{"id":223408,"date":"2026-01-08T15:25:17","date_gmt":"2026-01-08T15:25:17","guid":{"rendered":"https:\/\/www.newsbeep.com\/nz\/223408\/"},"modified":"2026-01-08T15:25:17","modified_gmt":"2026-01-08T15:25:17","slug":"transport-evidence-of-current-induced-nematic-dirac-valleys-in-a-parity-time-symmetric-antiferromagnet","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/nz\/223408\/","title":{"rendered":"Transport evidence of current-induced nematic Dirac valleys in a parity-time-symmetric antiferromagnet"},"content":{"rendered":"

To achieve high current density without significant current heating effects, we fabricated micro-devices (Fig.\u20092a<\/a>) capable of reaching a current density of jz\u00a0~5\u2009\u00d7\u2009107\u2009A\/m2 with an applied current of Iz\u2009=\u2009200\u2009\u03bcA. Fig.\u20092c<\/a> shows the AMR profile (i.e. azimuth angle \u03c6 dependence) of the first-harmonic component of interlayer resistivity \\({\\rho }_{zz}^{\\omega }\\) at 1.5\u2009K at 12\u2009T. As a result of precise alignment of the field perpendicular to the c axis using a two-axis rotation probe, we observed the four-fold \u03c6 dependence of \\({\\rho }_{zz}^{\\omega }\\). There, \\({\\rho }_{zz}^{\\omega }(\\varphi )\\) shows narrow dips for B|| [110] and \\([\\overline{1}10]\\) (\u03c6\u2009=\u20090\u00b0, 90\u00b0, \u22ef) while it shows broad peaks for B|| [100] and [010] (\u03c6\u2009=\u200945\u00b0, 135\u00b0, \u22ef), as reported previously45<\/a>,46<\/a>. The observed four-fold symmetry of \\({\\rho }_{zz}^{\\omega }(\\varphi )\\) is consistent with the four-fold rotoinversion symmetry of the Fermi surfaces at jz\u2009=\u20090, since \\({\\rho }_{zz}^{\\omega }(\\varphi )\\) involves integration over the full kz range (see Methods for a theoretical expression of the first-harmonic component of conductivity). Intuitively, the direction of the current-induced nematic deformation switches by 90\u00b0 depending on the sign of jz, and its overall effect on \\({\\rho }_{zz}^{\\omega }(\\varphi )\\) averages out, yielding four-fold symmetry in the linear transport. In contrast, the second-harmonic component of interlayer resistivity \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) exhibits distinct two-fold symmetry: sharp dips are located at \u03c6\u2009=\u20090\u00b0,\u00a0180\u00b0 (B||[110], \\([\\overline{1}\\overline{1}0]\\)), while sharp peaks are located at \u03c6\u2009=\u200990\u00b0,\u00a0270\u00b0 (\\({{{{\\bf{B}}}}}\\parallel [\\overline{1}10]\\), \\([1\\overline{1}0]\\)). This clearly indicates that the valleys A and B are non-equivalent when nonzero jz is applied, breaking the four-fold symmetry in the nonlinear transport. Reflecting that the deformation of each valley is driven by current, the peak height of \\({\\rho }_{zz}^{2\\omega }\\) (denoted by \\(\\Delta {\\rho }_{zz}^{2\\omega }\\) in Fig.\u20092d<\/a>) is almost proportional to jz (Fig.\u20092e<\/a>). It should be noted here that essentially the same two-fold symmetric \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) was observed in a microfabricated device with a different surface orientation (Fig.\u2009S3<\/a>), indicating that the present results are independent of the crystal cutting geometry.<\/p>\n

The profile of \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) strongly depends on magnetic field (Fig.\u20093b<\/a>). At 2 T, it exhibits a sine-like curve with two-fold symmetry. However, with increasing field, the dip (peak) structures located at \u03c6\u2009=\u20090\u00b0,\u00a0180\u00b0 (\u03c6\u2009=\u200990\u00b0,\u00a0270\u00b0) progressively evolve, accompanied by the gradual change in the weak background component. As discussed below, the observed variation in \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) is explained by the field dependence of \\({\\rho }_{zz}^{\\omega }(\\varphi )\\); the dips of \\({\\rho }_{zz}^{\\omega }(\\varphi )\\) (at \u03c6\u2009=\u20090\u00b0, 90\u00b0, 180\u00b0, \u22ef) become deeper and narrower with increasing field (Fig.\u20093a<\/a>).<\/p>\n

