Anomalous Hall effect is a prime example of electronic responses commonly associated with the spontaneous time-reversal symmetry breaking in the electronic structure of ferromagnets. More recently, the anomalous Hall effect and other time-reversal symmetry breaking responses were also theoretically and experimentally established in crystals with a vanishing net magnetization and a non-collinear magnetic order [1,2]. The experimental work presented in this talk has been inspired by theoretical predictions that the time-reversal symmetry breaking electronic structure and responses can occur within an abundant family of materials with a compensated collinear magnetic order [2-4]. The underlying unconventional magnetic phase forms in crystals whose opposite-spin sublattices are connected by a rotation symmetry-transformation [5]. Its characteristic feature is an alternating spin polarization in both real-space crystal structure and momentum-space electronic structure, which has suggested to term this emerging phase altermagnetism [5].

We will first present our experimental observation of a spontaneous anomalous Hall response in the absence of an external magnetic field in an epitaxial film of MnTe, which is a semiconductor with a collinear antiparallel magnetic ordering of Mn moments [6]. The anisotropic crystal environment of magnetic Mn atoms due to the non-magnetic Te atoms is essential for establishing the unconventional phase and generating the anomalous Hall effect in MnTe [5,6]. In the second part of the talk, we will present our observation of the spontaneous anomalous Hall effect in epitaxial thin-film Mn5Si3 [7]. We have studied Mn5Si3 epilayers grown on Si(111) substrate. We observe that epitaxial constraints stabilize a hexagonal unit cell in the magnetic state distinct from previously described phases in bulk Mn5Si3 crystals [8]. We observe a sizable spontaneous anomalous Hall conductivity of 5-20 S/cm, accompanied by a negligible net magnetization. Combined with the theoretical symmetry analysis and microscopic ab initio calculations, we conclude that our thin-film Mn5Si3 is a candidate for a d-wave Fermi-liquid instability form of the altermagnetic phase, generated by a compensated collinear ordering of magnetic moments on the lattice of Mn atoms [4,6].

[1] Nakatsuji and Arita, Annual Review of CMP 13, 119-142 (2022)[2] Smejkal et al. Nat. Rev. Mater., on-line 30 March (2022)

[3] Smejkal et al. Science Advances 6, 23 (2020)

[4] Mazin et al. PNAS 118 42 (2021)

[5] Smejkal et al. arXiv:2105.05820, arXiv:2204.10844

[6] Gonzales-Betancourt et al. arXiv:2112.06805

[7] Reichlova et al., arXiv:2012.15651

[8] Gottschilch et al., J. Mater. Chem., 22, 15275 (2012)

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Reliable and dynamic control of magnetic properties in technologically relevant magnetic materials is at the heart of a variety of emerging practical applications in spintronics. Gate voltage-controlled ionic diffusion in magnetic devices has shown to provide non-volatile control of perpendicular magnetic anisotropy, the Dzyaloshinskii Moriya interaction, as well as the velocity and pinning of magnetic domain walls, opening a solid path towards novel multifunctional spintronics devices. In this talk, I will present an overview of this exciting field, what it means for practical applications, and discuss the physical mechanisms involved.

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Two-dimensional spin-textured materials or interfaces are expected to exhibit high efficiency for the interconversion of spin current into charge current, even more efficient than conventional non-magnetic heavy metals [1,2]. Additionally, magnetic materials possessing strong spin-orbit coupling such as GdFeCo can also efficiently generate spin currents of different symmetries, spin anomalous Hall effect SAHE-like, and spin Hall effect SHE-like [3-5]. And one such symmetry, SHE-like, could produce what we have coined "self-torque" [6].

In the first part of the talk, I will show an example of “standard” or “external” spin-orbit torque in a W/CoTb/AlOx system. We use the strong spin-orbit coupling from W to exert spin-orbit torque and manipulate the perpendicular magnetization of CoTb amorphous ferrimagnetic layer [2] .

