Magnetoresistance effects in the metallic antiferromagnet Mn 2 Au
S.Yu.Bodnar, Y.Skourski, O. Gomonay, J. Sinova, M.Kläui, M.Jourdan
MMagnetoresistance effects in the metallic antiferromagnet Mn Au S.Yu. Bodnar, Y. Skourski, O. Gomonay, J. Sinova, M. Kl¨aui, and M. Jourdan Institut f¨ur Physik, Johannes Gutenberg-Universit¨at, Staudingerweg 7, D-55099 Mainz, Germany Hochfeld-Magnetlabor Dresden (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany
In antiferromagnetic spintronics, it is essential to separate the resistance modifications of purelymagnetic origin from other effects generated by current pulses intended to switch the N´eel vector.We investigate the magnetoresistance effects resulting from magnetic field induced reorientationsof the staggered magnetization of epitaxial antiferromagnetic Mn Au(001) thin films. The sampleswere exposed to 60 T magnetic field pulses along different crystallographic in-plane directions ofMn Au(001), while their resistance was measured. For the staggered magnetization aligned viaa spin-flop transition parallel to the easy [110]-direction, an ansiotropic magnetoresistance of (cid:39)− .
15 % was measured. In the case of a forced alignment of the staggered magnetization parallelto the hard [100]-direction, evidence for a larger anisotropic magnetoresistance effect was found.Furthermore, transient resistance reductions of (cid:39)
I. INTRODUCTION
In the emerging field of antiferromagnetic (AFM) spin-tronics [1–3], the orientation of the staggered magne-tization, or more general of the N´eel vector, is usedto encode information. For devices, the manipulationof the N´eel vector by current induced N´eel spin-orbittorques (NSOTs) [4] is most promising and in principlethe anisotropic magnetoresistance effect (AMR) can pro-vide a read-out mechanism. Thus, current pulse inducedreversible resistance changes demonstrated for CuMnAs[5–7] and Mn Au [8–10], were interpreted as originatingfrom the AMR associated with the reorientation of theN´eel vector.Current pulse generated resistance switching was ob-served also in polycrystalline metallic AFM MnN/Pt bi-layers [11] and insulating AFM NiO/Pt bilayers [12–14],which is assumed to result from interfacial spin-orbittorques and spin-Hall magnetoresistance for read-out.However, recently similar current pulse induced resis-tance changes were obtained investigating non-magneticcross structures consisting of pure Pt or Nb thin films.These experiments indicate that current pulse inducedannealing could produce electrical signals similar to thoseobserved in NiO/Pt [15, 16]. Thus it is of major impor-tance to investigate the obtainable magnetoresistance ef-fects independent of current pulse based manipulationof the AFMs, i. e. to investigate resistance modificationspurely associated with specific configurations of the N´eelvector of antiferromagnetic domain configurations.In this framework, we use a manipulation method ofthe N´eel vector of Mn Au thin films, which guaranteesthat only magnetism related properties of the AFM areaffected, explicitly excluding all kinds of Joule heatingrelated effects: N´eel vector reorientation by a large mag-netic field pulse of up to 60 T. For a collinear AFM, itis energetically favorable, if the magnetic moments arealigned perpendicular to the magnetic field, which allowsthem to slightly cant towards the field direction. This allows us to study the magnetoresistance effects origi-nating from a reorientation of the N´eel vector excludingall possible spurious effects. In general one can considerthree different magnetoresistance effects: First, the or-dinary magnetoresistance (OMR), which appears in non-magnetic metals as well. The field dependence of OMR isnon-hysteretic, depends on the details of the band struc-ture, and is in general positive [17]. The longitudinalas well as the transversal OMR can amount to severalpercent for large fields ( >
10 T) [18, 19]. Second, theanisotropic magnetoresistance (AMR), which, in AFMspintronics, is generally assumed to dominate the resis-tance modifications resulting from a current induced re-orientation of the N´eel vector. Third, the domain wallmagnetoresistance (DWMR). This is a relevant effect inAFM spintronics, as typically the thin films are patternedinto structures with lateral dimensions of several microm-eters, whereas the typical AFM domain size is muchsmaller [20–23]. In ferromagnets, the transport of spin-polarized currents leads to scattering by the non-collinearspin structure imparted by domain walls [24, 25]. Similareffects are possible for AFMs as well [26], but have beenstudied much less. One of the few AFM metals, whosedomain wall resistance has been experimentally investi-gated, is Cr [27].Here, we investigate the resistance changes inducedby an reorientation of the N´eel vector in epitax-ial Mn Au(001) thin films by a magnetic field pulse,i. e. we investigate pure magnetoresistance effects exclud-ing heating effects. We focus on the hysteretic magne-toresistance associated with the DWMR and AMR, as weare interested in the switching effects of AFM spintronics.
