France



Various types of Anomalous Hall effects have been widely investigated in recent years [1, 2]. In most of the cases, the predicted or measured Hall signal has been attributed to spontaneous magnetic moment arisen from the dynamics of the current flow [1]. In this work, we aim to investigate the role of anisotropic band dispersion of chiral Weyl fermions in generating a transverse current resulting in a Hall signal. For this purpose, the simplest Weyl semimetal phase consisting of two Weyl nodes with opposite chirality is adopted and the angular dependence of conductance is calculated [3, 4]. Multi-terminal devices with circular geometry as illustrated in Fig. 1 are commonly used to probe the dependence of the signal on transport direction in experiments [1, 3]. Therefore, in the proposed model, we adopt the circular channel geometry and calculate the conductance for arbitrary transport directions.&lt;br/&gt;&lt;br/&gt;The Hamiltonian of the simplest Weyl system is as follows,&lt;br/&gt;&lt;br/&gt;H = V&lt;sub&gt;0 &lt;/sub&gt;+ Σ&lt;sub&gt;i&lt;/sub&gt; hk&lt;sub&gt;i&lt;/sub&gt; τ (v&lt;sub&gt;i&lt;/sub&gt;σ&lt;sup&gt;i&lt;/sup&gt;+w&lt;sub&gt;i&lt;/sub&gt;),&lt;br/&gt;&lt;br/&gt;where σ’s are Pauli matrixes, v’s are velocities and their sign (τ = ±) carry the chirality of Weyl nodes. We assume symmetric velocities equal to v&lt;sub&gt;F&lt;/sub&gt; = 10&lt;sup&gt;6&lt;/sup&gt; m/s. The dispersion of Weyl fermion can be tilted along all three directions, and the strength of the tilt is denoted by w&lt;sub&gt;i&lt;/sub&gt;. In the current work, two Weyl nodes having opposite chirality are also tilted along opposite directions. The tilt direction is chosen to lie along the high anisotropy axis, which is close to one of the crystal axes in most of the Weyl semimetals reported up to date [e.g., Refs. 3, 5].&lt;br/&gt;&lt;br/&gt;The angular dependence of the conductance [3, 4, 5] can be calculated based on transmission probability along an arbitrary direction and integrated over all transverse wave vectors based on the following equation,&lt;br/&gt;&lt;br/&gt;G&lt;sub&gt;β&lt;/sub&gt; = G&lt;sub&gt;0&lt;/sub&gt; ∫ -(∂f/∂E)dE ∬&lt;sup&gt; &lt;/sup&gt;dS&lt;sub&gt;FS&lt;/sub&gt; T&lt;sub&gt;φ,γ&lt;/sub&gt; cosφ cosγ.&lt;br/&gt;&lt;br/&gt;In the above equation, γ is the angle between Fermi wave vector k and the x-y plane, φ is the azimuthal angle with respect to the x-axis, G&lt;sub&gt;0 &lt;/sub&gt;is the quantum conductance, dS&lt;sub&gt;FS&lt;/sub&gt; is the infinitesimal element of the elliptical Fermi surface per unit variation of the coordinates φ and γ. The anisotropy in crystal symmetry and the bandstructure make the conductance dependent on the angle between the transport direction and the crystal axis. Based on the conductance profile, the voltage difference between the transverse electrodes can be found as follows,&lt;br/&gt;&lt;br/&gt;V&lt;sub&gt;t&lt;/sub&gt; = V&lt;sub&gt;t1&lt;/sub&gt;-V&lt;sub&gt;t2&lt;/sub&gt; ∝ (S/ρ)[(G&lt;sub&gt;t1&lt;/sub&gt;-G&lt;sub&gt;t2&lt;/sub&gt;)/(L/√2)],&lt;br/&gt;&lt;br/&gt;where G&lt;sub&gt;t1 &lt;/sub&gt;= G&lt;sub&gt;β+(π/4)&lt;/sub&gt; and G&lt;sub&gt;t2 &lt;/sub&gt;= G&lt;sub&gt;β-(π/4)&lt;/sub&gt;. The longitudinal potential difference can be calculated similarly by replacing the respective conductance value and distance between the voltage probes.&lt;br/&gt;&lt;br/&gt;As shown in Fig. 2 and predicted by the above equation, transverse voltage emerges at some angles which are related to the imbalance of G&lt;sub&gt;t1&lt;/sub&gt; and G&lt;sub&gt;t2&lt;/sub&gt;. The highest V&lt;sub&gt;t&lt;/sub&gt; occurs at the maximum imbalance, where G&lt;sub&gt;t1&lt;/sub&gt; and G&lt;sub&gt;t2&lt;/sub&gt; coincide with the lowest and highest conductance points in the conductance profile shown in Fig. 1 (right). On the other hand, the conductance between source and drain is minimum in this direction as seen in Fig. 2. Our predicted results are quite consistent with the experimental results presented recently in literature [1] thus revealing a possible origin of the measured Hall signals in Weyl semimetals in the absence of a magnetic field.

**References:**

[1] Kang, K., Li, T., Sohn, E. &lt;i&gt;et al.&lt;/i&gt; Nonlinear anomalous Hall effect in few-layer WTe&lt;sub&gt;2&lt;/sub&gt;. &lt;i&gt;Nat.&lt;/i&gt; &lt;i&gt;Mater.&lt;/i&gt; 18, 324–328 (2019).&lt;br/&gt;[2] Ma, Q., Xu, SY., Shen, H. &lt;i&gt;et al.&lt;/i&gt; Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. &lt;i&gt;Nature&lt;/i&gt; 565, 337–342 (2019).&lt;br/&gt;[3] Qisheng Wang, Can Yesilyurt, Fucai Liu, Zhuo Bin Siu, Kaiming Cai, Dushyant Kumar, Zheng Liu, Mansoor B. A. Jalil, and Hyunsoo Yang &lt;i&gt;Nano Letters&lt;/i&gt; 2019 &lt;i&gt;19&lt;/i&gt; (4), 2647-2652&lt;br/&gt;[4] Yesilyurt, C., Siu, Z.B., Tan, S.G. &lt;i&gt;et al.&lt;/i&gt; Electrically tunable valley polarization in Weyl semimetals with tilted energy dispersion. &lt;i&gt;Sci Rep&lt;/i&gt; 9, 4480 (2019).&lt;br/&gt;[5] Soluyanov, A., Gresch, D., Wang, Z. &lt;i&gt;et al.&lt;/i&gt; Type-II Weyl semimetals. &lt;i&gt;Nature&lt;/i&gt; 527, 495–498 (2015).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/6d703c64fb6f07d5598af24065e4402f.jpg)
Illustration of the adopted model, i.e., circular multi-terminal circuit (left). Terminal A and B denote source and drain electrodes respectively, and the Hall signal is calculated as the voltage difference at two transverse points t&lt;sub&gt;1&lt;/sub&gt; and t&lt;sub&gt;2&lt;/sub&gt;.  Normalized anisotropic conductance profile of the Weyl system with two opposite chirality Weyl nodes (right). Blue (Red) arrow(s) indicates the conductance between the source and drain (transverse electrodes).

