwithvariouslevelsoflatticestrainin[010]
sample (bottom) at 4 K for angles φ between magnetic field directionranging,inequalsteps,fromthebiaxialpseudomor-
andcurrentdirection(alongstripe)from0◦ to90◦. Themag- phiccase(ǫ=−1.5·10−3,bottom,black)tothefullyrelaxed
netic field is swept from −0.3 T to 0.3 T for each scan. case (ǫ = 0, top, red). The strain in [100] remains fixed at
ǫ=−1.5·10−3.
a strong anisotropic magnetoresistance (AMR) is gener-
ally observed. The magnetoresistance is dependent on
theangleφbetweenthemagnetizationM~ andthecurrent
J~[7], witha minimum when M~ is parallelto the current mean energy per hole. The results support our inter-
[6]. Forthe measurement(see Fig.5), about250parallel pretation that strain is the key element in determin-
stripes are contacted from both ends. A series of mag- ing the magnetic anisotropy in (Ga,Mn)As nanostruc-
neticfieldsweepsfrom−0.3Tto0.3Tisperformed,with tures. Fig.6showstheevolutionoftheequivalentenergy
incrementalincreaseofthe angleφbetweenM~ andJ~af- minima along [100] and [010] for fully biaxially strained
ter each sweep. In both samples, all (hysteretically sym- (Ga,Mn)As(blackcurve)withincreasingdegreeofstrain
metric)curvesshareonelowresistancestateatB =0T. relaxationinthe[010]direction. Assuminghomogeneous
When the field sweep is performed in the [100] direc- strain distribution in the stripes and a moderate carrier
tion (φ = 0◦), the resistance remains at the low state. density 4·1020 cm−3, we can deduce from the calcula-
With increasing angle between M~ and J~, a high resis- tions, that the uniaxial contribution from strain domi-
tancestatedevelopsandreachesamaximumatφ=90◦. nates over the biaxial term to such a degree, that above
Atthisangle,themagnetizationstartsoutparalleltothe ǫ=−0.6·10−3 onlyasinglestablepoint, along[100],re-
stripes (low resistance) and is forced to the unfavorable mains. Thisischaracteristicofperfectuniaxialbehavior.
direction perpendicular to the stripes (high resistance) As we demonstrated above in connection with the X-ray
athighfields. As with the SQUID results,these findings data,ourpatternedsamplesexhibitstrainlevelsthatex-
fit perfectly into the picture of a strain induced uniaxial ceed this number. The difference by a factor of 2 in the
magneticanisotropy. Wealsoobservealargeropeningof anisotropy fields for the two differently strained samples
the curves from the additionally strained stripes (lower (Fig. 5) also agrees well with the model prediction (we
part of Fig. 5). This is a direct evidence of an increased findafactorof3). Weconcludethatourexperimentsand
anisotropy field, as more energy is necessary to rotate modeling unambiguously demonstrate that lithographic
the magnetization into the unfavorable hard [010] direc- pattering, when necessary combined with the (In,Ga)As
tion. According to [9], we determine the magnitude of stressortechnique,isareliableandversatiletoolforcon-
the anisotropy field from these openings to be ∼ 45 mT trollingthemagneticanisotropiesin(Ga,Mn)As. Wean-
for the pure (Ga,Mn)As stripes and∼80 mT for the ad- ticipatethatthislocaltechniqueshouldproveveryuseful
ditionally strainedstripes. As the strainin the magnetic for device applications.
layer of the second sample is demonstrably significantly
different with nominally identical physical dimensions, We thank T. Borzenko, A. Stahl, I. Gierz, and E.
this effect can clearly be attributed to the lattice strain, Umbach as well as the staff at HASYLAB for their
considering that shape anisotropy is identical for both help in this work. We acknowledge financial support
structures. from the DFG (BR 1960/2-2 and SFB 410) and the EU
Finally, we present the results of k·p calculations (NANOSPIN FP6-IST-015728 and the IHP programme
[10] of the magnetization-direction dependence of the “Access to Research Infrastructures“).
5
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