Nonreciprocal directional dichroism (NDD) is a phenomenon in which the optical absorption is changed by reversing the direction of light propagation or the sign of the magnetic order parameters. While the NDD has mostly been observed in materials with macroscopic magnetization, recent experiments have shown that the NDD can be induced by a specific antiferromagnetic (AFM) spin structure that breaks both space-inversion and time-reversal symmetries. This opens the possibility of visualizing the spatial distribution of AFM domains via the NDD effect. This article reviews the basic features of the NDD, a brief history of the NDD in AFM materials, and recent achievements in visualizing AFM domains via the NDD and related optical responses, and finally provides a perspective on applications of this method for future AFM spintronics research.

The behavior of electric current and electromagnetic waves (light) propagating in ordinary systems remains unchanged when the direction of propagation is reversed. However, this so-called reciprocity of behavior can be violated in several systems.1 The most famous example is the semiconductor diode, which rectifies electric current and is widely used as an indispensable component in modern technologies. Such a nonreciprocal phenomenon is also seen in optics, as represented by the optical isolator that allows for the unidirectional propagation of light. In general, the nonreciprocal optical response is based on the linear magneto-optical effect (Faraday or Kerr effect) associated with the macroscopic magnetization (M) of a medium. Recently, a distinct type of nonreciprocal optical response has been intensively studied. One of the most prominent examples is the so-called nonreciprocal directional dichroism (NDD), in which the optical absorption of a medium is changed by reversing the direction of light propagation or the sign of the magnetic order parameters,2–6 as illustrated in Figs. 1(a) and 1(b). The NDD has been observed in a wide wavelength range from microwave,7,8 terahertz wave,9–13 (near-)visible light,14–23 to x ray,24–26 highlighting the generality of the NDD. From a symmetry point of view, the NDD can occur in a material breaking both space-inversion and time-reversal symmetries (see Sec. II).4 In typical cases, the space-inversion symmetry is broken by electric polarization (P) and chirality, while the time-reversal symmetry is broken by M. Consequently, most NDD phenomena have been observed in materials with both M and P [e.g., materials in an electric field (E) and a magnetic field (H),27 polar/ferroelectric materials in H,28 and polar ferro(ferri)magnets16] and those with both M and chirality (e.g., chiral paramagnets in H,14,25 helical magnets in H,11 and chiral ferromagnets29). Specifically, the NDD in the latter case is referred to as a magneto-chiral dichroism.14 

FIG. 1.

Illustrations of nonreciprocal directional dichroism (NDD). (a) The NDD is characterized by a change in optical absorption when the direction of light propagation is reversed between +k and −k. The thick gray plate indicates a sample. The size of the diameter of the yellow cylinders represents the intensity of the incident and transmitted light. (b) By reversing the magnetic order parameter (here, antiparallel spins are indicated by green arrows), the sign of NDD is also reversed.

FIG. 1.

Illustrations of nonreciprocal directional dichroism (NDD). (a) The NDD is characterized by a change in optical absorption when the direction of light propagation is reversed between +k and −k. The thick gray plate indicates a sample. The size of the diameter of the yellow cylinders represents the intensity of the incident and transmitted light. (b) By reversing the magnetic order parameter (here, antiparallel spins are indicated by green arrows), the sign of NDD is also reversed.

Close modal

However, even in the absence of M, NDD can occur in an AFM material whose fully compensated spin arrangement breaks both space-inversion and time-reversal symmetries. Representative examples of such spin-arrangements are illustrated in Figs. 2(a) and 2(b), often called magnetic toroidal type and magnetic quadrupole type, respectively, in the research field of multiferroics.30–34 In addition, space-inversion and time-reversal symmetries can be broken even by a simple antiparallel spin arrangement if each spin site lacks local inversion symmetry.35–38 Therefore, the NDD in AFM materials is considered to be nothing special. As discussed in Special Topics, AFM materials have recently attracted considerable attention due to their excellent properties, including no stray field, robustness against external fields, and fast spin dynamics.39,40 While most AFM materials are useless due to the absence of net magnetization, recent studies show that AFM materials with broken symmetries can exhibit corresponding macroscopic physical responses. The NDD introduced here can be regarded as a new optical function in such symmetry-broken AFM materials. While the achievement of gigantic NDDs or, ultimately, the one-way transparency of light, is of great interest in terms of technological applications, this is beyond the main scope of this article. It is also noteworthy that the NDD, being sensitive to the sign of the magnetic order parameters, allows the optical visualization of AFM domains without the need for any intense pulsed lasers or large quantum-beam facilities that have traditionally been used for AFM domain imaging. The achievement of NDD-based imaging of AFM domains can not only contribute to the development of AFM-based memory devices but also help us study the behavior of AFM domains in external fields. This article focuses on recent developments in the optical visualization of AFM domains via the NDD and provides a perspective on applications of this method for future AFM spintronics research.

