Magneto-Seebeck microscopy of domain switching in collinear antiferromagnet CuMnAs

Antiferromagnets offer spintronic device characteristics unparalleled in ferromagnets owing to their lack of stray fields, THz spin dynamics, and rich materials landscape. Microscopic imaging of aniferromagnetic domains is one of the key prerequisites for understading physical principles of the device operation. However, adapting common magnetometry techniques to the dipolar-field-free antiferromagnets has been a major challenge. Here we demonstrate in a collinear antiferromagnet a thermoelectric detection method by combining the magneto-Seebeck effect with local heat gradients generated by scanning far-field or near-field techniques. In a 20 nm epilayer of uniaxial CuMnAs we observe reversible 180 deg switching of the N\'eel vector via domain wall displacement, controlled by the polarity of the current pulses. We also image polarity-dependent 90 deg switching of the N\'eel vector in a thicker biaxial film, and domain shattering induced at higher pulse amplitudes. The antiferromagnetic domain maps obtained by our laboratory technique are compared to measurements by the established synchrotron microscopy using X-ray magnetic linear dichroism.

Antiferromagnets offer spintronic device characteristics unparalleled in ferromagnets owing to their lack of stray fields, THz spin dynamics, and rich materials landscape. Microscopic imaging of antiferromagnetic domains is one of the key prerequisites for understanding physical principles of the device operation. However, adapting common magnetometry techniques to the dipolar-fieldfree antiferromagnets has been a major challenge. Here we demonstrate in a collinear antiferromagnet a thermoelectric detection method by combining the magneto-Seebeck effect with local heat gradients generated by scanning far-field or near-field techniques. In a 20 nm epilayer of uniaxial CuMnAs we observe reversible 180 • switching of the Néel vector via domain wall displacement, controlled by the polarity of the current pulses. We also image polarity-dependent 90 • switching of the Néel vector in a thicker biaxial film, and domain shattering induced at higher pulse amplitudes. The antiferromagnetic domain maps obtained by our laboratory technique are compared to measurements by the established synchrotron-based technique of x-ray photoemission electron microscopy using X-ray magnetic linear dichroism.
Writing and reading by electrical and optical means, high speed operation combined with neuromorphic memory characteristics, and novel topological phenomena are among the topics that have driven the research in the emerging field of antiferromagnetic spintronics 1-6 .
The development of devices whose operation is based on antiferromagnets was initiated by theoretical predictions 7,8 and subsequent experimental demonstrations of electrical detection and manipulation of the antiferromagnetic order by relativistic anisotropic magnetoresistance (AMR) and Néel spin-orbit torque (NSOT) effects in metallic antiferromagnets 9-12 .
From the early days of the antiferromagnetic spintronics research, a special attention is paid to complementing these electrical measurements by direct microscopic imaging of the typically multidomain states of the studied antiferromagnets 11,13-21 . The aim of these microscopies is to elucidate physical mechanisms of the switching which, e.g., in CuM-nAs have been associated with the Néel vector reorientation induced by the NSOT, and with electrical or optical pulse-induced quenching into paidnano-fragmented domain states of the antiferromagnet 20,21 . The microscopies are also essential for disentangling potential parasitic non-magnetic contributions to the resistive switching signals, as reported in metal/antiferromagnetic-insulator bilayers 19,22-26 .
However, established microscopy techniques for imaging antiferromagnets are rare and rely primarily on large-scale experimental facilities. Among these, X-ray magnetic linear dichroism combined with photoemission electron microscopy (XMLD-PEEM) 27 was used to visualize the electrical control of the Néel vector in CuMnAs, Mn 2 Au, or NiO 11, [13][14][15]18,19 .
In CuMnAs, the XMLD-PEEM images of the onset of current-induced NSOT reorientation of the Néel vector were directly linked to the onset of the corresponding electrical readout signals due to AMR 13,14 . 90 • Néel vector switching was observed by XMLD-PEEM for orthogonal writing currents 11,13 or, via domain wall motion, when reversing the polarity of the writing current 14 . Since XMLD-PEEM is a synchrotron-based technique, more accessible table-top microscopies are necessary for a systematic exploration of antiferromagnetic devices. An example here is the NV-diamond magnetometry 28,29 which was recently reported in antiferromagnetic Cr 2 O 3 , BiFeO 3 , and CuMnAs 20,30,31 , and which relies on stray-fields generated by uncompensated magnetic moments.
