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The interplay of symmetry and magnetism can determine the tensors of intrinsic anomalous Hall effect (AHE) [1]. In the past decades, AHE has been extensively researched in cubic crystals such as Fe ferromagnet [2], in which AHE σ&lt;sub&gt;xy&lt;/sub&gt; exists only when the magnetization has a component along the direction of J&lt;sub&gt;x&lt;/sub&gt; × E&lt;sub&gt;y&lt;/sub&gt;, where J&lt;sub&gt;x&lt;/sub&gt; is the Hall current and E&lt;sub&gt;y&lt;/sub&gt; is the electric field. The van der Waals ferromagnets provide opportunities to break this strict rule thanks to the low-symmetry structure. Here, we employed the VSe&lt;sub&gt;2&lt;/sub&gt; ferromagnet to study the tensor of intrinsic AHE with varying magnetization in different planes. The VSe&lt;sub&gt;2&lt;/sub&gt; monolayer, with the space group P-3m1 (No.164), can exhibit in-plane magnetic anisotropy and ferromagnetism at room temperature [3]. Using &lt;i&gt;ab-initio&lt;/i&gt; calculations, we have verified that in the VSe&lt;sub&gt;2&lt;/sub&gt; monolayer, the AHE σ&lt;sub&gt;xy&lt;/sub&gt; can be preserved with the absence of z-direction magnetization, and present a period of 2π/3. Moreover, for any plane, σ&lt;sub&gt;xy&lt;/sub&gt; exhibit nonlinear anisotropy with respect to magnetization, and xz-plane magnetization σ&lt;sub&gt;xy&lt;/sub&gt; slightly different from the yz-plane one. The symmetry analysis produces the AHE formulae, which fit well with &lt;i&gt;ab-initio&lt;/i&gt; data due to the higher-order terms. Our findings pave a new route to the emerging field of nonlinear spintronic phenomena.

**References:**

[1] R. R. Birss, Symmetry and Magnetism, North-Holland (1964)&lt;br/&gt;[2] Y. Yao &lt;i&gt;et al&lt;/i&gt;., &lt;i&gt;Phys. Rev. Lett.&lt;/i&gt; Vol. 92, p. 037204 (2004)&lt;br/&gt;[3] M. Bonilla &lt;i&gt;et al&lt;/i&gt;., &lt;i&gt;Nat. Nanotechnol.&lt;/i&gt; Vol. 13, p. 289 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e1affc1389eb8e1917c0a718c90c08bd.jpg)
Fig.1 Evolution of the AHE σ&lt;sub&gt;xy&lt;/sub&gt; when magnetization varies in different planes. Inset: Diagram of the variation of magnetization.



INTERMAG 2021

 Nonlinear anomalous Hall effect in van der Waals ferromagnet

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The interplay of symmetry and magnetism can determine the tensors of intrinsic anomalous Hall effect (AHE) [1]. In the past decades, AHE has been extensively researched in cubic crystals such as Fe ferromagnet [2], in which AHE σxy exists only when the magnetization has a component along the direction of Jx × Ey, where Jx is the Hall current and Ey is the electric field. The van der Waals ferromagnets provide opportunities to break this strict rule thanks to the low-symmetry structure. Here, we employed the VSe2 ferromagnet to study the tensor of intrinsic AHE with varying magnetization in different planes. The VSe2 monolayer, with the space group P-3m1 (No.164), can exhibit in-plane magnetic anisotropy and ferromagnetism at room temperature [3]. Using ab-initio calculations, we have verified that in the VSe2 monolayer, the AHE σxy can be preserved with the absence of z-direction magnetization, and present a period of 2π/3. Moreover, for any plane, σxy exhibit nonlinear anisotropy with respect to magnetization, and xz-plane magnetization σxy slightly different from the yz-plane one. The symmetry analysis produces the AHE formulae, which fit well with ab-initio data due to the higher-order terms. Our findings pave a new route to the emerging field of nonlinear spintronic phenomena.

**References:**

[1] R. R. Birss, Symmetry and Magnetism, North-Holland (1964) [2] Y. Yao et al., Phys. Rev. Lett. Vol. 92, p. 037204 (2004) [3] M. Bonilla et al., Nat. Nanotechnol. Vol. 13, p. 289 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e1affc1389eb8e1917c0a718c90c08bd.jpg)
Fig.1 Evolution of the AHE σxy when magnetization varies in different planes. Inset: Diagram of the variation of magnetization.

technical paper

Recent discoveries of magnetic van der Waals (vdW) materials provide the ideal platform for exploring intrinsic two-dimensional (2D) magnetism down to the 2D limit and potential opportunities for new spin-related applications. However, according to Ginzburg criterion, 2D magnetism is associated with strong intrinsic magnetization fluctuations, which will break down the approximation of mean field theory in the neighborhoods of critical points [1]. In this talk, we will show the evidence for the magnetization-fluctuation-induced effective g factor anisotropy in the 2D ferromagnetic insulators CrXTe3 (X = Si, Ge) by means of ferromagnetic resonance (FMR). After deriving the classical and quantum models of magnetic resonance [2, 3], we confirm the dramatic anisotropic shift of the measured g factor to originate from fluctuations with anisotropic interactions. The deduction of the g factor behind the fluctuations is consistent with the spin-only state (g≈2.050(10) for CrSiTe3 and 2.039(10) for CrGeTe3). In addition, we will show that the abnormal enhancement of g shift, supplemented by specific heat and magnetometry measurements. We believe the results presented in this talk strongly suggest that CrSiTe3 exhibits a more typical two-dimensional nature than CrGeTe3 and may be closer to the quantum critical point.

