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, USAsReceived 1 April 2005; published 14 June 2005d

We report the observation of anomalies in the longitudinal magnetoresistance of tensile-strainedGa1−xMnxAs epilayers with perpendicular magnetic anisotropy. Magnetoresistance measurements carried out inthe planar geometrysmagnetic field parallel to the current densityd reveal “spikes” that are antisymmetric withrespect to the direction of the magnetic field. These anomalies always occur during magnetization reversal, asindicated 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 domainwalls are located between the voltage probes. This interpretation is reinforced by carrying out angular sweeps

of HW , revealing an antisymmetric dependence on the helicity of the field sweep.

DOI: 10.1103/PhysRevB.71.241307 PACS numberssd: 75.50.Pp, 75.70.Ak, 75.60.2d

Contemporary interest in spintronics1 provides a strongmotivation for understanding the interplay between electricaltransport and domain wallssDWsd in both metallicferromagnets2–5 and in ferromagnetic semiconductors.6–9 De-spite a long history of magnetoresistancesMRd measure-ments in a variety of ferromagnetic materials, ongoing stud-ies continue to uncover effects such as an antisymmetric MRin metallic ferromagnets with perpendicular magneticanisotropy5 and a giant planar Hall effect in ferromagneticsemiconductors with in-plane magnetic anisotropy.6 The “ca-nonical” ferromagnetic semiconductor Ga1−xMnxAs is of par-ticular interest in the latter context because its physical prop-erties are the focus of extensive ongoing experimental andtheoretical studies.10–12

Here, we describe anomalies observed in MR measure-ments of tensile-strained Ga1−xMnxAs epilayers with a per-pendicular magnetic anisotropy. Although the backgroundMR in these samples is symmetric with respect to the direc-

tion of the magnetic fieldHW , we also observe resistance“spikes” with an antisymmetric deviationDR from the back-ground MR, i.e.,DRsHd=−DRs−Hd, similar to recent obser-vations in metallic ferromagnetic multilayers with perpen-dicular anisotropy.5 The anomalies always occur duringmagnetization reversal—indicated by a change in sign of theanomalous Hall effectsAHEd—and hence suggest an inti-mate connection with the nucleation of DWs. Unlike the re-cent observations of antisymmetric MR in metallic multilay-ers, we observe the field antisymmetricRxxsHd only inmagnetic field sweeps carried out in the planar geometry,

whereHW is nominally applied in the epilayer plane and par-allel to the current densitys jWd. Despite this difference, ourdata strongly suggest that the antisymmetric anomalies havethe same origin as in the metallic multilayer studies refer-enced above: circulating currents near DWs located betweenthe voltage probes produce AHE contributions toRxx, an ef-fect clearly enhanced during magnetization reversal. Thefield antisymmetry is then a direct consequence of the intrin-sic field dependence of the AHE.sWe note that such circu-lating currents are also known to create a strongRxy contri-bution to measurements ofRxx in ferromagnetic

semiconductors with in-plane anisotropy.7,13d Our interpreta-tion of the data is reinforced by carrying outangularsweepsof HW at constant field magnitude, revealing MR spikes thathave an antisymmetric dependence on the helicity of the fieldsweep. This unusual feature has a straightforward explana-tion within the circulating current picture.

We have fabricated and measured several Ga1−xMnxAssamples with perpendicular magnetic anisotropy. Full detailsof the sample growth by molecular beam epitaxy and post-growth annealing procedures are described elsewhere.14 Theanomalous magnetotransport behavior discussed in this pa-per is generic to all the samples studiedsboth as-grown andannealedd. We present data from two annealed samplessAandBd and one as-grown samplesCd with TC=135, 130, and125 K, respectively. All samples are grown ons001d semi-insulating GaAs substrates after the deposition of a bufferheterostructure that consists of 100 nm GaAssgrown at630 °Cd followed by 1-mm strain-relaxed Ga1−xInxAs sgrownat 480 °Cd. The magnetically active layer consists of a 30-nm-thick Ga1−xMnxAs epilayer grown on the Ga1−xInxAs sur-face at 230 °C. This creates a coherent in-plane tensile strainin the Ga1−xMnxAs, resulting in perpendicular magnetic an-isotropy, with the easy axis alongf001g. After removal fromthe molecular beam epitaxysMBEd chamber, the wafers arecleaved into smaller pieces and some of these pieces areannealed for 2 h at 250 °C. As found for standardGa1−xMnxAs grown on GaAs,15,16 the low temperature an-nealing increases the Curie temperature in these tensile-strained samples. Atomic force microscopy shows that thegrown surface has a cross-hatched pattern with ridges run-

