GaMnAs-based hybrid multiferroic memory device

0.48 MB·English

by  M. Overby

GaMnAs-based hybrid multiferroic memory device
M. Overby,1 A. Chernyshov,1 L. P. Rokhinson,1 X. Liu,2 and J. K. Furdyna2
1Department of Physics and Birck Nanotechnology Center,
Purdue University, West Lafayette, Indiana 47907 USA
2Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556 USA
(Dated: February 3, 2008)
8 A rapidly developing field of spintronics is
0 based on the premise that substituting charge
[ ]
0 with spin as a carrier of information can lead 100
2 to new devices with lower power consump- [ ]
110
n tion, non-volatility and highoperational speed1,2.
2m m
a Despite efficient magnetization detection3,4,5,
J
magnetization manipulation is primarily per-
8 formedbycurrent-generatedlocalmagneticfields H
2 [ ]
and is very inefficient. Here we report a 010
novel non-volatile hybrid multiferroic memory φH M
] φ
i cell with electrostatic control of magnetization m
c I
s based on strain-coupled GaMnAs ferromagnetic
[ ]
- semiconductor6 and a piezoelectric material. We 110
l
r use the crystalline anisotropy of GaMnAs to
t
m store information in the orientation of the mag-
V
netization along one of the two easy axes,
.
t which is monitored via transverse anisotropic
a
m magnetoresistance7. The magnetization orienta-
tion is switched by applying voltage to the piezo-
-
d electric material and tuning magnetic anisotropy
n of GaMnAs via the resulting stress field. I
o
In magnetic memories the information is stored in the
c
[ orientation of magnetization. The major weakness of
current MRAM implementations lies in the inherently
1
non-local character of magnetic fields used to flip ferro-
v
magnetic domains during the write operation. Neither FIG.1: Top: sketchoftheHallbarwithrelativeorientation
1
9 thermal switching8 nor current induced switching9 can ofelectricalcurrentI~,magneticfieldH~ andmagnetizationM~.
1 solve the problem completely. Bottom: an AFMimage of a 2µm-wide Hall bar is schemati-
4 Anattractivealternativetoconventionalferromagnets callyshownattachedtothepiezoelectric. Strainisappliedto
1. aremultiferroicmaterials10,whereferromagneticandfer- the sample along [100] and [010] directions, red dashed lines
on the sketch.
0 roelectric properties coexist and magnetization can be
8 controlled electrostatically via magnetoelectric coupling.
0 In single-phase and mixed-phase multiferroics ferromag-
:
v neticmaterialmustbeinsulatinginordertoavoidshort- orydevicecanberealized. Magneticanisotropyofdilute
i circuits. Alternatively, magnetoelectric coupling can be magnetic semiconductor GaMnAs films is largely con-
X
introduced between ferromagnetic and ferroelectric ma- trolled by epitaxial strain15,16, with compressive (ten-
ar terialsindirectlyviastrain,andinthiscasetheferromag- sile) strain inducing in-plane (out-of-plane) orientation
netic materialcan be conducting. A conceptual memory of magnetization. In GaMnAs compressively strained
device madeofferromagneticandpiezoelectric materials to (001) GaAs there are two equivalent easy axes of in-
has been proposed11, and permeability changes in mag- planemagnetization: along[100]andalong[010]crystal-
netostrictive films12, changes in coercive field13 and re- lographic directions. Lithographically-induced unidirec-
orientationofthe easyaxisfromin-plane toout-of-plane tional lateral relaxation can be used to select the easy
in Pd/CoPd/Pd trilayers14 have been recently demon- axis17,18. In addition to the large in-plane crystalline
strated. anisotropy there is an uniaxial anisotropy between [110]
Some ferromagnetic materials have a complex and [1¯10] directions which is probably due to the un-
anisotropic magnetocrystalline energy surface and sev- derlyinganisotropyofthe reconstructedGaAs surface19.
eral easy axes of magnetization. If the energy barrier We use this magnetocrystalline anisotropy in combina-
between adjacent easy-axis states can be controlled by tion with the magnetostrictive effect to demonstrate a
strain, then a multiferroic non-volatile multi-state mem- bi-stable memory device.