Fig. 3: Magnetic-field dependence and fitted results.\"figure<\/a><\/p>\n

a, b \u03c6 dependences of \\({\\rho }_{zz}^{\\omega }\\) (a) and \\({\\rho }_{zz}^{2\\omega }\\) (b) for SrMnBi2 at 1.5\u2009K for Iz=200\u2009\u03bcA for various magnetic fields. The solid curves are the fitted results of the experimental data on the basis of the empirical equation (see the main text). c, d Magnetic-field (B) dependence of the fitted parameters. \u03c32D (c) and r (c) represent the parameters of AMR, determined by fitting \\({\\rho }_{zz}^{\\omega }\\) [Eq. (1<\/a>)]. \u03b52D (d) and \u03b5r (d) represent the current-induced variations of \u03c32D and r, respectively, determined by fitting \\({\\rho }_{zz}^{2\\omega }\\) [Eq. (5<\/a>)]. The error bars indicate the uncertainties arising from the fitting.<\/p>\n

To formulate the relation between \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) and \\({\\rho }_{zz}^{\\omega }(\\varphi )\\), we here employ a phenomenological model of interlayer magnetoconductivity \\({\\sigma }_{zz}\\,(=1\/{\\rho }_{zz}^{\\omega })\\) taking account of the in-plane anisotropy of quasi-2D Dirac valley (Fig.\u20091d<\/a>)45<\/a>,46<\/a>,47<\/a>:<\/p>\n

$${\\sigma }_{zz}(\\varphi )=\\frac{2{\\sigma }_{{{{{\\rm{2D}}}}}}}{1+r{\\cos }^{2}\\varphi }+\\frac{2{\\sigma }_{{{{{\\rm{2D}}}}}}}{1+r{\\cos }^{2}(\\varphi+\\pi \/2)}+{\\sigma }_{3D},$$<\/p>\n

\n (1)\n <\/p>\n

where \u03c32D (\u03c33D) is the relative contribution of each quasi-2D Dirac valley (all 3D Fermi surfaces from the parabolic bands)45<\/a>,46<\/a>. r is the anisotropic factor of magnetoconductivity, resulting in the maximum (minimum) conductivity for the field along the shorter (longer) axis of the elliptic Dirac valley. Note here that the first (second) term corresponds to the contribution from the valley A (B), which gives \u03c3zz peaks, i.e. \\({\\rho }_{zz}^{\\omega }\\) dips at \u03c6\u2009=\u200990\u00b0,\u00a0270\u00b0 (\u03c6\u2009=\u20090\u00b0,\u00a0180\u00b0). The experimental profiles of \\({\\rho }_{zz}^{\\omega }(\\varphi )\\) at various magnetic fields are nicely fitted by Eq. (1<\/a>), as denoted by solid curves in Fig.\u20093a<\/a>. The fitted values of r and \u03c32D are summarised in Fig.\u20093c<\/a>. Reflecting the deeper and narrower dips in \\({\\rho }_{zz}^{\\omega }(\\varphi )\\) at higher fields, the r value monotonically increases with increasing field, whereas the \u03c32D is almost independent of field (the same is true for \u03c33D, see Fig.\u2009S2<\/a>). These fitted results are consistent with those reported in the literatures45<\/a>,46<\/a>.<\/p>\n

We now take account of the impact of the current-induced nematicity on Eq. (1<\/a>). Considering that the valleys A and B are non-equivalent in the presence of jz, the nematicity can be incorporated as current-induced changes in r and \u03c32D as follows<\/p>\n

$$r\\to r(1\\pm {\\epsilon }_{r}),$$<\/p>\n

\n (2)\n <\/p>\n

$${\\sigma }_{{{{{\\rm{2D}}}}}}\\to {\\sigma }_{{{{{\\rm{2D}}}}}}(1\\pm {\\epsilon }_{{{{{\\rm{2D}}}}}})$$<\/p>\n

\n (3)\n <\/p>\n

where \u03f5r(\u221djz) and \u03f52D(\u221djz) are dimensionless variations in r and \u03c32D, respectively. Note here that the \u00a0+\u00a0sign corresponds to the first term (valley A) in Eq. (1<\/a>), while the\u00a0\u2212\u00a0sign corresponds to the second term (valley B) in Eq. (1<\/a>). The resultant variation in \u03c3zz is given to the first order of \u03f5r and \u03f52D by (see \u201cMethods\u201d)<\/p>\n

$${\\sigma }_{zz}(\\varphi )\\to {\\sigma }_{zz}(\\varphi )+\\delta {\\sigma }_{zz}(\\varphi ),$$<\/p>\n