ning along thef110g direction that are higher than thoserunning along thef110g direction; the lateral spacing be-tween these ridges is,1 mm.

We measure the longitudinal and Hall resistancesRxx andRxy, respectivelyd in mesa-etched 800mm3400 mm Hallbars patterned using conventional photolithography and achemical wet etch, with electrical contacts made using in-dium solder and gold wire leads. For convenience, each Hallbar pattern consists of three arms oriented along three prin-

cipal crystalline directionsf110g, f010g, andf110g, as shown

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in Fig. 1. Both dc as well as low-frequency ac magnetotrans-port measurements are carried out from 300 mK to 300 K indifferent cryostats with superconducting magnets, includingone that contains a vector magnet that allows angular varia-tions of a 10-kOe field over the unit sphere. We also measuremagnetizationsMd as a function of temperature and magneticfield in a Quantum Design superconducting quantum inter-ference devicesSQUIDd magnetometer.

We first discuss the temperature dependence ofRxx andRxy at H=0. This is shown in Fig. 2sad for sampleA with thecurrent densityjWi f110g. Temperature- and field-dependentSQUID measurements on a separate piece of this sampleindicate the onset of ferromagnetism atTC=135 K with aneasy axis alongf001g. The zero-field behavior ofRxx andRxyconfirms the SQUID measurements:Rxx has a maximum inthe vicinity of TC, while Rxy reveals the emergence of theAHE below TC.10 A detailed analysis of the temperature de-pendence ofRxy and M at zero field yieldsRxy~RxxM overthe temperature range 20 KøTø120 K, empirically consis-tent with AHE in the presence of skew-scattering.17,18 Atlower temperatures, the temperature dependence does not fitany known pictures of the AHE.

We now discuss the magnetic field dependence ofRxx andRxy for the same sample in the perpendicular geometry,where the magnetic field is perpendicular to both the currentdensity and the sample planefsee Fig. 1sadg. The lower tracesin Figs. 2sbd and 2scd showRxysHd andRxxsHd, respectively,

atT=90 K with HW i f001g and jWi f110gd. The field dependenceof Rxy is dominated by the AHE and shows an easy axishysteresis loop that is proportional toMsHd, yielding a coer-cive field identical to that obtained in SQUID measurementssHCE,20 Oed. While the field dependence ofRxx shows re-producible featuresshysteresis and discontinuous resistancejumpsd associated with magnetization reversal, these effectsare relatively small and difficult to resolve, particularly athigh temperatures.

In contrast to the data measured in the perpendiculargeometry, we find surprising characteristics in the magneticfield dependence of bothRxy andRxx in the planar geometry,where the magnetic field is in the sample plane and parallelto the current densityfsee Fig. 1sadg. The upper tracesin Figs. 2sbd and 2scd showRxysHd andRxxsHd, respectively,

with jWiHW i f110g.19 The hysteretic Hall resistance loop nowhas an unusual shape and changes sign at a fieldHCH,2 kOe—almost two orders of magnitude larger than thecoercive fieldHCE observed in the easy axis configurationfFig. 2sbdg. Moreover, we find striking resistance “spikes” inRxx that areantisymmetricin magnetic field direction andthat occur whenRxy=0. This antisymmetry is at first sightsurprising because it appears to run counter to the Onsagerreciprocity requirement thatRxxsHd=Rxxs−Hd. Althoughasymmetric MR has been the focus of many discussionswithin the context of mesoscopic transport,20,21 macroscopicsamples are not expected to exhibit such asymmetric behav-ior. Figure 3 presents additional field dependent measure-

FIG. 1. sColord sad Schematic depiction of Hall bar orientation.

