Writing and Reading antiferromagnetic Mn 2 Au: Néel spin-orbit torques and large anisotropic magnetoresistance
S. Yu. Bodnar, L. ?mejkal, I. Turek, T. Jungwirth, O. Gomonay, J. Sinova, A.A. Sapozhnik, H.-J. Elmers, M. Kläui, M. Jourdan
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J un Writing and Reading antiferromagnetic Mn Au: N´eel spin-orbit torques and largeanisotropic magnetoresistance.
S. Yu. Bodnar, L. ˇSmejkal,
1, 2, 3
I. Turek, T. Jungwirth,
2, 4
O. Gomonay, J. Sinova, A.A. Sapozhnik, H.-J. Elmers, M. Kl¨aui, and M. Jourdan ∗ Institut f¨ur Physik, Johannes Gutenberg-Universit¨at, Staudinger Weg 7, 55128 Mainz, Germany Institute of Physics, Academy of Sciences of the Czech Republic,Cukrovarnicka 10, 162 00 Praha 6, Czech Republic Faculty of Mathematics and Physics, Charles University,Department of Condensed Matter Physics, Ke Karlovu 5, 12116 Praha 2, Czech Republic School of Physics and Astronomy, University of Nottingham,University Park, Nottingham NG7 2RD, United Kingdom (Dated: August 28, 2018)
PACS numbers:
Antiferromagnets are magnetically ordered ma-terials which exhibit no net moment and thusare insensitive to magnetic fields. Antiferromag-netic spintronics [1] aims to take advantage of thisinsensitivity for enhanced stability, while at thesame time active manipulation up to the natu-ral THz dynamic speeds of antiferromagnets [2]is possible, thus combining exceptional storagedensity and ultra-fast switching. However, the ac-tive manipulation and read-out of the N´eel vector(staggered moment) orientation is challenging.Recent predictions have opened up a path basedon a new spin-orbit torque [3], which couples di-rectly to the N´eel order parameter. This N´eelspin-orbit torque was first experimentally demon-strated in a pioneering work using semimetallicCuMnAs [4]. Here we demonstrate for Mn Au,a good conductor with a high ordering tempera-ture suitable for applications, reliable and repro-ducible switching using current pulses and read-out by magnetoresistance measurements. Thesymmetry of the torques agrees with theoreti-cal predictions and a large read-out magnetore-sistance effect of more than ≃ % is reproducedby ab initio transport calculations. For the key application operations of reading and writ-ing in antiferromagnets, different approaches have beenpreviously put forward. Initial experiments on spin-valvestructures with an antiferromagnet (AFM) as the ac-tive layer manipulated the N´eel vector by an exchange-spring effect with a ferromagnet (FM) and read-outvia Tunneling-Anisotropic Magnetoresistance (T-AMR)measurements [5]. Other related experiments were basedon the same effect [6], or on a FM to AFM phase tran-sition [7]. However, the most promising approach is touse current induced spin-orbit torques for switching theN´eel vector. It exhibits superior scaling and its counter- ∗ Electronic address: [email protected] part in ferromagnets is already established and consid-ered among the most efficient switching mechanisms formemory applications. [8, 9].Only two compounds, CuMnAs and Mn Au, areknown to provide at room temperature the collinear com-mensurate antiferromagnetic order and specific crystalstructure, which is predicted to result in the staggeredspin accumulation in the sublattice structure, leading tobulk N´eel spin-orbit torques allowing for current inducedswitching of the N´eel vector [3].Semimetallic CuMnAs was grown previously by molec-ular beam epitaxy (MBE) with a N´eel temperature of ≃
500 K [10] and current-induced switching of thesesamples was recently demonstrated for the first time[4, 11]. However, for spintronics applications the com-pound Mn Au provides several advantages, as it is a goodmetallic conductor and does not contain toxic compo-nents. Furthermore, its magnetic ordering temperatureis well above 1000 K [13], providing the necessary ther-mal stability for applications. Mn Au shows a simpleantiferromagnetic structure with the collinear magneticmoments in the (001)-plane [12–14]. Thin film sampleswere previously grown in (101)-orientation by MBE [15]and Fe/Mn Au(101) bilayers showed AMR effects of up2 . Au was the first