ARTICLE https://doi.org/10.1038/s42005-019-0150-8 OPEN Anisotropies and magnetic phase transitions in insulating antiferromagnets determined by a Spin-Hall magnetoresistance probe R. Lebrun 1, A. Ross 1,2, O. Gomonay1, S.A. Bender3, L. Baldrati1, F. Kronast4, A. Qaiumzadeh5, J. Sinova1,2, 1234567890():,; A. Brataas5, R.A. Duine3,5,6 & M. Kläui 1,2,5 Antiferromagnets possess a number of intriguing and promising properties for electronic devices, which include a vanishing net magnetic moment and thus insensitivity to large magnetic fields and characteristic terahertz frequency dynamics. However, probing the antiferromagnetic ordering is challenging without synchrotron-based facilities. Here, we determine the material parameters of the insulating iron oxide hematite, α-Fe2O3, using the surface sensitive spin-Hall magnetoresistance (SMR). Combined with a simple analytical model, we extract the antiferromagnetic anisotropies and the bulk Dzyaloshinskii-Moriya field over a wide range of temperatures and magnetic fields. Across the Morin phase transition, we show that the electrical response is dominated by the antiferromagnetic Néel vector rather than by the emergent weak magnetic moment. Our results highlight that the surface sen- sitivity of SMR enables access to the magnetic anisotropies of antiferromagnetic crystals, and also of thin films, where other methods to determine anisotropies such as bulk-sensitive magnetic susceptibility measurements do not provide sufficient sensitivity. 1 Institute for Physics, Johannes Gutenberg-University Mainz, 55099 Mainz, Germany. 2 Graduate School of Excellence Materials Science in Mainz, Staudingerweg 9, 55128 Mainz, Germany. 3 Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands. 4 Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein Str. 15, 12489 Berlin, Germany. 5 Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway. 6 Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. Correspondence and requests for materials should be addressed to R.L. (email: [email protected]) or to M.K. (email: [email protected]) COMMUNICATIONS PHYSICS | (2019) 2:50 | https://doi.org/10.1038/s42005-019-0150-8 | www.nature.com/commsphys 1 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-019-0150-8 n recent years, various new effects have been discovered which of domain wall motion. To understand the spin structures and the enable easy and efficient ways to probe and manipulate the switching mechanisms, knowledge of the anisotropies and I 1–3 fi antiferromagnetic order (or Néel vector) by electrical current . Dzyaloshinskii-Moriya (DMI) elds is crucial, which is however The Néel vector can be manipulated by electrical fields in mag- challenging in antiferromagnets using conventional approaches 4 5 netoelectric materials like Cr2O3 or multiferroics like BiFeO3 ,by requiring large scale facilities. bulk spin-galvanic effects in conducting antiferromagnets6,7,orby In this article, we determine the antiferromagnetic anisotropies interfacial spin-orbit torques in multilayers with the insulating and the bulk Dzyaloshinskii-Moriya field of the insulating iron 8–10 α NiO . For magneto-transport measurements, effects that are oxide hematite, -Fe2O3, using a surface sensitive spin-Hall even functions of the magnetic order parameter like magnetoresistance (SMR) technique. We develop an analytical anisotropic11,12 and spin-Hall magnetoresistance (SMR)13–15 could model that in combination with SMR measurements, allows for be used to probe the antiferromagnetic state and detect switching the identification of the material parameters of this prototypical events8–10. However, it is not obvious how one can extract the antiferromagnet over a wide range of temperatures and magnetic equilibrium state of an antiferromagnet and in particular determine field values. The SMR measurements are thus directly related to from the field dependence of the SMR key magnetic properties the equilibrium orientation of the Néel vector n calculated by such as the anisotropy values that are otherwise difficult to minimizing the magnetic energy of the sample. The SMR ascertain. response is shown to depend strongly on the direction of the The SMR technique can probe the magnetic state of bilayer charge current with respect to the magneto-crystalline aniso- systems consisting of a ferromagnetic or antiferromagnetic tropies axes. Both the small net magnetization induced by the insulator and a heavy metal. In the simplest modelsÀÁ [15,22,28], external magnetic field H or by the bulk Dzyaloshinskii-Moriya Δ À ðÞÁ μ 2 fi the longitudinal SMR signalÀÁR is proportional to 1 m HDMI above the Morin transition, do not signi cantly contribute for a ferromagnet and 1 À ðÞn Á μ 2 for an antiferromagnet to the electrical response in the canted easy-plane phase. These (where the unit vector μ of the spin-accumulation is perpendi- results demonstrate that the SMR technique is