**References:**

[1] B. Zappoli, D. Beysens, and Y. Garrabos, The ginzburg criterion, in Heat Transfers and Related Effects in Supercritical Fluids (Springer Netherlands, Dordrecht, 2015) pp. 371-372. [2] H. Beljers and J. Smit, Phil. Res. Rep 10 (1955). [3] K. Nagata, I. Yamamoto, H. Takano, and Y. Yokozawa, J. Phys. Soc. Jpn. 43, 857 (1977).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e990b75278b41650b030200dc271187b.png)
FIG. 1. (a) Coplanar waveguide with a rectangular single crystal placed parallel to the ab plane. The domain wall is represented by a blue solid line. (b) Illustration of three different resonant modes from the side view. (c) Frequency- and field-dependent FMR spectra (in-plane, β = π/2) for CrSiTe3 at 5 K. The solid lines represent fitting for the single domain mode and multi-domain mode. (d) Typical microwave transmission at 28 GHz sliced from (c). The resonant peak of the multidomain mode is formed by the superposition of a series of peaks with different angles α.

![](https://assets.underline.io/uploads/markdown_image/1/image/55280833cc11cb44be02ba76d089135f.jpg)
FIG. 3. (a,b) Temperature dependence of the effective g factor with the field applied both in-plane and out-of-plane for CST and CGT. The real g factor is calculated with g =1/3gab+2/3gc.

 Critical Fluctuations Induced g-factor Anisotropy in the Two-Dimensional Ferromagnetic Insulators CrXTe3 (X=Si, Ge)

Since the discovery of single-layer graphene in 2004, two-dimensional (2D) van der Waals (vdW) materials represented by it have demonstrated excellent electrical, magnetic, mechanical and optical physical properties under the structure of one or several layers of atomic thickness1. Based on these superior properties, 2D-layered vdW ferromagnetic materials have become the basis for constructing low-dimensional spintronics devices2, in which Fe3GeTe2 (FGT)3, Cr2Ge2Te64 and CrI35 as the main representative materials exhibit strong perpendicular magnetic anisotropy and other important characteristics in single layer. However, the Curie temperature (Tc) of above materials has not reached room temperature yet, which has greatly hinderer the subsequent development for device application. Therefore, recently researchers have been committed to explore 2D vdW ferromagnetic materials for room-temperature Tc in both theory and experiment. Here, we report that the interfacial engineering effect could effectively increase the Tc of the 2D vdW ferromagnetic material FGT from 230 K to 400 K, through heteroepitaxy with topological insulator of Bi2Te3. A theoretical calculation was further carried out to describe the magnetic properties by using first-principles calculations and the self-consistent Hubbard U approach (DFT+Uscf) together with the Monte Carlo (MC) simulations. After combination with Bi2Te3, the intralayer interactions in FGT was calculated to dramatically increase compared to that in pure FGT, well explaining the Tc enhancement. Our results may open up a new door to benefit the magnetic order in the 2D limit and realize spintronic devices based on 2D-layered vdW ferromagnetic materials with room temperature performances towards industrialization.

**References:**

1. Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6 (3), 183–191. 2. Lin, X.; Yang, W.; Wang, K. L.; Zhao, W. Two-Dimensional Spintronics for Low-Power Electronics. Nat. Electron. 2019, 2 (7), 274–283. 3. Liu, S.; Yuan, X.; Zou, Y.; Sheng, Y.; Huang, C.; Zhang, E.; Ling, J.; Liu, Y.; Wang, W.; Zhang, C.; Zou, J.; Wang, K.; Xiu, F. Wafer-Scale Two-Dimensional Ferromagnetic Fe3GeTe2 Thin Films Grown by Molecular Beam Epitaxy. npj 2D Mater. Appl. 2017, 1 (1), 30. 4. Gong, C.; Li, L.; Li, Z.; Ji, H.; Stern, A.; Xia, Y.; Cao, T.; Bao, W.; Wang, C.; Wang, Y.; Qiu, Z. Q.; Cava, R. J.; Louie, S. G.; Xia, J.; Zhang, X. Discovery of Intrinsic Ferromagnetism in Two-Dimensional van Der Waals Crystals. Nature 2017, 546 (7657), 265–269. 5. Huang, B.; Clark, G.; Navarro-Moratalla, E.; Klein, D. R.; Cheng, R.; Seyler, K. L.; Zhong, D.; Schmidgall, E.; McGuire, M. A.; Cobden, D. H.; Yao, W.; Xiao, D.; Jarillo-Herrero, P.; Xu, X. Layer-Dependent Ferromagnetism in a van Der Waals Crystal down to the Monolayer Limit. Nature 2017, 546 (7657), 270–273.

