Perspectives of antiferromagnetic spintronics

JID:PLA

AID:24916 /SSU

Doctopic: Perspectives

[m5G; v1.229; Prn:1/02/2018; 13:26] P.1 (1-7)

Physics Letters A ••• (••••) •••–•••

Contents lists available at ScienceDirect

Physics Letters A www.elsevier.com/locate/pla

Perspective article

Perspectives of antiferromagnetic spintronics Matthias B. Jungfleisch a,∗ , Wei Zhang a,b , Axel Hoffmann a a b

Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA Department of Physics, Oakland University, Rochester, MI 48309, USA

a r t i c l e

i n f o

Article history: Received 30 September 2017 Received in revised form 17 December 2017 Accepted 8 January 2018 Available online xxxx Invited by M. Wu Keywords: Antiferromagnets Spintronics Spin Hall effect Spin dynamics Magnons

a b s t r a c t Antiferromagnets are promising for future spintronic applications owing to their advantageous properties: They are magnetically ordered, but neighboring magnetic moments point in opposite directions, which results in zero net magnetization. This means antiferromagnets produce no stray fields and are insensitive to external magnetic field perturbations. Furthermore, they show intrinsic high frequency dynamics, exhibit considerable spin–orbit and magneto-transport effects. Over the past decade, it has been realized that antiferromagnets have more to offer than just being utilized as passive components in exchange bias applications. This development resulted in a paradigm shift, which opens the pathway to novel concepts using antiferromagnets for spin-based technologies and applications. This article gives a broad perspective on antiferromagnetic spintronics. In particular, the manipulation and detection of antiferromagnetic states by spintronics effects, as well as spin transport and dynamics in antiferromagnetic materials will be discussed. We will also outline current challenges and future research directions in this emerging field. © 2018 Published by Elsevier B.V.

1. Introduction In his noble lecture from 1970, Louis Néel stated that antiferromagnets “do not seem to have any applications” despite of being “extremely interesting from a theoretical viewpoint” [1]. This general perception prevailed until the early 1990s when the first commercial products employed exchange bias [2–4] in hard disk recording heads on larger industrial scales. Exchange bias, which originates from the exchange coupling of the magnetic spins in an antiferromagnet to the magnetization in an adjacent ferromagnet, gives rise to a preferred direction for the magnetization of a ferromagnet and thereby allows to establish a reference magnetization direction. On the other hand, the field of conventional spintronics is based on the precise control of magnetic moments in ferromagnets. Central concepts in conventional spintronics are electrical switching of magnetization (“writing”) via spin-transfer torque phenomena and readout of information using magnetoresistance effects. Spin-transfer torque effects refer to a scenario where a spin-polarized current injected into a ferromagnet exerts a torque on the magnetization causing the magnetization to precess and/or switch its direction [5]. On the other hand, magnetoresistance describes the change of electrical resistance in a

*

Corresponding author. Current address: Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA. E-mail address: jungfl[email protected] (M.B. Jungfleisch). https://doi.org/10.1016/j.physleta.2018.01.008 0375-9601/© 2018 Published by Elsevier B.V.

conductor when the magnetization is changed. The emerging field of antiferromagnetic spintronics aims at exploiting analog concepts in antiferromagnets rather than in ferromagnets. Moving from ferromagnetic to their antiferromagnetic counterparts offers distinct advantages: magnetic moments in antiferromagnets align in regular pattern with their neighboring magnetic moments pointing in opposite directions. This is a manifestation of an ordered magnetism, however, the total net magnetization is zero due to the opposing spin directions. This means antiferromagnets produce no stray fields and are mostly insensitive to external magnetic field perturbations. Typical resonance frequencies of antiferromagnets are much higher than in ferromagnets; i.e., in the terahertz frequency range, which make them promising candidates for technological applications [6]. The recent discovery of electrical switching and readout of an antiferromagnet by spin–orbit torque impressively shows that antiferromagnets can be controlled electrically in similar ways as their ferromagnetic counterparts [7]. This short Review presents a broad perspective on antiferromagnetic spintronics and discusses recent discoveries in the field. We briefly review various kinds of antiferromagnetic materials, which are promising candidates for spintronics applications. Then magneto-transport effects are discussed and fundamentals of electric manipulation of antiferromagnets via spin orbitronics are outlined. Furthermore, we review recent theoretical and experimental observations on antiferromagnetic dynamics, followed by a brief outlook and concluding remarks.

JID:PLA

AID:24916 /SSU

Doctopic: Perspectives

2

[m5G; v1.229; Prn:1/02/2018; 13:26] P.2 (1-7)

M.B. Jungfleisch et al. / Physics Letters A ••• (••••) •••–•••

2. Antiferromagnetic materials In nature, antiferromagnetic order is ubiquitous compared to ferromagnetic order. Antiferromagnetic order occurs commonly among transition metal oxides, such as NiO, and metallic alloys such as FeMn. In the following, we briefly present materials that are promising for antiferromagnetic spintronics. Metals. Metallic antiferromagnets are often times Mn-bases alloys, such as FeMn, PtMn or IrMn. The main advantage of this material class is their easy fabrication by sputtering deposition, which potentially allows for large scale industrial production. Furthermore, the manipulation of the antiferromagnetic properties by alloying different metals enables controlling spin–orbit effects. Being able to engineer those properties by adjusting the composition of the alloy is demanded by most technological applications. In addition, metallic antiferromagnets allow for studying spin-transfer effects, magnetoresistance, spin–orbit phenomena (such as spin Hall effect) [8–10], and spin pumping [11,12]. Those concepts, which can also be found in conventional ferromagnet-based spintronics, will be introduced below. Insulators. Recently, insulating antiferromagnets have attracted considerable attention as efficient spin-current sources; experimentally in microwave and thermal measurements, as well as in theoretical studies. Furthermore, they have been used in optical pump-probe experiments [6] and in studies on magnetoelectric effects [14]. Many insulating antiferromagnets are oxides, such as NiO, CoO, and Cr2 O3 . Another common class of antiferromagnetic insulators are fluorides, many of which have been investigated extensively with respect to their magnetic properties. One example is MnF2 , which undergoes a spin-flop transition at a magnetic field below 10 T for temperatures below the Néel temperature [15]. The spin-flop transition, where the magnetic spins rotate by almost 90◦ upon applying a sufficiently large magnetic field along the magnetic easy anisotropy axis is illustrated in Fig. 4(a). 3. Spin transport in antiferromagnets 3.1. Spin pumping and inverse spin Hall effect The spin Hall effect interconverts spin- and charge currents, which enables electrical generation and detection of diffusive spin currents and even collective spin excitations in magnetic solids [16,17]. The conversion efficiency is a material specific parameter, called spin-Hall angle. Studies on those effects in ferromagnetic/non-magnetic heterostructures are an important aspect of conventional spintronics, and magnetism research in general. In this subsection, we review similar studies on antiferromagnetbased heterostructures. The first part is devoted to the utilization of metallic antiferromagnets as spin-Hall detector materials. The second part, conversely, focuses on the implementation of antiferromagnets as spin-current amplifiers. Mendes et al. [10] demonstrated successfully that the hightemperature antiferromagnetic metal Ir20 Mn80 exhibits a significant spin Hall effect, which agrees with theoretical predictions [18]. In their experiment, a spin current from the ferrimagnetic insulator yttrium iron garnet (YIG) is injected into Ir20 Mn80 either by microwave spin pumping or spin Seebeck effect [19,20]. Spin pumping in ferromagnetic/non-magnetic bilayers refers to the transformation of magnetization dynamics in the ferromagnet into a spin-polarized electron current in the adjacent nonmagnetic conductor. This injection of a spin-polarized electron current from one layer into the other, depletes angular momentum from the magnetization precession, which leads in turn to a damping enhancement in the magnetic material [21]. Conversely,