compound for whichcurrent-induced internal staggered spin-orbit torqueswere predicted [3], corresponding experimental evidencehas been missing. Here we report current induced N´eelvector switching in Mn Au(001) epitaxial thin films,which is is easily read-out by a large AMR.Our Al O /Ta(10 nm)/Mn Au(75 nm)/Ta(3 nm)samples were prepared by sputtering as described else-where [17] and patterned into a star-structure as shownin Fig. 1. This geometry allows for electric writing of theN´eel vector orientation by pulsing currents along the twoperpendicular directions I pulse and I pulse and for electricread-out by measuring either the transversal resistivity ρ xy , i. e. the Planar Hall Effect (PHE), or the longitu-dinal resistivity ρ long , corresponding to the AMR of thesamples. Depending on the orientation of the patterned FIG. 1: Sample layout (star pattern) used for the currentinduced N´eel vector manipulation experiments with currentpulse directions I / pulse and probing contacts for PHE andAMR measurements indicated. structure, the pulse currents can be sent along differentcrystallographic directions.The AMR of a single domain sample is given byAMR hkl = ρ long ( φ = 0 o ) − ρ long ( φ = 90 o )¯ ρ long = ∆ ρ long ¯ ρ long , (1)where ρ long is longitudinal resistivity, φ is the angle be-tween the N´eel vector and current direction and [hkl] isthe N´eel vector orientation in the basis of the tetragonalconventional unit cell. The PHE usually observed in fer-romagnetic materials scales with the AMR and shows adependence on the angle φ given by [18, 19]: ρ xy = ∆ ρ long sin φ cos φ (2)Thus also in antiferromagnets ρ xy has its maximum valueand changes sign if φ switches from +45 o to − o .To study the switching, trains of 100 current pulseswith a pulse length of 1 ms and a delay between thepulses of 10 ms were applied. As after a pulse train ther-mal relaxation behaviour on a time scale of 1 s after wasobserved, the read-out was performed with a delay of10 s. Fig. 2 shows the transversal resistivity ρ xy versusthe number of applied pulse trains. First, a pulse currentdensity of 1 . × A/cm was applied along the [1¯10]direction, resulting in a small change of the correspond-ing Hall voltage. Without reaching saturation after 50pulse trains the pulse current direction was switched to[110], resulting in a reversal of the corresponding changeof the transversal resistivity. This sequence could be re-produced several times. Increased pulse current densitiesof 1 . × A/cm and 1 . × A/cm resulted in largerchanges of the corresponding Hall voltages. By increas-ing the number of pulse trains applied along the [110]direction to 500, a trend towards saturation of the Hallvoltage was obtained.Internal field like spin-orbit torques are expected togenerate reversible switching between distinct stablestates if the current is injected along biaxial easy direc-tions [3, 20]. However, we observed reversible switchingto stable states for pulse currents along both the crys-tallographic [110] and [100] axes (rotated star-pattern). xy ( c m ) No. of current pulse trains I pulse || [110] I pulse || [110] I pulse =1,4 1,7 1,8 x 10 A/cm FIG. 2: Probed transversal resistivity (DC probing currentdensity 10 A/cm ) vs. number of applied pulse trains alongdifferent directions. The crystallographic direction in whichthe current pulses were injected is indicated by the green andred color of the data points. The pulse current density wasincreased from 1 . × A/cm to 1 . × A/cm as indicatedin the graph. Thus we conclude that the in-plane magnetic anisotropyof our Mn Au thin films is weak. This is consistent withour calculations of the magnetocrystalline anisotropy en-ergy (MAE), which is almost negligible within the ab-plane (see
