France



Curvilinear magnetism is a rapidly developing research area of modern magnetism which deals with curved magnetic wires and curved magnetic films [1]. By extending planar geometries into three dimensional space, there appear new, sometimes, unexpected physical effects, stemming from mutual interplay between the geometrical properties of the underlying substrate and the magnetic order parameter. By tailoring curvature and topology of the conventional magnetic materials there appears a possibility to control material response leading to modification or even launching new functionalities [2, 3]. This is granted by complementary expertise and advances of fundamental researched, materials sciences and technologies.&lt;br/&gt;&lt;br/&gt;This talk focuses on the peculiarities emerging from geometrically curved magnetic objects, including 3D bent and twisted curved wires and films. The curvilinear geometry manifests itself in emergent anisotropy and chiral interactions. These curvature-induced interactions can be local stemming from the exchange energy [4, 5], but also can be nonlocal due to magnetostatics [6]. As a consequence, family of novel curvature-driven effects emerge, which include magnetochiral effects and topological patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking etc. Current and future challenges of the curvilinear magnetism will be discussed.

**References:**

[1] E. Y. Vedmedenko, R. K. Kawakami, D. D. Sheka et al, JPhysD, vol. 53 , p.453001 (2020)&lt;br/&gt;[2] R. Streubel, P. Fischer, F. Kronast et al, JphysD, vol. 49, p.363001 (2016)&lt;br/&gt;[3] P. Fischer P, D. Sanz-Hernández, R. Streubel et al, APL Materials, vol. 8, p. 010701 (2020)&lt;br/&gt;[4] Y. Gaididei, V. P. Kravchuk and D. D, Sheka, PRL, vol. 112, p. 257203 (2014)&lt;br/&gt;[5] D. D. Sheka, V. P. Kravchuk and Y. Gaididei, JPhysA, vol. 48, p.125202 (2015)&lt;br/&gt;[6] D. D. Sheka, O. V. Pylypovskyi, P. Landeros et ak, Communications Physics, vol. 3, p. 128 (2020)

**Images:**





INTERMAG 2021

 Curvilinear Magnetism INVITED

INTERMAG 2021 Welcome Video



	
<figure class="video_container">
 <iframe src="https://screencast-o-matic.com/player/crflqFVnUpZ?v=6&ff=1&title=0&controls=1" width=640 height=360 frameborder="0" allowfullscreen="true"> </iframe>
</figure>

Want to buy a ticket? 

Register for INTERMAG 2021 here

[![](https://assets.underline.io/uploads/markdown_image/1/image/17ce76e7960db633258024eef8d6da7f.png)](https://intermag.org/register)

Got your ticket, but still can’t access the event?

Contact us and our team will look into it.

Curvilinear magnetism is a rapidly developing research area of modern magnetism which deals with curved magnetic wires and curved magnetic films [1]. By extending planar geometries into three dimensional space, there appear new, sometimes, unexpected physical effects, stemming from mutual interplay between the geometrical properties of the underlying substrate and the magnetic order parameter. By tailoring curvature and topology of the conventional magnetic materials there appears a possibility to control material response leading to modification or even launching new functionalities [2, 3]. This is granted by complementary expertise and advances of fundamental researched, materials sciences and technologies. This talk focuses on the peculiarities emerging from geometrically curved magnetic objects, including 3D bent and twisted curved wires and films. The curvilinear geometry manifests itself in emergent anisotropy and chiral interactions. These curvature-induced interactions can be local stemming from the exchange energy [4, 5], but also can be nonlocal due to magnetostatics [6]. As a consequence, family of novel curvature-driven effects emerge, which include magnetochiral effects and topological patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking etc. Current and future challenges of the curvilinear magnetism will be discussed.

**References:**

[1] E. Y. Vedmedenko, R. K. Kawakami, D. D. Sheka et al, JPhysD, vol. 53 , p.453001 (2020) [2] R. Streubel, P. Fischer, F. Kronast et al, JphysD, vol. 49, p.363001 (2016) [3] P. Fischer P, D. Sanz-Hernández, R. Streubel et al, APL Materials, vol. 8, p. 010701 (2020) [4] Y. Gaididei, V. P. Kravchuk and D. D, Sheka, PRL, vol. 112, p. 257203 (2014) [5] D. D. Sheka, V. P. Kravchuk and Y. Gaididei, JPhysA, vol. 48, p.125202 (2015) [6] D. D. Sheka, O. V. Pylypovskyi, P. Landeros et ak, Communications Physics, vol. 3, p. 128 (2020)

**Images:**

technical paper

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

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.