FIG. 2.

(a) and (b) Magnetic toroidal type (a) and magnetic quadrupole type (b) spin arrangements that break both space-inversion and time-reversal symmetries. The green arrows indicate spins.

FIG. 2.

(a) and (b) Magnetic toroidal type (a) and magnetic quadrupole type (b) spin arrangements that break both space-inversion and time-reversal symmetries. The green arrows indicate spins.

Close modal

The NDD can be understood as a consequence of the linear magnetoelectric (ME) effect on electromagnetic waves.2,3 The linear ME effect is a cross-coupling between electric and magnetic dipole degrees of freedom, where M is induced by a static E or P is induced by a static H.41 Since both space-inversion and time-reversal symmetries must be broken for the linear ME effect to occur, the resulting NDD must also satisfy the same symmetry requirements. Extending the linear ME effect to the optical regime, one can see that an oscillating H (E) of light traveling in a medium can give rise to an oscillating electric polarization PHω (magnetization). This is often called the optical ME (OME) effect. If the ME tensor at the frequency ω (χω) has off-diagonal elements, PHω can have a component parallel or antiparallel to the ordinary oscillating electric polarization PEω induced by the electric field of light Eω, as shown in Fig. 3. Then, PHω and PEω can interfere with each other, either constructively or destructively. When the direction of light propagation is reversed, the sign of PHω is reversed with respect to that of PEω. As a result, the constructive interference is changed into destructive interference, which leads to nonreciprocal optical responses, including the NDD. For more detailed considerations on the NDD, including derivations based on the Maxwell equations, see, e.g., Ref. 10. Furthermore, since the sign of χω, and thus the sign of the NDD, is opposite between a pair of AFM domains associated with the time-reversal operation, the NDD can be used to distinguish such AFM domains. The NDD is classified as a linear optical response and can, therefore, be observed without the need for an intense light source such as a pulsed laser. This opens up the possibility of visualizing AFM domains using a standard optical microscope with less intense light sources such as a light-emitting diode (LED), as will be demonstrated in Sec. III.

FIG. 3.

Propagation of electromagnetic waves in a linear magnetoelectric (ME) medium with off-diagonal components of the ME tensor. In addition to an oscillating electric polarization PEω induced by an oscillating electric field Eω of light, an oscillating electric polarization PHω is also induced by the magnetic field of light Hω through the optical ME effect. PHω and PEω can interfere with each other either constructively or destructively. When the direction of light propagation (k) is reversed, the constructive interference is changed to destructive interference, resulting in nonreciprocal optical responses, including NDD.

FIG. 3.

Propagation of electromagnetic waves in a linear magnetoelectric (ME) medium with off-diagonal components of the ME tensor. In addition to an oscillating electric polarization PEω induced by an oscillating electric field Eω of light, an oscillating electric polarization PHω is also induced by the magnetic field of light Hω through the optical ME effect. PHω and PEω can interfere with each other either constructively or destructively. When the direction of light propagation (k) is reversed, the constructive interference is changed to destructive interference, resulting in nonreciprocal optical responses, including NDD.

Close modal

It is also worth noting that while the off-diagonal elements of the ME tensor contribute to the NDD, the diagonal elements can contribute to a distinct type of nonreciprocal optical responses. Examples include gyrotropic birefringence42,43 and nonreciprocal rotation (NRR) of the polarization angle of reflected light.42,44–46 Like NDD, these phenomena are of opposite sign for a time-reversed pair of AFM domains and can thus be used to visualize AFM domains.