2
[100] [010] [10 0] [010] [100] Vpzt (V)
10 -100 0 100
unstrained 10
M
0
) ) I
AMR (-1100 a) strained MR ( 5 1)0
erse 0 se A MR (5
Transv-1100 b) Transver 0 nsverse A-05
-5 a
0 200V Tr
-10
0V M 0.9 1.0
-10 c) -200V I (10-3)
-45 0 45 90 135 180 225 270 315 -10
0.9 1.0 1.1 1.2
H (degrees) (10-3)

FIG.2: TransverseAMRasafunctionofmagneticfieldangle
FIG. 3: Transverse AMR (TrAMR) for the strained Hall bar
ϕH for unstrained (a) and strained (b,c) samples. Arrows
as a function of uniaxial strain measured by a strain gauge.
indicate the field sweep directions. Magnetic field is H = 50
◦
mTandT =35K.VoltageappliedtothepiezoelectricVpzt = Static magnetic field H = 50 mT is applied at ϕH = 62 ,
0 for the curves(b) and Vpzt =±200 V and 0 for (c). the data is taken at T = 35 K. On the top axis approxi-
matevoltage on thepiezoelectric isindicated. Orientation of
magnetization relative to the current flow is shown schemat-
ically fortheTrAMR>0andTrAMR<0states. Intheinset
Molecular beam epitaxy at 265◦ C was employed to TrAMR is plotted for H =50 mT (red), 70 mT (green) and
100 mT (blue) measured at T =25 K.
grow 15-nm thick epilayers of Ga Mn As on semi-
0.92 0.08
insulating (001) GaAs substrates. The wafers were sub-
sequently annealed for 1 hour at 280◦ C in a nitrogen
similar strain.
atmosphere. Annealing increases the Curie temperature Directionofthein-planemagnetizationM~ ismeasured
of the ferromagnetic film to T ∼ 80 K and reduces
c via transverse anisotropic magnetoresistance (TrAMR),
the cubic anisotropy. The GaMnAs layer was patterned also known as giant planar Hall effect7
into 2 µm-wide Hall bars oriented along the [110] axis
by combination of e-beam lithography and wet etching, TrAMR=(ρ −ρ )sinϕ cosϕ , (1)
k ⊥ m m
see Fig. 1. After lithography 3 mm x 3 mm samples
were mechanically thinned to ∼100 µm and attached to where ρk and ρ⊥ are the resistivities for magnetization
a multilayer PZT (piezoelectric lead-zirconium-titanate oriented parallel and perpendicular to the current. The
ceramic)20 with epoxy, aligning the [010] axis with the sign and magnitude of TrAMR depend on the angle
axis of polarization of the PZT. Application of positive ϕm between magnetization M~ and current I~k[110], see
(negative) voltage V across the piezoelectric intro- schematic in Fig. 1. TrAMR reaches minimum (max-
PZT
ducestensile(compressive)straininthesamplealongthe imum) when M~k[010] (M~k[¯100]). Longitudinal AMR
[010] direction, and strain with the opposite sign along is ∝ cos2ϕ and is not sensitive to the magnetization
m
the[100]directionproportionaltothepiezoelectricstrain switching between 45◦ and 135◦.
coefficients d ≈−2d . Both coefficients decrease by a In Fig. 2 TrAMR is plotted for the strained and un-
33 31
factorof15betweenroomtemperatureand4.2K.Thein- strained Hall bars as magnetic field of constant magni-
ducedstrainε=∆L/Lforboth[010]and[100]directions tude H = 50 mT is rotated in the plane of the sample.