**Images:**

 Room-temperature ferromagnetism in 2D vdW Fe3GeTe2 and its potential application

Transition metal dichalcohedides (TMDs) are a group of compounds with the chemical formula MX2, where M is a transition metal (e.g. Mo, W), X is a chalcogen (Te, Se, S, etc.). Such materials have a layered structure, where metal atom sheets are sandwiched between two chalcogen sheets. The atomic bonding within the X-M-X layer is covalent, while the interlayer coupling is realized due to the van der Waals interaction. Therefore, such materials are considered structurally and electronically two-dimensional. In addition, TMDs attract attention for their promising electronic properties [1, 2]. TMD WTe2, MoTe2 and MoxW1-xTe2 are known to exhibit the topological Weyl semimetal (TWS) features when crystalized in an orthorhombic structure [3, 4]. Such materials have promising prospects for use in spintronics and micro- and nanoelectronics due to unusual electronic and magnetic properties (e.g. extremely large magnetoresistance, high charge carrier mobility, spin-polarized transport) owing to their nontrivial topology of the electronic band structure. Since TWSs were discovered relatively recently, at present such materials have not yet been extensively studied and are a hot research direction. Therefore, the purpose of this work is a comprehensive study of the electrical, galvanomagnetic and optical properties of the WTe2 single crystal. WTe2 single crystals were grown by the chemical vapour transport method as described in [5]. XRD analysis revealed that WTe2 have an orthorhombic structure with the lattice parameters a = 3.435(8) Å, b = 6.312(7) Å and c = 14.070(4) Å. The chemical composition of the samples was confirmed by X-ray microanalysis using a FEI Inspect F scanning electron microscope equipped with an EDAX attachment. The temperature dependences of the electrical resistivity ρ(T) and galvanomagnetic properties (magnetoresistivity and Hall Effect) were measured by the standard four-probe method in the temperature range from 1.8 to 300 K in magnetic fields of up to 9 T. An electric current flowed in the (00l) plane of the sample, and the magnetic field vector was directed perpendicular to the (00l) plane. The optical properties were measured using the Beattie method with one reflection from the (00l) plane of the samples in the spectral range of 0.17–5.0 eV at room temperature. The studies carried out showed that the temperature dependence of the electrical resistivity ρ(T) has a “metallic” behaviour and ρ monotonically increases with temperature from 20 to 860 μOhm×cm according to a quadratic law at T &lt; 60 K, reaches a linear dependence with a tendency to saturation at higher temperatures. T2 – dependence of ρ at low temperatures is known to be explained by several mechanisms, in particular, strong electron-electron scattering. In addition, in [6, 7], it is shown that the electron–phonon–surface interference scattering mechanism can lead to ρ ~ T2 in pure metals. Since the WTe2 single crystal has a layered structure, interface scattering of current carriers can cause ρ ~ T2. The magnetoresistivity Δρxx/ρ of the WTe2 single crystal is found to reach 1700% at T = 1.8 K in a magnetic field of 9 T. The field dependence Δρxx/ρ(B) changes according to a law close to quadratic in the investigated range of fields. This behaviour of the magnetoresistivity is inherent in compensated conductors with a closed Fermi surface in the region of high effective magnetic fields [8]. The state of electron-hole compensation leads to a high mobility of current carriers, which is also characteristic of TWSs. The Hall Effect data obtained allow us to conclude that the majority charge carriers are electrons with the concentration n ~ 1019 cm-3 and the mobility μ ≈ 7500 cm2/V×s at T = 1.8 K. Optical studies show that, in the investigated spectral region, the optical conductivity spectrum σ(E) is one broad band centered at 3.4 eV, formed by interband transitions. In the infrared region of the spectrum, low values of the imaginary part ε2 and positive values of the real part of ε1 of the complex permittivity are observed, which gives grounds to conclude that there is no contribution from free carriers of up to the boundary of the investigated spectral region. The revealed features, such as the large magnetoresistivity, high mobility of charge carriers, along with their relatively low concentration, insignificant contribution from free carriers to optical conductivity, are apparently the manifestation of the topological nature of the material, however, to clarify it, further studies are required. The research was carried out within the state assignment of the Ministry of Education and Science of the Russian Federation (theme “Spin”, No. AAAA-A18-118020290104-2), supported in part by RFBR (project No. 20-32-90069) and the Government of Russian Federation (Decree No. 211, Contract No. 02.A03.21.0006).

**References:**

1. J. A. Wilson and A. D. Yoffe, Adv. Phys., Vol. 18, p. 193 (1969). 2. P. K. Das, D. D. Sante, F. Cilento et al., Electron. Struct., Vol. 1, p. 014003 (2019). 3. Y. Wu, D. Mou, N. H. Jo et al., Phys. Rev. B, Vol. 95, p. 121113(R) (2016). 4. I. Belopolski, D. S. Sanchez, Y. Ishida et al., Nat. Commun., Vol. 7, p. 13643 (2016). 5. A. N. Domozhirova, S. V. Naumov, S. M. Podgornykh et al., Accepted for publication in Journal of Physics: Conference Series (2021). 6. V. E. Startsev, V. P. D'yakina, V. I. Cherepanov et al., Zh. Eksp. Teor. Fiz., Vol. 79, p. 1335 (1980). 7. V. V. Marchenkov, Low Temp. Phys., Vol. 37, p. 852 (2011). 8. I. M. Lifshitz, M. Ya. Azbel and M. I. Kaganov, Electronic Theory of Metals (Moscow: Nauka) (1971).

**Images:**

 Electrical Resistivity, Galvanomagnetic and Optical Properties of WTe2 Single Crystal