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d819182570aba9d154a697f1728aa977.jpg)
Angular dependence of anomalous Hall effect, where the Hall voltage V&lt;sub&gt;t&lt;/sub&gt; is calculated as the voltage difference between the points t1 and t2 (i.e., shown in Fig. 1). The longitudinal voltage V&lt;sub&gt;SD&lt;/sub&gt; is calculated as the voltage difference between points A and B (i.e., shown in Fig. 1)

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 Anomalous Hall Effect in Anisotropic Weyl Semimetals

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## Dr. Nishikant (Nish) Sonwalkar: Academician, Scientist, Musician

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Dr. Sonwalkar is regarded as a leading expert in the application of computers in education. He has extensive research and development experience in hypermedia authoring, mobile learning, adaptive learning, and brain-based synaptic learning, advanced scientific visualization, database management systems, and computer simulation.

After receiving doctoral degree from MIT in the area of Molecular Dynamics of Nano-interfaces, he joined MIT as faculty in Mechanical Engineering, but his passion for technology enabled education led him become the founding director of Hypermedia Teaching Facility (Hypermedia Lab) at MIT and later he was appointed as the Principal Educational Architect of MIT.

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NISH 2021

Various types of Anomalous Hall effects have been widely investigated in recent years [1, 2]. In most of the cases, the predicted or measured Hall signal has been attributed to spontaneous magnetic moment arisen from the dynamics of the current flow [1]. In this work, we aim to investigate the role of anisotropic band dispersion of chiral Weyl fermions in generating a transverse current resulting in a Hall signal. For this purpose, the simplest Weyl semimetal phase consisting of two Weyl nodes with opposite chirality is adopted and the angular dependence of conductance is calculated [3, 4]. Multi-terminal devices with circular geometry as illustrated in Fig. 1 are commonly used to probe the dependence of the signal on transport direction in experiments [1, 3]. Therefore, in the proposed model, we adopt the circular channel geometry and calculate the conductance for arbitrary transport directions. The Hamiltonian of the simplest Weyl system is as follows, H = V0 + Σi hki τ (viσi+wi), where σ’s are Pauli matrixes, v’s are velocities and their sign (τ = ±) carry the chirality of Weyl nodes. We assume symmetric velocities equal to vF = 106 m/s. The dispersion of Weyl fermion can be tilted along all three directions, and the strength of the tilt is denoted by wi. In the current work, two Weyl nodes having opposite chirality are also tilted along opposite directions. The tilt direction is chosen to lie along the high anisotropy axis, which is close to one of the crystal axes in most of the Weyl semimetals reported up to date [e.g., Refs. 3, 5]. The angular dependence of the conductance [3, 4, 5] can be calculated based on transmission probability along an arbitrary direction and integrated over all transverse wave vectors based on the following equation, Gβ = G0 ∫ -(∂f/∂E)dE ∬ dSFS Tφ,γ cosφ cosγ. In the above equation, γ is the angle between Fermi wave vector k and the x-y plane, φ is the azimuthal angle with respect to the x-axis, G0 is the quantum conductance, dSFS is the infinitesimal element of the elliptical Fermi surface per unit variation of the coordinates φ and γ. The anisotropy in crystal symmetry and the bandstructure make the conductance dependent on the angle between the transport direction and the crystal axis. Based on the conductance profile, the voltage difference between the transverse electrodes can be found as follows, Vt = Vt1-Vt2 ∝ (S/ρ)[(Gt1-Gt2)/(L/√2)], where Gt1 = Gβ+(π/4) and Gt2 = Gβ-(π/4). The longitudinal potential difference can be calculated similarly by replacing the respective conductance value and distance between the voltage probes. As shown in Fig. 2 and predicted by the above equation, transverse voltage emerges at some angles which are related to the imbalance of Gt1 and Gt2. The highest Vt occurs at the maximum imbalance, where Gt1 and Gt2 coincide with the lowest and highest conductance points in the conductance profile shown in Fig. 1 (right). On the other hand, the conductance between source and drain is minimum in this direction as seen in Fig. 2. Our predicted results are quite consistent with the experimental results presented recently in literature [1] thus revealing a possible origin of the measured Hall signals in Weyl semimetals in the absence of a magnetic field.

**References:**

[1] Kang, K., Li, T., Sohn, E. et al. Nonlinear anomalous Hall effect in few-layer WTe2. Nat. Mater. 18, 324–328 (2019). [2] Ma, Q., Xu, SY., Shen, H. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 (2019). [3] Qisheng Wang, Can Yesilyurt, Fucai Liu, Zhuo Bin Siu, Kaiming Cai, Dushyant Kumar, Zheng Liu, Mansoor B. A. Jalil, and Hyunsoo Yang Nano Letters 2019 19 (4), 2647-2652 [4] Yesilyurt, C., Siu, Z.B., Tan, S.G. et al. Electrically tunable valley polarization in Weyl semimetals with tilted energy dispersion. Sci Rep 9, 4480 (2019). [5] Soluyanov, A., Gresch, D., Wang, Z. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/6d703c64fb6f07d5598af24065e4402f.jpg)
Illustration of the adopted model, i.e., circular multi-terminal circuit (left). Terminal A and B denote source and drain electrodes respectively, and the Hall signal is calculated as the voltage difference at two transverse points t1 and t2. Normalized anisotropic conductance profile of the Weyl system with two opposite chirality Weyl nodes (right). Blue (Red) arrow(s) indicates the conductance between the source and drain (transverse electrodes).

