PHYSICAL REVIEW B 71, 241307sRd s2005d

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PHYSICAL REVIEW B 71, 241307͑R͒ ͑2005͒
Magnetoresistance anomalies in (Ga,Mn)As epilayers with perpendicular magnetic anisotropy
G. Xiang,1 A. W. Holleitner,2 B. L. Sheu,1 F. M. Mendoza,2 O. Maksimov,1 M. B. Stone,1
P. Schiffer,1 D. D. Awschalom,2 and N. Samarth1,2,*
1Physics Department and Materials Research Institute, Penn State University, University Park, Pennsylvania 16802, USA
2Center for Spintronics and Quantum Computation, University of California, Santa Barbara, California 93106, USA
͑Received 1 April 2005; published 14 June 2005͒
We report the observation of anomalies in the longitudinal magnetoresistance of tensile-strained
Ga1−xMnxAs epilayers with perpendicular magnetic anisotropy. Magnetoresistance measurements carried out in
the planar geometry ͑magnetic field parallel to the current density͒ reveal “spikes” that are antisymmetric with
respect to the direction of the magnetic field. These anomalies always occur during magnetization reversal, as
indicated by a simultaneous change in sign of the anomalous Hall effect. The data suggest that the antisym-
metric anomalies originate in anomalous Hall effect contributions to the longitudinal resistance when domain
walls are located between the voltage probes. This interpretation is reinforced by carrying out angular sweeps
ជ
of H, revealing an antisymmetric dependence on the helicity of the field sweep.
DOI: 10.1103/PhysRevB.71.241307 PACS number͑s͒: 75.50.Pp, 75.70.Ak, 75.60.Ϫd
Contemporary interest in spintronics1 provides a strong semiconductors with in-plane anisotropy.7,13͒ Our interpreta-
motivation for understanding the interplay between electrical tion of the data is reinforced by carrying out angular sweeps
transport and domain walls ͑DWs͒ in both metallic ជ
of H at constant field magnitude, revealing MR spikes that
ferromagnets2–5 and in ferromagnetic semiconductors.6–9 De- have an antisymmetric dependence on the helicity of the field
spite a long history of magnetoresistance ͑MR͒ measure- sweep. This unusual feature has a straightforward explana-
ments in a variety of ferromagnetic materials, ongoing stud- tion within the circulating current picture.
ies continue to uncover effects such as an antisymmetric MR We have fabricated and measured several Ga1−xMnxAs
in metallic ferromagnets with perpendicular magnetic samples with perpendicular magnetic anisotropy. Full details
anisotropy5 and a giant planar Hall effect in ferromagnetic of the sample growth by molecular beam epitaxy and post-
semiconductors with in-plane magnetic anisotropy.6 The “ca- growth annealing procedures are described elsewhere.14 The
nonical” ferromagnetic semiconductor Ga1−xMnxAs is of par- anomalous magnetotransport behavior discussed in this pa-
ticular interest in the latter context because its physical prop- per is generic to all the samples studied ͑both as-grown and
erties are the focus of extensive ongoing experimental and annealed͒. We present data from two annealed samples ͑A
theoretical studies.10–12 and B͒ and one as-grown sample ͑C͒ with TC = 135, 130, and
Here, we describe anomalies observed in MR measure- 125 K, respectively. All samples are grown on ͑001͒ semi-
ments of tensile-strained Ga1−xMnxAs epilayers with a per- insulating GaAs substrates after the deposition of a buffer
pendicular magnetic anisotropy. Although the background heterostructure that consists of 100 nm GaAs ͑grown at
MR in these samples is symmetric with respect to the direc- 630 °C͒ followed by 1-␮m strain-relaxed Ga1−xInxAs ͑grown
ជ
tion of the magnetic field H, we also observe resistance at 480 °C͒. The magnetically active layer consists of a 30-
“spikes” with an antisymmetric deviation ⌬R from the back- nm-thick Ga1−xMnxAs epilayer grown on the Ga1−xInxAs sur-
ground MR, i.e., ⌬R͑H͒ = −⌬R͑−H͒, similar to recent obser- face at 230 °C. This creates a coherent in-plane tensile strain
vations in metallic ferromagnetic multilayers with perpen- in the Ga1−xMnxAs, resulting in perpendicular magnetic an-
dicular anisotropy.5 The anomalies always occur during isotropy, with the easy axis along ͓001͔. After removal from
magnetization reversal—indicated by a change in sign of the the molecular beam epitaxy ͑MBE͒ chamber, the wafers are
anomalous Hall effect ͑AHE͒—and hence suggest an inti- cleaved into smaller pieces and some of these pieces are
mate connection with the nucleation of DWs. Unlike the re- annealed for 2 h at 250 °C. As found for standard
cent observations of antisymmetric MR in metallic multilay- Ga1−xMnxAs grown on GaAs,15,16 the low temperature an-
ers, we observe the field antisymmetric Rxx͑H͒ only in nealing increases the Curie temperature in these tensile-
magnetic field sweeps carried out in the planar geometry, strained samples. Atomic force microscopy shows that the
ជ
where H is nominally applied in the epilayer plane and par- grown surface has a cross-hatched pattern with ridges run-
ជ ¯
ning along the ͓110͔ direction that are higher than those
allel to the current density ͑j ͒. Despite this difference, our
data strongly suggest that the antisymmetric anomalies have running along the ͓110͔ direction; the lateral spacing be-
the same origin as in the metallic multilayer studies refer- tween these ridges is ϳ1 ␮m.