Chalcogenide thin films have become of interest in energy conversion, as thermoelectric materials, and for spintronic applications. Amongst them, antimony telluride (Sb2Te3) and bismuth telluride (Bi2Te3) have gained attention as Topological Insulators (TI) [1,2]. In order to make a step toward technology transfer, it is of major importance to achieve epitaxial quality-TI on large area, Si-based substrates. We have recently developed Metal Organic Chemical Vapor Deposition (MOCVD) processes to grow Bi2Te3 and Sb2Te3 thin films on top of 4” Si(111) substrates [1,3]. In this contribution we report clear evidence of the existence of topologically-protected surface states (TSS) in both ~90 nm-thick Bi2Te3 and ~30 nm-thick Sb2Te3 films by making use of magnetotransport (MR) and angle resolved photoemission spectroscopy (ARPES) studies. MR measurements were performed in the Van der Pauw configuration on ~1 x 1 cm2 samples without any processing or capping layers, in the 5-295 K temperature range. Following MR, samples were analysed by ex situ ARPES. In order to make this possible, prior to ARPES, the samples were cleaned under vacuum by 1.5 keV Ar ion sputtering for about 15 sec at 10-5 mbar. The sputtering cycles were repeated as many times as necessary to obtain a clean surface free of C and O contaminants, as verified by in situ X-ray photoelectron spectroscopy. As a final step, annealing under vacuum was performed at 290 °C for ~10 min, in order to recover the damage induced by Ar+ sputtering. Finally, flat and well-ordered surfaces were obtained, as checked by streaky reflection high-energy electron diffraction patterns. ARPES spectra were acquired at room temperature with a 100 mm hemispherical electron analyzer equipped with a 2D CCD detector (SPECS). The He I (21.22 eV) resonant line was used to excite photoelectrons and the energy resolution of the system was greater than 40 meV. Both Sb2Te3 and Bi2Te3 films exhibited a metallic behaviour, reaching a resistivity of 0.83 mΩ cm and 1.4 mΩ cm at 5 K, respectively. From Hall measurements, we identified the carrier type, being holes in Sb2Te3 and electrons in Bi2Te3, as expected. The evolution of the carrier density with the lowering of the temperature turned out to be different for the two samples: an increasing of the hole density for the Sb2Te3 and a decreasing of the electron density for the Bi2Te3 were observed. The corresponding mobilities displayed a maximum at 5 K, suggesting a suppression of bulk conduction at low temperature with a potentially higher contribution from the TSS. Quite interestingly, at 5 K, we detected a 430% increase of electron mobility in Bi2Te3, to be compared with a marginal 6% increase of hole mobility in the case of Sb2Te3. In both Sb2Te3 and Bi2Te3, MR measurements highlighted the presence of clear weak antilocalization (WAL) at low temperature, as shown in figures 1 and 2. WAL was interpreted in the framework of the Hikami-Larkin-Nagaoka (HLN) model as a first proof of the existence of 2D-conduction channels connected to TSS [4]. The two HLN parameters α (being connected to the number of conducting channels) and the coherence length (lφ) were extracted by fitting the magnetoconductance values (MC). The α values were 0.3 and 0.8 for Sb2Te3 and Bi2Te3 respectively, meaning that in Bi2Te3 the 2D-conduction is highly dominating when compared to Sb2Te3, in agreement with the corresponding temperature behaviour of electron and hole mobilities. At 5.5 K, the lφ reached the value of 74 nm in Bi2Te3 and 55 nm in Sb2Te3, again indicating a more favourable TSS-connected transport in Bi2Te3 than in Sb2Te3. Comparing the obtained α and lφ values with those reported in the literature for Bi2Te3 grown by MBE [5], we observe a very similar value for α and a slightly lower coherence length for our material. For what concerns Sb2Te3, the obtained α and lφ values are still lower than those previously reported for Sb2Te3 grown by MBE [6]. As clearly shown in the insets of figures 1 and 2, ARPES measurements evidenced the typical Dirac-like band structure represented by a linear dispersion relation in both Sb2Te3 and Bi2Te3 (Fermi level EF is placed at 0 eV). ARPES showed that for both Sb2Te3 and Bi2Te3, the Dirac point is not exactly at EF, cutting the valence band in Sb2Te3 and the conduction band in Bi2Te3, in accordance with Hall measurements. ARPES data were in nice agreement with the partial overlap between TSS and bulk conduction observed at low T in transport measurements. This is most likely the explanation why, for both materials, we did not reach the ideal α=1 value expected for a pure TSS conduction. Our results showed that the TI properties of Bi2Te3 and Sb2Te3 grown by MOCVD on large areas Si substrates, are approaching those obtained by state-of-the-art methods, such as MBE, thus making a fundamental step toward potential technology transfer of TI. On the other hand, to enhance the TSS contribution in the MOCVD-grown TIs and, therefore, their functionalities, the Fermi level must be moved in the bulk band gap, closer to the Dirac point. [7]

**References:**

[1] R. Cecchini, R. Mantovan,.. and M. Longo, Phys. Status Solidi PRL, Vol 12(8), 1800155 (2018) [2] Y. L. Chen, J. G. Analytis,.. and Z. X. Shen, Science 325, 178-181 (2009) [3] M. Rimoldi, R. Cecchini,.. and R. Mantovan, RSC Advances, Vol 10(34), 19936-19942 (2020) [4] S. Hikami, A. I. Larkin, Y. Nagaoka, Prog. Theor. Phys., Vol 63(2), 707-710 (1980) [5] A. Roy, S. Guchhait, .. and S. K. Banerjee, Apl, Phys. Lett., 102(16) 163118, (2013) [6] Y. Takagaki, A. Giussani, & R. Calarco, J. Phys.: Condens. Matter 25(34), 345801 (2013) [7] C. Chang, P. Tang,.. & Q. Xue, Phys. Rev. Lett.115(13) 136801 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/944d6ea6f697f1478d5927dfced2b881.jpg)
1) HLN fit of the magnetoconductance and ARPES analysis of a Sb2Te3 film.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc881fa1b2c83587acbe82b0640f1377.jpg)
2) HLN fit of the magnetoconductance and ARPES analysis of aBi2Te3 film.

 Magnetotransport and ARPES studies of large-area Sb2Te3 and Bi2Te3 topological insulators grown by MOCVD on Si

Superconductors (SCs) with Ising spin-orbit coupling (SOC), which internally pin electron spins to out-of-plane (OOP) directions such that OOP Cooper pairing can be stabilized against both orbital and paramagnetic effects of in-plane (IP) applied magnetic fields [1-3], have been of particular focus as a central ingredient for the topological protection of spin-triplet Cooper pairs and Majorana fermions [4,5]. Here, we experimentally examine how this so-called Ising superconductivity [1-3] affects the conversion efficiency of magnon spin to quasiparticle charge in a superconducting flake of 2-H NbSe2, transferred on top of Y3Fe5O12-based non-local magnon devices [6]. Comparing with a reference device composed of a spin-singlet superconducting Nb thin film [7], we show that the Y3Fe5O12-induced IP exchange spin-splitting in the NbSe flake is hindered by its inherent OOP SO-field, which in turn limits the transition-state enhancement of spin-to-charge conversion efficiency. Our results may have implications for proximity-controlled equal-spin tripet pairing [8] via tuning of IP exchange and OOP SO fields in Ising SC/insulating ferromagnet bilayers.

**References:**

[1] J. M. Lu, O. Zeliuk, I. Leermakers, N. F. Q. Yuan, U. Zeitler, K. T. Law, and J. T. Ye, Science 350, 1353 (2015). [2] Y. Saito et al., Nature Phys. 12, 144 (2016). [3] X. Xi, Z. Wang, W. Zhao, J. Park, K. T. Law, H. Berger, L. Forro, J. Shan, and K. F. Mak, Nat. Phys. 12, 139 (2016). [4] S. M. Frolov, M. J. Manfra, and J. D. Sau, Nat. Phys. 16, 718 (2020). [5] Benjamin T. Zhou, Noah F. Q. Yuan, Hong-Liang Jiang, and K. T. Law, Phys. Rev. B 93, 180501(R) (2016). [6] A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Nat. Phys. 11, 453 (2015). [7] K.-R. Jeon, J.-C. Jeon, X. Zhou, A. Migliorini, J. Yoon, and S. S. P. Parkin, ACS Nano 14, 15874 (2020). [8] J. Linder and J. W. A. Robinson, Nat. Phys. 11, 307 (2015).