Fig. 1. (Color online.) (a) A sketch illustrating the chemical structure of CuAu-Itype antiferromagnets, such as Pt50 Mn50 . (b) Thickness dependence of the inverse spin Hall contribution W ISHE to the rectified voltage measured by spin pumping and inverse spin Hall effect in Ni80 Fe20 (15)/Cu(4)/Pt50 Mn50 (tPtMn ). Using thicknessdependent measurements, a spin diffusion lengths of the order of 1 nm is found. Adapted from [8].

the spin-Seebeck effect is the creation of a spin-polarized electron current by a thermal gradient applied to such a heterostructure [22]. While these concepts were originally studied in ferromagnetic/non-magnetic bilayers, these concepts have now been applied to a variety of heterostructures, where either layer may be differently magnetically ordered. Mendes et al. find that the magnitude of the spin Hall effect in Ir20 Mn80 is of the same order as the standard non-magnetic spin Hall detector material Pt, demonstrating that antiferromagnetic materials are promising candidates as spin-current detectors in spintronic applications. Zhang et al. carried out extended, systematic studies on spin Hall effect in antiferromagnets and presented comprehensive investigations on CuAu-I-type metallic antiferromagnets [8], see Fig. 1(a). Nontrivial spin Hall effects were observed for FeMn, PdMn, and IrMn while a much higher effect was obtained for PtMn. Detailed thickness-dependent measurements revealed the spin-diffusion lengths of the various antiferromagnetic metals, see Fig. 1(b) as an example for PtMn. The estimated spin Hall angles of the four materials were found to follow the relationship PtMn > IrMn > PdMn > FeMn. This observation highlights the correlation between spin–orbit coupling of the non-magnetic species and magnitude of the spin Hall effect in their antiferromagnetic alloys. The experiments were compared with first-principles calculations and showed that the value of spin Hall conductivity can vary with crystal orientation and staggered antiferromagnetic magnetization [9]. Another aspect is the utilization of antiferromagnets for an enhanced spin transport. Hahn et al. [13] and Wang et al. [23] realized that the insertion of a thin NiO layer between yttrium iron garnet and Pt still enabled a significant transmission of spin current to the Pt layer even for rather thick NiO layers. In both experiments, microwave spin pumping was used to inject a spin current from the YIG into the Pt through a thin insulating NiO layer, see Fig. 2. This observation was highly surprising, since it was known that thin dielectric layers are very efficient at suppressing spin pumping, [24] but is was also later confirmed in spin Seebeck type measurement, see Sec. 3.2. A schematic of the experimental setup is shown in the inset of Fig. 2. Fig. 2(a) shows the YIG/Pt reference sample, whereas (b) illustrates the results for the trilayer YIG/NiO/Pt. Strikingly, there is still a clear inverse spin Hall voltage observed even with the NiO layer. Those results suggest a high spin transfer efficiency at both interfaces, YIG/NiO and NiO/Pt as well as a high conductivity for spin currents through the NiO. However, the spin diffusion length measured in NiO is very short, which is inconsistent with a picture of antiferromagnetic magnons, the elementary quanta of spin waves, that transport angular momentum through NiO. Confined antiferromagnetic fluctuations seem to be more likely to be responsible for the observed enhancement [13].

JID:PLA

AID:24916 /SSU

Doctopic: Perspectives

[m5G; v1.229; Prn:1/02/2018; 13:26] P.3 (1-7)

M.B. Jungfleisch et al. / Physics Letters A ••• (••••) •••–•••

Fig. 2. (Color online.) (a) Inverse spin Hall signal detected YIG/Pt generated by the spin current emitted by the YIG at resonance at ferromagnetic resonance (3.85 GHz, +10 dBm.) (b) Corresponding inverse spin Hall voltage for YIG/NiO(4)/Pt trilayer. Note the difference in scale for the measured voltages. The inset shows a sketch of the experimental setup. Adapted from [13].

Fig. 3. (Color online.) Spin transport through metallic antiferromagnets using measurements based on spin pumping combined with inverse spin Hall effects in Ni80 Fe20 /FeMn/W trilayers. Thickness dependence of the inverse spin Hall contribution W ISHE to the rectified voltage for frequencies from 4 to 9 GHz. Adapted from [25].