was monitored with a biaxial strain gauge glued to the For the unstrained sample (not attached to the piezo-
bottomofthe piezoelectric. Strainisproportionalto the electric) there are four extrema for the field angle ϕ
H
change of the gauge resistance,and was measuredin the around 45◦, 135◦, 225◦ and 315◦ with four switchings
Wheatstone bridge configuration: ∆ε = ε −ε = of magnetization by 90◦ near [110] and [1¯10] directions,
[010] [100]
(∆L/L) −(∆L/L) =α(R −R )/R,where which reflects the underlying crystalline anisotropy of
[010] [100] [010] [100]
α is the gauge sensitivity coefficient and R is the resis- GaMnAs. For the sample attached to the piezoelectric
tanceoftheunstrainedgauge. Ithasbeenshownbefore21 there is a gradual change in the angle of magnetization
that the strain gradient across the piezoelectric and the with only two abrupt 90◦ switchings of the direction of
sampleisnegligible: i.e.,gaugesgluedontopofthesam- magnetization per field rotation, which indicates strong
ple and on the opposite side of the piezoelectric measure uniaxial anisotropy due to a highly anisotropic thermal
3
Expe riment Mod el 90

200
8 [100] [010]
30 AMR () 04 unstrained Hall bar E/M (mT) 00 180 0 E/M (mT)20 100 mT
ansverse AMR () 1200 T--84 0 90H (de1g8)0 270 0 90H (de1g8)0 270 27000 [[a011)000]] 29700 m (Hd[e[10g010)0]] E/M (mT) 56000 dc)) 50 mT
Tr 0 Exp Model T)60 T)
Vpzt m m 90
200V 1.1•10-3 M (4400 180 0 M (
0V 0.92•10-3 E/ E/ H=0
-3
-10 -200V 0.75•10 60 e)
60
-90 -45 0 45 90 -90 -45 0 45 90 70 [010] [100] -90 0 90 180
H (deg) H (deg) b) 270 m (deg) m (deg)
FIG. 4: Experimentally measured (left panel) and modelled
FIG. 5: a) Polar plot of magnetostatic energy E/M as a
(right panel) transverse AMR for the strained sample at dif-
functionofmagnetizationangleϕm forH =0(black),50mT
ferent voltages on the piezoelectric (for comparison data for ◦
(blue)and100mT(red)forϕH =62 andVpzt=0(∆εKε=
an unstrained sample are shown in the inset). All data were 16mT).b-d)AngulardependenceofE/M for∆εKε =13−19
taken at T = 35 K and H = 50 mT. In the model we used
mT (black to magenta) for H =0 (e), H =50 mT (b,d) and
experimentally measured strain ∆ε, other model parameters H =100mT(c). BluelineandarrowmarkϕH =62◦,dashed
are discussed in thetext.
red lines indicate two stable orientations of magnetization.
non-volatile magnetic memory with electrostatic control
expansioncoefficientofthePZTstack(+1ppm/Kalong
of the state.
and -3 ppm/K perpendicular to the piezoelectric stack).
The center of the loop can be shifted by adjusting
By applying a finite voltage to the piezoelectric during
ϕ : e.g., a 1◦ change shifts the center of the loop by
cooldown we are able to control the thermally-induced H
stress within ∆ε<10−3 for T <50 K. ∆ε≈3.5·10−5. AsH increases,thesizeofthehysteresis
loop decreases, and the hysteresis vanishes for H > 100
Application of ±200 volts on the piezoelectric results
mT;seeinsetinFig.3. AtH <40mTtheloopincreases
in a shift of the angle of magnetization switching by
beyond the ±200 piezoelectric voltage span. In our ex-
∆ϕ ≈ 10◦, which is comparable to the size of the
H periments the magnetic field balances the residualstrain
hysteresis loop in TrAMR vs ϕ scans at V = 0,
H pzt due to anisotropic thermal expansion of the PZT. Alter-
Fig. 2(b,c). Applying a magnetic field of H = 50 mT
natively,intrinsicpiezoelectricpropertiesofGaAscanbe
oriented at ϕ = 62◦, which corresponds to the mid-
H utilized, in this case there will be no thermally induced
dle of the hysteresis loop, compensates for the thermally
strain and electrostatic switching of the magnetization
induced uniaxial strain anisotropy and restores the orig-
direction can be realized without applying an external
inal degeneracy between [010] and [¯100] magnetization
compensatingmagneticfield. Scalingofthe piezoelectric
directions of the unstrained GaMnAs for V ≈ 0. An
pzt element from 0.5 mm down to ∼ 1 µm will compensate
additionalstrainisthenappliedbyvaryingvoltageonthe forasmallstraincoefficientinGaAs(dpzt ≈10·dGaAsat
piezoelectric. InFig.3TrAMRisplottedasafunctionof 33 14
30 K), reduce operating voltage to a few volts and allow
measuredstrain∆ε, the correspondingV are approxi-
pzt electrostatic control of individual memory cells.