**Images:**

 Role of Ising Superconductivity in the Transition-State Enhancement of Magnon Spin to Quasiparticle Charge Conversion Efficiency

In contrast to the Hall effect, the nonlinear Hall effect (NLHE) can produce a transverse voltage in zero magnetic field [1]. The NLHE is a second-order phenomenon, which exhibits two components; one is the voltage oscillating at twice the frequency 2ω of the driving alternating current and the other is a d.c. component that is generated due to the rectification effect. Therefore, the NLHE can be utilized in applications requiring frequency doubling or rectification such as energy harvesting, wireless communications and IR detectors [2,3]. However, it requires NLHE to be detected at room temperature. Despite of several studies of NLHE in topological materials and 2D materials, the room-temperature NLHE has not yet been achieved [4,5]. In this work, we report the room-temperature NLHE in a type-II Weyl semimetal TaIrTe4, which hosts a robust NLHE due to broken inversion symmetry and large band overlapping at the Fermi level. The NLHE is present only when the electric field is applied along the axis of the mirror plane (a-axis of the crystal). We also observe a temperature-induced sign inversion of NLHE in TaIrTe4. Our theoretical calculations suggest that the observed sign inversion is a result of temperature-induced shift in the chemical potential indicating a direct correlation of NLHE with the electronic structure at the Fermi surface. Finally, based on the observed room-temperature NLHE in TaIrTe4 we demonstrate the wireless RF rectification with zero external bias and magnetic field. As shown in Fig. 1(b), an incident electric field along a-axis (Ea) generates a rectified voltage along b-axis (Vb), whereas, there is no rectification when the incident electric field is along b-axis (Eb) in consistent with the symmetry constraints of NLHE. This work opens a door to realizing room temperature applications based on the NLHE in Weyl semimetals.

**References:**

[1] I. Sodemann and L. Fu, Phys. Rev. Lett., 115, p.216806 (2015) [2] H. Isobe, S.-Y. Xu, and L. Fu, Sci. Adv., 6, p.eaay2497 (2020) [3] G. Pacchioni, Nat. Rev. Mater., 4, p.514 (2019) [4] Q. Ma, S.-Y. Xu, H. Shen, Nature, 565, p.337 (2019) [5] K. Kang, T. Li, E. Sohn, Nat. Mater., 18, p.324 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1c5c29957fb9c4db9817e1c9249c7463.jpg)
Fig. 1. (a) Schematic of the rectifier fabricated on Td-TaIrTe4. Patch antenna with a high directivity and gain of 3 dBi at ~2.4 GHz is used for electromagnetic radiation. The Hall bar device, utilizing the room-temperature NLHE in TaIrTe4, rectifies the incident electric field along a-axis (Ea) and generates a d.c. along the transverse direction b-axis (Ib). (b) The rectified d.c. voltage measured along b-axis (Vb) as a function of frequency while aligning the incident electric field at four different angles (θ = 0°, 90°, 180°, and 270°) relative to a-axis as shown in the inset.

 Room Temperature Nonlinear Hall Effect and Wireless RF Rectification in Weyl Semimetal TaIrTe4

An outstanding feature of topological quantum materials is their unique spin topology in the electronic band structures with novel charge to spin conversion effects. Here, I will present the novel charge to spin conversion phenomenon in topological insulators, Weyl semimetals, and its van der Waals heterostructures with graphene. The discovery of topological Weyl semimetals has revealed opportunities to realize several extraordinary physical phenomena in condensed matter physics. Weyl semimetals with strong spin orbit coupling, broken inversion symmetry, and novel spin textures are predicted to exhibit a charge to spin conversion effect that can efficiently convert the charge current to a spin current. We report a direct experimental observation of charge-spin conversion and its inverse effect in semimetal WTe2 at room temperature as shown in Fig. 1 (Ref. 1). We also observe an evolution of the charge to spin conversion signals from WTe2 and graphene hybrid device with a geometrical design (Ref. 2). The spin precession measurements of the signal at different gate voltages and ferromagnet magnetization show the robustness of the charge to spin conversion in WTe2 at room temperature. These results can be useful for designing heterostructure devices and in the architectures of 2D spintronic circuits. We could also detect an unconventional charge to spin conversion in WTe2, which is different from the conventional spin Hall and Rashba Edelstein effects (Ref. 3). Such a large and unconventional spin polarization can be possible in WTe2 due to a reduced crystal symmetry combined with its large spin Berry curvature, spin orbit interaction with a novel spin texture in the Fermi states. A robust and practical method is demonstrated for electrical creation and detection of such a spin polarization in WTe2 using both charge to spin conversion and its inverse phenomenon and utilized it for efficient spin injection and detection in the graphene channel up to room temperature. These findings open opportunities for utilizing Weyl materials WTe2 as nonmagnetic spin sources in all electrical van der Waals spintronic circuits and high performance nonvolatile spintronic technologies. Unique electronic spin textures in topological insulators are promising for emerging spin-orbit driven memory and logic technologies. However, there are several challenges related to enhancing their performance, electrical gate tunability, interference from trivial bulk states, and heterostructure interfaces. We address some challenges by integrating 2D graphene with a 3D topological insulator (TI) in van der Waals heterostructures to take advantage of their remarkable spintronic properties and engineer proximity induced spin orbit phenomena (Ref. 4). In these heterostructures, we experimentally demonstrate a gate tunable spin galvanic effect (SGE) at room temperature, allowing for efficient conversion of a nonequilibrium spin polarization into a transverse charge current (Ref. 5). Systematic measurements of SGE in various device geometries via a spin switch, spin precession, and magnetization rotation experiments establish the robustness of spin to charge conversion in the graphene and TI heterostructures. Importantly, using a gate voltage, we reveal a strong electric field tunability of both amplitude and sign of the spin galvanic signal. These findings provide an efficient route for realizing all electrical and gate tunable spin orbit technology using TIs and graphene in heterostructures. Fig. 1. Charge to spin conversion in WTe2 at room temperature. a. Device geometry and Hanle measurement of conventional charge to spin conversion in WTe2 (Ref. 1). B. Measurement of unconventional charge to spin conversion in WTe2. The measurement of spin valve and Hanle signals both in parallel and antiparallel configurations at room temperature show the unconventional nature of charge to spin conversion (Ref 3). Fig. 2. Spin galvanic effect in graphene and topological insulator heterostructure at room temperature. a. A schematic representing the spin galvanic effect, where spin polarized carriers diffuse in the graphene and TI heterostructure, acquire a transverse momentum and produce a charge current. b. A scanning electron microscopy picture of a graphene and TI hybrid device and measurement scheme. c. Schematics of band structures of proximitized graphene develop Rashba spin split bands in the valence and conduction bands. d. The SGE signal R measured with the inplane magnetic field Bx. e. The SGE was detected via spin precession with the out of plane field Bz at different gate voltages in the valence and conduction band of proximitized graphene (Ref 5).