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d819182570aba9d154a697f1728aa977.jpg)
Angular dependence of anomalous Hall effect, where the Hall voltage Vt is calculated as the voltage difference between the points t1 and t2 (i.e., shown in Fig. 1). The longitudinal voltage VSD is calculated as the voltage difference between points A and B (i.e., shown in Fig. 1)

technical paper

Periodic array sensor structures on metamaterials operating at THz ranges are developed and presented. In the proposed formulation, the mutual inductance effects between unit cells and the periodic structures are taken into account with the network synthesis method. The resonant characteristics of THz periodic arrays have been investigated and presented. The analytical results are verified with simulation results for several different cases. Prototypes have then been built and tested. It is confirmed that the proposed method can be used to design and develop THz sensors on metamaterials and implemented for several applications including biomedical. Main Body Metamaterial properties can be obtained by implementation of split-ring resonators (SRRs) [1]. SRRs are reported to be used in the design of biosensors at terahertz (THz) ranges in recent years. Terahertz thin-film sensors, plasmonic thin-film sensors, wireless strain sensors are designed with SRRs [2] to be used in biomedical applications. There are several advantages of using periodic structures due to their higher symmetry property than the unit cells [3]. Two of the other essential features of the periodic structures are their passband-stopband characteristics and the ability to support phase velocities which are much less than the light speed [4]. In this paper, closed-form relations for periodic arrays taking into account of complete effects of mutual inductances in the structure are developed with the network synthesis method from microwave frequencies to THz ranges. The step-by step design procedure from development of unit cell to formation of periodic arrays is detailed. The electromagnetic mutual inductance effects that take place between unit cells in the array and substrate are taken into account in the closed form relations for the first time according to the authors’ knowledge for periodic arrays. The accuracy of the formulations and models for THz operation are verified with 3D EM simulator and ADS circuit simulator. The proposed method have been implemented for 2x3 until cell as shown in Fig. 1 and the agreement between the simulation and analytical results are illustrated in Fig. 2. Several prototypes have been built and measured. All the analytical, simulation and measurement results are compared, and close agreement is confirmed for all cases.

**References:**

References: D. R. Smith, W. J. Padilla, D. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Physical review letters, vol. 84, no. 18, p. 4184, 2000. H. K. Kim, D. Lee, and S. Lim, “A fluidically tunable metasurface absorber for flexible large-scale wireless ethanol sensor applications,” Sensors, vol. 16, no. 8, p. 1246, 2016. F. Bayatur, “Metamaterial-Inspired Frequncy Selective Surfaces”, PhD Dissertation, 2009. R. Collin, “Foundation of Microwave Engineering”, McGraw-Hill Book Co, New York, 1966.

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/cb6792f9c684cac1a73b1de24d24215b.jpg)
Fig. 1 – 2x3 THz metamaterial periodic array sensor (a) EM Simulation (b) ADS Circuit Simulation

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/a789ffdaf6896a062e07d77a6d20fe18.jpg)
Fig. 2- Comparison of analytical and simulation results

 THz Periodic Array Sensor Design

We theoretically consider a possibility of generation of electromagnetic radiation due to transitions of electrons between spin subbands in a ferromagnet. It is known that such electro-dipole transitions are forbidden if a uniform ferromagnet is considered in a Vonsovsky s-d exchange model. One possible way to remove this limitation is to suggest that the exchange constant depends on the conduction electron momentum. This mechanism was suggested in [1]. At first, it seems to be fully exchange. However the dependence of the exchange constant on the electron momentum may appear only due to spin-orbit interaction in the subsystem of localized d- or f- electrons which are responsible for magnetization of the medium in this model, and no t in the conduction electron subsystem. In the present work, we consider several different mechanisms of electron transitions between spin subbands with photon emission. The most simple mechanism is the magneto-dipole electron transitions which exist due to the magnetic field of the wave. The effects governed by this mechanism are usually very small. Another mechanism appears due to the spin-orbit interaction which exists in the conduction electron subsystem. In our model calculations, we take the Rashba spin-orbit coupling that exists at the medium surfaces. Finally, a fully exchange mechanism of intersubband electron transitions that exists in magnetic medium with non-collinear magnetization distribution is investigated. An example of non-collinear ferromagnet that allows intersubband electrodipole electron transitions is a magnetic helicoid which may be realized either in natural (holmium, MnSi, FeGe at low temperature) or artificial (magnetic spring structures) materials. For all suggested mechanisms, probabilities of electron transitions between spin subbands are found and estimations are made for realistic parameters. We show that both spin-orbit coupling and exchange coupling in a non-collinear magnetic medium may give reasonable values of electron transition probabilities. Finally, a possibility to create devices based on the investigated mechanisms is discussed. This work was supported by the Russian Science Foundation (Grant #19-72-00130).

**References:**

[1] A. Kadigrobov, Z. Ivanov, T. Claeson, et al., Europhys. Lett. 67, 948 (2004)

**Images:**

 Electromagnetic wave generation in a ferromeagnet due to transitions between spin subbands

Anisotropic magnetoresistance (AMR) refers to an electrical phenomenon that the resistivity in a metallic ferromagnet depends on the mutual angle of the magnetization and electric current, which was first discovered by William Thomson in 1857 and is nowadays widely applied in magnetic sensors. Despite of a long history of study, AMR is usually explained vaguely as a complicated relativistic interaction of local magnetic moments and itinerant electrons. Nevertheless, the quantitative description of AMR for a particular magnetic material usually requires some tunable parameters that are determined by experimental measurement. Using first-principles transport calculations, we predict that the AMR of single-crystal CoFe alloys is strongly dependent on the current orientation and alloy concentration. An intrinsic mechanism for AMR is found to arise from the band crossing due to magnetization-dependent symmetry protection [1]. These special k points can be shifted towards or away from the Fermi energy by varying the alloy composition and hence the exchange splitting, thus allowing AMR tunability. The prediction is confirmed by delicate transport measurements, which further reveal a reciprocal relationship of the longitudinal and transverse resistivities along different crystal axes.

**References:**

[1] F. L. Zeng, Z. Y. Ren, Y. Li, J. Y. Zeng, M. W. Jia, J. Miao, A. Hoffmann, W. Zhang, Y. Z. Wu, and Z. Yuan, Physical Review Letters Vol. 125, p.097201 (2020).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/721d99ee7d03c6c285826d7d876f32b8.jpg)
Upper panel: Calculated band structure using the effective potentials of Fe in Co0.5Fe0.5 with the magnetization along [100]. The band gap at 0.25 eV above the Fermi level gradually shrinks when the magnetization is rotated towards [010], as shown in the inset. Lower panel: the nodal line formed by two energy bands in the (010) plane at M||[010] (left) and a gap opening up at M||[100] (right).