This interpretation is also supported by studies on all-metallic trilayers. Saglam et al. studied Ni80 Fe20 /FeMn/W trilayer samples by combined microwave spin pumping and inverse spin Hall effect measurements [25]. The key findings are shown in Fig. 3. The magnitude of the spin Hall angle of W and FeMn is relatively large, but opposite in sign. This allows for an unambiguous detection of spin currents transmitted through the FeMn layer thickness. Fig. 3 shows the FeMn-interlayer thickness dependence of the inverse spin Hall contribution W ISHE to the total measured voltage in the spin pumping experiment. It is important to note that if W ISHE is negative, the spin current pumped from permalloy into the FeMn layer can reach the W layer (W has a negative spin Hall angle), whereas a positive W ISHE indicates that most of spin current is converted within the FeMn layer. Three different regimes can be distinguished: (1) In the first regime <2 nm the spin current is pre-dominantly carried by electrons. (2) When the FeMn is sufficiently thick, antiferromagnetic order starts to develop and magnetic order fluctuations can effectively transmit spin angular momentum. This is indicated by a drop of W ISHE which means that more spin current is reaching the W top layer. (3) At a thickness of 9 nm antiferromagnetic order has fully developed and the majority of the spin current is transformed in the FeMn layer. Using this approach magnonic and electronic contribution to the spin transport process can be distinguished. The magnonic contribution can extend to relatively large distances (up to 9 nm) and is en-

3

hanced when the antiferromagnetic ordering temperature is close to the measurement temperature. Note that just as in the case of NiO the spin current absorbed in W is enhanced for intermediate thicknesses of FeMn compared to measurements without FeMn. Aside from utilizing antiferromagnets as spin Hall detectors or for enhancement of spin-charge conversion, Frangou et al. [11] and Qiu et al. [12] realized that fluctuations of the antiferromagnetic order affect the spin pumping process. Another outcome of these investigations is the possibility to easily detect magnetic phase transitions by spin pumping. Rather than amplifying and detecting spin currents in antiferromagnets, Zhang et al. used spin-Hall effect driven spin currents in Mn-based antiferromagnets to drive spin dynamics in an adjacent permalloy layer [9]. This mechanism is known as spin-torque ferromagnetic resonance and has been explored previously in conducting and insulating ferromagnetic materials [26–31]. In spin-torque ferromagnetic resonance a microwave charge current is passed through a bilayer consistent of a magnetic and spin-Hall material. The spin Hall effect converts this alternating charge current into in an oscillatory spin current, that subsequently drives the magnetization precession in addition to the microwave Oersted field in the magnetic layer. Detection of the resonant excitation is achieved by a rectification based on the anisotropic magnetoresistance that mixes with the microwave current. This detection is phase sensitive and since the driving torques from the Oersted fields and spin torques from the spin currents are 90◦ out-of-phase, this enables to quantify spin Hall effects. Zhang et al. observed that spin torques predominantly arise from diffusive transport of spin current generated by the spin Hall effect. They also found a growthorientation dependence of the spin torques by studying epitaxial samples, which may be correlated to the anisotropy of the spin Hall effect and demonstrates large tunable spin–orbit effects in magnetically ordered materials [9]. The fact that metallic antiferromagnets can give rise to sizable spin torques has direct applied consequences. In many applications, where the magnetization of a ferromagnetic layer is used to store information it is beneficial to have the magnetization perpendicular to the layer plane. While it has been shown that spin Hall effects can efficiently switch the magnetization of such perpendicularly magnetized films, it requires the application of an additional in-plane magnetic film to have a symmetry breaking for deterministic switching. However, if an antiferromagnetic layer is used for the spin Hall effect, then this layer can also provide an in-plane exchange bias field, which then allows to deterministically switch magnetizations without the necessity to apply additional external magnetic fields [32,33]. In addition, it was observed that such switching can be very gradual, which enabled the development of novel memristive devices that have already been employed in simple associative memory systems for pattern recognition [34]. 3.2. Spin-caloritronic effects Spin-caloritronics aims at exploring the interaction between spin, charge and heat currents [35]. In this context, past research efforts have mainly focused on ferromagnets, but there has also been considerable progress in using antiferromagnets for spin-caloric studies. We discuss here recent studies on thermallyinduced spin currents with a particular focus on spin-Seebeck type of studies. The seminal work by Uchida et al. revealed that spin currents can be induced in magnetic insulators by a thermal gradient and converted into a spin-polarized electron current at the interface to a normal metal [19,20]. Rezende et al. developed a bulk magnon spin current model for the spin Seebeck effect in the longitudinal configuration where the directions of spin-polarized electron current and temperature gra-

JID:PLA

4

AID:24916 /SSU

Doctopic: Perspectives

[m5G; v1.229; Prn:1/02/2018; 13:26] P.4 (1-7)

M.B. Jungfleisch et al. / Physics Letters A ••• (••••) •••–•••

Fig. 4. (Color online.) (a) Schematic illustration of a spin-flop transition in MnF2 . (b) Spin Seebeck voltage detected in a MnF2 /Pt thin film as a function of the applied magnetic field. The sharp increase of the voltage corresponds to the spin-flop transition. The inset illustrates the crystal structure of MnF2 and the antiferromagnetic spin structure. The (110) thin film crystal orientation plane is highlighted in blue. Adapted from [15].

dient coincide [36]. It is based on the spin current created by a temperature gradient across the thickness of a ferromagnetic insulator/normal metal bilayer. At the interface thermal magnons in excess of thermal equilibrium pump a spin current into the normal metal on account of the spin pumping process. In simple antiferromagnets the spin Seebeck effect in the bulk cancels due to the symmetry of the sublattices. In case of an easy axis antiferromagnet with two sublattices, the magnon bands are double degenerate, which means that two opposing spin currents develop in response to a temperature gradient [37]. This degeneracy can be lifted by applying a magnetic field along the easy axis. This has recently been shown experimentally in MnF2 [15] and Cr2 O3 [38]. Rezende et al. developed a model of the antiferromagnetic spin Seebeck effect that describes the experimental findings remarkably well [39]. The spin Seebeck voltage as a function of the magnetic field applied along the easy axis of a MnF2 thin film for various temperatures is shown in Fig. 4(b). A clear spin-flop transition corresponding to the sudden rotation of antiferromagnetic spins out of the easy axis is observed when large magnetic fields are applied parallel to the easy axis, see also Fig. 4(a). The spin-flop transition is absent when the magnetic field is applied perpendicular to the easy axis. As outlined in the previous section 3.1, a spin current in an antiferromagnetic insulator can be injected by coherent spin pumping from an adjacent ferromagnetic layer. This spin-current injection can be detected experimentally in ferromagnet/antiferromagnet/normal metal trilayers by rectification due to the inverse spin Hall effect in the normal metal. Khymyn et al. presented a theoretical model that describes this coherent spin injection and subsequent injection by evanescent magnon modes in the antiferromagnet [41]. Following the same idea, Lin et al. [40] and Hung et al. [42] carried out longitudinal spin Seebeck measurements in yttrium iron garnet (YIG)/nickel oxide (NiO) or chromium oxide (CoO)/platinum (Pt) trilayers. Fig. 5 illustrates the key observation: when a thin NiO layer of 1 nm thickness is sandwiched between the YIG and the Pt or Ta layer, an enhancement of the spin Seebeck voltage is observed. Ta and Pt have opposite spin Hall angles which causes the opposite polarity of the voltages, see Fig. 5(a) and (b). Lin et al. found an enhanced spin-current injection from the YIG into the Pt layer through a thin antiferromagnetic insulator by up to a factor of 10. Furthermore, a pronounced maximum in spin-current injection efficiency was observed near the Néel temperature. They also reveal the importance of the spin conductance in this process and relate the spin current amplification to spin fluctuations and antiferromagnetic magnons. Another interesting aspect of spin-caloritronic effects in antiferromagnets is the interaction of heat currents and/or thermallydriven magnons with antiferromagnetic spin textures and topolog-