II. EXPERIMENTAL TECHNIQUES
For the electric transport measurements, an epitaxialMn Au(001) thin film with a thickness of 80 nm was de-posited on a Al O (1¯102) substrate with a Ta(001) buffer a r X i v : . [ c ond - m a t . m t r l - s c i ] M a y layer (thickness 20 nm) as described in Ref. [28]. Thissample was capped with 2 nm of Ta to prevent oxidationof the Mn Au surface and shows the same morphology asthose investigated in Ref. [20]. For precise measurementsof the resistance, it was patterned by optical lithographyand ion beam etching into 3 stripes of 7 mm length and200 µ m width aligned parallel to the easy [110]-, easy[1¯10]- and hard [100]-directions of Mn Au, respectively.Separate contact pads at the ends of each stripe allowedfor 4-probe measurements of the resistivity along the dif-ferent crystallographic directions (see inset of Fig. 1).The sample was exposed to a magnetic field pulses withan amplitude of 60 T and a pulse duration of 150 ms atthe high field laboratory of the Helmholtz center Dres-den Rossendorf (HLD-EMFL) to generate an alignmentof the N´eel vector perpendicular to the field direction. Toensure the stable temperature required for magnetoresis-tance measurements, the sample was immersed in liquidhelium inside the cryostat within the field coil. Duringeach pulse, and afterwards for up to 10 s, the resistance R of one of the patterned Mn Au stripes was probed with asampling rate of 200 kHz using a numerical lock-in tech-nique with a probe current of 10 A / cm modulated witha frequency of 20 kHz. In parallel, the magnetic fieldwas obtained by numerical integration of the dB/dt sig-nal induced in a pick-up coil situated next to the sample.This lock-in technique enables resistance measurementsduring the field pulse application, while standard dc mea-surements are impossible due to the large induction effectgenerated by the magnetic field pulse. After each pulse,a waiting time of approximately 4 h is required for ther-malization of the magnet coil, before the next pulse canbe applied. III. RESULTS
The magnetoresistance effects discussed below can onlybe understood, if we first summarize our previous micro-scopic investigations of the persistent effects of large mag-netic field pulses on the AFM domain pattern of our sam-ples [20]. We showed by X-ray magnetic linear dichro-ism - photoelectron emission microscopy (XMLD-PEEM)that the AFM domain pattern of as-grown Mn Au(001)thin films consists of domains with an area of (cid:39) µ m with the N´eel vector aligned along both easy [110]- and[1¯10]-axes. Exposing the samples to a field pulse withan amplitude of B pulse = 30 T along one easy axis re-sulted in a significantly increased area of AFM domainswith the N´eel vector aligned perpendicular to the fieldpulse direction. The sample area covered by domainswith this N´eel vector alignment was observed to saturatefor B pulse = 50 T, i. e. an orientation of the N´eel vectorvia spin-flop happens between 30 T and 50 T. We showedthat these domains with the N´eel vector aligned perpen-dicular to the field pulse direction are typically of sightly FIG. 1. Field dependent resistances of a Mn Au(001) epi-taxial thin film measured during the exposure to magneticfield pulses along [110] with a duration of 150 ms, normalizedto the sample resistances directly before the application ofthe respective field pulse. Between both field pulses a waitingtime of about 4 h was required. larger sizes than in the as-grown state of the samples andare separated by narrow wormlike spin structures with awidth of (cid:39)
100 nm (about twice the resolution limit ofthe PEEM). However, after the application of field pulsesalong the hard [100]-direction, we observed an equal partof AFM domains with N´eel vector aligned parallel to botheasy [110]- and [1¯10]-axes, with as well a sightly largersizes than in the as-grown state [20].From the resistance measurements presented here, wefirst discuss the effect of field pulses (cid:126)B ( t ) along an easy[110]-direction of Mn Au, as this is associated with astraight forward modification of the magnetic state. Thepulse generates a spin flop of all AFM domains with theN´eel vectors (cid:126)N (cid:107) (cid:126)B , i. e. results in an persistent alignmentof (cid:126)N ⊥ (cid:126)B as discussed above. This alignment results ina relatively small, but persistent AMR effect, as we willdiscuss below. However, we first present the larger re-sistance modifications associated with the magnetic fieldpulse.The red curve in Fig. 1 shows the resistance R ofa Mn Au(001) thin film (normalized to the resistance R before the field pulse) probed along the easy [110]-direction during a 150 ms pulse generating a time depen-dent magnetic field B (t) applied along the same direc-tion.Up to B ( t ) (cid:39)
30 T, R ( B ) is governed by the non-hysteretic positive OMR. However, we focus on the hys-teretic resistance modifications originating from DWMRand AMR. Such effects appear above 30 T, which is ex-actly the magnetic field at which we previously observeda spin-flop of most AFM domains with (cid:126)N (cid:107) (cid:126)B (cid:107) [110].The hysteretic resistance reduction saturates at (cid:39)
50 T,which is the magnetic field, at which the N´eel vectorsof all corresponding domains have completed the spin-flop alignment [20]. With decreasing field below 30 T, R ( B ) hysteretically reproduces the previous curve witha negative shift of the resistivity of (cid:39) .