In the second part, I will show our study on ferrimagnetic FiM GdFeCo alloys in which the 5d band of Gd induces large spin-orbit coupling. We demonstrate the giant spin current emission (SAHE+SHE) by GdFeCo from the current-induced modulation of the ferromagnetic resonance linewidth of NiFe in GdFeCo/Cu/NiFe. Overall efficiency is 25 times more important in GdFeCo/Cu/NiFe than in Pt/Cu/NiFe [3].

The study of the self-torque is carried out by harmonic Hall voltage measurements in samples where the GdFeCo layer exhibits out-of-plane magnetization. We compare the self-torque in GdFeCo/Cu with torques induced by Pt or Ta in Pt/Cu/GdFeCo and Ta/Cu/GdFeCo [3]. Thus, These “self-torques” can be tuned by adjusting the spin absorption outside the GdFeCo layer. Moreover, taking advantage of the different characteristics temperatures in ferrimagnets [2,6,7], we show the features that differentiate self-torque from what we know so far, the "external" spin-orbit torque [6].

These results pave the way for new architectures to achieve switching by self-SOT and skyrmions manipulation.

Work performed with co-authors in Refs. 1,2,6 and 7. This work was supported from Agence Nationale de la Recherche (France) under contract ANR-19-CE24-0016-01 (TOPTRONIC), and related projects in Ref. 2,6-7.

[2] Pham, TH et al, Thermal contribution to the spin-orbit torque in metallic-ferrimagnetic systems. Phys. Rev. Appl. 9, 064032 (2018).

[3] Taniguchi et al. Spin-Transfer Torques Generated by the Anomalous Hall Effect and Anisotropic Magnetoresistance. Phys Rev Appl. 3, 044001 (2015).

[4] Amin et al., Intrinsic spin current in ferromagnets. Phys. Rev. B 99, 220405 (2019)

[5] Kim & Lee, Generalized Spin Drift-Diffusion Formalism in the Presence of Spin-Orbit Interaction of Ferromagnets. Phys. Rev. L 125, 207205 (2020)

[6] Céspedes-Berrocal D., Damas H. et al. Current-Induced Spin Torques on Single GdFeCo Magnetic Layers. Adv. Materials 33, 2007047 (2021)

[7] Damas H. et al. PSS-Rapid Res. Lett., https://doi.org/10.1002/pssr.202200035

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Magnetisation dynamics usually takes place at non-zero temperatures, i.e. in a thermodynamical environment. Many recent applications (e.g. heat-assisted magnetic recording) make use of temperature to influence the spin dynamics. On the contrary, others application (e.g. magnetocaloric) use magnetization changes to produce heat. In the present talk I will discuss our multi-scale framework to model both situations. I will review some recent results concerning the influence of temperature on domain wall width [1] or skyrmion size [2] and illustrate their motion under thermal gradient via the spin-Seebeck effect. Typically, domain walls or skyrmion are moving to the hot region, abeit for skyrmions with a skyrmion Hall angle. For the domain wall motion, especially in the perpendicular materials, we observed their oscillations as a function of time, particularly in the presence of pinning centers. For skyrmions, we also report a motion to the cold region in multilayered systems contrary to what happens in the ultrathin single layer case.

Since temperature can change magnetisation, there is a well-known reciprocal effect: magnetisation changes produce heat, used for example in magnetic hyperthermia for cancer treatment. These effects are typically considered through the area of hysteresis cycle, while I will underline the important role of local heating and magnetization dynamics [3]. Similarly, since the domain wall can be moved under thermal gradient, one can expect the reciprocal effect - the domain wall motion could be accompanied by a temperature release (the spin-Peltier effect for domain wall [4]). In this case the released temperature is proportional to the ratio of domain wall velocity/width. Here we consider the antiferromagnetic MnAu material, where ultra-high velocities are predicted when the domain wall is moved under current by spin-orbit torque. Importantly, when the domain wall velocities are high, its width decreases due to relativistic effects. We estimate that the domain wall motion in this material can be accompanied by a localized ultrafast heat pulse as strong as 0.1K, much higher than for coherent magnetization switching. The energy release is especially efficient under elastic collision of domain walls with the same topological charge [5].