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d17485d5cd6a1e42a3fa03d642fe1e36.jpg)
Calculated and experimental resistivity of CoFe alloy for different magnetization and current orientations, as well as the dependence on the alloy concentration.

 Intrinsic mechanism for anisotropic magnetoresistance and experimental confirmation in CoFe alloys INVITED

In spintronics, one of the long standing questions is why the MgO barrier is almost the only option to achieve a large tunnelling magnetoresistance (TMR) ratio at room temperature (RT) but not as large as the theoretical prediction [1]. This can be due to the spin fluctuation at the ferromagnet/MgO tunnel barrier interfaces and/or spin-independent hopping within the barrier in a magnetic tunnel junction (MTJ) [2]. One of the approaches to overcome these issues is to employ the lattice softening of the ferromagnetic layers in MTJ. Recently a metastable body-centred cubic (bcc) CoxMn100-x (CoMn) ferromagnetic films have been reported to exhibit the enhancement of their magnetic moments with an ideal lattice matching with MhO [3], which can be an ideal candidate for the TMR enhancement in MTJ. MTJ stacks were grown using conventional magnetron sputtering on MgO(001) substrates with the structure of Cr (40)/CoxMn100-x (10)/MgO (2.4)/CoxMn100-x (4)/Co3Fe(1.5)/IrMn (10)/Ru (5) (thickness in nm) [4]. For CoMn, four different compositions of x = 66, 75, 83 and 86 were used, allowing to control the CoMn lattice constants. To promote the crystallisation of the seed and CoMn layers, in-situ annealing was performed after the deposition of the Cr seed layer and CoxMn100-x layers at 700oC and 200oC, respectively. MTJs were then post-annealed at 325oC for their crystallisation after patterned into pillars with Ti/Au electrodes by photolithography. TMR measurements were carried out using the conventional four-terminal setup with elevating temperature, showing two distinctive TMR ratios of 229% and 142% at room temperature for x = 75 and 86, respectively. The corresponding atomic structures were imaged by cross-sectional transmission electron microscopy (TEM, JEOL JEM-2100 Plus) at 600k magnification. Figures 1(a) shows a cross-sectional high-resolution (HR) TEM image of the MTJ with x = 75 showing the larger TMR ratio. Fully epitaxial growth of the entire MTJ is confirmed with some dislocations, of which period is calculated to be (11.4 ± 0.3) nm. This indicates that the Co75Mn25 layer may induce plastic deformation rather than elastic deformation with inducing dislocations at the boundaries between crystals. The x = 86 sample, on the other hand, shows dark black regions at the CoMn/MgO interfaces indicating CoMn/MgO is not fully crystallised within the CoMn layer [see Fig. 1(b)]. These features are found to be induced by dislocations formed at the CoMn/MgO/CoMn interface with the period of (8.9 ± 0.3) nm. These dislocations may be the origin of the interfacial spin fluctuation. In the MgO layer for x = 75, two distinctive crystallographic phases are observed as shown as the regions (i) and (ii), which are crystallised along MgO[001] and [100] directions, respectively, as similarly reported in previous reports [5]. For x = 86, an additional partially crystallised MgO grains are found, which induces spin-independent hopping to reduce the corresponding TMR ratio. By measuring the lattice constants of CoMn and MgO in the HRTEM images, the top CoMn lattice constants are almost constant across MTJs apart from x = 86, confirming the lattice softening of these layers with forming almost strain-free MTJ. These results were compared with ab initio calculations on the lattice stability of the CoMn alloys. Calculations confirm the crystalline deformation stability across a broad compositional range in CoMn, proving a strain-free interface for larger TMR ratios. Further optimisation of the CoMn-based MTJs can achieve &gt; 1,000% TMR ratio at RT.

**References:**

[1] A. Hirohata et al., J. Magn. Magn. Mater., vol. 509, p. 166711 (2020). [2] C. H. Shang et al., Phys. Rev. B, vol. 58, p. R2917 (1998). [3] R.J. Snow et al., J. Magn. Magn. Mater., vol. 419, p. 490 (2016). [4] K. Kunimatsu et al., Appl. Phys. Exp., vol. 13, p. 083007 (2020). [5] G. X. Miao et al., Appl. Phys. Lett., vol. 93, p. 142511 (2008).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/cd295ebb917f5d44588a534b3c4a60c8.jpg)
Fig. 1 HRTEM images taken on the x = (a) 75 and (b) 86 sample.

 Strain-Free Magnetic Tunnel Junction with Metastable bcc CoxMn100-x(001) Ferromagnetic Layers