75 %, by whichthe sample resistivity directly after the pulse is reducedcompared to its initial value.As we will discuss below, this resistance reduction re-laxes on a time scale of (cid:39)
10 s. So if the experiment isrepeated some hours later with another field pulse, onestarts with the same resistance, which the as-grown sam-ple had before the first field pulse plus a small AMRcontribution, which we will discuss below. However, firstwe continue to discuss the relatively large resistance re-duction, which appears at the spin flop field of (cid:39)
30 T.The blue curve in Fig. 1 shows
R/R of the sameMn Au(001) thin film in a second field pulse along thesame [110]-direction 4 h later, but this time probed withcontacts along the perpendicular [1¯10]-direction: R ( B )shows a similar hysteresis as described above for the lon-gitudinal resistance measurements, i. e. a reduction of theresistance at a magnetic field corresponding to the spin-flop field by a very similar value as discussed above forthe probe current (cid:107) [110].For further investigation of the field pulse related re-sistance changes, the field was next applied along thehard [010]- and [100]-directions of the Mn Au thin films,while probing always with the current direction paral-lel to [010] (see inset of Fig. 2). For these hard axis di-rections of the magnetic field, no spin-flop is possible.Instead, the N´eel vectors of the different AFM domainswill rotate smoothly from the easy directions towards analignment perpendicular to the field pulse direction (hardaxis), which they will reach at the spin-flop field. Thismeans, that a continuously growing contribution of theAMR effect to the total resistance change is expected forthis field direction, which becomes zero again in zero fieldwith the N´eel vector aligned again along the easy [110]and equivalent directions. Indeed, the dependence of thesample resistance on the current direction as shown inFig. 2 is much stronger for the field along the hard [100]direction than for (cid:126)B (cid:107) [110]. Although the directionaldependence of the OMR, which also contributes, is un-known, this provides evidence for a large AMR in theorder of some percent associated with the alignment ofthe N´eel vector parallel to the hard [100] direction inagreement with our previous calculations [8]. Addition-ally, also for the hard axis field direction, a hystereticresistance reduction is observed. It amounts to about1 .
75 %, which is about twice as large as for the easy fielddirection.To understand the origin of these changes of the sam-ple resistance, we next probe their temporal stability.These hysteretic resistance reductions are not persistent,i. e. they relax towards values relatively close to the orig-inal resistance of the sample before application of a field
FIG. 2. Field dependent resistances of a Mn Au(001) epi-taxial thin film measured during the exposure to a magneticfield pulses along [010] and [100] with a duration of 150 ms,normalized to the sample resistances directly before the ap-plication of the respective field pulse. Note that between bothfield pulses the waiting time was about 4 h.FIG. 3. Time dependence of the normalized resistances of aMn Au(001) epitaxial thin film probed along different currentdirections after the exposure to magnetic field pulses along thehard as well as along the easy in-plane axis. The resistancerelaxes with a logarithmic time dependence as shown by thefits (dashed curves). pulse: As shown in Fig. 3, the resistance reduction gen-erated by the magnetic field exceeding the spin-flop fieldrelaxes for pulses along the hard [010] as well as alongthe easy [110] direction of the Mn Au(001) thin films ona time scale of 10 s. Its decay can be fitted by a logarith-mic time dependence, which is typical for the relaxationof the magnetization of ferromagnets of different types[29, 30]. Theoretically, this type of relaxation behaviorwas first associated with a flat-topped distribution of en-
FIG. 4. Time dependent resistance for different probe cur-rent directions (see inset) of a Mn Au(001) thin film in theas-grown state and after the application of the first 60 T fieldpulse at t (cid:39)
250 s along the direction indicated in the inset.The standard dc-measurement is unable to produce meaning-ful data for the first (cid:39)
15 s after the field pulse due to over-loading of the nanovoltmeter by the pulse induced induction.The blue boxes indicate the alignment of the N´eel vector. ergy barriers [31], while later it was shown, that it israther universal for any distribution of energy barriers[32].However, when checking the relaxation of the differentsignals, we find that not all resistance modifications as-sociated with the field pulse are transient, as we discussnext:After applying a field pulse along one of the easy axisdirections to a sample in the as-grown state, which con-sists of AFM domains with an equal distribution of do-mains with the N´eel vector aligned along all four equiv-alent easy directions (see images in ref. [20]), the resis-tance does not relax completely to its original value. InFig. 4, the time dependent sample resistivity is shown forthe first 20 min after application of a 60 T field pulseto an as-grown sample, measured by a standard DC-measurement. Please note that with this measurementtechnique no meaningful data is obtained for the first (cid:39)
15 s after the field pulse due to overloading of the DCnanovoltmeter by the pulse induced induction. A per-sistent probe current direction J dependent increase anddecrease of the sample resistance is observed (see inset ofFig. 4). Correspondingly, if the resistance measurementshown in Fig. 2 is performed for the first time with a sam-ple in the as-grown state and than 4 h later repeated withexactly the same configuration, the initial resistance ischanged by exactly the value of the persistent resistancemodification discussed here. This long term persistentresistance change of ∆ R (cid:39) − .