Methods ).An example of the resulting changes of the transver-sal and longitudinal resistivities generated by pulse cur-rents along the [100] and [010] directions is displayed inFig. 3. The upper panel (Fig. 3a) shows the longitudi-nal resistivity probed after each of the first 1600 pulsetrains consisting of 100 pulses each with a current density1 . × A/cm . For the first sequences only small varia-tions of the longitudinal resistivity were observed. How-ever, with the application of subsequent pulse trains themagnitude of the effect increased. This training-like be-haviour may be associated with the motion and pinningof AFM domain walls in the sample. After 1600 pulsetrains a constant resistance change of ∆ ρ long / ¯ ρ = 2 . ρ xy = 0 . µ Ωcm.Based on these numbers the identification of the lon-gitudinal and transversal resistivities with the AMR andPHE can be verified: If both effects originate from thesame anisotropic electron scattering, they have to be re-lated by equation (2). We assume a switching of the
FIG. 3: (a) Longitudinal resistivity (DC probing currentdensity 10 A/cm ) vs. number of applied pulse trains. (b)Transversal resistivity of the same sample vs. number of ap-plied pulse trains. The crystallographic direction in which thecurrent pulses were injected is indicated by the green and redcolor of the data points. N´eel-vector in parts of the sample corresponding to achange of φ in equation (2) from +45 o to − o , i. e.∆ ρ xy = ρ xy (+45 o ) − ρ xy ( − o ) = ∆ ρ long , (3)Thus we find that ρ xy = 0 . µ Ωcm corresponds again to∆ ρ long / ¯ ρ = 2 . ρ xy = 1 . µ Ωcm was reached, which based on equation(3) corresponds to an AMR of 6 .
25 %. This is one ofthe largest found in metallic magnetic thin films, andits size bodes well for easy read-out of the antiferromag-netic state as necessary for device applications. Whilesmall variations exist between samples, we observe con-sistently larger AMR effects for pulse currents along the[100] than for the [110] directions.To understand the origin of the magnetoresistance ef-fects, we calculated the AMR of single domain Mn Au,assuming a complete 90 o switching of the N´eel vector(see Methods ). In general, AMR originates from the ef-fects of spin-orbit coupling on the band structure andfrom scattering from an extrinsic disorder potential [22].When incorporating the effects of realistic disorder inthe calculations (see
Methods ), two types were consid-ered: Off-stoichiometry and inter-site swapping betweenMn and Au atoms. Experimentally, the former was ana-lyzed by energy dispersive x-ray spectroscopy (EDX) of500 nm thick Mn Au films resulting in a stoichiometry of66 . ± . . ± . and AMR . Fig. 4a, showsthe results for different degrees of disorder in Mn Au.Large AMR values consistent with our experiments wereobtained for small degrees of disorder reaching a maxi-mum value of 6 . AM R > AM R , which reproduces the ex-perimentally observed trend for the two crystalline direc-tions. The corresponding calculated residual resistivitiesas shown in Fig. 4b are consistent with the experimen-tally obtained values ( ≃ µ Ωcm [17]), corroborating therelevance of the simulated type of disorder.In summary, in-plane switching of the N´eel vector inthe antiferromagnetic metal Mn Au by current pulseswas realized using intrinsic spin-orbit torques. Consis-tent measurements of the AMR and PHE showed pulsecurrent direction dependent reversible changes, provid-ing direct evidence for N´eel vector switching. Easy read-out of the switching is provided by a large amplitudeof the AMR of more than 6%, which is more than anorder of magnitude higher than previously observed forother antiferromagnetic systems and one of the highestAMR amplitudes found for metallic magnetic thin films.We can reproduce the magnitude of the effect theoret-ically by including realistic disorder and, in particular,find the same dependence of the amplitude on the crys-tallographic directions in the experiment as in the calcu-lation. With the basic principles of writing and read-outdemonstrated, combined with a theoretical understand-ing of the underlying spin-orbit torques, and the large
FIG. 4: (a) Calculated AMR of Mn Au for different degrees ofdisorder due to Au excess and due to Mn - Au site swappingwith dependence on the N´eel vector orientation. (b) Cal-culated residual resistivities of Mn Au for different degreesdisorder due to Au excess and due to Mn - Au site swapping. magnetoresistive effects, the metallic compound Mn Auis a prime candidate to enable future AFM spintronics.