enced above: circulating currents near DWs located between We measure the longitudinal and Hall resistance ͑Rxx and
the voltage probes produce AHE contributions to Rxx, an ef- Rxy, respectively͒ in mesa-etched 800 ␮m ϫ 400 ␮m Hall
fect clearly enhanced during magnetization reversal. The bars patterned using conventional photolithography and a
field antisymmetry is then a direct consequence of the intrin- chemical wet etch, with electrical contacts made using in-
sic field dependence of the AHE. ͑We note that such circu- dium solder and gold wire leads. For convenience, each Hall
lating currents are also known to create a strong Rxy contri- bar pattern consists of three arms oriented along three prin-
bution to measurements of Rxx in ferromagnetic ¯
cipal crystalline directions ͓110͔, ͓010͔, and ͓110͔, as shown
1098-0121/2005/71͑24͒/241307͑4͒/$23.00 241307-1 ©2005 The American Physical Society

2. RAPID COMMUNICATIONS
XIANG et al. PHYSICAL REVIEW B 71, 241307͑R͒ ͑2005͒
FIG. 1. ͑Color͒ ͑a͒ Schematic depiction of Hall bar orientation.
ជ ជ
The field directions HЌ and Hʈ relative to the current density ជ j
correspond to the perpendicular and planar geometries discussed in
the text. ͑b͒ The schematic depiction of one of the angular field
sweeps discussed in the text.
in Fig. 1. Both dc as well as low-frequency ac magnetotrans-
port measurements are carried out from 300 mK to 300 K in
different cryostats with superconducting magnets, including
one that contains a vector magnet that allows angular varia-
tions of a 10-kOe field over the unit sphere. We also measure
magnetization ͑M͒ as a function of temperature and magnetic
field in a Quantum Design superconducting quantum inter-
ference device ͑SQUID͒ magnetometer.
We first discuss the temperature dependence of Rxx and FIG. 2. ͑Color͒ ͑a͒ Temperature dependence of Rxx and Rxy for
Rxy at H = 0. This is shown in Fig. 2͑a͒ for sample A with the sample A with ជ ʈ ͓110͔ in the absence of an external magnetic field.
j ¯
current density ជ ʈ ͓110͔. Temperature- and field-dependent
j ¯ Panels ͑b͒ and ͑c͒ show the magnetic field dependence of Rxy and
SQUID measurements on a separate piece of this sample Rxx, respectively, at T = 90 K for the same sample in the planar
ជ ¯
geometry ͑H ʈ ͓110͔, upper trace and inset͒ and the perpendicular
indicate the onset of ferromagnetism at TC = 135 K with an
easy axis along ͓001͔. The zero-field behavior of Rxx and Rxy geometry ͑H ជ ʈ ͓001͔, lower trace and inset͒. In both cases, the Hall
confirms the SQUID measurements: Rxx has a maximum in bar is oriented such that ជ ʈ ͓110͔. The data in ͑b͒ and ͑c͒ are offset
j ¯
the vicinity of TC, while Rxy reveals the emergence of the along the y axis for clarity.