[2] R.Tomasello et al Phys. Rev. B 97, 060402(R) (2018)

[3] C.Muñoz-Mendez, Phys. Rev.B 102, 214412 (2020)

[4] R.M.Otxoa et al Comm. Phys 3, 31 (2020)

[5] R.M.Otxoa et al Phys.Rev.Res. 3, 043069 (2021)

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Spin-orbit torques (SOTs) in bilayers of ferromagnetic (FM) and nonmagnetic (NM) materials, such as spin Hall [1] and Rashba [2, 3] torques, enable energy efficient manipulation of magnetization by electric currents. In this talk, I will discuss the discovery [4] of a damping-like SOT arising from planar Hall current in FM conductors [5, 6]. The magnitude of this planar Hall torque (PHT) is similar to that of the giant spin Hall torque in FM/Pt bilayers and strong PHT can be present in a system with negligibly small spin Hall torque such as FM/Au bilayers. We also show that PHT is large enough to cancel magnetic damping of the FM and excite auto-oscillations of the FM magnetization. The discovery of PHT expands the class of materials and systems for energy efficient manipulation of magnetization by giant SOTs.

1. Liu L. et al. (2012) Spin-torque switching with the giant spin Hall effect of tantalum. Science. 336, 555.

2. Miron I. M. et al. (2011) Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189.

3. Kurebayashi H. et al. (2014) An antidamping spin–orbit torque originating from the Berry curvature, Nature Nanotech. 9, 211.

4. Safranski C., Montoya E.A., Krivorotov I.N. (2019) Spin–orbit torque driven by a planar Hall current. Nat. Nanotech. 14, 27.

5. Taniguchi T., Grollier J., Stiles M.D. (2015) Spin-Transfer Torques Generated by the Anomalous Hall Effect and Anisotropic Magnetoresistance. Phys. Rev. Appl. 3, 1.

6. Ochoa H., Zarzuela R., Tserkovnyak Y. (2021) Self-induced spin-orbit torques in metallic ferromagnets, J. Magn. Magn. Mater. 538, 168262.

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**PDF file of the talk available here**

In this talk, we show that the phenomenon known as "Valley Hall Effect", whereby a an electric field induces a transverse valley current, is better described as an instance of the Orbital Hall Effect (OHE), where the ambiguous ``valley'' indices are replaced by a physical quantity, the orbital magnetic moment, which can be defined uniformly over the entire Brillouin zone. This description removes ambiguities that are present in the definition of the valley Hall current, as the conductivity in the orbital Hall effect is unambiguously defined as the Brillouin zone integral of a new quantity, called the orbital Berry curvature. The reformulation in terms of OHE is illustrated in the case of gapped graphene, which has been previously proposed to be a good platform to observe the valley Hall effect. The new formulation provides a direct explanation to the orbital moments accumulated at the edges of the sample, which were observed in previous Kerr rotation measurements.

]]>Two-dimensional materials such as graphene and black phosphorus hold great promises for room temperature spintronics applications requiring long-distance spin communication [1]. In this talk, I will focus on spin transport in ultra-thin black phosphorus. After introducing its exceptional spin transport properties (e.g. gate-tunable nanosecond spin lifetimes and record non-local spin signals) [2], I will discuss our recent efforts focused on investigating the impact of its unique crystal structure on spin dynamics. The observation of strong anisotropic spin transport provides opportunities to realize directional control of spin propagation.

[1] A. Avsar et al., Rev. Mod. Phys. 92, 021003 (2020)[2] A. Avsar et al., Nat. Phys. 13, 888-894 (2017) ]]>

An insulating ferromagnet (FM)-topological insulator (TI)-FM trilayer heterostructure can be operated as an adiabatic quantum motor by virtue of the combined effect of voltage-induced torque and its reverse effect—topological charge pumping. Unlike traditional current-driven systems, such a voltage-driven system can achieve 100% mechanical efficiency because the output current is purely adiabatic which does not incur Joule heating as dissipative currents do. This mechanism enables the excitation of the high-frequency exchange mode resonance in an FM-TI-FM system, where the two FM precess with a 180° phase difference, without producing any waste heat. Even in the presence of leakage currents and other imperfections, our proposed setup can still realize a mechanical efficiency two orders of magnitude larger than current-driven magnetic resonances. On the theoretical side, the voltage-induced torque is determined by the Berry curvature jointing time and crystal momentum, which has been previously overlooked in the study of topological materials. Our findings will facilitate the development of ultrafast spintronic devices consuming extremely low power.