 Nonlinear anomalous Hall effect in van der Waals ferromagnet

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%.

 Tunable Electronic and Magnetic Properties of Two-dimensional Janus Magnetic Materials

Two-dimensional magnetic (2DM) van der Waals (vdW) materials have attracted significant attention over the last few years, after the first experimental demonstration of ferromagnetism persisting down to the monolayer limit [1]. Since then, new vdW 2DM materials emerge frequently, covering a broad spectrum of diverse properties also found in other 3D counterpart systems – ferro/antiferromagnetism (FM/AFM), metallic/semiconducting behaviour and many non-trivial electronic phases. Out of this expanding pool of 2DM, one category that stands out is FMs with strong out-of-plane anisotropy, which present superior qualities desirable for magnetic random-access memory and other spintronic applications. Fe3GeTe2 (FGT) is a prominent member of this family that features a lot of interesting properties, such as a relatively high, thickness-dependent Tc (150 K – 220 K) that can be tuned to room temperature by doping, high spin-orbit coupling originating from a strongly correlated electronic system, application in spin valves, topological phases and Kondo behaviour, amongst others [2]. FGT is a quasi-2D itinerant ferromagnetic metal, and its structure consists of Fe3Ge layers sandwiched by single-atom layers of Te. Among the FGT layers, Te atoms are bonded together by vdW forces, allowing for exfoliation of the material in ultra-thin flakes with the scotch-tape exfoliation technique. Despite the considerable efforts that have already taken place in order to determine the underlying micromagnetic structure and behaviour of FGT, its highly anisotropic and non-trivial nature has not yet allowed for a consensus in the relevant scientific community. Our work therefore aims to shed light for the case of quasi-bulk FGT, by combining magnetic susceptibility measurements and Raman spectroscopy [3]. Our magnetometry study picks up the main point of controversy around FGT, which is a kink found below the Curie temperature, roughly at 150 K. This possible magnetic transition has been shown to represent a FM to AFM interlayer coupling between the vdW bonded layers [5], however it has been argued that this can be due to different reasons, such as domain wall pinning effects. A temperature dependent Raman study can provide further insight by indirectly detecting a phase change – electronic reconfiguration leads to a qualitative change in the Raman signal, and that is what our results suggest (Fig. 1). The separation between the Raman peaks is a possible sign of this magnetic transition, a signature that often accompanies other 2D material related properties and transitions however rarely related to magnetic properties. Additionally, it has been shown that variations in the sample history, i.e. temperature and applied magnetic field (as well as number of atomic layers), result in different magnetic phases, such as labyrinth and stripe domains, bubble-like lattice and possibly skyrmion phases [4]. Our systematic magnetometry study provides insight regarding the formation of these different magnetic states, following three different magnetization protocols, namely: zero-field cooling (ZFC), field cooling (FC) and field warming (FW) methods (Fig. 2). The magnetometry results are correlated to Raman responses, examined up to 2nd order. Particular interest arises from a prominent feature (a 2nd kink below 150 K) that has not been observed before – suggesting the existence of possibly another magnetic phase. Our results advance the understanding of the underlying mechanisms of Fe3GeTe2, an important 2DM that is often incorporated in spintronic vdW heterostructures and devices.

**References:**

C. Gong, L. Li and X. Zhang, Nature, Vol 546, p. 265-269 (2017) Y. Deng, Y. Yu and Y. Zhang, Nature, Vol 563, p. 94-99 (2018) L. Du, J. Tang and Z. Sun, Adv. Funct. Mat., Vol 29 (2019) H. Wang, C. Wang and J. Li, APL, Vol 116 (2020) J. Yi, H. Zhuang and Z. Gai, 2D Materials, Vol 4 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c55428df00e41337ff9c7e60ce6809c6.jpg)
Fig. 1: Temperature-dependent Raman response: a) 2nd order Raman susceptibility. b) Temperature dependent separation of the peaks @150 and @120 cm-1