**References:**

1. Observation of charge to spin conversion in Weyl semimetal at room temperature. B Zhao, D Khokhriakov, Y Zhang, H Fu, B Karpiak, AM Hoque, X Xu, Y Jiang, B Yan, SP Dash. Phys. Rev. Res. 2 (1), 013286 (2020). 2. Charge-spin conversion signal in WTe2 van der Waals hybrid devices with a geometrical design. B. Zhao, A. Md. Hoque, D. Khokhriakov, B. Karpiak, S.P. Dash. Appl. Phys. Lett. 117, 242401 (2020). 3. Unconventional charge-to-spin conversion Weyl Semimetal WTe2. B Zhao, B Karpiak, D Khokhriakov, A Johansson, AM Hoque, X Xu, Y Jiang, I Mertig, SP Dash. Advanced Materials, 2000818 (2020). 4. Tailoring emergent spin phenomena in Dirac material heterostructures. D Khokhriakov, A. W. Cummings, K Song, M Vila, B Karpiak, A Dankert, S Roche and SP. Dash. Science Advances, 4, 9, eaat9349 (2018). 5. Gate-tunable Spin-Galvanic Effect in Graphene - Topological insulator van der Waals Heterostructures at Room Temperature. D Khokhriakov, AM Hoque, B Karpiak, SP Dash. Nature Communication 11, 3657 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/42eab8e2dc3b7cce2be8f59122fff436.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/4c4b9ee8b0fe7d9ef3c951698c9f42bd.jpg)

 Charge Spin Conversion in Topological Materials and Heterostructures INVITED

Topological chiral spin textures, such as chiral domain walls and magnetic skyrmions, offer a unique opportunity to bring topology into room-temperature spintronic devices [1]. The stability of chiral spin textures is defined by the competition of Heisenberg exchange coupling, magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction (DMI) [2], which can be engineered by the customized magnetic interfaces. Fe4N has been considered as a promising material in spintronic devices thanks to the high saturation magnetization, high Curie temperature and high spin polarization [3]. However, low magnetocrystalline anisotropy seriously prevents it from being an ideal candidate for magnetic information storage. The traditional approach for perpendicular magnetic anisotropy (PMA) and interfacial DMI engineering is to use ferromagnet (FM)/oxide interfaces [4], multilayer structures comprising FM/nonmagnetic metal (NM) interfaces [5], or graphene/FM interfaces [6]. Recent theoretical prediction and experimental evidence have triggered interest in the hybrid interfaces between 3d FMs and two-dimensional transition-metal dichalcogenides (2D TMDs) [7,8]. The potentials of 2D TMDs in pushing magnetic information storage to the atomic thin limit, the ability to form hybrid interfaces without the need for lattice matching, as well as the attractive semiconducting electronic band structures, provide advantages for magnetization manipulation at atomic-scale interfaces. For 2D TMDs, The lack of inversion center in the crystal structure provides significant advantage, which is already used to obtain unconventional PMA at 2D TMDs/FM interfaces. In addition, 2D TMDs are very promising to enhance the DMI parameter at 2D TMDs/FM interfaces owing to their intrinsic spin-orbit coupling (SOC). In this work, the magnetic anisotropy and DMI of MoS2/Fe4N(111) interfaces are investigated via first-principles calculations. It is found that the large PMA and anticlockwise chiral DMI appear at the MoS2/Fe4N(111) interface. Strong variations of the PMA and DMI parameters are demonstrated by applying in-plane biaxial strain of the interfaces. The variations of PMA and DMI under strain can be attributed to the hybridization of in-plane and out-of-plane d orbitals in interfacial Fe atom layer, respectively. These results show the possibility of stabilizing chiral spin textures in the 2D TMDs/FM systems. Further, the method of strain controlling PMA and DMI at MoS2/Fe4N interface opens another pathway for the development of spintronic devices using 2D TMDs. This work is supported by National Natural Science Foundation of China (51871161 and 52071233).

**References:**

[1] A. Fert, N. Reyren and V. Cros, Nat. Rev. Mater. 2, 17031 (2017). [2] A. Fert and P. M. Levy, Phys. Rev. Lett. 44, 1538 (1980). [3] W.B. Mi, Z.B. Guo, X.P. Feng, et al, Acta Mater. 61, 6387 (2013). [4] S. Ikeda, K. Miura, H. Yamamoto, et al, Nat. Mater. 9, 721 (2010). [5] H. Yang, A. Thiaville, S. Rohart, et al, Phys. Rev. Lett. 115, 267210 (2015). [6] H. Yang, G. Chen, A. A. C. Cotta, et al, Nat. Mater. 17, 605 (2018). [7] B. Peng, Q. Li, X. Liang, et al, ACS Nano 11, 12257 (2017). [8] A. Kumar, A. K. Chaurasiya, N. Chowdhury, et al, Appl. Phys. Lett. 116, 232405 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/df9e4fd5d68e952257b4cf29776310b7.jpg)
Figure 1. Top views of Fe4N(111)-1×1 and MoS2-√3×√3. (b) Side view of optimized MoS2/Fe4N interface. (a) Magnetic anisotropy energy as a function of strain at the MoS2/Fe4N interface