The field directionsHW ' and HW i relative to the current densityjW

correspond to the perpendicular and planar geometries discussed inthe text. sbd The schematic depiction of one of the angular fieldsweeps discussed in the text.

FIG. 2. sColord sad Temperature dependence ofRxx andRxy for

sampleA with jWi f110g in the absence of an external magnetic field.Panelssbd and scd show the magnetic field dependence ofRxy andRxx, respectively, atT=90 K for the same sample in the planar

geometrysHW i f110g, upper trace and insetd and the perpendicular

geometrysHW i f001g, lower trace and insetd. In both cases, the Hall

bar is oriented such thatjWi f110g. The data insbd andscd are offsetalong they axis for clarity.

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ments ofRxy andRxx at different temperatures showing thatthe characteristics observed in Fig. 2scd are generic and canbe readily observed at temperatures as high as 100 K.

The unusual shape of the hysteretic Hall loops observedin the planar geometry can be explained by assuming that thenominally in-plane magnetic field is slightly misaligned, re-sulting in an AHE contribution from the magnetization com-ponent along the easy axisszd. To illustrate the physics un-derlying the Hall loop, we followRxysHd from negative topositive magnetic field, starting atH=−10 kOe nominallyapplied in-plane and parallel tojW, but with a small uninten-tional misalignment towards +z scharacterized by an angled

between HW and jW. At this large magnetic field,Mz!M in-plane, resulting in a negligible AHE, consistent with the

data in Figs. 2sbd and 3sad. As uHW u→0,MW gradually changesorientation from in-planes−xd towards +z sthe easy axisd,with the symmetry between +z and −z broken by the fieldmisalignment. This results in a positive value ofRxy at

H=0. When we reverse the direction ofHW and increase its

magnitude, the misalignment ofHW is now towards −z. Thisinitiates a reversal of the sample magnetization via the nucle-ation and propagation of DWs, and is accompanied by achange in sign ofRxy. While we do not presently have anydirect information about the domain structure in thesesamples, scanning Hall probe imaging of similar samples hasshown the presence of striped domains with widths that areas large as,30 mm.22 Further increases in the magnitude of

HW gradually orient the magnetization in-plane, so that theAHE decreases and eventually becomes negligible. We notethat while we might expect additional contributions toRxyfrom the planar Hall effect, these appear to be small com-pared with the AHE in samples with tensile strain.

The Hall loop provides a crucial insight into the differentbehavior ofRxxsHd in the planar and perpendicular geom-etries: the data show that large-scale switching occurs in theplanar geometry only whenHzùHCH sind=HCE. Using thecoercive fields observed for the perpendicular and planar ge-

ometriesfFig. 2sbdg, we estimate that the misalignment angled,0.6°. Since the typical magnetic field sweep rate is10 Oe/s, thez component only increases at a rate of,0.1 Oe/s. Consequently, magnetization reversal in theplanar geometry case occurs quasistatically, allowing theslow propagation of DWs during the magnetic field sweep.This is in strong contrast with the perpendicular geometrycase where magnetization reversal occurs very rapidlysina couple of secondsd with our typical sweep rates. Theantisymmetric jumps inRxx in the planar geometry can nowbe qualitatively understood using the picture developed inRef. 5. When the magnetization is homogeneous,RxxsHd=Rxxs−Hd: this situation applies to most of the magnetic fieldregime in Figs. 2scd and 3sbd. However, when DWs areformed, creating a spatially inhomogeneous magnetization,the current density is perturbed bysstaticd circulating cur-rents that flow in the vicinity of DWs.5,13

These circulating currents lead to an admixture ofRxy intomeasurements ofRxx. BecauseRxysHd=−Rxys−Hd, the contri-bution is antisymmetric with respect to the field direction. To

FIG. 4. sColord Panelssad and sbd show Rxx and Rxy, respec-

tively, T=90 K for sampleB as HW is swept through an angleu=360° in the plane perpendicular to the current density with

uHW u=730 Oe. The angleu is defined betweenHW and f001g. Theupper traces correspond tojWi f110g, while in the lower traces

jWi f110g. The data are offset along they axis for clarity. Panelscdshows measurements ofRxx taken with higher angular resolution on

another samplesCd at T=4.2 K. Here, jWi f010g and HW are againswept throughu=360° in the plane perpendicular to the current

with uHW u=730 Oe.