Magnetic tunnel junctions (MTJs) show great promise for implementation in high-performance spin transfer torque magnetic random-access memory (STT-MRAM) [1] and novel computing regimes such as magnetic domain wall logic [2] and neuromorphic computing [3]. MTJs consist of an insulating thin film tunneling barrier sandwiched between two ferromagnet electrodes. By altering the magnetization of the electrodes, the rate of tunneling across the barrier can be varied. This provides a mechanism to convert nonvolatile magnetic information to electrical information via modifying the resistivity of the device, achieving on/off tunnel magnetoresistance ratios (TMR) of over 600% at room temperature in state-of-the-art CoFeB/MgO/CoFeB MTJs [4]. Unfortunately, a handful of material setbacks stand in the way of the widespread adoption of even leading MgO MTJs over other emerging technologies, such as Resistive-RAM junctions, in next-generation architectures. MgO’s wide bandgap (7.8 eV) is associated with a high junction resistance-area (RA) product, greatly increasing power-draw and necessitating high operating voltages, which leads to device variability challenges and dielectric breakdown [5]. Additionally, MgO creates magnetic dead layers through the oxidation of interfacial Fe atoms and requires ultra-thin barrier layers that are difficult to fabricate and may contain pinholes [6]. These setbacks result in a reduction of the effective TMR and an increase in the RA-product, which motivates the search for new barrier materials. Here, we explore the properties of rock-salt structured Scandium Nitride (ScN) magnetoresistive junctions and find it a promising barrier material given its novel electron symmetry filtering properties, high TMR, and low RA-product. Fe/ScN/Fe MTJ supercells were constructed for 3,5,6,7 and 8 atomic layers of ScN, with the ScN lattice rotated by 45 degrees such that the N anions rest over the interfacial Fe, analogous to the Fe/MgO interface. Using the plane-wave basis density functional theory (DFT) package VASP [9], the MTJ supercells were converged and exported to Quantum Espresso [10] to calculate the complex bands, symmetry properties, and to perform spin-polarized electron transport calculations under the Landauer-Büttiker formalism as implemented in PWCOND [9]. A Hubbard +U correction of 4.5 eV was applied to Sc’s 3d orbital to correct the electronic band gaps using the PBE-GGA pseudopotentials. In this manner, the indirect Γ-X gap of the ScN was matched near to experimental values [7] at 1.31 eV. The conductance calculations find TMR ratios exceeding 1900% for sufficiently thick systems (&gt; 6 atomic layers of ScN), with spin-dependent transport dominated by unique Δ2’ band filtering through Sc’s 3d orbital in the 6-layer system analysed [12]. This mechanism is different from the spin filtering in Fe/MgO/Fe MTJs, where MgO selects for the half-metallic Δ1 band present in bcc Fe or CoFe electrodes [8]. Instead, ScN selects for Fe’s Δ2’ electrons with large crystal momentum, which is only provided in the majority spin of the Fe band structure at the fermi energy. Even with the high TMR and symmetry filtering in ScN, the layer-dependent calculations predict that the devices remain highly conductive with respect to barrier thickness, unlike in MgO systems where the dominant Δ1 electron wavefunctions decay rapidly across the barrier [8]. Fabricated in a system with minimal symmetry mixing and atomic dislocations, magnetoresistive ScN junctions could operate with a fraction of the power of MgO MTJs, while allowing for thicker barriers with more lenient manufacturing tolerances and maintaining high TMRs characteristic of MgO MTJs. Partial funding from Sandia National Lab (SNL). SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525

**References:**

[1] H. Noguchi, K. Ikegami, S. Takaya, ISSCC 132, (2016) [2] J. A. Currivan-Incorvia, S. Siddiqui, S. Dutta, Nat. Comms. 7, 3 (2016). [3] N. Hassan, X. Hu, L. Jiang-Wei, J. Appl. Phys. 124, (2018). [4] S. Ikeda, J. Hayakawa, Appl. Phys. Lett. 93, 1 (2008) [5] L. Xue, A. Kontos, IEEE Trans. Magn. 51, 1 (2015). [6] W. S. Zhao, Y. Zhang, T. Devolder, Microelectron. Reliab. 52, 1848 (2012). [7] D. Gall, M. Städele, Phys. Rev. B - Condens. Matter Mater. Phys. 63, 1251191 (2001). [8] W. H. Butler, STAM, 9(1), 014106. (2008) [9] G. Kresse and J. Furthmüller, Phys. Rev. B, 54:11169, (1996) [10] Giannozzi, P., Baroni, S., Bonini, N. Journal of Physics: Condensed Matter, 21(39), 395502 (2009) [11] A. Smogunov, A. Dal Corso, E. Tosatti, Phys. Rev. B 70, 045417 (2004) [12] S. Karki, V. Rogers, (under review) arXiv 2008.12770 (2020)

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2eacbc5c29f6d3c4ffb033cdca39b0e2.jpg)
Fig. 1 Scattering states of parallel-magnetized Fe/6ScN/Fe majority spin (a) and minority spin (b) sampled at a high-transmission spike at kx = 0.02 (2π/a) and ky = 0.05 (2π/a).

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/9627d3f44227554116317204d460b021.jpg)
Fig. 2 Complex bands of Scandium Nitride sampled at the Γ and X point, with the symmetry-resolved real bands set in between. A small Hubbard +U bandgap correction is applied.

 Large magnetoresistance in symmetry-filtering scandium nitride junctions using first principles

