Evidence of metallic clustering in annealed Ga1-xMnxAs from atypical scaling behavior of the anomalous Hall coefficient
ABSTRACT We report on the anomalous Hall coefficient and longitudinal resistivity scaling relationships on a series of annealed Ga1-xMnxAs epilayers (x~0.055). As-grown samples exhibit scaling parameter n of ~ 1. Near the optimal annealing temperature, we find n ~ 2 to be consistent with recent theories on the intrinsic origins of anomalous Hall Effect in Ga1-xMnxAs. For annealing temperatures far above the optimum, we note n > 3, similar behavior to certain inhomogeneous systems. This observation of atypical behavior agrees well with characteristic features attributable to spherical resonance from metallic inclusions from optical spectroscopy measurements. Comment: 3 pages, 3 figures
Evidence of metallic clustering in annealed Ga1-xMnxAs from atypical scaling behavior of
the anomalous Hall coefficient
H.K. Choi, W.O. Lee, Y.S. Oh, K.H. Kim, and Y.D. Parka)
CSCMR & School of Physics, Seoul National University, Seoul 151-747 Korea
S.S.A. Seo and T.W. Noh
ReCOE and School of Physics, Seoul National University NS50, Seoul 151-747 Korea
Y.S. Kim, Z.G. Khim, I.T. Jeong, and J.C. Woo
School of Physics, Seoul National University NS50, Seoul 151-747 Korea
Department of Physics and Institute of Fundamental Physics, Sejong University, Seoul 143-747 Korea
We report on the anomalous Hall coefficient (Rs) and longitudinal resistivity (ρxx) scaling relationship
(RS ∝ ρxx
parameter n of ~ 1. Near the optimal annealing temperature, we find n ≈ 2 to be consistent with recent
theories on the intrinsic origins of anomalous Hall Effect in Ga1-xMnxAs. For annealing temperatures far
above the optimum, we note n > 3, similar behavior to certain inhomogeneous systems. This
observation of atypical behavior agrees well with characteristic features attributable to spherical
resonance from metallic inclusions from optical spectroscopy measurements.
n) on a series of annealed Ga1-xMnxAs epilayers (x ≈ 0.055). As-grown samples exhibit scaling
Ever since the first reports of carrier mediated
ferromagnetic ordering in III-V
semiconductors (DMS), anomalous Hall Effect (AHE)
measurements have had an important role in their
characterization1. First, observation of AHE was tacitly
believed to be attributed from a single phase carrier
mediated DMS materials2,3. AHE has been utilized to
indirectly measure magnetic properties, especially where
direct magnetization measurements are difficult, with novel
demonstrations of carrier mediated ferromagnetic ordering
manipulated by electric fields4 and even with reports of
AHE near room temperature for GaAs-based DMS
systems5. Whether observations of AHE are indeed unique
to a single phase DMS materials is best illustrated in AHE
measurements of Ti1-xCoxO2 system6; whether to carrier-
mediated DMS materials has been studied in both Mn:Ge
system7 as well as digitally doped Mn/GaAs system8.
The origins of DMS magnetic ordering, especially
whether the carriers are spin-polarized or the magnetization
is due to secondary phases, are essential issues to be
considered for the applicability of DMS for spintronic
device applications. Even for Ga1-xMnxAs, the seminal III-
V DMS, there have been reports of secondary phases which
may contribute to the observed magnetic properties9 as well
as localization of spin-polarized carriers near the magnetic
impurity10. Recently, a means to increases magnetic
coercivities of Ga1-xMnxAs by inclusion of small concen-
tration of nanometer-sized MnAs has been reported11. AHE
in Ga1-xMnxAs has been studied theoretically by many
groups with its origins ranging from Berry phase in the
momentum space12 to phonon-assisted hopping of holes
between localized states in the impurity band8,13. In this
letter, we illustrate the sensitivity of the Hall Effect
measurements to metallic inclusions within the Ga1-xMnxAs
host by atypical scaling relationship of the anomalous Hall
coefficient (RS) to resistivity (ρxx).