matelymarkedonthetopaxis(thereisasmallhysteresis
We model the strain along [100] and [010] direc-
in ∆ε vs V ). As additional compressive strain is ap-
pzt tions as an extra magnetostatic energy density term
plied along [010], this direction becomes the easy axis of 2ε K sin2(ϕ + 45◦) + 2ε K sin2(ϕ − 45◦) =
magnetizationandmagnetizationalignsitself with[010]. [100] ε m [010] ε m
∆εK sin(2ϕ )+const. Then, for a single domain mag-
ε m
As additional tensile strain is applied along [010] direc-
net the free energy density can be written as
tion, the [¯100] direction becomes the easy axis and po-
larizationswitchesby90◦. Theswitchingoccursinafew E = K sin2(ϕ )+K /4cos2(2ϕ )
u m 1 m
steps,indicatingafew-domaincompositionofourdevice.
+HMcos(ϕ −ϕ )+∆εK sin(2ϕ ) (2)
m H ε m
At V = 0 the magnetization has two stable orienta-
pzt
tions, M~k[¯100] and M~k[010], and the orientation can be omittingconstantoffset,whereK ,K andK arecubic,
1 u ε
switched by applying a negative or a positive voltage on uniaxialandstrainanisotropyconstants;H istheapplied
thepiezoelectric. Thus,thedeviceperformsasabi-stable in-plane magnetic field; and ϕ and ϕ are the angles
m H
4
between[110]directionandmagnetizationandmagnetic To illustrate the mechanism of magnetization switch-
field respectively; see schematic in Fig. 1. We assume ing we plot magnetic energy density normalizedby mag-
that K is the same for [100] and [010] directions. netization E/M (Eq. 2) as a function of ϕ in Fig. 5.
ε m
In equilibrium the magnetization orientation ϕ min- AtH =0 there areonlytwominima alongthe [100]axis
m
imizes the free energy, dE/dϕ = 0 and d2E/dϕ2 > 0. due to the large uniaxial strain (see Fig. 5 (a,e)), caused
m m
TheTrAMRcanbecalculatedfromEq.1foragivenan- byanisotropicthermalexpansioncoefficientofthepiezo-
gleϕ oftheexternalfieldH. Fromthefitstotheexper- electric.
H
imentalTrAMR data we canextractthe anisotropycon- With external magnetic field H = 50 mT applied at
stantsK ,K andK . Themodelcapturesalltheessen- ϕ = 62◦ E/M has two minima: at ϕ = 32◦ and at
1 u ε H m
tialfeaturesofthedata,andcorrespondingfitsareshown 123◦, i.e., close to [010] and to [¯100] crystallographic di-
inFig.4forthestrainedandunstraineddevices. Forun- rections. For the strain field ∆εK /M = 13 mT the
ε
strained device anisotropy fields 2K /M = 40 mT and global minimum is at ϕ = 32◦, and in equilibrium the
1 m
2K /M = 6 mT. These values are significantly smaller magnetization is oriented along the [010] direction. As
u
thanthepreviouslyreportedvaluesforas-grown(notan- thestrainfieldincreasesto19mTthetwominimaswitch,
nealed)wafers7,22. Forthe sample attachedtothe piezo- andϕ =123◦ becomestheglobalminimum. Itisinter-
m
electricthecrystallineanisotropyfieldremainsthesame, estingtonotethatthereisalwaysasmallbarrierbetween
but the uniaxial anisotropy increases to 2K /M = 50 the two minima. Unless the barrier is an artifact of our
u
mT. The strain-inducedanisotropyfield ∆εK /M varies model, the switching of magnetization should be either
ε
between13mTand19mTfordifferentV between-200 temperature activated or should occur via macroscopic
pzt
V and 200 V, the coefficient K /M =17 T. quantum tunnelling.