Magnetic tunnel junctions (MTJs) are a key element for various spintronic devices such as magnetic random-access memories including novel ones, i.e., brain-morphic devices and magnetic logic circuits. For future applications, room temperature (RT) TMR ratios of 1000% are targeted [1]. However, fabricating MTJs with a TMR ratio much larger than 200% is difficult because the spin-polarized tunneling current strongly depends on the ferromagnet (FM)/oxide interfaces quality. MTJs suffer from imperfect interfaces due to dislocations, formation of unfavorable oxide layers at the electrode/barrier interfaces or oxygen vacancies [2,3]. Especially, the fabrication of high-quality FM electrodes on the oxide barrier is difficult due to their different chemical properties which is challenging for fabrication of sharp interfaces. Such imperfections disturb highly spin polarized electron tunneling and lead to reduced TMR ratios experimentally. In fact, the TMR ratio of well-studied Fe/MgO/Fe merely exceed 200% at RT even though theoretical calculations predicted &gt;1000% TMR ratios [2]. Here, we report giant enhancement in RT-TMR ratios of Fe/MgO/Fe by tuning the growth condition of each layer and optimization of barrier interfaces: maximum 417% at RT and 914% at 5 K in a single-crystal, spin-valve-type Fe/MgO/Fe MTJ [4]. Exchange-spin-valve MTJ structures were fabricated in an ultrahigh vacuum magnetron sputtering system (base pressure: 4×10-7 Pa) with the structure: MgO(001) substrate//Cr (60)/Fe (30 or 50)/CoFe (0 or 2.24)/Mg (0.5)/wedge-shaped MgO (dMgO = 0.5 – 2.5)/Fe (5)/IrMn (10)/Ru (20) (number in brackets in nm). The MgO barrier was deposited using electron-beam evaporation method and a linear shutter for the wedge-shaped barrier. In-situ post-annealing was performed for each layer. After deposition, the wafers were ex-situ annealed in a 0.7 T magnetic field at 200°C and subsequently, the TMR ratio and resistance area product (RA) was measured using current in-plane tunneling (CIPT) method. The TMR ratio is defined as TMR = (RAP – RP)/RP × 100%, where RP (RAP) are the resistance for the parallel (antiparallel) state. Thereafter, the wafers were pattered into micrometer scale MTJs using photo- and EB-lithography. The transport properties were investigated using a standard dc 4-probe method. In Fig. 1 (a) and (b), RA and TMR ratio vs. dMgO for the MTJ with a 30 nm and 50 nm bottom-Fe is shown, respectively, for the patterned MTJs (dc 4-probe). For the MTJ with 30 nm bottom-Fe the unpatterned wafer (CIPT) results are also shown. As expected, a linear relationship between log(RA) and dMgO in a wide dMgO range was observed, suggesting good MgO barrier formation. For dMgO &lt; 1 nm, the MgO barrier may be discontinuous. For dMgO &gt; 1 nm, the TMR ratio increases with dMgO and it finally reaches &gt;400%. The inset of Fig. 1 (b) shows the MR loop of the Fe (50 nm)/MgO/Fe MTJ with a maximum 417% TMR ratio which almost doubles previously reported values of Fe/MgO/Fe. Improved Fe/MgO interfaces and well-controlled (001)-orientation of our Fe/MgO/Fe resulted in this significant enhancement of the TMR ratio. In addition, it shows significant oscillatory behavior with dMgO. The oscillation period is 0.31 nm, which agrees with the previous Fe/MgO/Fe report [2]. The oscillation is clearly observed in both the patterned and unpatterned cases, which excludes possible errors of our measurements. The peak-to-valley difference of the oscillation reaches ~80%, which is ~7 times larger than the previous report [2]. The RA curves also possess an oscillatory component as seen in Fig.1 (a). Furthermore, the TMR ratio was increased to 497% at RT by using a Fe/CoFe/MgO/Fe structure (red square in Fig. 1 and MR loop in inset of Fig. 1(b)). This value is larger than other ones of exchange-spin-valve MTJs such as Co/MgO/Co (410%) [5] and Co2(FeMn)Si/MgO/Co2(FeMn)Si (429%) [6]. In Fig. 2, the temperature dependence of the TMR ratio for an Fe (30 nm)/MgO/Fe MTJ is shown. The TMR ratio is 386% at RT and increases to 914% at 3 K. The respective MR loops are displayed in the inset of Fig. 2. The low temperature (LT) value is around three times larger as compared to other reported values of Fe/MgO/Fe MTJs (250-370%) [2,7]. Our Fe/MgO/Fe MTJ exhibits a giant TMR ratio close to 1,000% at LT, which is often referred as a theoretical value of Fe/MgO/Fe. The study demonstrated that there is more room for improving TMR ratios of Fe/MgO/Fe MTJs by the optimization of each layer and interface. Further improvement in TMR ratios using the technology in the present study can be expected as demonstrated by the CoFe insertion result. This work was partly supported by the ImPACT Program of the Council for Science, Technology and innovation (Cabinet Office, Government of Japan), JSPS KAKENHI Grant No. 16H06332, TIA collaborative research program “Kakehashi”, and JPNP16007, commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

**References:**

[1] D. Ielmini and S. Ambrogio, Nanotechnology, Vol. 31, p. 092001 (2020). [2] S. Yuasa et al., Nat. Mater., Vol. 3, p. 868 (2004). [3] X.-G. Zhang, et al., Phys. Rev. B, Vol. 68, p. 092402 (2003). [4] T. Scheike et al., Appl. Phys. Lett., in press; arXiv: 2011.08739. [5] S. Yuasa et al., Appl. Phys. Lett., Vol. 89, p. 042505 (2006). [6] H.-x. Liu, et al., J. Phys. D: Appl. Phys., Vol. 48, p. 164001 (2015). [7] S. G. Wang, et al., Phys. Rev. B, Vol. 78, p. 180411(R) (2008).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/fcd71b3caf74c7f35790944728c9ec6d.jpg)
Fig. 1 RA (a) and TMR ratio (b) vs. dMgO for Fe/MgO/Fe MTJs with 30 nm (circle and cross) and 50 nm (diamond) bottom-Fe and Fe(50 nm)/CoFe(2.24 nm)/MgO/Fe (square) MTJ. Inset: MR loops of both MTJs at their maximum TMR ratios.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d4a9e77a8c2d894c8d8c4e9022dcd09d.jpg)
Fig. 2 TMR ratio vs. temperature of a Fe(30 nm)/MgO/Fe MTJ. Inset: MR loops at 300 K and 5 K.

 Giant tunnel magnetoresistance up to 417% at room temperature using Fe/MgO/Fe magnetic tunnel junctions

Perpendicular magnetic tunnel junctions (p-MTJs) utilizing tetragonal Mn-based alloy films attracts attention as key devices for magnetic random access memory and THz frequency devices 1. There were many past studies demonstrating those devices, whereas their TMR ratios were much smaller than those predicted by first-principles calculations2. Interlayers between the Mn-based alloy and the barrier effectively enhance those TMR ratio, and the TMR ratio of 60% was reported in MnGa/MgO MTJs with FeCo interlayer3. It is crucial to find new interlayer materials to further enhance the TMR ratio for realizing Mn-based p-MTJs for practical applications. Recently, we have reported in-plane type MTJs using bcc-Co75Mn25 electrodes. Bcc-Co75Mn25 is known for its metastable bcc-phase and for ferromagnetism having high Curie temperature4. Those MTJs showed a high TMR ratio of over 200%, which may be due to highly spin-polarized △1 band in bcc-Co75Mn25 5. Here we demonstrate high TMR ratio in ultrathin MnGa-based p-MTJs with the bcc-Co3Mn alloy interlayer. The result indicates that bcc-CoMn alloy is one of the promising interlayer materials for obtaining high TMR ratio in Mn-based p-MTJs6,7. The samples were prepared using a magnetron sputtering system. The stacking structure of the samples was MgO(001) substrate/Cr(40)/Co55Ga45(30)/ Mn61Ga39(3)/ CoxMn100-x(0.8) /Mg(0.4)/MgO(2)/Fe60Co20B20(1.2)/Ta(3)/Ru(5) (thickness is in nanometers) Here, the CoxMn100-x interlayer was deposited using a co-sputtering technique with Co and Mn targets. All the layers were deposited at room temperature, and the deposition process for the buffer and seed layers was adopted from a previous study6. Micro-fabrication of MTJs was performed by standard ultraviolet photolithography, and Ar ion milling etching. After microfabrication, the MTJs were annealed at 250 °C in a vacuum furnace. TMR measurements were performed by a physical property measurement system (PPMS, Quantum Design) using a standard four-probe method at a bias voltage of 1 mV. Figure 1 shows the TMR curves of the MTJs with/without Co75Mn25 interlayer measured at 300 K. The Co75Mn25 interlayer shows the TMR ratio up of approximately 80%, which is much enhanced as compared with that for MnGa-MTJs, ~ 10 %. Meanwhile, the shape of the TMR curve and the increase of coercivity indicate that Co75Mn25 interlayer strongly and antiferromagnetically couples with perpendicularly-magnetized MnGa layer. Figure 2 shows the composition x dependence of the TMR ratio for the MTJs with 0.8-nm-thick CoxMn100-x interlayer. The TMR ratio for the x=0 MTJ is 70% (145%) at 300 K (10K), which is larger than the value expected from Julliere’s relation with spin-polarization of fcc-Co and CoFe(B). Moreover, the TMR ratio increases by up to 85% (209%) at 300 K(10 K) for the case of x=0.8. Those high TMR ratio would originate from coherent tunneling between highly spin-polarized Δ1 bands in bcc-Co (Co-Mn) and CoFe(B) electrodes, even though the Co-Mn interlayer thickness is very small, 0.8 nm. This may be also consistent with the temperature dependence of resistance or conductance in these MTJs, which was similar to those observed in Fe/MgO/Fe MTJs. Acknowledgement We would like to thank Y. Kondo for his technical assistance. This work was partially supported by JST CREST (No. JPMJCR17J5).