Fig. 5. (Color online.) Inverse spin Hall voltage V as a function of the applied field H in (a) Pt(3)/YIG, Pt(3)/NiO(1)/YIG, Pt(3)/NiO(1)/SiOx and (b) Ta(3)/YIG, Ta(3)/NiO(1)/ YIG, thickness in parentheses in nm. The longitudinal temperature gradient across the YIG is about 10 K/mm. Adapted from [40].

ical solitons. The discussion of those effects is beyond the scope of this perspective and the interested reader is referred to the literature, e.g., [37,43–45]. 4. Spin-orbitronics: electrical writing and reading of antiferromagnets The utilization of spin-orbitronic effects to electrically switch the magnetization sublattices of an antiferromagnet and to read out the state thereafter encompasses many interesting phenomena. A detailed discussion of those effects, such as anisotropic magnetoresistance [46], tunneling anisotropic magnetoresistance [47], anomalous Hall effect [48] and spin Hall magnetoresistance [42] in antiferromagnets are beyond the scope of this perspective and the interested reader is referred to the literature; e.g., [37,49]. In the following we will focus on a key observation in the field: It was shown recently that current-driven internal fields whose sign periodically alternate in the antiferromagnetic sublattices can be used to reverse the order parameter in CuMnAs [7]. Although the full CuMnAs crystal is centrosymmetric, CuMnAs possesses a local inversion symmetry breaking in the bulk [see Fig. 6(a)], which enables the inverse spin galvanic effect to induce a nonequilibrium spin polarization in the bulk of the crystal with the same staggered symmetry as the antiferromagnetic order. This allows for electrical switching between stable configurations in antiferromagnetic CuMnAs thin-film devices using current densities of the order 106 A/cm2 . Fig. 6(b) shows an optical microscopy image of the device and the measurement geometry. The direction of the write current J write is either horizontal or vertical, while the read current J read is applied in the diagonal direction and the voltage measured perpendicular to J read . Fig. 6(c) shows the transverse resistance after applying three successive 50 ms writing pulses J write alternately along different [100] crystal directions of CuMnAs. This observation unambiguously demonstrates that antiferromagnets can be used as memory elements in the same way as their ferromagnetic counterparts. In addition, it was recently shown by direct imaging of the magnetic domains in CuMnAs, how the anisotropic magnetoresistance is related to magnetic domain reorientations [50]. Interestingly, compared to ferromagnetic material based memory, antiferromagnetic memories are potentially faster and the absence of stray fields allows for more closely packed individual elements leading to higher storage density. Those memories are also insensitive to magnetic fields and radiation which makes them interesting components for satellite and aircraft electronics. Recently, similar electric switching has also been demonstrated for Mn2 Au [51], which has been the material where antiferromagnetically staggered spin accumulations were first theoretically proposed [52]. Interestingly the anisotropic magnetoresistance in this material is rather large with around 6%, but also the current densities required for the switching is fairly large. Thus heating is

JID:PLA

AID:24916 /SSU

Doctopic: Perspectives

[m5G; v1.229; Prn:1/02/2018; 13:26] P.5 (1-7)

M.B. Jungfleisch et al. / Physics Letters A ••• (••••) •••–•••

Fig. 6. (Color online.) Electrical switching of antiferromagnetic CuMnAs. (a) Illustration of the CuMnAs crystal structure and antiferromagnetic ordering. The two Mn spin-sublattices A and B (red and purple) are inversion partners. This enables the inverse spin galvanic effect to induce a non-equilibrium spin polarization in the bulk of the crystal with the same staggered symmetry as the antiferromagnetic order. The full CuMnAs crystal is centro-symmetric around the interstitial position, which is highlighted by the green ball. (b) Optical microscopy image of the device and illustration of the measurement geometry. (c) Change in the transverse resistance after applying three successive 50 ms writing pulses J write alternately along the [100] crystal direction of CuMnAs indicated by black arrow (b) and black points in (c) and along the [010] axis indicated by red arrow in (b) and red points in (c). Reading current J read is applied along the [110] axis, and transverse resistance R ⊥ signals are recorded 10 s after each writing pulse. Adapted from [7].

significant, as can also be deduced from the strong non-linearity of the switching [53]. Another interesting new recent development is the electric switching and readout of antiferromagnetic insulators. Towards this end it had been theoretically suggested that the magnetic order in Cr2 O3 can be electrically switched via the magnetoelectric effect of this material [54]. At the same time for the right crystallographic orientation Cr2 O3 has a net magnetization at its surface and the concomitant boundary magnetization can be electrically measured via the Hall effect [55]. Combining these two ideas together enabled already the demonstration of a simple functional memory cell [56]. 5. Antiferromagnetic dynamics Current-induced switching by spin-transfer torque effects as discussed in the previous section and excitation of spin dynamics are governed by the same physics. When a compensation of damping in the magnetic material occurs, the magnetization either switches to another direction or starts steady-state oscillations. A great advantage of antiferromagnets is that such spin-torque oscillators can potentially be operated at much higher frequencies when antiferromagnets are used since they feature higher resonance frequencies. It was recently shown theoretically that spintorque can indeed trigger spontaneous excitation of antiferromagnetic dynamics in a similar way as in ferromagnets [57,58]. This is not necessarily obvious due to the fact that common antiferromagnets have two magnetic sublattices with opposite magnetizations. This means that spin-transfer torque effects on the two sub-lattice magnetizations may be opposing each other and thus cancel each other out. Very recently, it was shown theoretically that this problem can be circumvented by two different mecha-

5

Fig. 7. (Color online.) (a) Schematic of a THz-frequency oscillator based on a Pt/antiferromagnet bilayer. The hard axis lies in the bilayer plane perpendicular to the direction of the DC bias current and parallel to the direction of polarization of the spin current. The spin-transfer torque induced by the DC bias current can excite a rotation of the antiferromagnetic sublattice magnetizations that is non-uniform in time resulting in an AC spin-pumping signal at THz frequencies which is subsequently transformed into an AC electric field via the inverse spin-Hall effect in the Pt layer. (b) Calculated frequency as a function of the DC electric current density for NiO(5)/Pt(20). Adapted from [57].