![](https://assets.underline.io/uploads/markdown_image/1/image/5131d011fc9a59caf031435ea40dcbe4.jpg)
Fig. 2: Magnetization measurements of quasi-bulk FGT: FC, FW and ZFC protocols obtained under different applied magnetic fields. a) Happl. = 10 mT, b) Happl. = 50 mT, c) Happl. = 100 mT, d) a magnetometry feature (kink) position in temperature under varied applied H field (arrows in a, b, c)

 Correlation of Magnetic Properties of van der Waals Itinerant Magnet Fe3GeTe2 using Magnetometry and Raman Spectroscopy

Magnetic domain walls (DWs) in a Weyl semimetal can induce localized charges and be treated as local axial gauge fields.[1] Dynamics and textures of magnetic DWs may largely alter the electronic behaviors in a Weyl semimetal system.[2] In this work, we imaged the spontaneous magnetization and magnetic susceptibility of a ferromagnetic (FM) Weyl semimetal candidate CeAlSi using scanning SQUID microscopy [3], [4]. We observed the ferromagnetic DWs lined-up with [100] direction (or other degenerate directions) and the coexistence of stable and metastable domain phases, which arise likely due to the magnetoelastic and magnetostriction effects and are highly tunable with small strains. The temperature evolution of the FM domains shows that stable domains shrink while metastable domains grow and eventually collapse to narrow domain-wall-like features as temperature rises towards Tc ~ 8.3K.(fig.1) We applied in-plane external field as the CeAlSi sample was cooled down to ~8K, showing that the pattern of FM domains is strongly correlated with both the amplitude and the orientation of the external field. The area of stable domains increases with field (fig.2) and reaches maximum when the field is parallel to the easy axis of the CeAlSi crystal. Our results suggest these heterogeneous phases can be manipulated and therefore provide a practical way to study the interplay between magnetism and electronic properties in Weyl system.

**References:**

[1] Y. Araki, A. Yoshida, and K. Nomura, Phys Rev B, vol. 98, no. 4, p. 045302, Jul. 2018 [2] J. D. Hannukainen, Y. Ferreiros, A. Cortijo, and J. H. Bardarson, Phys. Rev. B, vol. 102, no. 24, p. 241401, Dec. 2020 [3] H.-Y. Yang et al., ArXiv200607943 Cond-Mat, Jun. 2020 [4] B. Xu, J. Franklin, H.-Y. Yang, F. Tafti, and I. Sochnikov, ArXiv201106168 Cond-Mat, Nov. 2020

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/03e8ecc3bef65d96e91883ee81c1252f.jpg)
Figure 1. The temperature evolution of the magnetic domains in the CeAlSi crystal. Upper row: dc magnetizations in flux units. Middle and lower rows are the in-phase component and the out-of-phase component of the ac susceptibility. Dark green and dark marine areas in the in-phase and out-of-phase components, respectively, are stable in-plane domains. Light green and light marine areas in the in-phase and out-of-phase components, respectively, are metastable domains. The stable domains shrink, while the metastable grow towards the transition, and eventually collapse to narrow features reminiscent of the domain boundaries roughly lined up with the crystallographic <1 0 0> direction. The dc magnetization contrast reduces towards the transition, while the amplitude of the in-phase and out-of-phase signals grow. The metastable regions show enhanced signals. Immediately above the transition temperature, all signals collapse to small values, and no domains persist.

![](https://assets.underline.io/uploads/markdown_image/1/image/954b2477fcd8048e89881b7176b39e5d.jpg)
Figure 2. The growth of domains with magnetic field in a CeAlSi crystal that was as-cooled through the transition at ~8K. The stable and metastable domains in the in-phase and out-of-phase components are represented the same way as in fig 1.

 Direct observation of tunable magnetic domains in noncentrosymmetric ferromagnetic Weyl semimetal CeAlSi