![](https://assets.underline.io/uploads/markdown_image/1/image/6667324b8ab4d9d9029055b1f0d7d374.jpg)
Figure 2. (a) Total DMI strength dtot and micromagnetic DMI parameter D as a function of strain at the MoS2/Fe4N interface. (b) Layer resolved SOC energy differences associated DMI under strains

 Strain-Tailored Magnetic Anisotropy and Dzyaloshinskii-Moriya Interaction at MoS2/Fe4N(111) Interface

The interplay between symmetry breaking and topological electronic structure is crucial to design anomalous transport properties in materials. Materials with strong or quantum electromagnetic responses have an extensive impact on the development of data storage, information processing, energy conversion, etc. In magnetic materials, the anomalous transport of anomalous Hall effect, anomalous Nernst effect, and magneto-optical effect et al. can be understood from the Berry curvature of the electronic band structures. Two typical band structures of Weyl points and nodal line band structures host strong local Berry curvature. Since the Berry curvature is time-reversal symmetry odd, such strong Berry curvatures can lead to strongly enhanced anomalous transport signals. With this guiding principle, we studied the anomalous Hall effect in magnetic Weyl semimetal Co3Sn2S2 [1-3] and magnetic nodal line semimetal in Heusler compound Co2Mn(Ga/Al) [4]. With a mirror symmetry, the inverted band structure forms a nodal loop in the absence of spin-orbital coupling. This nodal line can be broken by spin-orbital coupling and a bandgap opens, which generates non-zero Berry curvature in the bandgap and forms a hot loop, see Figure 1a-b. Such strong Berry curvature in the magnetic system can lead to a strongly enhance or even quantized anomalous Hall effect. We applied this idea to real materials of magnetic Heusler compounds Co2Mn(Ga/Al). Protected by mirror symmetries the band inversion between the bands with opposite mirror eigenvalue forms three gapless nodal lines in the kx=0, ky=0, and kz=0 mirror planes, respectively. With spin-orbital coupling, the symmetry of the system is reduced. Taking magnetic along z, the mirror symmetries in kx=0 and ky=0 planes are broken, which leads to band anti-crossings with strong local Berry curvature locating in the opened bandgap around original nodal lines, see Figure 1d. Integral of the Berry curvature in the whole k-space gives a large intrinsic anomalous Hall conductivity reaching ~1500 to ~2000 S/cm [4]. Weyl points is another typical band structure and present as the Berry curvature monopole, and therefore naturally results in a strong anomalous Hall effect. In ideal models with only one pair of Weyl points locating at the Fermi level, the intrinsic anomalous Hall conductivity can be presented as the combination distance of Weyl points and the quantized anomalous Hall conductance. Inspired by these excellent relations, we studied the anomalous Hall effect in Co3Sn2S2, and a new record of three-dimensional anomalous Hall angel (~20%) was observed, which offers the 1st three-dimensional material with both strong anomalous Hall conductivity and anomalous Hall angle [1]. It indeed shows as a Weyl semimetal from electronic band structure analysis. One crucial symmetry in Co3Sn2S2 is the three mirror planes parallel to the c direction, which results in three pairs of nodal lines connected by a c3z rotation symmetry. Because the magnetization is aligned along the z-direction, the mirror symmetries are broken by spin-orbital coupling. Meanwhile, one pair of Weyl points with opposite chirality remains along each of the former nodal lines, leading to the so large anomalous Hall effect. Though the strong anomalous Hall effect provides a promising signature for the existence of Weyl and nodal line band structure. Our transport work about Co3Sn2S2 and Co2MnGa/Al inspired the direct band structure detection by ARPES and STM [5-7], and they are in turn became the 1st experimentally verified magnetic Weyl semimetal and nodal line semimetal, respectively. Applying temperature gradient instead of the electrical field, the Weyl points and nodal lines induced Berry curvature can also lead to strongly enhanced anomalous Nernst effect. From our theoretical calculations and experimental measurements, the anomalous Nernst conductivity can reach around 3 and 6 A/(m-K) in Co3Sn2S2 [8] and Co2MnGa [9], respectively, with Co2MnGa keeping the record. Owing to the large anisotropy, Co3Sn2S2 is, so far, the only material with a large anomalous Nernst effect with zero magnetic fields. In addition, very recently, a giant magneto-optical response was observed in Co3Sn2S2 with the applied field from polarized light [10]. Very recently, a strong interest in antiferromagnets is rising. In an antiferromagnet without such kind of joint TO symmetry to reverse Berry curvature, it allows the existence of anomalous Hall effect, anomalous Nernst effect, magneto-optical responses, and special spin current, etc. The nonzero anomalous Hall effect in antiferromagnets was proposed as early as 2001 in distorted non-linear magnetic structures [11]. However, its experimental realization was not successful until 2015 [12-16]. This understanding can be further expanded into collinear antiferromagnets. Different from non-linear antiferromagnets, the collinear antiferromagnetic structure can be usually understood from two sublattices connected by translation of inversion operation. Therefore, there are mainly two ways to break the joint symmetry, to replace the magnetic atoms connected by the joint TO symmetry, or change the the nonmagnetic sites. With this understanding, we predicted the anomalous Hall and Nernst effect in anti-Heusler Weyl semimetal Ti2MnAl [17-18].