Several 100 nm thick Ga1-xMnxAs samples (x ≈ 0.055)
are prepared by LT-MBE on epi-ready SI GaAs(001)
substrates after 500 nm GaAs buffer layers are first grown,
which details are reported elsewhere14. After growth, high-
resolution x-ray diffraction (HRXRD) measurements is used
to verify x of 0.052, 0.052, and 0.056 for sample A, sample
B, and sample C, respectively. The samples are fashioned
into electrically isolated 300 μm x 1900 μm Hall bar
structures. As-grown, the magnetic ordering temperature
(TC), as estimated by SQUID magnetometry and/or by
transport measurements, is found to be 50 - 62 K. Samples
are then annealed in a tube furnace in a flowing dry N2
environment for one hour with annealing temperature (TA),
measured by a thermocouple near the sample, ranging from
200°-400° C. After annealing, indium contacts are fashioned
and verified as ohmic for transport measurements in a
closed-cycle cryostat and/or in a Quantum Design PPMS
with customized ac lock-in technique capabilities.
Our observed effects due to annealing on the transport
and magnetic properties are similar to those reported by
a) Electronic mail: firstname.lastname@example.org
FIG. 1: Log-log plot of ρxy and ρxxfor samples A-C series.
Measurements of ρxy and ρxx are conducted simultaneously
by ac lock-in technique with excitation current of 10 – 40
μA at 17 Hz. Each cluster of data points represents an
isotherm of a particular sample from a series annealed at TA
measured at Tm (< TC). Insets plot ρxy and ρxx as function of
applied field for Tm < TC for sample A series annealed at
200° C (A-200) and at 290° C (A-290). Dotted line
representing n = 1 is provides as a guide.
others15-17. Resistivities of the three samples initially
decrease (along with corresponding increase in TC) with
increasing TA as donor impurities such as Mn interstitial
concentrations (MnI) are reduced by out-diffusion to the
surface and passivated17. We find our optimal TA, in terms
of lowest ρxx and highest TC, to be ~ 250° C. As TA is
further increased, we observe corresponding increase in ρxx
and decrease in TC, as Mn leaves the Ga1-xMnxAs solution.
For TA > ~350° C, ρxx was too large to measure accurately,
even at room temperature (ρxx > 1 Ω-cm). For even the
highest TA, we have not detected any evidence of secondary
precipitates such as α-MnAs from SQUID magnetometry
or HRXRD measurements. In short, by annealing three
samples with nearly identical total Mn concentration, series
of samples with resistivity spanning nearly two orders of
magnitude, exhibiting both ‘metallic’ and insulator-like
behaviors, and TC varying over 100 K are realized.
Hall measurements show typical anomalous behavior
along with negative magneto-resistance for each sample
below TC. In AHE literature18, the Hall resistivity (ρxy) is
generally expressed as ρxy = RoB + μoRsM, an empirical
relationship valid for both intrinsic and extrinsic origins of
magnetic material systems19, where the first term is the
ordinary term with B as the magnetic induction and Ro is
the ordinary Hall coefficient related to the nature and
amount of carriers, and the second term is the anomalous
term with M as the magnetization of the sample with RS
related to spin polarization of carriers and the spin-orbit
interaction. A scaling relationship for Hall resistivity can
be expressed as ρxy ∝ ρxx
nearly constant. The value of the scaling parameter (n) can
take on values of between one and two. Experimentally, n
n in cases where magnetization is
can be determined by measuring ρxy while varying ρxx by
both the measurement temperature (Tm) and solute
concentration. Here, we vary the Mn concentration
primarily by varying TA. For all magneto-transport mea-
surements, we plot ρxy as function of ρxx for each sample
below its TC (Fig. 1). We note that our data along with those
from other groups2,16 generally follow a weakly universal
linear scaling relationship (n ≈ 1).