nisms. Cheng et al. proposed THz-frequency generation in NiO/Pt bi-layers via a nonlinear feedback mechanism, which stabilizes the antiferromagnetic precession around the easy axis [58]. In their model the spin current is polarized along the easy axis of the ferromagnet. Another approach was presented by Khymyn et al. [57], see Fig. 7. Here, the spin polarization is along the hard axis of the antiferromagnet. The spin current with spin polarization along the hard axis generates a torque acting on the antiferromagnetically ordered moments parallel to the direction of spin polarization. As a result the sublattice magnetizations cant and internal exchange torques causes rotation of the sublattices [59], see Fig. 7(a). This means that spin-transfer torques induced by DC currents excite a rotation of the antiferromagnetic sublattice magnetizations that is non-uniform in time. As consequence of this non-uniform rotation an AC spin-pumping signal at THz frequencies is induced and subsequently transformed into an AC electric field via the inverse spin-Hall effect in the Pt layer [57], Fig. 7(b). Another pivotal aspect of antiferromagnetic dynamics is optical generation of coherent magnons in antiferromagnets. Kampfrath et al. demonstrated that the magnetic component of intense THz transients enables ultrafast control of the spin degree of freedom [6]. They used single-cycle THz pulses to turn on and off coherent magnons in NiO at room temperature with a resonance frequency of about 1 THz. An ultrashort optical pulse probes the THz-induced spin dynamics directly in the time domain through time-resolved Faraday rotation, which is the magnetic field induced polarization change of the probing laser light. A sketch of the experimental setup and the mechanism is shown in Fig. 8(a) and the result is depicted in Fig. 8(b). A harmonic oscillation with a period of 1 ps is observed within a single cycle. It reaches its maximum amplitude at 3 ps and then decays exponentially with a time constant of 29 ps [6]. The corresponding Fourier transform of the Faraday transient and the incident THz pulse is shown in the inset of Fig. 8(b). Clearly, the Faraday transient consists of a narrow peak at 1.0 THz, which links the signal to the magnonic resonance in NiO [60,61].

JID:PLA

AID:24916 /SSU

Doctopic: Perspectives

6

[m5G; v1.229; Prn:1/02/2018; 13:26] P.6 (1-7)

M.B. Jungfleisch et al. / Physics Letters A ••• (••••) •••–•••

Fig. 8. (Color online.) (a) Schematic of femtosecond THz spin resonance. An intense free-space THz transient (red curve) interacts with the electron spins of the NiO thin film and excites magnons. A femtosecond near-infrared (NIR) probe pulse (green curves) samples the induced net magnetization by means of the Faraday effect (Faraday rotation θF ) after a variable delay time t. (b) Time trace of magnetic field of the incident terahertz pulse, top panel. Ultrafast Faraday rotation θF induced in the NiO sample at room temperature, bottom panel. Harmonic oscillations with a period of 1 ps are due to an antiferromagnetic spin precession. Inset shows amplitude spectra of the Faraday transient and driving THz field. Adapted from [6].

An interesting consequence of the very fast dynamics of antiferromagnets is that it may lead to much faster device operation compared to devices based on ferromagnetic materials. Towards this end switching of the sublattice magnetization with THz pulse has already been observed for CuMnAs [62]. Interestingly, the total energy required for switching the antiferromagnet is constant even for frequencies above 1 GHz. This is in stark contrast to ferromagnetic materials, where the switching energy required increases significantly at higher frequencies [63]. Similarly it is possible that the manipulation of domain walls may be much faster in antiferromagnets [64]. This trend has already been observed in experiments that use the ferrimagnet FeCoGd, where the angular momentum can be compensated for specific temperatures and compositions [65]. These experiments show electrically driven domain wall motion with a speed up to 1.7 km/s, which exceeds the velocities in similar experiments using ferromagnetic materials. The real speed limit is still unclear, although theoretically it has been suggested that ultimately the domain wall speed might be limited by the emission of THz spin waves [66]. 6. Concluding remarks Over the course of the past decade antiferromagnets have transitioned from being considered as a curious phenomenon in magnetism to a promising research direction in spintronics beyond its passive role in exchange-bias application. Recent advancements such as the observation of spin pumping, spin Hall effect, spin Seebeck effect, and spin–orbit torques in antiferromagnetic-based devices have broadened our horizon and promise thrilling future developments in the field. This renewed interest in antiferromagnetic materials also spurred novel developments for probing the spin structure in these materials. While bulk probes like neutron scattering have historically been an excellent tool to get intricate information, these are not suitable to probe the magnetic structure in small patterned devices. Towards this end there are a variety of new encouraging techniques being developed. One approach is to use the above discussed spin transport effects, which has already been used to explore the spin flop transition in NiO [67,68]. Novel optical approaches are also promising [69]. But most excitingly, local microscopy based on spin excitations in nitrogen vacancy centers of diamond may provide a truly novel way to probe local spin structures in antiferromagnets with ultimate sensitivity [70]. Many challenges on the road towards antiferromagnetic spintronics remain. Basic fundamental characterization of many anti-