In this work we investigate current pulse-induced changes of the domain structure in the compensated collinear antiferromagnet CuMnAs 32,33 , focusing on 90 • and 180 • Néel vector switching as well as domain fragmentation. For the microscopic imaging we utilize a thermoelectric response due to the magneto-Seebeck effect (MSE), which is a thermal analog of AMR. The MSE can be applied to the large class of conductive antiferromagnets and is not limited to either uncompensated antiferromagnets that still produce detectable magnetic stray fields, or to systems whose additional broken symmetries allow for the anomalous Nernst effect or the magnetooptical Kerr effect, such as non-collinear antiferromagnets.
The MSE response is mapped to a laser-induced localized temperature gradient in the device. A thermoelectric voltage signal is measured across the entire bar device when the scanning probe is placed on top of an antiferromagnetic texture with spatially varying Néel vector.
We employ two techniques: The first one is based on the scanning far-field optical microscopy (SFOM) 34 , which in combination with anomalous Nernst or spin-Seebeck thermoelectric response was employed in earlier studies of a non-collinear antiferromagnet Mn 3 Sn and a metal/antiferromagnetic-insulator bilayer Pt/NiO, respectively 16,17 . In the second, high-resolution approach we utilize photocurrent nanoscopy in a scattering-type scanning near-field optical microscope (SNOM) [35][36][37] . Here a metal-coated tip of an atomic force mi-croscope (AFM) placed in close proximity to the CuMnAs surface acts as an optical antenna for light focused on the tip. The incident electric field is strongly confined around the tip apex, providing a nanoscale near field point source. Since, to the best of our knowledge, the scanning optical microscopy combined with MSE has not been applied to antiferromagnets prior to our work, we provide comparisons to images obtained by the established synchrotron XMLD-PEEM technique.
Comparison of optical-thermoelectric and X-ray microscopies of CuMnAs domains In Fig. 1a we illustrate our SFOM-MSE technique on two neighbouring antiferromagnetic domains separated by a 90 • domain wall. We use a 800 nm wavelength cw-laser beam of 1 mW power focused to a spot with a full-width at half-maximum (FWHM) of ≈ 1 µm on the surface of the CuMnAs antiferromagnet. The laser spot generates a lateral radially symmetric temperature gradient and we monitor the laser-induced thermoelectric voltage, V T , at the two ends of the bar device. Non-zero V T may occur when the temperature gradient crosses an antiferromagnetic domain boundary, as shown schematically in Fig. 1a. This is because the Néel vector reorients and, therefore, the magneto-Seebeck coefficient changes 38 so that the net thermoelectric signal does not cancel. As we show in the Supplementary Note 1, we can reproduce the sign and magnitude of the measured V T signal with a magneto-Seebeck coefficient ∆S = S c − S p = 4 µV/K by considering the boundary conditions of our open circuit configuration, thermal conductivities of 200 W/(K·m) and 75 W/(K·m) for the metallic CuMnAs film and for the insulating GaP substrate, respectively, and by assuming that 50 % of the laser power is absorbed within the metallic CuMnAs layer. Here S c (S p ) is the Seebeck coefficient when the Néel vector is collinear (perpendicular) to the temperature gradient. Note that the calculated maximum temperature rise at 5 mW laser power, the highest power used in our SFOM-MSE experiments, is not greater than 6 K (see Supplementary Note 1). We also verified that anisotropies of the conductivity, e.g., due to AMR, give a negligible contribution to the thermoelectric voltage signal.
The optical micrograph in Fig. 1b   The analogous overall structure of the SFOM-MSE and XMLD-PEEM images confirms that the main contribution to the thermoelectric voltage signal comes from the antiferromagnetic texture and the corresponding variation of the magneto-Seebeck coefficient. Quantitative differences between the two measurements can be ascribed to different lateral resolution and depth sensitivity of the two techniques. The lateral resolution of the XMLD-PEEM in the metallic antiferromagnet CuMnAs is about 50 nm while the resolution of the SFOM-MSE is limited by the thermal gradient generated by the ∼ 1 µm wide Gaussian shaped laser spot.