We apply an alternative scaling relationship in terms of
the anomalous Hall coefficient (RS ∝ ρxx
properties as well as ρxx are inevitably related to carrier
concentration (nh). For Ga1-xMnxAs, the anomalous term is
much larger than the ordinary term. Its influence along with
difficulties in achieving technical magnetization saturation
affects accurate determination of nh (along with accurate
determination of RS). We estimate RS at low applied fields
from ∂ρxy/∂B=(μoRsM)∂ΜΖ/∂BZ with μoRsM >> RoB and RS
being independent of B. For Ga1-xMnxAs during Hall
measurement, ∂ΜΖ/∂BZ can be expressed, from the Stoner-
Wolfarth model, as MS[μoMS – 2(Ku⊥ − KC)]-1 here Ku⊥ and
KC are the perpendicular uniaxial and the cubic anisotropy
constants, respectively20. Recently, Titova et al. reports that
the perpendicular uniaxial fields (μoMS – 2 Ku⊥) to be nearly
independent of carrier concentration21, and for x > 0.05, we
expect KC to be negligible due to the large built-in com-
pressive strain during LT-MBE20. A good agreement in the
temperature dependence of normalized magnetization from
SQUID magnetometer measurements, from Arrott plots of
AHE data, as well as from M ∝ ρxy(∂ΜΖ/∂BZ)-1 or M ∝ ρxy/RS
validates our assumption (Fig. 2.a).
n) as magnetic
FIG. 2: a) Plot of sample C-250 normalized magnetization
as function of temperature. b) Log-log plot of cRS (∂ρxy/∂B)
as function of ρxx for sample C annealed at 200° – 300° C to
fit the scaling parameter n ranging from ~1 to ~ 3. Each
data point reflects isotherm measurements of ΑΗΕ. c) Plot
of scaling parameter n as function of ρxx at 15 K for sample
C series (from as-grown to 315° C anneal). Arrow indicates
increasing annealing temperature. ‘Bars’ span ρxx measured
up to TC. d) Similar non-monotonic behavior of scaling
parameter n is seen in sample A (triangle) & B (square)
FIG. 3: Absorption spectra of sample series C annealed at
differing temperatures (300° - 400° C) shows increased
absorption near ~1 eV for samples annealed between 315° C
and 370° C. Plot of ρxx for sample series A (triangle), B
(square), and C (circle) for differing annealing temperatures
Now, we plot cRS (as ∂ρxy/∂B) as function of ρxx, again
for all samples and Tm below sample’s TC to fit n (Fig. 2.b).
We note a clear transition from n = 2 to n = 1 for ρxx > ~ 10
mΩ-cm, similar to what had been observed where only ρxx
had been varied by temperature22. For ρxx < 10 mΩ-cm, n
= 2 is consistent with intrinsic origins of AHE12,22,23. For n
= 1 regime, further study is required to discern whether the
origins of AHE is due to hopping transport13 or from
extrinsic skew scattering24 as linear scaling behavior is
expected in both. For the highest ρxx, individually fitting
the scaling relationship RS ∝ (ρxx(Tm))n where ρxx is varied
by measurement temperature results in atypical values of n
(> 3). We plot n as fitted to each sample (Fig. 2.c&d). For
all three series of samples, as-grown samples up to the
optimal TA show n ≈ 1. Near the optimal TA, n equals ~ 2,
with further increase in TA results in n > 3, corresponding to
decreases in nh and TC along with increase in ρxx. Similar
scaling behavior of AHE has been seen in inhomogeneous
granular systems where nanometer-sized super-para-
magnetic clusters are randomly distributed in a non-
magnetic matrix such as CoAg systems (n = 3.7)25,
although exact origins of such atypical scaling behavior are
To determine whether our observations can be
attributed to inclusion of metallic nanometer-sized particles,
optical absorption measurements on sample C series are
conducted (Fig. 3). Annealing the sample up to 300° C, the
absorption increases and it is dominant near the low photon
energy region. For TA > 300° C, the low photon energy
absorption decreases which trend is consistent with
dependence of ρxx to TA from transport measurements (Fig.
3 inset). However, at TA of 330° C, it is noteworthy that the
broad region of photon absorption around 1 eV increases.