1. Brief history

At the end of this section, we briefly review the history of OME research on AFM materials. The OME effects were first predicted by theoretical studies as early as the 1960s,42,47–49 soon after the first discovery of the static linear ME effect in the insulating AFM material Cr2O3.41 The possibility of visualizing AFM domains via the OME effect was also proposed in 1963.50 Since then, however, there has been no observation of the OME-related optical responses for AFM materials until Pisarev and co-workers observed the gyrotropic birefringence at a near-infrared wavelength for Cr2O3 in 1991.44 Subsequently, in 1993, Krichevtsov and co-workers reported NRR at a visible wavelength for Cr2O3.45 They also reported the switching of the sign of the NRR between a time-reversed pair of AFM domains. To our knowledge, this is the first demonstration of AFM domain identification via the OME effect. Then, after a long hiatus, in 2018, Kocsis and co-workers demonstrated the optical identification of AFM domains via the NDD at terahertz wavelengths for the insulating ME material LiCoPO4.13 More recently, in 2020, Kimura and co-workers reported the NDD-based visualization of the spatial distribution of AFM domains in the insulating ME material Pb(TiO)Cu4(PO4)4 using an optical microscope,21 as will be reviewed in Sec. III. After the initial demonstration, the OME-based AFM-domain visualization has been extended to several AFM materials and has helped to reveal their intriguing properties. Some of these will be reviewed in the following.

First, we describe a principle for visualizing AFM domains via NDD. For an AFM material exhibiting the NDD, the absorption coefficient for a fixed light propagation direction is different between the opposite AFM domain states (labeled as A+ and A−). As shown in Fig. 4, when light is incident on a single-crystal sample with both A+ and A−, the transmitted light intensity after passing through the A+ and A− regions will be different from each other. Accordingly, the spatial distribution of the light intensity directly reflects that of the AFM domains, which can be visualized with a standard optical microscope using a low-cost light source such as LEDs. The quality of the domain images can be improved by additional image processing (e.g., background subtraction and light polarization analysis).

FIG. 4.

Principle of optical visualization of antiferromagnetic (AFM) domains via NDD using optical microscopy. A+ and A− denote a time-reversed pair of AFM domains. Green arrows represent spins. The diameters of the cyan circles correspond to the incident and transmitted light intensities. Double-headed arrows indicate the direction of light polarization. The spatial distribution of the AFM domains is translated into that of the transmitted light intensity and can thus be visualized by a camera.

FIG. 4.

Principle of optical visualization of antiferromagnetic (AFM) domains via NDD using optical microscopy. A+ and A− denote a time-reversed pair of AFM domains. Green arrows represent spins. The diameters of the cyan circles correspond to the incident and transmitted light intensities. Double-headed arrows indicate the direction of light polarization. The spatial distribution of the AFM domains is translated into that of the transmitted light intensity and can thus be visualized by a camera.

Close modal

As described earlier, the NDD-based optical visualization of AFM domains was first achieved on an insulating antiferromagnet Pb(TiO)Cu4(PO4)4. As illustrated in Figs. 5(a) and 5(b), this material has a tetragonal crystal structure and exhibits a highly complex spin structure below TN = 7 K. The spin structure is of the magnetic quadrupolar type [see Fig. 2(b)], thus breaking the space-inversion and time-reversal symmetries. The plus and minus signs of the quadrupoles correspond to the opposite AFM domains (Q+ and Q−), which are related to time reversal. The magnetic point group is 4′22′, where symmetric off-diagonal components in χω can be finite. Solving the Maxwell equations suggests that NDD appears for light traveling along the z axis (±kz), and the sign of NDD is reversed by switching the light polarization direction Eω between the x||[110] and y||[1¯10] axes. In this sense, the NDD in Pb(TiO)Cu4(PO4)4 should be referred to as nonreciprocal linear dichroism (NLD), but we will continue to use the term NDD for simplicity.

FIG. 5.

Optical visualization of antiferromagnetic (AFM) domains in Pb(TiO)Cu4(PO4)4. (a) and (b) Magnetic structures for (a) Q+ and (b) Q− AFM domains. (c) Absorption coefficient spectra for Q+ [α(Q+)] and Q− [α(Q−)] in the photon energy range 1.2 < Eph < 2.5 eV. (d) Subtraction spectra Δαα(Q+) − α(Q−) for opposite directions of light propagation (+kz and −kz). (e) Light polarization (Eω) dependence of Δα. (f) Two-dimensional map of Δα obtained at 5 K < TN. The color contrast corresponds to the AFM domains. Adapted from Ref. 21.

FIG. 5.

