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Magnetoresistance anomalies in (Ga,Mn)As epilayers with perpendicular magnetic anisotropy


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PHYSICAL REVIEW B 71, 241307sRd s2005d

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Magnetoresistance anomalies in (Ga,Mn)As epilayers with perpendicular magnetic anisotropy

  1. 1. RAPID COMMUNICATIONS 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 sweepstransport and domain walls ͑DWs͒ in both metallic ជ of H at constant field magnitude, revealing MR spikes thatferromagnets2–5 and in ferromagnetic semiconductors.6–9 De- have an antisymmetric dependence on the helicity of the fieldspite 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−xMnxAsin metallic ferromagnets with perpendicular magnetic samples with perpendicular magnetic anisotropy. Full detailsanisotropy5 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 Thenonical” 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 anderties are the focus of extensive ongoing experimental and annealed͒. We present data from two annealed samples ͑Atheoretical 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 bufferpendicular magnetic anisotropy. Although the background heterostructure that consists of 100 nm GaAs ͑grown atMR in these samples is symmetric with respect to the direc- 630 °C͒ followed by 1-␮m strain-relaxed Ga1−xInxAs ͑grown ជtion 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 strainvations 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 frommagnetization reversal—indicated by a change in sign of the the molecular beam epitaxy ͑MBE͒ chamber, the wafers areanomalous Hall effect ͑AHE͒—and hence suggest an inti- cleaved into smaller pieces and some of these pieces aremate connection with the nucleation of DWs. Unlike the re- annealed for 2 h at 250 °C. As found for standardcent 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 ជwhere 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 thoseallel to the current density ͑j ͒. Despite this difference, ourdata 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 andthe voltage probes produce AHE contributions to Rxx, an ef- Rxy, respectively͒ in mesa-etched 800 ␮m ϫ 400 ␮m Hallfect clearly enhanced during magnetization reversal. The bars patterned using conventional photolithography and afield 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 Halllating 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 shown1098-0121/2005/71͑24͒/241307͑4͒/$23.00 241307-1 ©2005 The American Physical Society
  2. 2. RAPID COMMUNICATIONSXIANG et al. PHYSICAL REVIEW B 71, 241307͑R͒ ͑2005͒ FIG. 1. ͑Color͒ ͑a͒ Schematic depiction of Hall bar orientation. ជ ជThe field directions HЌ and Hʈ relative to the current density ជ jcorrespond to the perpendicular and planar geometries discussed inthe text. ͑b͒ The schematic depiction of one of the angular fieldsweeps discussed in the 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 measuremagnetization ͑M͒ as a function of temperature and magneticfield 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 forRxy 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 andSQUID 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 perpendicularindicate the onset of ferromagnetism at TC = 135 K with aneasy axis along ͓001͔. The zero-field behavior of Rxx and Rxy geometry ͑H ជ ʈ ͓001͔, lower trace and inset͒. In both cases, the Hallconfirms 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 perpendicularthe temperature range 20 K ഛ T ഛ 120 K, empirically consis- geometry, we find surprising characteristics in the magnetictent 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 parallelany 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 HCHdensity and the sample plane ͓see Fig. 1͑a͔͒. The lower traces ϳ 2 kOe—almost two orders of magnitude larger than thein Figs. 2͑b͒ and 2͑c͒ show Rxy͑H͒ and Rxx͑H͒, respectively, coercive field HCE observed in the easy axis configuration ជat T = 90 K with H ʈ ͓001͔ and ជ ʈ ͓110͔͒. The field dependence j ¯ ͓Fig. 2͑b͔͒. Moreover, we find striking resistance “spikes” inof Rxy is dominated by the AHE and shows an easy axis Rxx that are antisymmetric in magnetic field direction andhysteresis loop that is proportional to M͑H͒, yielding a coer- that occur when Rxy = 0. This antisymmetry is at first sightcive field identical to that obtained in SQUID measurements surprising because it appears to run counter to the Onsager͑HCE ϳ 20 Oe͒. While the field dependence of Rxx shows re- reciprocity requirement that Rxx͑H͒ = Rxx͑−H͒. Althoughproducible features ͑hysteresis and discontinuous resistance asymmetric MR has been the focus of many discussionsjumps͒ associated with magnetization reversal, these effects within the context of mesoscopic transport,20,21 macroscopicare 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- 241307-2