Such feature may originate from photon scattering by
metallic clusters such as MnAs nano-crystals, whose
diameters should be much smaller than the wavelength of
the photon (1 eV = 1240 nm) and found to have average
diameters of 20-30 nm from cross-sectional transmission
electron microscopy in a previous study27. For annealing
temperatures at 370° C and 400° C, overall photon
absorption decreases. This observation suggests that the
conducting carrier concentration dramatically decreases, and
that the clusters size increases to a point that they cannot
scatter photons by ‘spherical resonance’ process28.
In summary, we have systematically measured the
magneto-transport properties of annealed Ga1-xMnxAs (x ≈
0.055), which samples did not exhibit characteristics of
secondary phases from SQUID magnetometry and HRXRD
measurements. By determining the scaling relationships
between the anomalous Hall coefficient and resistivity,
samples annealed higher than 300° C exhibit scaling
parameters that cannot be explained by current theories on
the origins of AHE in DMS, and most likely due to
formation of nanometer-sized metallic inclusions in a DMS
This work is supported by Samsung Electronics
Endowment and KOSEF through CSCMR. YDP & KHK
acknowledges partial support from the City of Seoul R&BD
Program. We would like to thank H.C. Kim of MSL at
KBSI for assistance with the SQUID magnetometry
1 A. H. Macdonald, P. Schiffer, and N. Samarth, Nat. Mat. 4, 195
2 H. Ohno, Science 281, 951 (1998).
3 M. Tanaka, J. Vac. Sci. Tech. B 16, 2267 (1998).
4 H. Ohno et al., Nature (London) 408, 944 (2000); Y. D. Park et
al., Science 295, 651 (2002).
5 Y.D. Park et al., Phys. Rev. B 68, 085210 (2003); A.M. Nazmul
et al., Phys. Rev. Lett. 95, 017201 (2005).
6 H. Toyosaki et al., Nat. Mat. 3, 221 (2004); S.R. Shinde et al.,
Phys. Rev. Lett. 92, 166601 (2004).
7 A.P. Li et al., Phys. Rev. B 72, 195205 (2005).
8 W. Allen et al., Phys. Rev. B 70, 125320 (2004).
9 K. Hamaya et al., Phys. Rev. Lett. 94, 147203 (2005).
10 V.F. Sapega et al., Phys. Rev. Lett. 94, 137401 (2005).
11 K.Y. Wang et al., Appl. Phys. Lett. 88, 022510 (2006).
12 T. Jungwirth, Q. Niu, and A. H. MacDonald, Phys. Rev. Lett. 88,
13 A.A. Burkov and L. Balents, Phys. Rev. Lett. 91, 057202 (2003).
14 Y.S. Kim et al., J. Kor. Phys. Soc. 47, 306 (2005).
15 T. Hayashi et al., Appl. Phys. Lett. 78, 1691 (2001); S.J.
Potashnik et al., Appl. Phys. Lett. 79, 1495 (2001).
16 K.W. Edmonds et al., Appl. Phys. Lett. 81, 4991 (2002).
17 K.W. Edmonds et al., Phys. Rev. Lett. 92, 037201 (2004).
18 C.M. Hurd, The Hall Effect and its applications, edited by C.
Chien and C.R. Westgate. (Penum, New York, 1980), pp.1-54.
19 Z. Fang et al., Science 302, 92 (2003).
20 X. Liu et al., J. Appl. Phys. 98, 063904 (2005).
21 L.V. Titova et al., Phys. Rev. B 72, 165205 (2005).
22 D. Ruzmetov et al., Phys. Rev. B 69, 155207 (2004).
23 R. Karplus and J.M. Luttinger, Phys. Rev. 95, 1154 (1954).
24 J. Smit, Physica (Ultrecht) 21, 877 (1955).
25 P. Xiong et al., Phys. Rev. Lett. 69, 3220 (1992).
26 A. Gerber et al., Phys. Rev. B 69, 224403 (2004).
27 S.S.A. Seo et al., J. Appl. Phys. 95, 8172 (2004).
28 S.S.A. Seo et al., Appl. Phys. Lett. 82, 4749 (2003).