15 % is positive for probecurrent parallel and negative for probe current perpen- dicular to the field pulse direction, which corresponds toan AMR effect. An AMR of similar size but with a dif-ferent sign was recently reported for CuMnAs [33].
IV. DISCUSSION AND CONCLUSIONS
Thus we conclude that in Mn Au there is a negativeAMR of (cid:39) − .
15 % at 4 K associated directly withthe spin-flop driven N´eel vector reorientation. This ex-perimentally observed AMR is in good agreement withour previously published calculations [8]: we consideredthe AMR of Mn Au(001) theoretically for alignments ofthe N´eel vector parallel to the [110] as well as parallelto the [100] direction. In the first case, we obtained
AM R [110] (cid:39) − . AM R [100] (cid:39)
AM R [110] in the order of several percent is consistent with the ex-perimentally observed anisotropy of the resistance withthe N´eel vector forced by the field pulse to align alongthe hard axis (Fig. 2).However, AMR cannot account for the field pulse gen-erated hysteretic transient resistance reductions, whichappear for all field directions at the spin-flop field. Thiseffect can be explained based on DWMR. Independentfrom the physical mechanism of the DWMR, the largemagnetic field during the pulse makes any alignment ofthe N´eel vector parallel to the field energetically unfa-vorable. Thus it is likely that during a field pulse with amagnitude above the spin-flop field all domain walls areremoved. However, we know from the XMLD-PEEM in-vestigation of our samples performed weeks after the fieldpulses, that even in samples with a persistent spin-flop in-duced reorientation of the N´eel vector domain walls exist.We also know that in all configurations the field pulsesreduce the resistance of the Mn Au thin films at the spin-flop field followed by an increase of the resistance afterthe pulse. Thus we can consistently assume that the do-main walls produce a significant DWMR, which is identi-fied by removing the domain walls during the field pulse.After the pulse, on the time scale of 10 s (at 4 K) givenby the measured relaxation time of the resistance, the do-main walls reform. As the density of the domain walls isvery similar in the as grown and in the field manipulatedsamples [20], the contribution of the DWMR to the sam-ple resistance is before and after the field pulse is verysimilar as well. A microscopy based verification of thismodel is highly desired, but unfortunately not possible asXMLD-PEEM imaging of the domain of Mn Au cannotbe realized on the time scale of 1 s after a 50 T field pulse.Furthermore, we can only speculate about the physicalorigin of the relatively large DWMR, which is implied byour analysis: We propose, that it is related to the specificanisotropies in the band structure of Mn Au, from whichalso the large calculated
AM R [100] (cid:39)
AM R [110] (cid:39) − .
15 %. Thus we can now exclude theAMR of AFM domains with the N´eel vector aligned bycurrent pulses as the origin of these large resistance mod-ifications. However, here we have provided evidence for apotentially large DWMR in Mn Au, which could well ex-plain the observed resistance changes in the current pulseexperiments. Clearly, this requires further investigationscombining the microscopic observation of current inducedAFM domain manipulation with in-situ resistance mea-surements.
V. SUMMARY
In summary, we have identified the magnitude of theAMR (cid:39) − .
15 % in Mn Au associated with the per-sistent alignment of the N´eel vector along the magneticeasy [110] axis. Forcing the N´eel vector to align parallelto the hard [110] axis, we provided experimental evidencefor an AMR of several percent for this orientation of thestaggered magnetization. These experimental values areconsistent with our previous calculations of the AMR [8].Furthermore, we observed field pulse induced transientresistance reductions of (cid:39) Au. Such largedomain wall resistances would provide opportunities inantiferromagnetic spintronics such as race track memory[34] or multi-level switching [35] and could explain thelarge resistance changes generated by current pulsesapplied to our Mn Au(001) thin films [8].
ACKNOWLEDGMENTS
Funded by the Deutsche Forschungsgemeinschaft(DFG, German Research Foundation) TRR 173268565370 (projects A01, A05 and B12). We acknowl-edge the support of the HLD at HZDR, member of the European Magnetic Field Laboratory (EMFL). [1] T. Jungwirth et al., The multiple directions of antiferro-magnetic spintronics,
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