Regarding the depth sensitivity, the photo-electrons in the XMLD-PEEM are detected only from a few-nm surface layer of the antiferromagnet while the thermoelectric measurements probe the full thickness of the antiferromagnetic film. Note also that the XMLD-PEEM measurements were performed about 10 days before the SFOM-MSE measurements.

Optical thermoelectric imaging of the current-induced switching
We now use the SFOM method to correlate the local magnetic domain structure to electrical resistance variation after current pulse excitation, which further evidences that the image contrast we detect is indeed of magnetic origin. We simultaneously measure the thermoelectric signals along the vertical and horizontal bars in a symmetric 5 µm wide cross bar geometry, shown in Fig. 2a . The vertical and horizontal SFOM-MSE voltages   This is consistent with the NSOT switching mechanism which was identified in the earlier XMLD-PEEM study at comparable amplitudes of the current pulses 14 . Note that we observe a change in resistance of about 4%. This is larger than the expected AMR due to 90 • Néel vector reorientation inside a domain 14,39 and indicates that additional effects contribute to the variation of R || in our multidomain state.
To further evidence the reversible NSOT switching controlled by the current polarity we measure a 10 µm wide symmetric cross bar device, shown in  Figure 5b shows a micrograph of a 2 µm wide CuMnAs bar device below the cantilever with the AFM tip. The thermoelectric voltage, V T , generated in the channel is analyzed by a lock-in amplifier at the AFM tip modulation frequency Ω. For tip enhanced focusing we use a scattering-type SNOM operated in the tapping mode. A gold coated Si cantilever with a typical tip diameter below 50 nm oscillates with an amplitude of 80 nm above the sample surface at its mechanical resonance frequency Ω ≈ 240 kHz. The continuous wave emission of a quantum cascade laser is focused onto the tip apex which acts as an antenna transmitting a strongly confined near-field to the sample surface. In contrast to our diffraction-limited SFOM method with λ = 800 nm excitation wavelength, we use here a laser emission with mid-infrared wavelength because the longer wavelength couples more efficiently into the AFM tip and the resolution of this near-field method is not diffraction limited. Figure 5c shows, from left to right, the AFM topography image, the magnitude of the thermoelectric voltage |V T |, and its sign sgn(V T ), all detected simultaneously during the SNOM-MSE measurement. As evident from the comparison between the SNOM-MSE signal and the AFM topography, the majority of the features appearing in the MSE map do not correlate with defects in the topography. We therefore conclude that also in this uniaxial material the contrast originates dominantly from the antiferromagnetic texture. In order to highlight the position of the 180 • domain walls, we plot the absolute value of the measured signal alongside with its polarity. We can then identify the 180 • domain walls as meandering zero-signal lines that surround micron-size antiferromagnetic domains.
In order to investigate the effect of current-induced NSOT on the 180 • domain walls we manipulate the magnetic texture by sending current pulses through the bar device, as illustrated in Fig. 6. We apply current pulses of |j p | ≈ 2.5 × 10 11 A/m 2 with a duration of 1 ms and with alternating polarity in order to illustrate the reversible switching; the current direction is shown by the red and blue arrows. Note that the onset current amplitude for switching in the 20 nm CuMnAs film is higher than in the above switching experiments in the 45 nm film. We do not attribute it to the difference of intrinsic properties of the two films.
It results from the heat-assisted nature of switching 21, 46 and from an interplay of device geometry and heat dissipation during the writing pulse. For ultrashort pulses (with lengths in the ns-scale or smaller), the temperature increase of the CuMnAs device is determined by the energy density delivered by the pulse. Hence, the onset current density for switching does not depend on the dimensions of the CuMnAs device 46 . For longer pulses, including those used in the present work, the effect of heat dissipation from the device during the pulse becomes important. Consequently, the current density required to achieve the same switching temperature increases with decreasing film thickness.