ferromagnet materials is still lacking, such as what are the exact spin structures especially in heterostructures, magnitude of anisotropies, and bandstructures of magnetic excitations. This is especially true for more complex non-collinear antiferromagnets, where chirality of the spin structure opens up additional pathways for influencing transport phenomena. Thus especially, a full understanding and experimental investigation of the dynamics remains a formidable challenge. At the same time, it is clear that recent developments have just scratched the surface on the wide variety of antiferromagnetic materials to be explored. From the viewpoint of its applied impact, the scientific progress and new discoveries are inherently unpredictable. The post-Moore era with an upsurge of mobile devices and cloud technologies as well as a tighter integration of internet-of-things devices embedded in our life does not only demand new computing concepts, but also novel and versatile materials. It seems unlikely that antiferromagnetic spintronics alone will solve all of the current challenges in information technologies. However, the unique characteristics of antiferromagnets including non-volatility, no fringing stray fields, THz dynamics, robustness versus external magnetic fields make antiferromagnetic spintronics to be a promising building block in “More than Moore” concepts and technologies [59,71,72]. Acknowledgement This work was supported by the U.S. Department of Energy, Office of Science, Materials Science and Engineering Division. References [1] L. Néel, Magnetism and the local molecular field, Science 174 (1971) 985–992. [2] W.H. Meiklejohn, C.P. Bean, New magnetic anisotropy, Phys. Rev. 105 (1957) 904–913. [3] J. Nogués, I.K. Schuller, Exchange bias, J. Magn. Magn. Mater. 192 (1999) 203–232. [4] W. Zhang, K.M. Krishnan, Epitaxial exchange-bias systems: from fundamentals to future spin-orbitronics, Mater. Sci. Eng., R Rep. 105 (2016) 1–20. [5] J.C. Slonczewski, Current-driven excitation of magnetic multilayers, J. Magn. Magn. Mater. 159 (1996) L1. [6] T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, R. Huber, Coherent terahertz control of antiferromagnetic spin waves, Nat. Photonics 5 (2011) 31–34. [7] P. Wadley, B. Howells, J. Železný, C. Andrews, V. Hills, R.P. Campion, V. Novak, K. Olejník, F. Maccherozzi, S.S. Dhesi, S.Y. Martin, T. Wagner, J. Wunderlich, F. Freimuth, Y. Mokrousov, J. Kuneš, J.S. Chauhan, M.J. Grzybowski, A.W. Rushforth, K.W. Edmonds, B.L. Gallagher, T. Jungwirth, Electrical switching of an antiferromagnet, Science 351 (2016) 587–590. [8] W. Zhang, M.B. Jungfleisch, W. Jiang, J.E. Pearson, A. Hoffmann, F. Freimuth, Y. Mokrousov, Spin Hall effects in metallic antiferromagnets, Phys. Rev. Lett. 113 (2014) 196602. [9] W. Zhang, M.B. Jungfleisch, F. Freimuth, W. Jiang, J. Sklenar, J.E. Pearson, J.B. Ketterson, Y. Mokrousov, A. Hoffmann, All-electrical manipulation of magnetization dynamics in a ferromagnet by antiferromagnets with anisotropic spin Hall effects, Phys. Rev. B 92 (2015) 144405. [10] J.B.S. Mendes, R.O. Cunha, O.A. Santos, P.R.T. Ribeiro, F.L.A. Machado, R.L. Rodríguez-Suárez, A. Azevedo, S.M. Rezende, Large inverse spin Hall effect in the antiferromagnetic metal Ir20 Mn80 , Phys. Rev. B 89 (2014) 140406. [11] L. Frangou, S. Oyarzun, S. Auffret, L. Vila, S. Gambarelli, V. Baltz, Enhanced spin pumping efficiency in antiferromagnetic IrMn thin films around the magnetic phase transition, Phys. Rev. Lett. 116 (2016) 077203. [12] Z. Qiu, J. Li, D. Hou, E. Arenholz, A.T. N’Diaye, A. Tan, K.-i. Uchida, K. Sato, S. Okamoto, Y. Tserkovnyak, Z.Q. Qiu, E. Saitoh, Spin-current probe for phase transition in an insulator, Nat. Commun. 7 (2016) 12670. [13] C. Hahn, G. De Loubens, V.V. Naletov, J. Ben Youssef, O. Klein, M. Viret, Conduction of spin currents through insulating antiferromagnetic oxides, Europhys. Lett. 108 (2014) 57005. [14] C. Binek, B. Doudin, Magnetoelectronics with magnetoelectrics, J. Phys. Condens. Matter 17 (2005) L39–L44. [15] S.M. Wu, W. Zhang, A. KC, P. Borisov, J.E. Pearson, J.S. Jiang, D. Lederman, A. Hoffmann, A. Bhattacharya, Antiferromagnetic spin Seebeck effect, Phys. Rev. Lett. 116 (2016) 097204. [16] A. Hoffmann, Spin Hall effect in metals, IEEE Trans. Magn. 49 (2013) 5172. [17] M.B. Jungfleisch, W. Zhang, W. Jiang, A. Hoffmann, New pathways towards efficient metallic spin Hall spintronics, SPIN 05 (2015) 1530005.

JID:PLA

AID:24916 /SSU

Doctopic: Perspectives

[m5G; v1.229; Prn:1/02/2018; 13:26] P.7 (1-7)