Acknowledgments:
This work is supported by theGerman Research Foundation (DFG) through the Tran-sregional Collaborative Research Center SFB/TRR173
Spin+X , Projects A03 and A05. J.S., L.S., O.G.,and T.J. acknowledge the support of the Alexandervon Humboldt Foundation, the ERC Synergy GrantSC2 (No. 610115), the Ministry of Education of theCzech Republic Grant No. LM2015087, and the GrantAgency of the Czech Republic grant no. 14-37427G, L.S. acknowledges support from the Grant Agency ofthe Charles University, no. 280815. Access to computingand storage facilities owned by parties and projects con-tributing to the National Grid Infrastructure MetaCen-trum provided under the program ”Projects of LargeResearch, Development, and Innovations Infrastruc-tures” (CESNET LM2015042), is greatly appreciated.TheworkofI.T.wassupportedbytheCzechScience Founda-tion(GrantNo. 14-37427G).
Author contributions
S.Yu.B. and M.J. mainly wrote the paper and per-formed the transport measurements; L.S. performed theAMR and anisotropy calculations and wrote the cor-responding part of the manuscript, I.T. developed thecodes for the transport calculations, S.Yu.B. and A.A.S.prepared the samples, H.-J.E, M.K., O.G., T.J., I.T, andJ.S. discussed the results and contributed to the writingof the manuscript; M.J. coordinated the project.
Methods
Measurement Procedure
The current pulse trains were gen-erated by a Keithley 2430 Source Meter. After each pulse train adelay of 10 s for thermal relaxation was followed by a measurementof the transversal or longitudinal voltage across the central part ofthe patterned structure resulting from a probe current density of10 A/cm . Typically this procedure was repeated several timesbefore the pulse trains were sent along the perpendicular directionof the cross structure, keeping the probing contacts unchanged.Based on time resolved resistivity measurements during the ap-plication of pulse trains and temperature dependent resistivitymeasurements of Mn Au thin films the local temperature of therelevant sample region was estimated: Values of up to 600 K in thestable regime and ≃
800 K at current densities, which finally de-stroyed the samples, were obtained. The local temperature rapidlydecays after the application of a current pulse train, therefore ther-moelectric voltages can be neglected.
MAE and AMR calculation
The MAE was calculated usingthe FLAPW (Full Potential Linearized Augmented Plane Wave)method in combination with the GGA (Generalized Gradiend Ap-proximation). We found the MAE in line with previous reports [23] ≃ µ eV per formula unit, which is at the resolution limit of ourmethod based on the magnetic force theorem.To calculate the AMR in Mn Au ab initio we employed the fullyrelativistic Dirac tight binding-linear muffin-tin orbital plus coher-ent potential approximation (FRD-TB-LMTO+CPA) method incombination with the Kubo formula [24, 25]. We used the s-, p-,and d-type orbitals in the basis and the LSDA (Local Spin DensityApproximation) Vosko-Wilk-Nusair exchange-correlation potentialparametrization [26]. The ground-state magnetization and den-sity of states was reproduced consistently with a previous reports[3, 12]. In the transport calculation we used up to 10 k-points inthe Brillouin zone and for the residual resistivity calculations weset the imaginary part of the complex energy to Γ = 10 − Ry. [1] Jungwirth, T., Marti, X., Wadley, P. & Wunderlich, J.Antiferromagnetic spintronics.
Nat. Nanotech. , 231(2016).[2] Kampfrath, T. et al . Coherent terahertz control of anti-ferromagnetic spin waves. Nat. Phot. , 31 (2011). [3] Zelezny, J. et al . Relativistic Neel-order fields induced byelectrical current in antiferromagnets. Phys. Rev. Lett. , 157201 (2014).[4] Wadley, P. et al . Electrical switching of an antiferromag-net.
Science , 587 (2016). [5] Park, B. G., et al . A spin-valve-like magnetoresistance ofan antiferromagnet-based tunnel junction.
