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PHYSICAL REVIEW B 88, 214431 (2013)

Testing dependence of anomalous Hall effect on resistivity in SrRuO3 by its increase with electron irradiation Noam Haham,1 Marcin Konczykowski,2 Bouwe Kuiper,3 Gertjan Koster,3 and Lior Klein1 1

Department of Physics, Nano-magnetism Research Center, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel 2 Laboratoire des Solides Irradis, Ecole Polytechnique, 91128 Palaiseau Cedex, France 3 Faculty of Science and Technology and MESA + Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands (Received 26 October 2013; published 30 December 2013) We measure the anomalous Hall effect (AHE) in several patterns of the itinerant ferromagnet SrRuO3 before and after the patterns are irradiated with electrons. The irradiation increases the resistivity of the patterns due to the introduction of point defects and we find that the AHE coefficient Rs scales with the total resistivity before and after irradiation which indicates that the AHE is determined by the total resistivity. We discuss possible origins of slight deviations from scaling that are observed at low temperature, particularly below 70 K. DOI: 10.1103/PhysRevB.88.214431

PACS number(s): 75.47.−m, 72.25.Ba, 75.50.Cc, 72.15.Gd

I. INTRODUCTION

Magnetic conductors exhibit transverse resistivity linked to their magnetic moments. This phenomenon, known as the anomalous Hall effect (AHE),1 is one of the most intriguing manifestations of a transport phenomenon that is sensitive to spin and topology and therefore it has motivated intense theoretical and experimental efforts. Extrinsic and intrinsic mechanisms were proposed to explain the AHE. The extrinsic mechanism includes skew scattering2 and side jumps3 which provide for the transverse resistivity linked to the AHE (ρxy ), ρxy = Rs μ0 M⊥ ,

(1)

where Rs is the anomalous Hall coefficient which is a function of the longitudinal resistivity ρxx . On the other hand, the intrinsic Berry phase mechanism (Karplus-Luttinger)1,4 2  where σxy (M)  (the transverse provides ρxy = −ρxx σxy (M) conductivity) reflects the dependence of the band structure  However, when the band structure on the magnetization M. is temperature independent, the intrinsic contribution to the AHE reduces to the form of Eq. (1).4 The itinerant ferromagnet SrRuO3 (Ref. 5) has played an important role in the study of the different contributions to the AHE. Berry phase calculations that assume a temperaturedependent exchange gap that closes at Tc seemed to be consistent with the data.6,7 However, it has been found that the AHE vanishes at a specific resistivity, and not at a specific magnetization as one might expect from such a model.8 Recently, it was found that the AHE is consistent with a combination of two contributions: (a) a side jumps contribution and (b) a Berry phase contribution with a temperature independent band when taking into account the temperature dependence of the scattering time.9,10 The applicability of the model to SrRuO3 was demonstrated by measuring SrRuO3 films with a wide range of thicknesses that vary considerably in the temperature dependence of their resistivity9 and showing a scaling relation of Rs normalized with its maximum value as a function of the resistivity ρxx normalized with the resistivity at which the AHE vanishes. While there are justifications for normalizing Rs and ρxx , it is desirable to show the existence of scaling without normalization. This can be achieved by changing the 1098-0121/2013/88(21)/214431(4)

resistivity of a pattern and comparing the dependence of the AHE on resistivity before and after the induced change. Low-temperature electron irradiation has been used before to induce a small change in the resistivity of SrRuO3 films without a significant change of film quality.11 Here we measure the AHE in several patterns of SrRuO3 before and after electron irradiation and find that overall a good scaling is obtained, in support of previous claims. However, at low temperatures, strongly irradiated patterns show slight deviations from scaling, suggesting a nontrivial effect of the induced point defects. II. SAMPLES AND EXPERIMENT