ε
1 G. A. Prinz, Magnetoelectronics. Science 282, 1660-1663 in Co50Fe50 interdigitated electrodes on piezoelectric sub-
(1998). strates. J. Appl. Phys. 101, 54903 - 1 (2007).
2 S. A. Wolf et al., Spintronics: a spin-based electronics vi- 14 J.-W. Lee, S.-C. Shin,and S.-K. Kim, Spin engineering of
sion for thefuture. Science 294, 1488 (2001). CoPd alloy films via the inverse piezoelectric effect. Appl.
3 M. Baibich et al., Giant magnetoresistance of Phys. Lett. 82, 2458 - 60 (2003).
(001)Fe/(001)Cr magnetic superlattices. Phys. Rev. 15 U. Welp et al.,Magnetic Domain Structureand Magnetic
Lett. 61, 2472 (1988). Anisotropy in Ga1−xMnxAs.Phys. Rev. Lett. 90, 167206
4 G.Binasch,P.Gru¨nberg,F.Saurenbach,andW.Zinn,En- (2003).
hanced magnetoresistance in layered magnetic structures 16 X. Liu, Y. Sasaki, and J. K. Furdyna, Ferromagnetic res-
with antiferromagnetic interlayer exchange. Phys. Rev. B onance in Ga1−xMnxAs : Effects of magnetic anisotropy.
39, 4828–4830 (1989). Phys. Rev. B 67, 205204 (2003).
5 J. Moodera, L. Kinder, T. Wong, and R. Meservey, Large 17 S. Hu¨mpfner et al., Lithographic engineering of
magnetoresistance at room temperature in ferromagnetic anisotropies in (Ga,Mn)As. Appl. Phys. Lett. 90, 102102
thin film tunnel junctions. Phys. Rev. Lett. 74, 3273 (2007).
(1995). 18 J. Wenisch et al., Control of Magnetic Anisotropy in
6 H. Ohno, Making nonmagnetic semiconductors ferromag- (Ga,Mn)As by Lithography-Induced Strain Relaxation.
netic. Science 281, 951 - 6 (1998). Phys. Rev. Lett. 99, 077201 (2007).
7 H. Tang, R. Kawakami, D. Awschalom, and M. Roukes, 19 U. Welp et al., Uniaxial in-Plane Magnetic Anisotropy of
Giant planar Hall effect in epitaxial (Ga,Mn)As devices. Ga1−xMnxAs. Appl. Phys. Lett. 85, 260 - 2 (2004).
Phys. Rev. Lett. 90, 107201 - 1 (2003). 20 Part No. PSt 150/5x5/7, from Piezomechanik, Munich,
8 M.Kerekesetal.,Dynamicheatinginsubmicronsizemag- Germany.
netic tunneljunctions with exchangebiased storage layer. 21 M.Shayeganetal.,Low-temperature,insitutunable,uni-
J. Appl. Phys. 97, 10 - 501 (2005). axialstressmeasurementsinsemiconductorsusingapiezo-
9 E. Myers et al., Current-induced switching of domains in electric actuator. Appl. Phys. Lett. 83, 5235 - 7 (2003).
magneticmultilayerdevices.Science285,867-70(1999). 22 D. Y. Shin et al., Temperature dependence of magnetic
10 W. Eerenstein, N. Mathur, and J. Scott, Multiferroic and anisotropy in ferromagnetic (Ga,Mn)As films: Investiga-
magnetoelectric materials. Nature 442, 759 - 65 (2006). tion by the planar Hall effect. Phys. Rev. B 76, 035327
11 V.Novosad et al.,Novelmagnetostrictive memory device. (2007).
J. Appl. Phys. 87, 6400 - 2 (2000).
12 K. Arai, C. Muranaka, and M. Yamaguchi, A new hybrid Acknowledgements The work was supported by
device using magnetostrictive amorphous films and piezo- NSF under the grants ECS-0348289 (Purdue) and
electricsubstrates.IEEETrans.Magn.30,916-18(1994). DMR-0603752(Notre Dame).
13 H. Boukari et al., Voltage assisted magnetic switching