  3. 3. RAPID COMMUNICATIONSMAGNETORESISTANCE ANOMALIES IN ͑Ga,Mn͒As … PHYSICAL REVIEW B 71, 241307͑R͒ ͑2005͒ FIG. 3. ͑Color͒ Magnetic field dependence of ͑a͒ Rxy and ͑b͒ Rxxin 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 yaxis for clarity.ments of Rxy and Rxx at different temperatures showing thatthe characteristics observed in Fig. 2͑c͒ 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 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 anglepositive magnetic field, starting at H = −10 kOe nominally ␪ = 360° in the plane perpendicular to the current density withapplied 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. Thetional misalignment towards +z ͑characterized by an angle ␦ ˆ upper traces correspond to ជ ʈ ͓110͔, while in the lower traces j ជbetween 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 ជdata 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 jorientation from in-plane ͑−x͒ towards +z ͑the easy axis͒, ˆ ˆ swept through ␪ = 360° in the plane perpendicular to the current ˆ ˆwith 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 ជH = 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 ismagnitude, the misalignment of H is now towards −z. This ˆ 10 Oe/ s, the z component only increases at a rate ofinitiates a reversal of the sample magnetization via the nucle- ϳ0.1 Oe/ s. Consequently, magnetization reversal in theation and propagation of DWs, and is accompanied by a planar geometry case occurs quasistatically, allowing thechange in sign of Rxy. While we do not presently have any slow propagation of DWs during the magnetic field information about the domain structure in these This is in strong contrast with the perpendicular geometrysamples, scanning Hall probe imaging of similar samples has case where magnetization reversal occurs very rapidly ͑inshown the presence of striped domains with widths that are a couple of seconds͒ with our typical sweep rates. Theas large as ϳ30 ␮m.22 Further increases in the magnitude of antisymmetric jumps in Rxx in the planar geometry can now ជH gradually orient the magnetization in-plane, so that the be qualitatively understood using the picture developed inAHE decreases and eventually becomes negligible. We note Ref. 5. When the magnetization is homogeneous, Rxx͑H͒that while we might expect additional contributions to Rxy = Rxx͑−H͒: this situation applies to most of the magnetic fieldfrom the planar Hall effect, these appear to be small com- regime in Figs. 2͑c͒ and 3͑b͒. However, when DWs arepared 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.5,13etries: the data show that large-scale switching occurs in the These circulating currents lead to an admixture of Rxy intoplanar 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 241307-3
  4. 4. RAPID COMMUNICATIONSXIANG et al. PHYSICAL REVIEW B 71, 241307͑R͒ ͑2005͒test the correctness of this interpretation, we have carried out ¯ ͑C͒ patterned along ͓010͔. The reproducible, fine structure insimultaneous measurements of Rxx using contacts on oppo- each of the resistance spikes, suggests the presence of smallsite sides of a Hall bar which should show opposite signs for magnetic domains. It is pertinent to question whether thethe circulating current contribution to Rxx. Our measurements resistance spikes indicate a transient state or a stable one. Toindeed 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 aversal. Further, we find that the data follow the “sum rule” configuration where a resistance spike approximately reachesRxxup − Rxxdown = Rxyleft − Rxyright,7 again consistent with the pic- its maximum value and then holding the field direction andture that the resistance anomalies arise from transverse elec- magnitude fixed for several minutes. Our measurementstric 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 confirmnetic field angle. Figure 4͑a͒ shows angle-dependent mea- that the resistance spikes do not have an extrinsic origin suchsurements of Rxx in a different sample ͑B͒ when the magni- as inductive effects. ជtude of H is held constant while its direction is changed In summary, we have observed field-antisymmetricusing a vector magnet ͓see for example Fig. 1͑b͔͒. The data anomalies in the longitudinal MR of Ga1−xMnxAs epilayersare 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 whenazimuthal angle ␪ through 360° in the plane normal to the DWs are located in between the measuring contacts, but arecurrent density. As in the field-swept data, the angular only observed in the planar geometry when the magneticsweeps 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 multilayerschanges 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 currentsurprising, 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 experimentssweep: 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-strainedmagnetization reversal at −␪ and +␪ always occur towards Ga1−xMnxAs.the same direction, hence creating an AHE contribution ofthe 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 ofhigh-resolution angle-dependent magnetoresistance measure- California-Santa Barbara subcontract KK4131, and NSFments at 4.2 K with angular steps of 0.1° on another sample DMR-0305238, DMR-0305223, and DMR-0401486. 15 T.*Electronic address: 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. 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