The surface states of three-dimensional topological insulators (TIs) exhibit a large spin-orbit coupling leading to spin-momentum locking, the electron spin being locked perpendicularly to the electron momentum. This property is promising for spintronic applications, as the Rashba Edelstein effect can create, from a charge current at the conducting surface of a TI, a spin accumulation. Reciprocally, the injection of a spin current creates a net charge current by inverse Edelstein effect. Recently, we have demonstrated a large spin-to-charge conversion efficiency in strained mercury telluride (HgTe) TI at room temperature [1], with conversion rates one order of magnitude higher compared to conventional materials. Achieving the mirror charge-to-spin conversion would be of great interest for memory and logic applications, with two effects in particular that could be exploited. First, the spin-orbit torques (SOT), in which the spin accumulation induces a torque on the magnetization [2], which can be used as a switching mechanism in a magnetoresistive random access memories (SOT-MRAM). Second, the unidirectional spin-hall magnetoresistance (USMR), in which depending on the relative directions between the spin accumulation and the magnetization, the system holds high or low resistance state [3]. While conventional SOT devices suffer from a three-terminal geometry, this USMR effect has potential to be used as a new reading mechanism for developing a novel type of SOT-MRAM with a two-terminal geometry and smaller footprint. Here we report unidirectional spin-Hall magnetoresistance in HgTe topological insulator-ferromagnet heterostructures up to room temperature. Results are shown from a 3 µm wide Hall bar device made of a NiFe ferromagnetic layer with in-plane magnetization on top of a HgTe layer with a thin HgCdTe insertion to protect the TI surface state (Figure 1). Harmonic measurements of the longitudinal and Hall resistance are performed to investigate both USMR and spin-orbit torque effects. A change in the nonlinear magnetoresistance upon switching the magnetization from +y to –y direction is demonstrated (Figure 1b), corresponding to the signature of the USMR driven by Eldelstein effect. Anomalous Nernst and spin Seebeck effects are measured from the nonlinear magnetoresistance in the x direction, showing negligible contributions. The results show USMR efficiency of 2.6 ppm A cm-1 at 10K, three times higher than in ferromagnet-normal bilayer and on the same order of low temperature Bismuth Selenide TI. USMR signal is seen to increase linearly with the current density, confirming the unidirectional nature of USMR in HgTe (Figure 2). Experimental results at room temperature further show comparable USMR efficiency, bringing HgTe compatible for room temperature applications. Ongoing material engineering is discussed to improve further the USMR efficiency on HgTe system, the high efficiency observed in this first demonstration constituting an important step towards SOT-MRAM with two-terminal geometry at room temperature.

**References:**

[1] P. Noel et al., Phys. Rev. Lett. 120, 167201 (2018). [2] I. M. Miron et al., Nature 476, 189–193 (2011). [3] C. O. Avci et al., Nature Physics 11, 570–575 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f2e1172201ca3e61e64fb3ee032e8b46.jpg)
Sample layout and nonlinear magnetoresistance (a) Structure of the sample and measurement geometry. (b) Second harmonic longitudinal resistance as a function of the magnetic field along the y direction. (c) Second harmonic Hall resistance as a function of the magnetic field along the x direction. All measurement were performed with a current density of j2D = 3.3 A cm-1 at a temperature of 10K.

![](https://assets.underline.io/uploads/markdown_image/1/image/0aec57feaef1307ba3166b3fc3a3daa8.jpg)
XY angular dependence and extraction of USMR efficiency. (a) Angular dependence of the second harmonic longitudinal resistance when the magnetic field is rotated in the xy plane. (b) Current dependence of the USMR resistance at 10K. Inset shows USMR as a function of the temperature.