Optical visualization of antiferromagnetic (AFM) domains in Pb(TiO)Cu4(PO4)4. (a) and (b) Magnetic structures for (a) Q+ and (b) Q− AFM domains. (c) Absorption coefficient spectra for Q+ [α(Q+)] and Q− [α(Q−)] in the photon energy range 1.2 < Eph < 2.5 eV. (d) Subtraction spectra Δαα(Q+) − α(Q−) for opposite directions of light propagation (+kz and −kz). (e) Light polarization (Eω) dependence of Δα. (f) Two-dimensional map of Δα obtained at 5 K < TN. The color contrast corresponds to the AFM domains. Adapted from Ref. 21.

Close modal

Figure 5(c) shows the absorption coefficient (α) spectra for a single-crystal sample with Q+ [α(Q+)] and Q− [α(Q−)] in the visible to near-infrared regions, whose energies correspond to Cu2+ dd transitions. It is found that α is changed by switching between Q+ and Q− domains. Moreover, the sign of the subtraction spectra Δαα(Q+) − α(Q−) is reversed upon reversing the light propagation direction (+kz ↔ −kz) [Fig. 5(d)] and switching of Eω between x and y [Fig. 5(e)], confirming the NDD expected for the magnetic symmetry. Notably, the relative change in the absorption coefficient Δα/α0 [α0 is an average of α(Q+) and α(Q−)] is up to 4% at about 1.8 eV (=700 nm), which is more than an order of magnitude larger than the previously reported value of NDD or related effects for AFM materials at visible to near-infrared wavelengths. Therefore, Pb(TiO)Cu4(PO4)4 is considered suitable for demonstrating the NDD-based optical visualization of AFM domains.

Figure 5(f) shows an image of a single crystal sample at 5 K obtained by conventional optical microscopy using a 700 nm LED light source. The image was obtained as the difference of two images taken at x and y polarizations. A clear contrast with a stripe-pattern is observed, which corresponds to the spatial distribution of the AFM domains. The direction of the stripe pattern does not coincide with any high symmetry axes in this compound. Therefore, thermal stress during cooling and/or a possible crystalline defect formed in the single-crystal sample are likely origins. We also display in Fig. 6(a) a series of images of another crystal taken at different electric field strengths under a constant magnetic field. Electric-field switching of the AFM domains is clearly observed, and its hysteretic behavior is revealed by an electric-field dependence of the AFM domain fraction [Fig. 6(b)]. These results illustrate that the NDD efficiently visualizes AFM domains responding to external fields.

FIG. 6.

Visualization of AFM domains in Pb(TiO)Cu4(PO4)4 in response to external fields. (a) AFM domain images in a sequentially applied electric field (E) in the presence of a biased magnetic field (B). Both E and B are along the a axis. More red (blue) color corresponds to a larger fraction of domain Q+ (Q−). (b) The E dependence of a volume fraction of Q+. The Roman numerals in (b) correspond to the images in (a). Adapted from Ref. 21.

FIG. 6.

Visualization of AFM domains in Pb(TiO)Cu4(PO4)4 in response to external fields. (a) AFM domain images in a sequentially applied electric field (E) in the presence of a biased magnetic field (B). Both E and B are along the a axis. More red (blue) color corresponds to a larger fraction of domain Q+ (Q−). (b) The E dependence of a volume fraction of Q+. The Roman numerals in (b) correspond to the images in (a). Adapted from Ref. 21.

Close modal

In this section, we review a more recent study that extended the NDD-based approach to the visualization of multi-state AFM domains.22 The material of interest here is Bi2CuO4, which can be viewed as an insulating version of the representative spintronic AFM material CuMnAs.51 Similar to CuMnAs, Bi2CuO4 has a tetragonal crystal structure and undergoes a transition (TN = 44 K) to a collinear AFM phase in which the spins are antiparallel aligned and oriented in the tetragonal xy plane, as shown in Fig. 7(a). This leads to the formation of four types of AFM domain states with Néel vectors (L) parallel to the +x, −x, +y, and −y directions, which are labeled as Lx+, Lx, Ly+, and Ly, respectively [Fig. 7(b)]. Here, the direction of L is defined as parallel to the Cu1 spin. Due to the lack of local inversion symmetry at the Cu sites, this collinear spin structure (magnetic point group m′mm) breaks both space-inversion and time-reversal symmetries, thus inducing NDD for light traveling in the xy plane and perpendicular to L. The NDD-induced change in the absorption coefficient δα has a sin θ dependence, where θ denotes an angle between L and the light propagation vector k. Therefore, as shown in Fig. 7(b), when light is incident along the x (or y) axis, the NDD takes three different values depending on the spin direction, allowing for optical visualization of three out of four AFM domains.