FIG. 3. sColord Magnetic field dependence ofsad Rxy andsbd Rxx

in sampleA at T=40, 60, 80, 100 K. The data are all taken in the

planar geometry withHW i jWi f110g. The data are offset along theyaxis for clarity.

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test the correctness of this interpretation, we have carried outsimultaneous measurements ofRxx using contacts on oppo-site sides of a Hall bar which should show opposite signs forthe circulating current contribution toRxx. Our measurementsindeed reveal this asymmetry, showing that the sumRxx

upsHd+RxxdownsHd is symmetric with respect to field re-

versal. Further, we find that the data follow the “sum rule”Rxx

up−Rxxdown=Rxy

left−Rxyright,7 again consistent with the pic-

ture that the resistance anomalies arise from transverse elec-tric field contributions due to circulating currents.

Further evidence for AHE contributions toRxx emergesfrom MR measurements carried out as a function of the mag-netic field angle. Figure 4sad shows angle-dependent mea-surements ofRxx in a different samplesBd when the magni-

tude of HW is held constant while its direction is changedusing a vector magnetfsee for example Fig. 1sbdg. The dataare shown for Hall bars patterned along two different crys-

talline directionssjWi f110g and jWi f110gd, while we sweep theazimuthal angleu through 360° in the plane normal to thecurrent density. As in the field-swept data, the angular

sweeps also show spikes inRxx wheneverRxy sand henceMW dchanges signfFig. 4sbdg. The spikes have an asymmetric de-pendence on the helicity of the sweep. While this is initiallysurprising, the reason becomes clear if we assume that thefield rotation nucleates DWs just as in the case of a field

sweep: whenHW is swept in theyz plane, DWs are nucleatedwheneverHz.HCE. For sweeps of opposite helicity, themagnetization reversal at −u and +u always occur towardsthe same direction, hence creating an AHE contribution ofthe same sign.

The angular scans also reveal that the DW structure dur-ing these angular sweeps is quite complex. Figure 4scd showshigh-resolution angle-dependent magnetoresistance measure-ments at 4.2 K with angular steps of 0.1° on another sample

sCd patterned alongf010g. The reproducible, fine structure ineach of the resistance spikes, suggests the presence of smallmagnetic domains. It is pertinent to question whether theresistance spikes indicate a transient state or a stable one. Toexamine this issue, we carried out time-dependent measure-ments ofRxx after sweeping the magnetic field angle to aconfiguration where a resistance spike approximately reachesits maximum value and then holding the field direction andmagnitude fixed for several minutes. Our measurementsshow that the value ofRxx does not change over this timescale, indicating that the magnetic state creating the resis-tance spike is a stable one. These observations also confirmthat the resistance spikes do not have an extrinsic origin suchas inductive effects.

In summary, we have observed field-antisymmetricanomalies in the longitudinal MR of Ga1−xMnxAs epilayerswith perpendicular magnetic anisotropy. These antisymmet-ric anomalies arise from AHE contributions toRxx whenDWs are located in between the measuring contacts, but areonly observed in the planar geometry when the magneticfield is parallel to the current density. This contrasts withsimilar observations in metallic ferromagnetic multilayerswith perpendicular magnetic anisotropy where such antisym-metric MR is observed with the field normal to the currentand the sample plane. Our observations are likely to be im-portant for the analysis of MR measurements in experimentsfocusing on the control and measurements of DWs in later-ally patterned structures fabricated from tensile-strainedGa1−xMnxAs.

This research has been supported by Grants NO. ONRN0014-05-1-0107, DARPA/ONR N00014-99-1-1093,N00014-99-1-1096, and N00014-00-1-0951, University ofCalifornia-Santa Barbara subcontract KK4131, and NSFDMR-0305238, DMR-0305223, and DMR-0401486.

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