**References:**

[1] S. Mizukami et al., Scripta Materialia 118, 70 (2016). [2] J. Jeong et al., Nat. Commun., 7, 10276 (2016). [3] Q. L. Ma et al., Phys. Rev. Lett. 112, 157202 (2014). [4] R. J. Snow et al., J. Magn. Magn. Mater. 419, 490 (2016). [5] K. Kunimatsu et al., Appl. Phys. Express 13, 083007 (2020). [6] K. Z. Suzuki et al., Sci. Rep. 6 , 30249 (2016). [7] K. Z. Suzuki et al., submitted.

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/cd118f0c5f1c2b5dda5eeec663df1850.jpg)
Figure1 TMR curves measured at 300 K for the MnGa-based p-MTJs with/without Co75Mn25 interlayer.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/ec9d8f4d534d71d7d5602117fd1c8e27.jpg)
Figure 2 The Co composition dependence of the TMR ratio in MnGa-based p-MTJs with CoxMn100-x interlayer at 300 and 10 K.

 High Tunnel magnetoresistance in ultrathin MnGa-based perpendicular magnetic tunnel junctions utilizing ferromagnetic bcc-CoMn interlayers

Spin-orbitronics, which takes advantage of spin-orbit coupling (SOC), has expanded the research objects of spintronics to nonmagnetic materials. Here, we report the emerging nonlinear spintronic phenomena in the inversion-asymmetric nonmagnetic quantum materials with SOC. For instance, the surface state of three-dimensional topological insulator (TI) owns helical spin textures with the spin and momentum perpendicularly locked. We show the observation of a nonlinear magnetoresistance (called bilinear magneto-electric resistance, BMER) [1] and nonlinear Hall effect [2] in a prototypical TI Bi2Se3, which scale linearly with both the applied electric and magnetic fields. We further reveal that these effects are originated from the conversion of a nonlinear spin current to charge current under the application of an external magnetic field. A close link between the BMER and the spin texture was established in TI surface states, which enables a novel transport probe of spin textures. We further extended the observation of BMER effect to the d-orbital two-dimensional electron gas (2DEG) at a SrTiO3 (STO) (111) surface [3]. The BMER probes a three-fold out-of-plane spin texture, in addition to an in-plane one at the STO (111) surface 2DEG. This novel spin texture is in contrast to the conventional one induced by the Rashba effect. By performing tight-binding supercell calculations, we find that this 3D spin texture is fully described by the confinement effects of the STO t2g conduction band in the (111) plane. We recently reported the observation a sign reversal of nonlinear magnetoresistance with temperature in a semimetal WTe2 [4]. Theoretical calculations revealed the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These findings open a new branch in spintronics, which discusses the nonlinear transport effects in spin-polarized quantum materials, and is therefore referred as nonlinear spintronics.

**References:**

[1] Pan He, et al. Nature Physics 14, 495 (2018) [2] Pan He, et al. Phys. Rev. Lett. 123, 016801 (2019) [3] Pan He, et al. Phys. Rev. Lett. 120, 266802 (2018) [4] Pan He, et al. Nature commun., 10, 1290 (2019)

**Images:**

 Nonlinear spintronics in quantum materials with inversion symmetry breaking INVITED