 ferromagnet heterostructures

Topological insulators (TI) are gaining attention from a technological point of view due to their foreseen highly efficient capability to control adjacent magnetic media through spin to charge (S2C) conversion [1]. However, in order to make a decisive step toward technology transfer, it is necessary to develop fabrication methods suitable to guarantee their large-scale production. We developed a Metal Organic Chemical Vapour Deposition technique (MOCVD) process to grow epitaxial-quality antimony telluride (Sb2Te3) topological insulator (TI) on 4” Si(111) substrates [2]. When compared to granular-Sb2Te3 grown on SiO2 [3], the epitaxial-Sb2Te3 on top of Si(111), shows improved magnetoconductance (MC) performances, especially upon proper annealing, as described in [2]. Figure 1 displays the MC signal emerging from the epitaxial (annealed) Sb2Te3 on Si(111), at 5.5 K. Clearly, the MC displays a non-parabolic shape, which we attribute to weak antilocalization. In the framework of the Hikami-Larkin-Nagaoka (HLN) model [3], we extract the parameters α (being connected to the number of conducting channels), and coherence length (lφ), as depicted in the inset of Figure 1. The values of α and lφ for the annealed sample are 0.3 and 55 nm, respectively, thus indicating a 2D-type of conduction due to the existence of topologically-protected surface states (TSS). The as-deposited sample shows a much smaller MC signal, and the extracted α and lφ are comparable with those previously obtained for granular-Sb2Te3 on SiO2 [3]. Following the MC studies, both the as-deposited and epitaxial Sb2Te3 samples have been covered with evaporated 57Fe(5nm) and subsequently in situ capped with Au(5nm) to prevent Fe oxidation. To investigate the potential role of the Sb2Te3 preparation on S2C efficiency, terahertz (THz) emission spectroscopy has been conducted on both samples. The Fe layer is saturated by an external in-plane magnetic field. The multilayer system is excited using femtosecond laser pulses, which launch a longitudinal spin-polarized electron current. Through S2C conversion, the spin current is converted into a transverse charge current concomitantly ejecting a THz pulse which we record in the time domain via electro-optic (EO) detection (see Figure 2) [4,5]. Our results show a considerable impact of Sb2Te3 annealing on the THz signal amplitude suggesting a S2C conversion contribution from the Fe/Sb2Te3 interface. Conversion-electron Mössbauer spectroscopy (CEMS) has been conducted on the same samples studied by THz emission spectroscopy. The Fe/as-deposited-Sb2Te3 spectrum resembles those previously reported for the Fe/granular-Sb2Te3 system [6], and CEMS reports that a large fraction of Fe atoms (≤60%) coordinates paramagnetically with Te in a “FeTe” type of bonding. Surprisingly, this fraction collapses to ≤10% at the interface with annealed (epitaxial) Sb2Te3, with a CEM-spectrum mostly dominated by pure Fe, reflecting a remarkable improvement of the chemical-structural-magnetic quality of the Fe/annealed- Sb2Te3 interface. We propose the suppression of the “FeTe”-type of bonding at the interface as being the main source for the enhancement of the S2C conversion as observed by THz emission spectroscopy. To conclude, the annealed epitaxial Sb2Te3 develops TSS-connected conduction as shown by MC (Figure 1), which turns out in an enhancement of the THz signal in Fe/Sb2Te3 heterostructures as due to S2C conversion (Figure 2). By means of CEMS, the evolution of the S2C efficiency with the Sb2Te3 annealing is attributed to a remarkable suppression of intermixing occurring at the Fe/Sb2Te3 interface, when Fe is deposited in direct contact on top of annealed and epitaxial Sb2Te3.

**References:**

[1] A. Soumyanarayanan, N. Reyren, A. Fert et al., Nature 539, 509 (2016) [2] M. Rimoldi, R. Cecchini, C. Wiemer et al., RSC Advances 10(34), 19936 (2020) [3] R. Cecchini, R. Mantovan, C. Wiemer et al., Phys. Status Solidi RRL 12, 1800155 (2018) [4] T. Seifert, S. Jaiswal, U. Martens et al., Nat. Photonics, 10, 483 (2016) [5] T. Seifert, S. Jaiswal, J. Barker et al., Nat Commun 9, 2899 (2018). [6] E. Longo, C. Wiemer, R. Cecchini et al., Adv. Mater. Interfaces 7, 2000 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6fdf4a13fdf66c175dd0d951784e14b2.jpg)
Fig.1. Magnetoconductance signal of the epitaxial (annealed) Sb2Te3 on Si(111), at 5.5 K. The inset shows the fit in the framework of the Hikami-Larkin-Nagaoka model, from which the α and lφ parameters are extracted.

![](https://assets.underline.io/uploads/markdown_image/1/image/a97ebfc4c249fdb79705013e0f677e76.jpg)
Fig.2. THz emission signals of the Au/Fe/as-deposited-Sb2Te3 (black curve) and Au/Fe/epitaxial-Sb2Te3 (red curve) heterostructures.

Curvilinear Magnetism INVITED

Downloads

Next from INTERMAG 2021

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

Similar lecture

Dynamic state transitions in vortex-based magnetic tunnel junctions for high frequency data transmission

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES

Curvilinear Magnetism INVITED

.css-70qvj9{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}Downloads

Next from INTERMAG 2021

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

Similar lecture

Dynamic state transitions in vortex-based magnetic tunnel junctions for high frequency data transmission

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES

Downloads