Nat. Mat. ,347 (2011).[6] Fina, I. et al . Anisotropic magnetoresistance in an an-tiferromagnetic semiconductor. Nat. Commun. , 4671(2014).[7] Marti, X. et al . Room-temperature antiferromagneticmemory resistor. Nat. Mat. , 367 (2014).[8] Gambardella, P., and Miron, I. M. Current-induced spin-orbit torques. Phil. Trans. R. Soc. A
Nat. Nanotech. , 86 (2014).[10] Wadley, P. et al . Tetragonal phase of epitaxial room-temperature antiferromagnet CuMnAs. Nat. Commun. , 2322 (2013).[11] Grzybowski, M. J. et al . Imaging Current-InducedSwitching of Antiferromagnetic Domains in CuMnAs.Phys. Rev. Lett. , 057701 (2017).[12] Shick, A. B., Khmelevskyi, S., Mryasov, O. N., Wun-derlich, J. & Jungwirth, T. Spin-orbit coupling inducedanisotropy effects in bimetallic antiferromagnets: A routetowards antiferromagnetic spintronics. Phys. Rev B ,212409 (2010).[13] Barthem, V. M. T. S., Colin, C. V., Mayaffre, H., Julien,M.-H. & D. Givord, Revealing the properties of Mn Aufor antiferromagnetic spintronics.
Nat. Commun. , 2892(2013)[14] Barthem, V. M. T. S. et al . Easy moment directionand antiferromagnetic domain wall motion in Mn2Au. J. Magn. Magn. Mater. , 289 (2016).[15] Han-Chun Wu et al . Mn Au: Body-Centered-TetragonalBimetallic Antiferromagnets Grown by Molecular BeamEpitaxy.
Adv. Mat. , 6374 (2012).[16] Han-Chun Wu et al . Anomalous Anisotropic Magne-toresistance of Antiferromagnetic Epitaxial BimetallicFilms: Mn Au and Mn Au/Fe Bilayers.
Adv. Funct. Mat. et al . Epitaxial Mn Au thin films for an-tiferromagnetic spintronics.
J. Phys. D: Appl. Phys. ,385001 (2015).[18] Thompson, D. A., Romankiw, L. T., & Mayadas, A. F.Thin film magnetoresistors in memory, storage, and re-lated applications. IEEE Trans. Magn. , 1039 (1975).[19] Seemann, K. M. et al . Origin of the planar Hall effectin nanocrystalline Co60Fe20B20. Phys. Rev. Lett. ,086603 (2011).[20] Roy, P. E., Otxoa, R. M. & Wunderlich, J. Robust pi-cosecond writing of a layered antiferromagnet by stag-gered spin-orbit fields.
Phys. Rev. B , 014439 (2016).[21] Turek, I., Kudrnovsky, J. & Drchal, V. Ab initio theoryof galvanomagnetic phenomena in ferromagnetic metalsand disordered alloys. Phys. Rev. B , 014405 (2012).[22] De Ranieri, E. et al . Lithographically and electrically con-trolled strain effects on anisotropic magnetoresistance in(Ga,Mn)As. New J. Phys. , , 065003, (2008).[23] Shick, A. B., Khmelevskyi, S., Mryasov, O. N., Wun-derlich, J. & Jungwirth, T. Spin-orbit coupling inducedanisotropy effects in bimetallic antiferromagnets: A routetowards antiferromagnetic spintronics, Phys. Rev. B , ,212409 (2010).[24] Turek, I., Kudrnovsky, J., Drchal, V., Szunyogh, L.& Weinberger, P. Interatomic electron transport bysemiempirical and ab initio tight-binding approaches. Phys. Rev. B , 125101, (2002).[25] Turek, I., Kudrnovsky, J. & Drchal, V. Fermi sea term inthe relativistic linear muffn-tin-orbital transport theoryfor random alloys. Phys. Rev. B , 064405, (2014).[26] Vosko, S. H., Wilk, L. and Nusair, M. Accurate spin-dependent electron liquid correlation energies for localspin density calculations: a critical analysis. Can. J.Phys. ,58