FIG. 7.

Visualization of four-state AFM domains in Bi2CuO4. (a) Magnetic structure of Bi2CuO4. Magenta arrows indicate Cu spins. (b) Four types of AFM domains, indicated by the direction of the Néel vector L. The direction of L is defined as parallel to the Cu1 spins. When light is incident in the xy plane with the propagation vector k, a change in the absorption coefficient (δα) due to NDD has a sin θ dependence, where θ is an angle between L and k. For fixed k||+x, δα takes three different values for the respective domains (shown at the bottom), as conceptually represented by three colors (blue, red, and white). (c) Absorption coefficient spectra for Ly+ and Ly at 5 K in the photon energy range of 1.5 < Eph < 2.0 eV. (d) Subtraction spectra for opposite directions of light propagation (+kx and −kx). (e) A sequence of two-dimensional maps of α′ at 5 K in varying magnetic fields of (e) 0, (f) 0.36, and (g) 0.58 T applied along the y axis. Here, α′ is the variation of the absorption coefficient from 50 K (>TN). Blue, red, and white colors correspond to Ly+, Ly, and Lx+ (or Lx−) domains, respectively. Adapted from Ref. 22.

FIG. 7.

Visualization of four-state AFM domains in Bi2CuO4. (a) Magnetic structure of Bi2CuO4. Magenta arrows indicate Cu spins. (b) Four types of AFM domains, indicated by the direction of the Néel vector L. The direction of L is defined as parallel to the Cu1 spins. When light is incident in the xy plane with the propagation vector k, a change in the absorption coefficient (δα) due to NDD has a sin θ dependence, where θ is an angle between L and k. For fixed k||+x, δα takes three different values for the respective domains (shown at the bottom), as conceptually represented by three colors (blue, red, and white). (c) Absorption coefficient spectra for Ly+ and Ly at 5 K in the photon energy range of 1.5 < Eph < 2.0 eV. (d) Subtraction spectra for opposite directions of light propagation (+kx and −kx). (e) A sequence of two-dimensional maps of α′ at 5 K in varying magnetic fields of (e) 0, (f) 0.36, and (g) 0.58 T applied along the y axis. Here, α′ is the variation of the absorption coefficient from 50 K (>TN). Blue, red, and white colors correspond to Ly+, Ly, and Lx+ (or Lx−) domains, respectively. Adapted from Ref. 22.

Close modal

Figures 7(c) and 7(d) show the visible to near-infrared absorption coefficient (α) spectra at fixed k||+x for opposite AFM domains, Ly+ (sinθ = 1) and Ly (sin θ = −1), and corresponding subtraction spectra for opposite signs of k, respectively. As in Pb(TiO)Cu4(PO4)4, the α in Bi2CuO4 is changed by switching either L or k, confirming the NDD. Remarkably, the relative change in α (i.e., the magnitude of the NDD) reaches up to 40% at 1.65 eV (750 nm), which is an order of magnitude larger than ∼4% in Pb(TiO)Cu4(PO4)4. This result highlights the potential of AFM materials as novel types of nonreciprocal optical devices. The observed giant NDD originates from Cu2+ dd transitions. Details are described in Ref. 22.

Figure 7(e) displays an optical microscopy image of a Bi2CuO4 single crystal at 5 K and zero field using a standard optical microscope with a 750 nm LED light source. The image is based on the two-dimensional map of Δα′ = α(5 K) − α(50 K). Unexpectedly, there is only a two-level contrast, meaning that there are only Ly+ (blue) and Ly (red) domains. In contrast, as can be seen in Fig. 7(g), in a high magnetic field of 0.58 T applied along the existing spin axes (||y), the image becomes completely uniform (white). This indicates that Ly+ and Ly in the entire sample region have been transformed by the field into Lx+ and Lx, most likely by a spin-flop process. Here, Lx+ and Lx cannot be distinguished because the light is incident along the x axis. However, as demonstrated in Fig. 8, Lx+ and Lx can be distinguished using a slightly tilted incident light. These results show that all four AFM domains can be optically visualized using the NDD.

FIG. 8.

Visualization of “hidden” AFM domains with slightly tilted incident light. As seen in the left panel, in an applied magnetic field of 0.58 T, the AFM domains (Lx+ and Lx) are indistinguishable when the light propagation direction is parallel to the x axis. In contrast, as seen in the right panel, the two AFM domains are clearly distinguishable when the light propagation direction is slightly tilted by ∼8° from the x axis to the y axis. Adapted from Ref. 22.