M.B. Jungfleisch et al. / Physics Letters A ••• (••••) •••–•••

[18] Z. Qiao, W. Ren, H. Chen, L. Bellaiche, Z. Zhang, A.H. MacDonald, Q. Niu, Quantum anomalous Hall effect in graphene proximity coupled to an antiferromagnetic insulator, Phys. Rev. Lett. 112 (2014) 116404. [19] K. Uchida, J. Xiao, H. Adachi, J. Ohe, S. Takahashi, J. Ieda, T. Ota, Y. Kajiwara, H. Umezawa, H. Kawai, G.E.W. Bauer, S. Maekawa, E. Saitoh, Spin Seebeck insulator, Nat. Mater. 9 (2010) 894–897. [20] K.-i. Uchida, H. Adachi, T. Ota, H. Nakayama, S. Maekawa, E. Saitoh, Observation of longitudinal spin-Seebeck effect in magnetic insulators, Appl. Phys. Lett. 97 (2010) 172505. [21] Y. Tserkovnyak, A. Brataas, G.E.W. Bauer, Enhanced Gilbert damping in thin ferromagnetic films, Phys. Rev. Lett. 88 (2002) 117601. [22] K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, E. Saitoh, Observation of the spin Seebeck effect, Nature 455 (2008) 778–781. [23] H. Wang, C. Du, P.C. Hammel, F. Yang, Antiferromagnonic spin transport from Y3 Fe5 O12 into NiO, Phys. Rev. Lett. 113 (2014) 097202. [24] O. Mosendz, J.E. Pearson, F.Y. Fradin, S.D. Bader, A. Hoffmann, Suppression of spin-pumping by a MgO tunnel-barrier, Appl. Phys. Lett. 96 (2010) 022502. [25] H. Saglam, W. Zhang, M.B. Jungfleisch, J. Sklenar, J.E. Pearson, J.B. Ketterson, A. Hoffmann, Spin transport through the metallic antiferromagnet FeMn, Phys. Rev. B 94 (2016) 140412. [26] J. Sklenar, W. Zhang, M.B. Jungfleisch, H. Saglam, S. Grudichak, W. Jiang, J.E. Pearson, J.B. Ketterson, A. Hoffmann, Unidirectional spin-torque driven magnetization dynamics, Phys. Rev. B 95 (2017) 224431. [27] M.B. Jungfleisch, W. Zhang, J. Sklenar, W. Jiang, J.E. Pearson, J.B. Ketterson, A. Hoffmann, Interface-driven spin-torque ferromagnetic resonance by Rashba coupling at the interface between nonmagnetic materials, Phys. Rev. B 93 (2016) 224419. [28] J. Sklenar, W. Zhang, M.B. Jungfleisch, W. Jiang, H. Chang, J.E. Pearson, M. Wu, J.B. Ketterson, A. Hoffmann, Driving and detecting ferromagnetic resonance in insulators with the spin Hall effect, Phys. Rev. B 92 (2015) 174406. [29] M.B. Jungfleisch, W. Zhang, J. Sklenar, J. Ding, W. Jiang, H. Chang, F.Y. Fradin, J.E. Pearson, J.B. Ketterson, V. Novosad, M. Wu, A. Hoffmann, Large spin-wave bullet in a ferrimagnetic insulator driven by the spin Hall effect, Phys. Rev. Lett. 116 (2016) 057601. [30] L. Liu, T. Moriyama, D.C. Ralph, R.A. Buhrman, Spin-torque ferromagnetic resonance induced by the spin Hall effect, Phys. Rev. Lett. 106 (2011) 036601. [31] A.R. Mellnik, J.S. Lee, A. Richardella, J.L. Grab, P.J. Mintun, M.H. Fischer, A. Vaezi, A. Manchon, E.A. Kim, N. Samarth, D.C. Ralph, Spin-transfer torque generated by a topological insulator, Nature 511 (2014) 449–451. [32] S. Fukami, C. Zhang, S. DuttaGupta, A. Kurenkov, H. Ohno, Magnetization switching by spin–orbit torque in an antiferromagnet–ferromagnet bilayer system, Nat. Mater. 15 (2016) 535–541. [33] Y.-W. Oh, S.-h.C. Baek, Y.M. Kim, H.Y. Lee, K.-D. Lee, C.-G. Yang, E.-S. Park, K.-S. Lee, K.-W. Kim, G. Go, J.-R. Jeong, B.-C. Min, H.-W. Lee, K.-J. Lee, B.-G. Park, Field-free switching of perpendicular magnetization through spin–orbit torque in antiferromagnet/ferromagnet/oxide structures, Nat. Nanotechnol. 11 (2016) 878–884. [34] W.A. Borders, H. Akima, S. Fukami, S. Moriya, S. Kurihara, Y. Horio, S. Sato, H. Ohno, Analogue spin–orbit torque device for artificial-neural-network-based associative memory operation, Appl. Phys. Express 10 (2017) 013007. [35] G.E.W. Bauer, E. Saitoh, B.J. van Wees, Spin caloritronics, Nat. Mater. 11 (2012) 391–399. [36] S.M. Rezende, R.L. Rodríguez-Suárez, R.O. Cunha, J.C. López Ortiz, A. Azevedo, Bulk magnon spin current theory for the longitudinal spin Seebeck effect, J. Magn. Magn. Mater. 400 (2016) 171–177. [37] V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, Y. Tserkovnyak, Antiferromagnetic spintronics, arXiv:1606.04284, 2016. [38] S. Seki, T. Ideue, M. Kubota, Y. Kozuka, R. Takagi, M. Nakamura, Y. Kaneko, M. Kawasaki, Y. Tokura, Thermal generation of spin current in an antiferromagnet, Phys. Rev. Lett. 115 (2015) 266601. [39] S.M. Rezende, R.L. Rodríguez-Suárez, A. Azevedo, Theory of the spin Seebeck effect in antiferromagnets, Phys. Rev. B 93 (2016) 014425. [40] W. Lin, K. Chen, S. Zhang, C.L. Chien, Enhancement of thermally injected spin current through an antiferromagnetic insulator, Phys. Rev. Lett. 116 (2016) 186601. [41] R. Khymyn, I. Lisenkov, V.S. Tiberkevich, A.N. Slavin, B.A. Ivanov, Transformation of spin current by antiferromagnetic insulators, Phys. Rev. B 93 (2016) 224421. [42] Y.-M. Hung, C. Hahn, H. Chang, M. Wu, H. Ohldag, A.D. Kent, Spin transport in antiferromagnetic NiO and magnetoresistance in Y3Fe5O12/NiO/Pt structures, AIP Adv. 7 (2017) 055903. [43] S.K. Kim, Y. Tserkovnyak, O. Tchernyshyov, Propulsion of a domain wall in an antiferromagnet by magnons, Phys. Rev. B 90 (2014) 104406. [44] S. Takei, B.I. Halperin, A. Yacoby, Y. Tserkovnyak, Superfluid spin transport through antiferromagnetic insulators, Phys. Rev. B 90 (2014) 094408. [45] P. Wadley, K. Oleynik, A. Hoffmann, H. Ohno, Spin-transport, spin-torque and memory in antiferromagnetic devices: part of a collection of reviews on antiferromagnetic spintronics, Nat. Phys., in press, arXiv:1705.10675, 2017. [46] X. Martí, I. Fina, C. Frontera, J. Liu, P. Wadley, Q. He, R.J. Paull, J.D. Clarkson, J. Kudrnovský, I. Turek, J. Kuneš, D. Yi, J.-H. Chu, C.T. Nelson, L. You, E. Arenholz, S. Salahuddin, J. Fontcuberta, T. Jungwirth, R. Ramesh, Room-temperature antiferromagnetic memory resistor, Nat. Mater. 13 (2014) 367–374.