In Figs. 6a,b we plot a zoom of the measured |V T | and sgn(V T ) after applying a train of 22 current pulses before applying the train of current pulses again with opposite polarity. We found that depending on the polarity of the applied pulses, the antiferromagnetic domains change their size by reversibly displacing domain walls, consistent with the NSOT driven antiferromagnetic domain wall motion 47,48 . The corresponding resistance changes are plotted in Figs. 6c,d. After applying pulses of amplitude |j p | = 2.5 × 10 11 A/m 2 , we observe in

Conclusions
We have introduced a laboratory method for imaging antiferromagnetic domain structure by mapping the local magneto-Seebeck effect using a far-field or near-field optical scanning approach. In uniaxial CuMnAs, we identify narrow 180 • domain walls of sub-micron width and their pulse induced displacements. These reversible, polarity-dependent modifications of the antiferromagnetic domain maps are consistent with the current-induced NSOT switching mechanism. We link the imaged domain changes to resistive switching signals which we attribute to scattering on the 180 • domain walls. In biaxial CuMnAs, we confirm large micron size domains and their Current-pulse-induced modifications. We conclude that AMR from the 90 • Néel vector reorientation in the antiferromagnetic domains can explain only part of the measured resistance variations. We suggest that magnetic scattering on domain walls gives a strong additional contribution to the observed resistive switching. Apart from the polarity dependent NSOT reorientation of the Néel vector at lower pulse amplitudes we also confirm shattering into fragmented metastable multi-domain states with sub-micron feature sizes after applying larger amplitude pulses, and the subsequent relaxation towards the pre-pulsed state of the antiferromagnet.             Since the electromotive force generated by the Seebeck effect depends on the temperature gradient, we compare both the laser-spot-induced temperature gradient in the direction perpendicular to the surface, Fig. S1b, and in the sample plane, Fig. S1c. Interestingly, these gradients are of similar size but the voltage signal that can be measured between the external contacts is only generated by the in-plane temperature gradient, since the Néel vectors are oriented everywhere within the sample plane.
The electromotive force generated by the Seebeck effect E emf = −S∇T , where S is the Seebeck tensor, is not necessarily aligned with the temperature gradient ∇T since anisotropies of the magneto-Seebeck effect can be generated by the symmetry-breaking magnetic order. For the sake of simplicity, we chose the main axis of the Seebeck tensor S to be aligned collinear with the Néel vector. The electric current density j results as a combined action of thermally generated electromotive force and the electrostatic Coulomb force: where ϕ is the electric potential and σ is the electric conductivity tensor. Both the matrix elements of the electric conductivity and the Seebeck tensor are connected with the magnetic order due to AMR and MSE, respectively, and both can contribute to the thermoelectric voltage signal when local variations of σ and S are located within the temperature gradient.
For the open circuit geometry of our experiments, the stationary solution is derived from the continuity equation, with the boundary conditions j · n = 0 on the surface , where n is the unit vector locally normal to the sample surface. Since the electrostatic potential ϕ is determined by the charge density ρ in the sample volume, we solve Eq. the relative change of the MSE signal by AMR is enhanced by a factor of 3000 and 500, respectively, i.e., we find again no significant effect of AMR.
Our simulations presented in Fig. S2 show that conductivity variations due to the AMR of ±10% do only insignificantly modify the thermoelectric voltage signal V T . We therefore neglect magnetoresistive contributions in the following calculations.
In the case of homogeneous and isotropic Seebeck coefficient (without the magnetic order) and far from sample boundaries, the equation ( In this area, we expect domain wall displacements only along vertical directions. We therefore average the data along horizontal lines and further dis-cretize along the x-axis into p = 100 segments, "samples", to obtain the resulting functions V T (n, x i ) with i = 1, . . . p, as plotted in Fig. S7a. The Index n stands for the state after the n th pulse sequence. The PCA was performed by first standardizing the data V T (n, x i ) with the 9-dimensional column vectors v ( where w (k) = (w x 1 (k) , w x 2 (k) , . . . , w xp(k) ) are the eigenvectors of the correlation matrix Cov with Cov() being the covariance between the column vectors v (x i ) . The scores are sorted such that the strongest variation with n is associated with the smallest k, so that the number l of required eigenvectors to describe the variation of the measurements is ideally much less than p. The variance ratios of the scores in the above measurement are 0.68, 0.16, and 0.06 for k=1, 2 and 3, respectively, showing that the main variation is contained in the first 2 principal components.
More specifically, V T (n, x i ) can now be decomposed into a set of basis functions, v k T (x i ), as