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Antiferromagnetic spintronics present a promising approach to overcome limitations of current information technology. Owing to the vanishing net magnetization, antiferromagnetic materials exhibit spin dynamics on sub-picosecond timescales potentially allowing for not only data storage and logic circuit applications that are orders of magnitude faster than their established ferromagnetic counterparts, but also the development of new paradigms for device architectures with greater functionality. The tremendous interest in the realization of antiferromagnet-based devices has triggered an ongoing exploration of tools for controlling and manipulating antiferromagnets.

In this talk, I will present recent advances in the ultrafast optical excitation and probing of antiferromagnetic spin precessions. Based on the inverse magneto-optical effects [1,2], laser pulses can act like ultrafast magnetic field pulses, thereby enabling efficient non-thermal optical excitation of coherent spin precessions in fully compensated antiferromagnets. We show that the initial phase of the spin precession contains valuable information about the excitation, which allows us not only to distinguish between different excitation mechanisms [3], but also to reveal an ultrafast damping torque which can even become the dominant excitation mechanism in antiferromagnets [4]. The ensuing coherent spin precession leads to a transient symmetry reduction. Using symmetry-sensitive nonlinear optical probes, we track the antiferromagnetic order parameter quantitatively in three dimensions [5]. We observe a strongly elliptical precession – typical for antiferromagnetic dynamics. I will conclude with an outlook on how these results can contribute to emerging topics in ultrafast magnetization dynamics [6].

[2] A.M. Kalashnikova, A.V. Kimel, R.V. Pisarev, V.N. Gridnev, A. Kirilyuk, and Th. Rasing, Phys. Rev. Lett. 99, 167205 (2007)

[3] C. Tzschaschel, K. Otano, R. Iida, T. Shimura, H. Ueda, S. Günther, M. Fiebig, and T. Satoh, Phys. Rev. B 95, 174407 (2017)

[4] C. Tzschaschel, T. Satoh, and M. Fiebig, Nat. Commun. 11, 6142 (2020)

[5] C. Tzschaschel, T. Satoh, and M. Fiebig, Nat. Commun. 10, 3995 (2019)

[6] J. Li, C.-J. Yang, R. Mondal, C. Tzschaschel, and S. Pal, Appl. Phys. Lett. 120, 050501 (2022)

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The nature of the counter-intuitive heat induced ferromagnetism in FeRh has been a subject of ongoing debates for about 60 years, resembling a dispute about the chicken-or-egg causality dilemma. FeRh is antiferromagnetic at low temperatures and becomes ferromagnetic, when heated above 370 K. These magnetic changes are accompanied by an expansion of the unit cell. It is, however, still unknown whether this a magnetic phase transition that drives the lattice expansion or a structural phase transition that causes the magnetic changes. To resolve this magnetism-or-lattice causality dilemma, we heated FeRh with femtosecond laser pulse and traced structural and magnetic changes by measuring reflectivity and the magneto-optical Kerr effect, respectively. Alternatively, we performed ultrafast magnetometry and traced formation of ferromagnetic domains with the help of double-pulse THz emission spectroscopy. We show that while a femtosecond laser pulse indeed generates ferromagnetic nuclei in FeRh, it takes of about 10 ps before the nuclei acquire a net magnetization. We argue that this latency is intrinsic to the phase transition from collinear antiferromagnetic to ferromagnetic states and must be present even in the case when the sign of the exchange interaction changes instantaneously. Using high magnetic fields up to 25 T, we could accelerate the magnetic phase transition and eventually discovered the fastest possible emergence of ferromagnetism in step with the lattice. As a result, we show that both spins and lattice evolve simultaneously. This finding practically resolves the magnetism-or-lattice causality dilemma.

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