7

[47] B.G. Park, J. Wunderlich, X. Martí, V. Holý, Y. Kurosaki, M. Yamada, H. Yamamoto, A. Nishide, J. Hayakawa, H. Takahashi, A.B. Shick, T. Jungwirth, A spinvalve-like magnetoresistance of an antiferromagnet-based tunnel junction, Nat. Mater. 10 (2011) 347–351. [48] C. Sürgers, G. Fischer, P. Winkel, H. von Löhneysen, Large topological Hall effect in the non-collinear phase of an antiferromagnet, Nat. Commun. 5 (2014) 3400. [49] T. Jungwirth, X. Martí, P. Wadley, J. Wunderlich, Antiferromagnetic spintronics, Nat. Nanotechnol. 11 (2016) 231–241. [50] M.J. Grzybowski, P. Wadley, K.W. Edmonds, R. Beardsley, V. Hills, R.P. Campion, B.L. Gallagher, J.S. Chauhan, V. Novak, T. Jungwirth, F. Maccherozzi, S.S. Dhesi, Imaging current-induced switching of antiferromagnetic domains in CuMnAs, Phys. Rev. Lett. 118 (2017) 057701. [51] S.Y. Bodnar, I. Turek, T. Jungwirth, O. Gomonay, J. Sinova, A.A. Sapozhnik, H.J. Elmers, M. Kläui, M. Jourdan, Writing and reading antiferromagnetic Mn2 Au: Néel spin–orbit torques and large anisotropic magnetoresistance, Nat. Commun. 9 (2018) 348. [52] J. Železný, H. Gao, K. Výborný, J. Zemen, J. Mašek, A. Manchon, J. Wunderlich, J. Sinova, T. Jungwirth, Relativistic Néel-order fields induced by electrical current in antiferromagnets, Phys. Rev. Lett. 113 (2014) 157201. [53] M. Meinert, D. Graulich, T. Matalla-Wagner, Key role of thermal activation in the electrical switching of antiferromagnetic Mn2Au, arXiv:1706.06983, 2017. [54] K.D. Belashchenko, Equilibrium magnetization at the boundary of a magnetoelectric antiferromagnet, Phys. Rev. Lett. 105 (2010) 147204. [55] T. Kosub, M. Kopte, F. Radu, O.G. Schmidt, D. Makarov, All-electric access to the magnetic-field-invariant magnetization of antiferromagnets, Phys. Rev. Lett. 115 (2015) 097201. [56] T. Kosub, M. Kopte, R. Hühne, P. Appel, B. Shields, P. Maletinsky, R. Hübner, M.O. Liedke, J. Fassbender, O.G. Schmidt, D. Makarov, Purely antiferromagnetic magnetoelectric random access memory, Nat. Commun. 8 (2017) 13985. [57] R. Khymyn, I. Lisenkov, V. Tiberkevich, B.A. Ivanov, A. Slavin, Antiferromagnetic THz-frequency Josephson-like oscillator driven by spin current, Sci. Rep. 7 (2017) 43705. [58] R. Cheng, D. Xiao, A. Brataas, Terahertz antiferromagnetic spin Hall nanooscillator, Phys. Rev. Lett. 116 (2016) 207603. [59] O. Gomonay, V. Baltz, A. Brataas, Y. Tserkovnyak, Part of a collection of reviews on antiferromagnetic spintronics. Antiferromagnetic dynamics, spin-textures, and nanostructures, arXiv:1705.10377, 2017. [60] J. Milano, L.B. Steren, M. Grimsditch, Effect of dipolar interaction on the antiferromagnetic resonance spectra of NiO, Phys. Rev. Lett. 93 (2004) 077601. [61] M. Grimsditch, L.E. McNeil, D.J. Lockwood, Unexpected behavior of the antiferromagnetic mode of NiO, Phys. Rev. B 58 (1998) 14462–14466. [62] K. Olejník, V. Schuler, X. Martí, V. Novak, Z. Kašpar, P. Wadley, R.P. Campion, K.W. Edmonds, B.L. Gallagher, J. Garces, M. Baumgartner, P. Gambardella, T. Jungwirth, Antiferromagnetic CuMnAs multi-level memory cell with microelectronic compatibility, Nat. Commun. 8 (2017) 15434. [63] K. Garello, C.O. Avci, I.M. Miron, M. Baumgartner, A. Ghosh, S. Auffret, O. Boulle, G. Gaudin, P. Gambardella, Ultrafast magnetization switching by spin–orbit torques, Appl. Phys. Lett. 105 (2014) 212402. [64] T. Shiino, S.-H. Oh, P.M. Haney, S.-W. Lee, G. Go, B.-G. Park, K.-J. Lee, Antiferromagnetic domain wall motion driven by spin–orbit torques, Phys. Rev. Lett. 117 (2016) 087203. [65] K.-J. Kim, S.K. Kim, T. Tono, S.-H. Oh, T. Okuno, W.S. Ham, Y. Hirata, S. Kim, G. Go, Y. Tserkovnyak, A. Tsukamoto, T. Moriyama, K.-J. Lee, T. Ono, Fast domain wall motion induced by antiferromagnetic spin dynamics at the angular momentum compensation temperature of ferrimagnets, Nat. Mater. 16 (2017) 1187–1192. [66] S.-H. Oh, S.K. Kim, D.-K. Lee, G. Go, K.-J. Kim, T. Ono, Y. Tserkovnyak, K.-J. Lee, Coherent terahertz spin-wave emission associated with ferrimagnetic domain wall dynamics, Phys. Rev. B 96 (2017) 100407. [67] L. Baldrati, A. Ross, T. Niizeki, C. Schneider, R. Ramos, J. Cramer, O. Gomonay, M. Filianina, T. Savchenko, D. Heinze, A. Kleibert, E. Saitoh, J. Sinova, M. Kläui, Full angular dependence of the spin Hall and ordinary magnetoresistance in epitaxial antiferromagnetic NiO(001)/Pt thin films, arXiv:1709.00910, 2017. [68] G.R. Hoogeboom, A. Aqeel, T. Kuschel, T.T.M. Palstra, B.J. van Wees, Negative spin Hall magnetoresistance of Pt on the bulk easy-plane antiferromagnet NiO, Appl. Phys. Lett. 111 (2017) 052409. [69] V. Saidl, P. Nemec, P. Wadley, V. Hills, R.P. Campion, V. Novak, K.W. Edmonds, F. Maccherozzi, S.S. Dhesi, B.L. Gallagher, F. Trojanek, J. Kuneš, J. Železný, P. Maly, T. Jungwirth, Optical determination of the Néel vector in a CuMnAs thin-film antiferromagnet, Nat. Photonics 11 (2017) 91–96. [70] I. Gross, W. Akhtar, V. Garcia, L.J. Martínez, S. Chouaieb, K. Garcia, C. Carrétéro, A. Barthélémy, P. Appel, P. Maletinsky, J.V. Kim, J.Y. Chauleau, N. Jaouen, M. Viret, M. Bibes, S. Fusil, V. Jacques, Real-space imaging of non-collinear antiferromagnetic order with a single-spin magnetometer, Nature 549 (2017) 252–256. [71] M.M. Waldrop, The chips are down for Moore’s law, Nat. News 530 (2016) 144–147. [72] O. Gomonay, T. Jungwirth, J. Sinova, Concepts of antiferromagnetic spintronics, Phys. Status Solidi RRL 11 (2017) 1700022.