**References:**

[1] Enke Liu, Yan Sun, Nitesh Kumar, et al. Nat. Phy., 14, 1125 (2018) [2] Qiunan Xu, Enke Liu, Wujun Shi, et al. Phy. Rev. B 97, 235416 (2018) [3] Lukas Muechler, Enke Liu, Jacob Gayles, et al. Phy. Rev. B 101, 115106 (2020) [4] Kaustuv Manna, Lukas Muechler, Ting-Hui Kao et al. Phy. Rev. X 8, 041045 (2018) [5] D. F. Liu, et al. Science 365, 1282 (2019) [6] Noam Morali, et al. Science 365, 1286 (2019) [7] Ilya Belopolski et al. Science 365, 1278 (2019) [8] Satya N. Guin, Praveen Vir, Yang Zhang et al. Adv. Mater. 31, 1806622 (2019) [9] M. Ikhlas, T. Tomita, and T. Koretsune, et al. Nat. Phys. 13, 1085 (2017) [10] Y. Okamura, S. Minami, Y. Kato et al. Nat. Comm. 11, 4619 (2020) [11] R. Shindou, and N. Nagaosa, Phys. Rev. Lett. 87, 116801 (2001) [12] H. Chen, H., Q. Niu, and A. H. MacDonald, A., Phys. Rev. Lett. 112, 017205 (2014) [13] J. Kübler, and C. Felser, Europhys. Lett. 108, 67001 (2014) [14] S. Nakatsuji, N. Kiyohara, and T. Higo, Nature 527, 212–215 (2015) [15] A. Nayak, et al. Sci. Adv. 2, e1501870 (2016). [16] Z. Q. Liu1, H. Chen, J. M. Wang, et al. Nat. Elec. 1, 172 (2018) [17] Wujun Shi, Lukas Muechler, Kaustuv Manna, et al. Phy. Rev. B 97, 060406(R) (2018) [18] Jonathan Noky, Jacob Gayles, Claudia Felser, and Yan Sun, Phy. Rev. B 97, 220405(R) (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d01cd4614a8a3acd393ef3a3b74c6d6d.jpg)
Figure 1 (a-b) Nodal line band structure generated and non-zero Berry curvature hot ring located in the bandgap. (c-d) Crystal structure and Berry curvature distribution for Co2MnGa. [Ref.4]

 Anomalous transport in magnetic topological materials

Two-dimensional magnetic materials have attracted much attention since they provide new opportunities for the development of multifunctional devices.1-2 Half-metal materials with 100% spin polarization are highly desired in spin-based devices. Because they are not only the ideal electrode materials for the magnetic tunneling junctions (MTJ),3 but also can realize high efficient spin injection to the semiconductors.4 Janus magnetic materials have broken the time and space symmetries simultaneously, which may show novel physical properties comparing with their counterparts.5-6 However, the electronic and magnetic properties of Janus half-metal materials are still unclear, so we selected the half-metal, 1T-FeCl2 monolayer,7-8 as the prototype to study the electronic and magnetic properties of its Janus structures, and the stains are applied to tunable their properties in this work. The FeXY (X, Y = Cl, Br and I) monolayers are half-metals and their ferromagnetism stem from the super-exchange interaction according to the GKA theory. The Curie temperature (Tc) of Janus FeClBr, FeClI and FeBrI are 28, 21 and 29 K, respectively (Figure 1 (a)). In the meantime, the Tc under biaxial strains is investigated and the Tc are 54, 42 and 61 K at e = -6%, increasing about 100% comparing with the unstrained FeXY monolayer. Besides, the MAE of FeXY strongly relies on the angle of magnetization and increases considerably under compressive strain. The MAE of FeBrI as an example is shown in Fig. 1 (c), the unstrained FeBrI is IMA, but translating from IMA to PMA when e &lt; 0 and e &gt; 2%, this will help to increase the density of storage. And the absolute value of MAE enhances one order magnitude when the e = -6%. It is demonstrated that the compressive strains effectively enhance the ferromagnetism of FeXY. The atom-resolved MAE shows that the main contributions of MAE come from Fe and I atoms. Additionally, the MAE of I atom translates from IMA to PAM when e &lt; -2% which induce the translation of total MAE. To further explicate the change of MAE, the orbital-resolved MAE of FeBrI is calculated and the results plotted in Figure 2. The I atom is IMA at e = 0%, because the matrix element differences between px and py orbitals are negative and the absolute value is larger than the py and pz orbitals. However, the px and py orbitals hybridization translate to the positive at e = -6%, which make the magnetic anisotropy translate from IMA to PMA. Our studies provide an example of the 2D Janus half-metal materials and enrich the 2D magnetic material library. This work is supported by National Natural Science Foundation of China (51871161 and 52071233).

**References:**

[1] B. Huang, G. Clark, E. N. Moratalla, et al, Nature, 546, 270-273 (2017). [2] C. Gong, L. Li, Z. Li, et al, Nature, 546, 265-269 (2017). [3] K. I. Kobayashi, T. Kimura, H. Sawada, et al, Nature, 395, 677-680 (1998). [4] S. Sugahara and M. Tanaka, Appl. Phys. Lett., 84, 2307-2309 (2004). [5] Q. F. Yao, J. Cai, W. Y. Tong, S. J. et al, Phys. Rev. B, 95, 165401 (2017). [6] A. Y. Lu, H. Zhu, J. Xiao, et al, Nat. Nanotechnol., 12, 744-749, (2017). [7] E. Torun, H. Sahin, S. K. Singh et al, Appl. Phys. Lett., 106, 192404 (2015). [8] M. Ashton, D. Gluhovic, S. B. Sinnott, et al, Nano Lett., 17, 5251-5257 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ff113acc1f69a9ea300e35dc593fafd1.jpg)
Figure 1. The Curie temperature of Janus FeXY (X, Y = Cl, Br and I) monolayers as a function of temperature at e=0 (a) and -6% (b). Angular dependence MAE of FeBrI monolayer under different strain (c)

![](https://assets.underline.io/uploads/markdown_image/1/image/bcf570ab2cd2948b644687dfd355892c.jpg)
Figure 2. Orbital-resolved MAE of FeBrI monolayer under e = -6%, 0% and 6%.

Nonlinear anomalous Hall effect in van der Waals ferromagnet

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Nonlinear anomalous Hall effect in van der Waals ferromagnet

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Critical Fluctuations Induced g-factor Anisotropy in the Two-Dimensional Ferromagnetic Insulators CrXTe3 (X=Si, Ge)

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Ultra-thin Heusler films and lamellae that host non-collinear spin textures

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