Nowadays, our lives are greatly enriched by information society. Meanwhile, energy resource issue is becoming a serious problem, leading to the demand for devices with lower power consumption. When we focus on the memory, the spread of non-volatile memory, represented by the racetrack memory [1] based on current induced domain wall motion (CIDWM), has been longed for. To realize this, our groups have been investigating anti-perovskite Mn4N films as candidate materials for the racetrack memory. They show a small saturation magnetization (MS) of 80 kA m-1 and clear perpendicular magnetic anisotropy (PMA) [2], contributing to high velocity and low threshold current density, respectively. We experimentally demonstrated the domain wall velocity (vDW) of 900 ms-1 at 1.3×1012 Am-2 only by spin-transfer torque (STT) [2]. Note that we achieved this record by rare-earth free material unlikely other reports. Our recent work also pays attention to Mn4-xNixN films because they have compensation point at x ~ 0.15 where vDW takes its maximum value [3]. In Mn3.85Ni0.15N, we recorded vDW of 2000 m/s at 1.16×1012 Am-2, the fastest purely STT-driven CIDWM [4]. Despite of these amazing performances, large parts of magneto-transport properties in Mn4-xNixN films are still unknown although they are deeply linked to the relationship between conduction electrons and localized ones. Interestingly, we confirmed large anomalous Hall effect (AHE) with a relatively large anomalous Hall angle (θAHE = ρAHE/ρxx) of 2% in Mn4N films although they don’t contain any heavy metal with large spin-orbit coupling [2]. There were attempts to discover the origin of such large AHE, however, it has not been proved by now. In this work, we performed AHE and conductivity measurements at temperatures in the range of 5-300 K, and we plotted σAHE against σxx to find out the origin of AHE [6]. Also, we performed anisotropic magnetoresistance (AMR) measurements for the better understanding of spin-dependent scattering in these materials. Mn4-xNixN films (30 nm) were fabricated onto SrTiO3 (STO)(001) substrates by molecular beam epitaxy. Epitaxial growth was confirmed by X-ray diffraction, and the thickness of each layer was examined by X-ray reflectivity. AHE and AMR measurements were performed by physical properties measurement system. Before measurements, film samples were processed into Hall bars with a width of 200 mm by Ar ion milling. During AMR measurements, DC current was set to flow in the [100] azimuth and a magnetic field of 9 T was applied parallel to the plane. Figure 1 shows the σxx dependence of σAHE in Mn4-xNixN/STO in the temperature range of 5-300 K. Note that σxx became larger at lower temperatures, a typical behavior in metals. The region of σxx &lt; 104 Ω-1cm-1 is called “Bad metal regime”, where σAHE is proportional to σxxα (α~1.8) in many 3d transition metals [5]. Mn4-xNixN films (x &gt; 0) also followed this trend, while Mn4N showed rather constant σAHE relative to σxx. On the other hand, the region of σxx &gt; 104 Ω-1cm-1 is called “Good metal regime”, where σAHE did not change so much against σxx. In Mn4-xNixN at small x (x = 0 and 0.05), however, σAHE decreased with increasing σxx, thereby, with decreasing temperature. It’s also remarkable that σAHE remained almost unchanged when x = 0.15 and 0.2. This discrepancy can be explained in the following. Figure 2 shows the Fourier coefficients C2 (cos2θ) and C4 (cos4θ) of AMR curves of Mn4-xNixN/STO. θ is the angle made by the current and magnetization. C2 and C4 components derive from cubic and tetragonal crystalline fields, respectively [6]. Thus, large C4 components at temperatures lower than 100 K at x = 0 and 0.05 originate from tetragonal one although they have cubic structures. Note that C4 component was very small at x = 0.15, and AMR was barely observed at x &gt; 0.2. In 3d transition metals, intrinsic AHE comes from hopping of electrons between electronic states dyz and dzx [7]. However, these states rise under the tetragonal crystalline field due to the resolution of degeneracy, leading to smaller number of electrons related to the origin of AHE. Therefore, reflecting our experimental results, unexpected decrease in σAHE at low temperatures in Mn4-xNixN (x= 0, 0.05) can be explained by the emergence of tetragonal field. On the basis of these discussions, we conclude that large AHE in Mn4-xNixN originates from intrinsic AHE at low temperatures. Although we have not fully revealed the case at room temperature due to a limited number of reports on AHE in “Bad metal regime”, we suggest that it originates from intrinsic AHE and extrinsic AHE such as phonon-scattering. We believe this work opens the interest in the band structure of Mn4-xNixN films.

**References:**

[1] S. Parkin and S.-H. Yang, Nat. Nanotechnol. Vol.10, p.195 (2015). [2] T. Gushi, L. Vila and T. Suemasu et al., Nano. Lett. Vol.19, p.8716 (2019). [3] T. Komori, K. Amemiya and T. Suemasu et al., J. Appl. Phys. Vol.127, p.043903 (2020). [4] S. Ghosh, T. Komori and L. Vila et al., IEEE MMM Virtual Conference, R1-11, Nov. (2020). [5] N. Nagaosa, S. Onoda and N. P. Ong et al., Rev. Mod. Phys. Vol.82, p.1539 (2010). [6] S. Kokado and M. Tsunoda, Mater. Today Proceedings Vol.33, p.1864 (2020). [7] H. Kotani, T. Tanaka, K. Yamada Phys. Rev. B Vol.75, p.184416 (2007).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/cb1bf1328229c6aeb2d2d6ad95de27fd.jpg)
Fig. 1 σxx dependence of σAHE in Mn4-xNixN at temperatures (5-300 K). A dashed line indicates the border of Good metal and Bad metal regime.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/185d297e24af6e838eb29c195a960292.jpg)
FIg. 2 Fourier coefficients C2 and C4 of AMR curves of Mn4-xNixN.

 Magneto-transport properties in Mn4-xNixN films with large current induced domain wall mobility and investigation in their large anomalous Hall effect

Magnetotransport properties of magnetic materials receive considerable interests, because of they make an important role in basic science and technological applications[1]. Anomalous Hall Effect (AHE), as an important topic in condensed matter, contains extensive physics for their many different mechanisms, such as intrinsic mechanism associated with the Berry curvature in entangled Bloch electronic bands, extrinsic mechanism including skew scattering and side jump scattering[2]. In this study, the magnetotransport properties in antiferromagnetic half-Heusler single crystals of TbPtBi, a magnetic-field-induced topological semimetal with simple band structure, were investigated. We found a non-monotonic dependence of the anomalous Hall resistivity on the magnetic field in a strong magnetic field (B&gt;7T), which comes from the change of band structure caused by the Zeeman-like splitting when an external magnetic field is applied. The experimental results show that credible anomalous Hall resistivity and conductivity reach up to 0.68mΩcm and 125Ω-1cm-1, respectively. A large anomalous Hall angle (AHA) up to 33% is achieved in TbPtBi, which is comparable to a typical ferromagnetic Weyl semimetal Co3Sn2S2[3]. The analysis of the results shows that this should be attributed to topological band around EF and low carrier density.

**References:**

[1] Science advances 4 : eaar7880 (2018). [2] Rev. Mod. Phys. 82 (2), 1539 (2010); Physical Review 95 (5), 1154 (1954); Physica 24, 39 (1958); Physica 21, 877 (1955); Phys. Rev. B 2 (11), 4559 (1970). [3] Nat. Phys. 14, 1125 (2018); Adv. Funct. Mater., 2000830 (2020); Nano Lett. 7476–7481, (2020).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/72c83298ed580c527c76631a5810d453.jpg)
Figure 1. Dependence of the longitudinal resistivityρxx(a) and Hall resistivity ρxy (b) on magnetic field B at temperatures from 1.8K to 50K. (c) Separation progress of normal Hall resistivity ρxyN and anomalous Hall resistivity ρxyA at 1.8K. The inset shows the normal Hall resistivity obtained by linear fitting for low magnetic field curves at corresponding T. (d) The anomalous Hall resistivity ρxyA after subtracting the fitting normal Hall resistivity ρxyN. The inset is the maximum value of ρxyA at different temperatures.

Anomalous Hall Effect in Anisotropic Weyl Semimetals

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Anomalous Hall Effect in Anisotropic Weyl Semimetals

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