∼ 5.53 A, ˚ Epitaxial thin films of orthorhombic SrRuO3 (a = ˚ and c ∼ ˚ were grown on slightly miscut b∼ = 5.57 A, = 7.85 A) (∼0.1◦ ) SrTiO3 substrates using pulsed laser deposition (PLD). The substrates were chemically treated to achieve a TiO2 surface termination.12 A sample temperature of 700 ◦ C and a growth pressure of 0.3 mbar in a gas mixture consisting of 50% argon and 50% oxygen were set for the deposition. A 248-nm KrF excimer laser was used to ablate the material at a repetition rate of 1 Hz with an energy density of 2.1 J/cm2 and a spot size of 2.3 mm2 . A postanneal during cooldown was performed in a 100-mbar oxygen pressure with a ramp rate of 25◦ /min. Before and after deposition the surface morphology was studied using a Bruker Icon Dimension AFM and the film thickness and crystallinity were measured using a Bruker D8 diffractometer by x-ray reflectivity and reciprocal space maps. The films have a Cuire temperature Tc ∼ 150 K and they exhibit uniaxial magnetocrystalline anisotropy with an easy axis which varies with temperature between 45◦ from the film normal at 150 K and 30◦ at the low-temperature limit.13 The anisotropy field exceeds 7 T as a result of which the remanent magnetization does not break into domains up to a few degrees below Tc ,14 and has a component perpendicular to the film even in the absence of a magnetic field. These features enable us to directly measure the zero-field antisymmetric transverse resistivity which can be fully attributed to AHE, ρxy . The films were patterned to allow transverse and longitudinal resistivity measurements, and the patterns were irradiated by an electron beam with an energy of 2.5 MeV and an

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©2013 American Physical Society

HAHAM, KONCZYKOWSKI, KUIPER, KOSTER, AND KLEIN

III. EXPERIMENTAL RESULTS

Figure 1 shows the temperature dependence between 2 and 150 K of the longitudinal resistivity ρxx before and after 160

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FIG. 1. (Color online) Longitudinal resistivity ρxx vs temperature before (blue circles) and after (red crosses) irradiation of four patterns.

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average dose of 1.6 C/cm2 at the low-temperature beam line CRYO-1 of SIRIUS facility at Ecole Polytechnique based on a Pelltron-type NEC accelerator coupled with a close-cycle refrigerator. During the irradiation the sample was immersed in liquid hydrogen and kept at a temperature below 22 K. There is a variety of defects which can be induced by irradiation in a compound, however, since the energy of the irradiated electrons is relatively low, it is not enough to induce cascades and amorphous tracks, and only Frenkel pairs are created on all three sublattices of SrRuO3 . The creation of antisite defects is possible but it has much lower probability involving a sequence of interstitial defect creation. Thus the relevant induced defects are exclusively Frenkel pairs. Upon removal of the sample and warming up to room temperature, a partial annealing of damage occurs. Since interstitials have in general much lower migration energy than vacancies, we presume that the remaining damage contributing to the increase of resistivity is mainly vacancies15 and that interstitial defects either recombine with nearby vacancies or migrate to the sample surface which is the dominant sink in our case. Based on numerical simulations we estimate the density of defects as ∼7.5 × 1019 cm1 3 assuming a threshold energy of ∼20 eV for all of the sublattices. The AHE resistivity and longitudinal resistivity were measured at zero field as a function of temperature before and after irradiation with a Quantum Design PPMS-9. The field-antisymmetric transverse resistivity ρxy was extracted by changing the voltage and current leads.16 The data shown here are for a 34-nm film with resistivity ratio of 5.

PHYSICAL REVIEW B 88, 214431 (2013)

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FIG. 2. (Color online) AHE resistivity ρxy as a function of temperature before (blue circles) and after (red crosses) irradiation for four patterns.

