Nanoscale imaging and management of altermagnetism in MnTe

Our vector mapping includes native, real-space detection of the path of the choice magnetic order vector, to = M₁– M₂ with respect to the MnTe crystal axes within the (0001) aircraft by X-ray magnetic linear dichroism (XMLD)-PEEM, and marked to for a particular crystallographic orientation by embedding X-ray magnetic round dichroism (XMCD)-PEEM. In antimagnets with sublattices of reverse rotation and linked by translation or inversion, it’s ({mathcal{T}})– Odd XMCD is excluded by symmetry. Solely in such instances to The axis might be detected ({mathcal{T}})-Even XMLD-PEEM, however the tag to stays unresolved^{25,26,27,28,29,30}. In distinction, current theoretical and experimental spectroscopic examine of MnTe variable magnets confirmed the presence of great XMCD, which displays ({mathcal{T}})-Breaking symmetry within the digital construction by spin-polarization variation of the g wave¹². Furthermore, the spectral form of XMCD is because of to The sign within the (0001) aircraft is qualitatively totally different from the XMCD spectral type as a consequence of internet magnetization M= M₁ + M₂ Alongside the axis (0001).¹². This was demonstrated in Ref. ¹² By evaluating the XMCD spectral profiles measured in a zero magnetic area and in a 6-T area utilized alongside the (0001) axis. Within the earlier case, M Weak and the measured spectral form agrees with the anticipated spectral form as a result of to . Within the final case, M It’s massive in measurement and qualitatively modifies the spectral form, which is once more per idea. We carried out regular X-ray PEEM, which is the perfect geometry for measuring each the in-plane Néel axis within the XMLD, and the magnetic variational XMCD. Photos have been taken at zero exterior area, the place the XMCD sign is because of weak relative relaxation M It’s negligible in comparison with the magnetic variable XMCD as a result of ({bf{L}}parallel langle 1bar{1}00rangle ) Tendencies in degree (0001).¹². The latter results in the measured XMCD-PEEM distinction as confirmed by its spectral dependence (Knock Prolonged information format. 1). By analogy to the DC anomalous Corridor impact, XMCD might be described by the Corridor vector, ({bf{h}}=({sigma }_{zy}^{a},{sigma }_{xz}^{a},{sigma }_{yx}^{a}) )the place p_IY = –p_YI They’re the uneven elements of the frequency-dependent conduction tensor. to to At degree (0001) of MnTe, H Factors alongside the (0001) axis, ie ({sigma }_{zy}^{a} = {sigma }_{xz}^{a} = 0) and ({sigma }_{r}^{a}ni 0)besides ({bf{L}}parallel langle 2bar{1}bar{1}0rangle ) axes the place ({sigma }_{y}^{a} = 0) By symmetry.

mix XMCD-PEEM and XMLD-PEEM photos right into a vector map for toIt’s proven within the determine. 1 b. as to The vector subtends the angle, ϕwithin the MnTe(0001) aircraft with respect to ((1bar{1}00)) axis, XMCD is proportional to cos(3ϕ), with a most measurement ({bf{L}}parallel langle 1bar{1}00rangle ) -Axes and invisibility ({bf{L}}parallel langle 2bar{1}bar{1}0rangle ) Interviewer¹². XMCD-PEEM picture of 25–micrometer² The unpatterned area of MnTe is proven in Determine 1. 1 cthe place constructive and unfavorable XMCD seem as mild and darkish distinction, respectively. The corresponding three-color XMLD-PEEM map is proven in Determine 1. 1 dobtained from a set of PEEM photos taken utilizing X-ray linear polarization, inside the MnTe (0001) aircraft, in 10° steps from -90° to +90° relative to the horizontal ((1bar{1}00)) axis. On this native photograph to -The vector axis is highlighted (in crimson, inexperienced, and blue), however the absolute path stays unspecified. This data is embedded by combining XMCD-PEEM and XMLD-PEEM right into a six-color vector map, as proven in Determine 1. 1 e, fthe place constructive XMCD areas change the colour (crimson, inexperienced, blue to orange, yellow, and purple) of the XMLD-PEEM map and unfavorable XMCD areas depart them unchanged. Manna l_2,3The X-ray absorption and paramagnetic XMCD spectra are proven in Determine 1. 1 gram. XMCD-PEEM photos are acquired at a continuing vitality equivalent to the height within the paramagnetic XMCD at L₂edge. The XMCD distinction is mirrored between the constructive and unfavorable peaks of the XMCD spectrum, as proven in Determine 1 (Prolonged Information). 1and disappears at excessive temperatures the place the spontaneous anomalous Corridor impact is absent, as proven within the expanded information Determine 1. 2.

Characteristic vector mapping for toWithin the unpatterned MnTe movie, as proven in Determine 1. 1 e, freveals a wealthy panorama of secure (epitaxial) tissue much like earlier stories in compensated magnets^{26,27,28,29,30}. There are 60° and 120° area partitions separating the domainsto Alignment alongside totally different simple axes, plus swirl-like textures. Highlighted within the determine. 1f That is an instance of another magnetic vortex and antivortex pair, and is much like the magnetic textures beforehand found in antiferromagnets akin to CuMnAs (ref. 1). ³⁰). Nonetheless, solely XMLD-PEEM was accessible in antimagnet³⁰that’s, solely the spatially various Néel-vector axis might be decided, much like our XMLD-PEEM picture in Determine 1 . 1 d. In our various magnetic case, we are able to add the data from the measured XMCD-PEEM (Determine 1). 1 c). This permits us to attract a vector map ofto as proven within the determine. 1 e, f. We straight decide experimentally thattoThe vector makes a 360° clockwise rotation across the first nanotextile, indicated by the purple-white circle, whereas the opposite nanotextile is an antivortex with an reverse spin to the nanotexture.toVector, indicated by a cyan-white circle.