AHE below TC.10 A detailed analysis of the temperature de-
pendence of Rxy and M at zero field yields Rxy ϰ RxxM over In contrast to the data measured in the perpendicular
the temperature range 20 K ഛ T ഛ 120 K, empirically consis- geometry, we find surprising characteristics in the magnetic
tent with AHE in the presence of skew-scattering.17,18 At field dependence of both Rxy and Rxx in the planar geometry,
lower temperatures, the temperature dependence does not fit where the magnetic field is in the sample plane and parallel
any known pictures of the AHE. to the current density ͓see Fig. 1͑a͔͒. The upper traces
We now discuss the magnetic field dependence of Rxx and in Figs. 2͑b͒ and 2͑c͒ show Rxy͑H͒ and Rxx͑H͒, respectively,
Rxy for the same sample in the perpendicular geometry, j ជ
with ជ ʈ H ʈ ͓110͔.19 The hysteretic Hall resistance loop now
¯
where the magnetic field is perpendicular to both the current has an unusual shape and changes sign at a field HCH
density and the sample plane ͓see Fig. 1͑a͔͒. The lower traces ϳ 2 kOe—almost two orders of magnitude larger than the
in Figs. 2͑b͒ and 2͑c͒ show Rxy͑H͒ and Rxx͑H͒, respectively, coercive field HCE observed in the easy axis configuration
ជ
at T = 90 K with H ʈ ͓001͔ and ជ ʈ ͓110͔͒. The field dependence
j ¯ ͓Fig. 2͑b͔͒. Moreover, we find striking resistance “spikes” in
of Rxy is dominated by the AHE and shows an easy axis Rxx that are antisymmetric in magnetic field direction and
hysteresis loop that is proportional to M͑H͒, yielding a coer- that occur when Rxy = 0. This antisymmetry is at first sight
cive field identical to that obtained in SQUID measurements surprising because it appears to run counter to the Onsager
͑HCE ϳ 20 Oe͒. While the field dependence of Rxx shows re- reciprocity requirement that Rxx͑H͒ = Rxx͑−H͒. Although
producible features ͑hysteresis and discontinuous resistance asymmetric MR has been the focus of many discussions
jumps͒ associated with magnetization reversal, these effects within the context of mesoscopic transport,20,21 macroscopic
are relatively small and difficult to resolve, particularly at samples are not expected to exhibit such asymmetric behav-
high temperatures. ior. Figure 3 presents additional field dependent measure-
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MAGNETORESISTANCE ANOMALIES IN ͑Ga,Mn͒As … PHYSICAL REVIEW B 71, 241307͑R͒ ͑2005͒
FIG. 3. ͑Color͒ Magnetic field dependence of ͑a͒ Rxy and ͑b͒ Rxx
in sample A at T = 40, 60, 80, 100 K. The data are all taken in the
ជ j ¯
planar geometry with H ʈ ជ ʈ ͓110͔. The data are offset along the y
axis for clarity.
ments of Rxy and Rxx at different temperatures showing that
the characteristics observed in Fig. 2͑c͒ are generic and can
be readily observed at temperatures as high as 100 K.
The unusual shape of the hysteretic Hall loops observed
in the planar geometry can be explained by assuming that the
nominally in-plane magnetic field is slightly misaligned, re-
sulting in an AHE contribution from the magnetization com-
ponent along the easy axis ͑z͒. To illustrate the physics un-
ˆ
FIG. 4. ͑Color͒ Panels ͑a͒ and ͑b͒ show Rxx and Rxy, respec-
derlying the Hall loop, we follow Rxy͑H͒ from negative to ជ
tively, T = 90 K for sample B as H is swept through an angle
positive magnetic field, starting at H = −10 kOe nominally ␪ = 360° in the plane perpendicular to the current density with
applied in-plane and parallel to ជ, but with a small uninten-
j ជ ជ
͉H͉ = 730 Oe. The angle ␪ is defined between H and ͓001͔. The
tional misalignment towards +z ͑characterized by an angle ␦
ˆ
upper traces correspond to ជ ʈ ͓110͔, while in the lower traces
j
ជ
between H and ជ. At this large magnetic field, M z
j ជ ʈ ͓110͔. The data are offset along the y axis for clarity. Panel ͑c͒
j ¯
Ӷ M in-plane, resulting in a negligible AHE, consistent with the shows measurements of Rxx taken with higher angular resolution on
ជ ជ
data in Figs. 2͑b͒ and 3͑a͒. As ͉H͉ → 0 , M gradually changes ជ
another sample ͑C͒ at T = 4.2 K. Here, ជ ʈ ͓010͔ and H are again
j
orientation from in-plane ͑−x͒ towards +z ͑the easy axis͒,
ˆ ˆ swept through ␪ = 360° in the plane perpendicular to the current
ˆ ˆ
with the symmetry between +z and −z broken by the field ជ
with ͉H͉ = 730 Oe.