irradiation. Four independent Hall bar patterns are measured on one sample to confirm that the observed phenomena are intrinsic to the film. We note a significant change in resistivity due to the irradiation. The change in the residual resistivity is ∼10% for patterns 1 and 2 and ∼17% for patterns 3 and 4. We attribute the differences in the resistivity increase to local variations in the irradiation dose. We note that the irradiation-induced increase in resistivity is larger at low temperatures, consistent with previous results.11 Figure 2 shows the temperature dependence of the transverse resistivity ρxy at zero field before and after electron irradiation. The curves differ significantly, with the largest difference at low temperatures where the irradiation-induced increase in resistivity is the largest. To test the claim that the AHE coefficient Rs scales with resistivity,9 we divide ρxy by M⊥ , and extract Rs according to Eq. (1). Figure 3 shows the extracted Rs as a function of ρxx before and after the irradiation. The curves before and after irradiation collapse on a single curve with small deviations. We note that for all the patterns the resistivity for which the AHE vanishes, ρ0 , increases slightly after irradiation. We find that the ratio between ρ0 after irradiation and ρ0 before irradiation is ∼1.01 for all four patterns. A possible source for the consistent change might be a change in the effective thickness of the film due to the migration of irradiation-induced interstitial defects to the surface of the sample. A change of 1% in effective thickness which corresponds to approximately one monolayer may account for the observed change. This scenario implies the need to correct ρxx and Rs by the same geometrical factor. Figure 4 shows the corrected AHE coefficient Rs∗ as a ∗ function of the corrected longitudinal resistivity ρxx before and after the irradiation, assuming a thickness change of 1%. We note that the scaling is improved; we obtain an excellent

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TESTING DEPENDENCE OF ANOMALOUS HALL EFFECT . . . Pattern 2

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FIG. 3. (Color online) Rs as a function of resistivity ρxx before (blue circles) and after (red crosses) irradiation for four patterns.

scaling for patterns 1 and 2 and a reasonably good scaling for patterns 3 and 4. The scaling indicates that the AHE is sensitive only to the total resistivity irrespective of its sources. The weights of phonons, magnons, and point defect scattering in resistivity change as a result of the irradiation, yet the AHE is sensitive only to the total resistivity. Patterns 3 and 4 which exhibit a larger increase in resistivity exhibit deviations from scaling below 70 K. A possible source for the deviation is an irradiation induced suppression of the magnetization (which is assumed unchanged in our analysis). Changes in magnetic properties due to irradiation induced damage has been previously reported in other materials including changes in the magnetic susceptibility in paramagnetic materials17–20 and even an induced ferromagnetism in graphite.21 However, we expect a suppression of the magnetization to yield deviations from scaling at all temperatures and not only below 70 K as observed. Another possibility is that the deviations are related to an intrinsic effect of the irradiation-induced point defects. The nature of defects induced by electron irradiation is vacancies which are expected to occur in all the sublattices of SrRuO3 . It has been found that in SrRuO3 , Ru vacancies enhance electronic correlation22 which may affect the band structure. Thus, it is possible that for the strongly irradiated patterns, the

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PHYSICAL REVIEW B 88, 214431 (2013)

N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Rev. Mod. Phys. 82, 1539 (2010). 2 J. Smit, Physica 21, 877 (1955); ,24, 39 (1958). 3 L. Berger, Phys. Rev. B 2, 4559 (1970); ,5, 1862 (1972).

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FIG. 4. (Color online) Corrected AHE coefficient Rs∗ as a func∗ before (blue circles) and after (red tion of corrected resistivity ρxx crosses) irradiation for four patterns.

irradiation induces a change in the band structure. A change in the band structure is expected to affect mainly the Berry phase contribution to the AHE,9 which is dominant at low temperatures and decays at higher temperatures which may explain why the deviations are at low temperatures. IV. CONCLUSIONS

We study the effect of electron irradiation on the AHE in SrRuO3 . We measure the temperature dependence of the AHE and longitudinal resistivity before and after the irradiation, and find that the AHE coefficient Rs scales with the total resistivity. The observation reinforces previous findings that the AHE is sensitive only to the total resistivity irrespective of its sources or nature of scattering (elastic or inelastic). Slight deviations from scaling are observed at temperatures below 70 K for strongly irradiated patterns suggesting a nontrivial effect of irradiation induced point defects on the AHE, possibly related to enhanced electronic correlations. ACKNOWLEDGMENTS

L.K. acknowledges support by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. We acknowledge the support of SIRIUS facility at Ecole Polytechnique.

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