a powerful and cular to the charge current J in the heavy metal and m and n are alternative tool to the complex neutron scattering33 or X-ray29 the magnetization and the Néel vector, respectively). As the based measurements to ascertain not only the orientation of the magnetization in ferromagnets aligns along the external magnetic Néel vector as demonstrated previously, but also to extract key field, while the Néel vector of an antiferromagnet tends to align parameters such as the magnetic anisotropies and DMI fields in perpendicularly, ferro- and antiferromagnets should exhibit a antiferromagnets. different field dependence of the SMR signal on the external magnetic field. When the magnetic field is applied parallel to the Results current, the SMR contribution to the longitudinal resistance Analytical Model.Wefirst develop the necessary model that should increase for a ferromagnet (positive SMR) and should allows us to analyze the results of the SMR transport experiments. decrease for antiferromagnets (negative SMR). However, recent We assume that the SMR signal depends only on the components experiments show a more complicated behavior of SMR in of the Néel vector22,28: 16 antiferromagnets, with positive SMR in SrMnO3 , negative SMR in the easy-plane NiO17,18, and both positive19,20 and negative21 ( SMR measured in the easy-axis antiferromagnet Cr O .To ΔR 1 À ðÞn Á μ 2; j ¼ k; 2 3 jk ¼ ρ ð1Þ explain the different SMR signs, there were suggestions of R 0 n n ; j ≠ k; mechanisms such as contributions from proximity jk j k induced magnetization21 or canted moments22. Additional complications stem from the possible strong dependence of the where j, k = x, y, are the coordinates along and perpendicular to SMR response on the magneto-crystalline anisotropy resulting the current direction within the sample plane, the constant ρ from structural symmetries23. However, such effects, can be 0 17,24 depends on the spin-mixing conductance at the Pt-hematite concealed in multi-domain states by the presence of interface and is considered as a fitting parameter. The unit vector magneto-elastic coupling. α of spin-accumulation µ lays within the xy plane and is perpen- Hematite, -Fe2O3, is not only the main component of rust, but dicular to the current. The equilibrium orientation of the Néel also a prototypical insulating antiferromagnet that lends itself to vector n is calculated by minimizing the potential energy (per disentangle the origins of the SMR signals in antiferromagnets unit volume) and identify the role of easy-axis and easy-plane symmetries in the magnetoresistance response. This iron oxide has a hexagonal crystal structure R3c, and at room temperature shows an easy- ¼ 1 2 þ ðÞÀÀ Á þ plane canted antiferromagnetic ordering in the basal crystal- wpot 2Ms Hexm HDMI nXmY nY mX H m wani lographic plane. It undergoes a magnetic phase transition at the 2 Morin temperature25–27 (at about 260 K), below which it exhibits ð2Þ an easy-axis antiferromagnetic ordering along the c-axis. It also possesses a bulk Dzyaloshinskii-Moriya internal field28,29 along fi the c-axis, which is thus hidden in the easy-axis phase and which where Hex parametrizes the exchange eld which keeps the leads to a small (less than a millirad) canting angle between the magnetic sublattices antiparallel, HDMI is the Dzyaloshinskii- fi magnetic sublattices, generating a weak moment in the easy-plane Moriya eld, Ms is the sublattice magnetization, n and m are the phase. Furthermore, hematite shows an accessible spin-flop field Néel vector and magnetization of the antiferromagnet related by below 10 Tesla so that the Néel vector fully reorients perpendi- the conditions n Á m = 0 and n2 þ m2 ¼ 1. The coordinate frame cular to external magnetic fields30. The size of the magnetic XYZ is related to the crystallographic axes and differs from the domains can exceed ten micrometers in both single crystals (see xyz frame defined by the surface plane of the R-cut hematite Supplementary Fig. 1) and thin films31 enabling long distance sample (x being the projection of the easy axis Z in the sample spin transport32, and domain redistribution in the easy-plane can plane, y the axis perpendicular to it) and its normal z. The ani- be dominated by the coherent rotation of the Néel vector instead sotropy energy of the antiferromagnet depends on two 2 COMMUNICATIONS PHYSICS | (2019) 2:50 | https://doi.org/10.1038/s42005-019-0150-8 | www.nature.com/commsphys COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-019-0150-8 ARTICLE parameters: required for a reorientation is ÀÁ H2 À H2 χ ¼ DMI;sf sf χ Hcr H sin H ÀÁÀÁÀÁ 2H ; ¼ À 1 ð Þ 2 À 1 2 À 2 2 À 2 2À 2 þ 2 2 : qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDMI sf ð4Þ wani 2Ms H2jj T nZ H? nX nY 4 nX nY 3 nX nY 2 6 þ 1 ð 2 À 2 Þ2 2 χ þ 2 2 : HDMI;sf Hsf sin H 4HDMI;sf Hsf ð3Þ 2HDMI;sf By fitting the angular dependence of the critical field with Eq.