FIG. 8.

Visualization of “hidden” AFM domains with slightly tilted incident light. As seen in the left panel, in an applied magnetic field of 0.58 T, the AFM domains (Lx+ and Lx) are indistinguishable when the light propagation direction is parallel to the x axis. In contrast, as seen in the right panel, the two AFM domains are clearly distinguishable when the light propagation direction is slightly tilted by ∼8° from the x axis to the y axis. Adapted from Ref. 22.

Close modal

It has been shown that the field-induced transformation of AFM domains proceeds in a spatially inhomogeneous manner. As shown in Fig. 7(f), as the field is increased, the Lx+ (Lx) domains (white color) appear in such a way that they form a stripe pattern intersecting the low-field Ly+ and/or Ly domains. This leads to the coexistence of four AFM domains at about 0.36 T before the uniform state is formed at a higher field. Furthermore, it was also found that the shape of the boundary between Ly+ and Ly, namely, the 180° AFM domain wall, is changed by an applied magnetic field: it is rounded at zero-field and straight at 0.36 T. Such a field-induced change in the shape of the 180° AFM domain wall is unexpected and surprising, and elucidating this behavior is an interesting future topic. These observations highlight that the NDD-based AFM-domain visualization provides much new information about the responses of AFM to external fields.

As further research progresses, we present here a recent demonstration of AFM-domain visualization via NRR in the reflection geometry. As briefly described in Sec. II, NRR is another manifestation of the OME effect, which is induced by the diagonal components of χω. Its physical appearance is essentially the same as the magneto-optical Kerr effect (although their mechanisms are different), i.e., the polarization angle of linearly polarized incident light is rotated upon the reflection at the surface of a single-crystal sample. While the NRR was observed for Cr2O3 as early as the 1990s, the rotation angle θ was found to be small, on the order of 10−3 (deg) at visible wavelengths,45,52 making the NRR-based AFM-domain visualization a challenge. Nevertheless, in 2022, Hayashida and co-workers46 successfully visualized the AFM domains of Cr2O3 using optical microscopy combined with a polarization-modulation technique.53 The experimental setup is shown in Fig. 9(a). In this technique, a liquid-crystal variable retarder is used to switch the polarization state of the incident light, and reflection microscopy images were taken alternately with linearly polarized (ILP) and right-circularly polarized (IRCP) incident light. The transmission axis of an analyzer placed behind the sample is 45° to the polarization direction of the linearly polarized incident light. If θ and the associated circular dichroism are small enough, θ is calculated for each pixel of the camera as ΔI/I0θ(π/180), where ΔIILPIRCP and I0 ≡ (ILP + IRCP)/2. By taking a large number (15 000) of ΔI/I0 maps and averaging them, one can detect a small θ signal of the order of ∼10−4 (deg). Figure 9(c) shows an AFM domain image of a Cr2O3 single crystal at 270 K obtained using visible light (1.91 eV), where bright and dark regions correspond to a time-reversal pair of AFM domains with opposite θ signs [L+ and L−, see Fig. 9(b)]. The result confirms that the AFM domains of ME materials with diagonal components of χω can be visualized via the NRR in the reflection geometry.

FIG. 9.

(a) A schematic illustration of the optical setup for the NRR-based AFM-domain imaging. P: Polarizer; L: Lens; S: Sample; A: Analyzer; D: Si-detector; Q: Quarter-wave plane; LED: LED light source; OL: Objective lens; C: sCMOS camera; LC: Liquid crystal variable retarder; BS: Beam splitter. (b) A time-reversed pair of AFM domains in Cr2O3 (L+ and L−). The Cr spins of sites A and B are indicated by red arrows for L+ and blue arrows for L−. (c) AFM domains of Cr2O3 visualized by the NDD at 1.91 eV. Adapted from Ref. 46.

FIG. 9.

(a) A schematic illustration of the optical setup for the NRR-based AFM-domain imaging. P: Polarizer; L: Lens; S: Sample; A: Analyzer; D: Si-detector; Q: Quarter-wave plane; LED: LED light source; OL: Objective lens; C: sCMOS camera; LC: Liquid crystal variable retarder; BS: Beam splitter. (b) A time-reversed pair of AFM domains in Cr2O3 (L+ and L−). The Cr spins of sites A and B are indicated by red arrows for L+ and blue arrows for L−. (c) AFM domains of Cr2O3 visualized by the NDD at 1.91 eV. Adapted from Ref. 46.