misalignment. This results in a positive value of Rxy at
ជ
H = 0. When we reverse the direction of H and increase its ometries ͓Fig. 2͑b͔͒, we estimate that the misalignment angle
ជ ␦ ϳ 0.6°. Since the typical magnetic field sweep rate is
magnitude, the misalignment of H is now towards −z. This ˆ 10 Oe/ s, the z component only increases at a rate of
initiates a reversal of the sample magnetization via the nucle- ϳ0.1 Oe/ s. Consequently, magnetization reversal in the
ation and propagation of DWs, and is accompanied by a planar geometry case occurs quasistatically, allowing the
change in sign of Rxy. While we do not presently have any slow propagation of DWs during the magnetic field sweep.
direct information about the domain structure in these This is in strong contrast with the perpendicular geometry
samples, scanning Hall probe imaging of similar samples has case where magnetization reversal occurs very rapidly ͑in
shown the presence of striped domains with widths that are a couple of seconds͒ with our typical sweep rates. The
as large as ϳ30 ␮m.22 Further increases in the magnitude of antisymmetric jumps in Rxx in the planar geometry can now
ជ
H gradually orient the magnetization in-plane, so that the be qualitatively understood using the picture developed in
AHE decreases and eventually becomes negligible. We note Ref. 5. When the magnetization is homogeneous, Rxx͑H͒
that while we might expect additional contributions to Rxy = Rxx͑−H͒: this situation applies to most of the magnetic field
from the planar Hall effect, these appear to be small com- regime in Figs. 2͑c͒ and 3͑b͒. However, when DWs are
pared with the AHE in samples with tensile strain. formed, creating a spatially inhomogeneous magnetization,
The Hall loop provides a crucial insight into the different the current density is perturbed by ͑static͒ circulating cur-
behavior of Rxx͑H͒ in the planar and perpendicular geom- rents that flow in the vicinity of DWs.5,13
etries: the data show that large-scale switching occurs in the These circulating currents lead to an admixture of Rxy into
planar geometry only when Hz ജ HCH sin ␦ = HCE. Using the measurements of Rxx. Because Rxy͑H͒ = −Rxy͑−H͒, the contri-
coercive fields observed for the perpendicular and planar ge- bution is antisymmetric with respect to the field direction. To
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XIANG et al. PHYSICAL REVIEW B 71, 241307͑R͒ ͑2005͒
test the correctness of this interpretation, we have carried out ¯
͑C͒ patterned along ͓010͔. The reproducible, fine structure in
simultaneous measurements of Rxx using contacts on oppo- each of the resistance spikes, suggests the presence of small
site sides of a Hall bar which should show opposite signs for magnetic domains. It is pertinent to question whether the
the circulating current contribution to Rxx. Our measurements resistance spikes indicate a transient state or a stable one. To
indeed reveal this asymmetry, showing that the sum examine this issue, we carried out time-dependent measure-
Rxxup͑H͒ + Rxxdown͑H͒ is symmetric with respect to field re- ments of Rxx after sweeping the magnetic field angle to a
versal. Further, we find that the data follow the “sum rule” configuration where a resistance spike approximately reaches
Rxxup − Rxxdown = Rxyleft − Rxyright,7 again consistent with the pic- its maximum value and then holding the field direction and
ture that the resistance anomalies arise from transverse elec- magnitude fixed for several minutes. Our measurements
tric field contributions due to circulating currents. show that the value of Rxx does not change over this time
Further evidence for AHE contributions to Rxx emerges scale, indicating that the magnetic state creating the resis-
from MR measurements carried out as a function of the mag- tance spike is a stable one. These observations also confirm
netic field angle. Figure 4͑a͒ shows angle-dependent mea- that the resistance spikes do not have an extrinsic origin such
surements of Rxx in a different sample ͑B͒ when the magni- as inductive effects.