Close modal

With the above-mentioned recent achievements in visualizing AFM domains via NDD and related optical responses, this section provides perspectives on the future applications of this method for AFM spintronics research.

The dynamics of AFM domain walls driven by external fields, such as a magnetic field, an electric field, a laser pulse, temperature change, etc., has been one of the central topics in AFM spintronic research. Domains are spatially inhomogeneous objects, and their dynamics are usually indeterministic. Therefore, an external-field-pump-optical-probe technique, which is often used to track the ultrafast dynamics of repeatable phenomena, may not work well for the study of domain dynamics. As emphasized in Sec. II, the NDD is classified as linear optics and can, therefore, produce much larger signals than nonlinear optics. Thanks to this advantage, it is not difficult to obtain a “single-shot” AFM domain image in a time as short as ∼1 ms, even using a less-expensive commercial camera and less-intense light sources such as LEDs. The combination of a high-speed camera or a streak camera with a more intense light source can further reduce the image acquisition time, presumably down to ∼1 ns or less. Therefore, NDD-based imaging may be a unique and powerful technique for tracking the temporal evolution of AFM domains. So far, NDD-based imaging has only been applied to the relatively slow (millisecond) motion of AFM domain walls in the insulating material MnTiO3 with a collinear spin structure.54 The application of this method to other different AFM materials can greatly contribute to a deeper understanding of the physics of AFM domain wall dynamics. In particular, the electric-field-driven dynamics of the AFM domain walls through the ME couplings is worth investigating for the development of future low-power devices based on AFM materials.

As presented earlier, NDD-based domain imaging has been successfully applied to several AFM insulators. However, because of the transmission geometry in the experiments, NDD-based imaging can hardly be applied to AFM materials with strong light absorption. Such materials include metallic AFM materials and topological AFM insulators, the cutting-edge systems in materials science. By contrast, NRR-based imaging can overcome this difficulty as it utilizes reflected light from a single-crystal sample of a target AFM material. Therefore, applications of NRR-based imaging to the study of metallic or topological AFM materials are an interesting future research direction. We note that during the preparation of the present manuscript, Qiu and co-workers55 reported an exciting discovery of an axion induction of AFM order in the topological insulator MnBi2Te4, where the OME-induced circular dichroism (imaginary part of the NRR) was used to visualize its AFM domains. This exemplifies the efficiency of NRR-based domain imaging in the study of exotic AFM materials. As described in Secs. II and IV, the NRR can be observed in AFM materials with diagonal components of χω, and many such AFM materials can be found in the literature and magnetic structure databases. We believe that NRR-based domain imaging will provide new insight into the physics of exotic AFM materials.

In this article, we reviewed the recent developments in the detection of antiferromagnetic (AFM) domains by nonreciprocal directional dichroism (NDD), with particular emphasis on the optical visualization of the spatial distribution of AFM domains in single-crystal samples. Although the first success of this visualization via NDD was achieved only recently (in 2020), its efficiency and applicability were immediately demonstrated by subsequent studies on several AFM materials. The method has been further extended to the use of nonreciprocal rotation (NRR) of reflected light, a phenomenon closely related to NDD, which allows us to visualize AFM domains not only in conventional insulators but also in metals and topological insulators. These techniques will greatly contribute to a deeper understanding of AFM domain physics in various AFM materials, including AFM domain formation mechanisms and domain-wall motion driven by external stimuli such as thermal gradients, voltage pulses, electric currents, and light pulses.

The authors are grateful to T. Hayashida, K. Arakawa, T. Ohshima, Y. Otake, S. Kimura, N. Abe, and T. Arima for fruitful discussions. The schematics of the crystal structures were drawn using the software VESTA.56 K. K. acknowledges support from JSPS KAKENHI under Grant No. JP19H01847, the MEXT Leading Initiative for Excellent Young Researchers (LEADER), the Murata Science Foundation, and the Iketani Science and Technology Foundation. T. K. acknowledges support from JSPS KAKENHI under Grant Nos. JP19H05823, JP21H04436, and JP21H04988. This work was partly performed at the High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University (Project No. 202112-HMKGE-0013).

The authors have no conflicts to disclose.

Kenta Kimura: Funding acquisition (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Tsuyoshi Kimura: Funding acquisition (equal); Writing – review & editing (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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