ជ
tude of H is held constant while its direction is changed In summary, we have observed field-antisymmetric
using a vector magnet ͓see for example Fig. 1͑b͔͒. The data anomalies in the longitudinal MR of Ga1−xMnxAs epilayers
are shown for Hall bars patterned along two different crys- with perpendicular magnetic anisotropy. These antisymmet-
talline directions ͑j ʈ ͓110͔ and ជ ʈ ͓110͔͒, while we sweep the
ជ j ¯ ric anomalies arise from AHE contributions to Rxx when
azimuthal angle ␪ through 360° in the plane normal to the DWs are located in between the measuring contacts, but are
current density. As in the field-swept data, the angular only observed in the planar geometry when the magnetic
sweeps also show spikes in Rxx whenever Rxy ͑and hence M ͒ ជ field is parallel to the current density. This contrasts with
similar observations in metallic ferromagnetic multilayers
changes sign ͓Fig. 4͑b͔͒. The spikes have an asymmetric de-
with perpendicular magnetic anisotropy where such antisym-
pendence on the helicity of the sweep. While this is initially
metric MR is observed with the field normal to the current
surprising, the reason becomes clear if we assume that the
and the sample plane. Our observations are likely to be im-
field rotation nucleates DWs just as in the case of a field
ជ portant for the analysis of MR measurements in experiments
sweep: when H is swept in the yz plane, DWs are nucleated focusing on the control and measurements of DWs in later-
whenever Hz Ͼ HCE. For sweeps of opposite helicity, the ally patterned structures fabricated from tensile-strained
magnetization reversal at −␪ and +␪ always occur towards Ga1−xMnxAs.
the same direction, hence creating an AHE contribution of
the same sign. This research has been supported by Grants NO. ONR
The angular scans also reveal that the DW structure dur- N0014-05-1-0107, DARPA/ONR N00014-99-1-1093,
ing these angular sweeps is quite complex. Figure 4͑c͒ shows N00014-99-1-1096, and N00014-00-1-0951, University of
high-resolution angle-dependent magnetoresistance measure- California-Santa Barbara subcontract KK4131, and NSF
ments at 4.2 K with angular steps of 0.1° on another sample DMR-0305238, DMR-0305223, and DMR-0401486.
15 T.
*Electronic address: nsamarth@psu.edu Hayashi, Y. Hashimoto, S. Katsumoto, and Y. Iye, Appl. Phys.
1 S. A. Wolf et al., Science 294, 1488 ͑2001͒. Lett. 78, 1691 ͑2001͒.
2 A. D. Kent et al., J. Phys.: Condens. Matter 13, R461 ͑2001͒. 16 S. J. Potashnik, K. C. Ku, S. H. Chun, J. J. Berry, N. Samarth, and
3 T. Ono et al., Science 284, 468 ͑1999͒. P. Schiffer, Appl. Phys. Lett. 79, 1495 ͑2001͒.
4 D. A. Allwood et al., Science 296, 2003 ͑2002͒. 17 C. M. Hurd, The Hall Effect in Metals and Alloys ͑Plenum, New
5 X. M. Cheng et al., Phys. Rev. Lett. 94, 017203 ͑2005͒. York, 1972͒.
6 H. X. Tang et al., Phys. Rev. Lett. 90, 107201 ͑2003͒. 18 J. Smit, Physica ͑Amsterdam͒ 21, 877 ͑1955͒.
7 H. X. Tang et al., Nature ͑London͒ 431, 52 ͑2004͒. 19 Because the magnetic field is applied along a hard axis in this
8 A. W. Holleitner et al., Appl. Phys. Lett. 85, 5622 ͑2004͒. geometry, cooling down a sample in zero applied field and then
9 M. Yamanouchi, D. Chiba, F. Matsukura, and H. Ohno, Nature starting magnetic field sweeps can create unstable magnetic do-
͑London͒ 428, 539 ͑2004͒. main patterns. Hence, to produce consistently reproducible data
10 H. Ohno, in Semiconductor Spintronics and Quantum Computa- when the magnetic field is then swept through a loop, we carry
tion, edited by D. D. Awschalom, D. Loss, and N. Samarth out magnetoresistance measurements after cooling the sample
͑Springer-Verlag, Berlin, 2002͒. down from room temperature in an in-plane magnetic field of
11 N. Samarth, in Solid State Physics, edited by H. Ehrenreich and F. −20 kOe.
Spaepen ͑Elsevier Academic Press, San Diego, 2004͒, Vol. 58. 20 M. Buttiker, Phys. Rev. Lett. 57, 1761 ͑1986͒.
12 A. H. MacDonald, P. Schiffer, and N. Samarth, Nat. Mater. 4, 21 A. D. Benoit, S. Washburn, C. P. Umbach, R. B. Laibowitz, and
195 ͑2005͒. R. A. Webb, Phys. Rev. Lett. 57, 1765 ͑1986͒.
13 H. Tang and M. L. Roukes, Phys. Rev. B 70, 205213 ͑2004͒. 22 T. Shono, T. Hasegawa, T. Fukumura, F. Matsukura, and H.
14 O. Maksimov et al., J. Cryst. Growth 269, 298 ͑2004͒. Ohno, Appl. Phys. Lett. 77, 1363 ͑2000͒.
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