\n (4)\n <\/p>\n

where<\/p>\n

$$\\delta {\\sigma }_{zz}(\\varphi )=\t– 2{\\sigma }_{{{{{\\rm{2D}}}}}}r\\left\\{{\\left(\\frac{\\cos \\varphi }{1+r{\\cos }^{2}\\varphi }\\right)}^{2}-{\\left(\\frac{\\cos (\\varphi+\\pi \/2)}{1+r{\\cos }^{2}(\\varphi+\\pi \/2)}\\right)}^{2}\\right\\}{\\epsilon }_{r} \\\\ \t+2{\\sigma }_{{{{{\\rm{2D}}}}}}\\left\\{\\frac{1}{1+r{\\cos }^{2}\\varphi }-\\frac{1}{1+r{\\cos }^{2}(\\varphi+\\pi \/2)}\\right\\}{\\epsilon }_{{{{{\\rm{2D}}}}}}$$<\/p>\n

\n (5)\n <\/p>\n

Since \u03f5r and \u03f52D are proportional to jz, \u03b4\u03c3zz is also proportional to jz, corresponding to the nonreciprocal component of the interlayer conductivity. By converting the nonreciprocal conductivity to resistivity using the relation \\({\\rho }_{zz}^{2\\omega }=-\\frac{\\delta {\\sigma }_{zz}}{{({\\sigma }_{zz})}^{2}}\\) (see \u201cMethods\u201d), we fit the experimental \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) profiles at various fields, as shown in Fig.\u20093b<\/a>. For this fitting, \u03f52D and \u03f5r were treated as adjustable parameters, while \u03c32D and r were fixed to the values obtained from fitting \\({\\rho }_{zz}^{\\omega }(\\varphi )\\) at each field (Fig.\u20093c<\/a>). The experimental \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) profiles are well reproduced by Eq. (5<\/a>) regardless of field, as indicated by the solid curves in Fig.\u20093b<\/a>. This demonstrates that the field dependence of \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) arises solely from the field dependence of \\({\\rho }_{zz}^{\\omega }(\\varphi )\\). The extracted values of \u03f52D and \u03f5r are nearly field-independent and are of the order of 10\u22125 (Fig.\u20093d<\/a>). Consequently, the magnitude of current-induced nematicity is estimated to be of the order of 10\u22125 for jz\u00a0~5\u2009\u00d7\u2009107 A\/m2 (Iz\u2009=\u2009200\u2009\u03bcA). In the previous study, current-induced lattice displacement was measured in EuMnBi2, where the largest strain was \u00a0~1.4\u2009\u00d7\u200910\u22128 at jz\u00a0~4\u2009\u00d7\u2009104 A\/m2 at the lowest temperature36<\/a>. This corresponds to the strain of \u00a0~2\u2009\u00d7\u200910\u22125 at jz\u00a0~5\u2009\u00d7\u2009107 A\/m2 (the same jz used in this study). Thus, the nematicity estimated from the AMR profile is of the same order of magnitude as that revealed by the lattice displacement measurements.<\/p>\n

Here, we discuss the temperature dependence of \u03c12\u03c9(\u03d5). The amplitude of the \u03c12\u03c9(\u03d5) peaks and dips decreases with increasing temperature and nearly vanishes above 30\u2009K (Fig.\u2009S4d<\/a>), which is well below the N\u00e9el temperature TN\u2009=\u2009295\u2009K40<\/a>. This arises primarily from the suppression of the AMR \\({\\rho }_{zz}^{\\omega }(\\phi )\\) at elevated temperatures (Fig.\u2009S4c<\/a>), since \\({\\rho }_{zz}^{2\\omega }(\\phi )\\) originates from the current-induced modulation of \\({\\rho }_{zz}^{\\omega }(\\phi )\\). Additionally, a decrease in the current-induced nematicity (i.e. \u03f52D and \u03f5r) with increasing temperature, as was previously reported in the lattice displacement measurements in EuMnBi236<\/a>, may further contribute to the more rapid suppression of \u03c12\u03c9(\u03d5) compared to \\({\\rho }_{zz}^{\\omega }(\\phi )\\). These results suggest that the temperature dependence of \u03c12\u03c9(\u03d5) involves multiple underlying mechanisms.<\/p>\n

Finally, we demonstrate the detection and control of magnetic domains in the present \\({{{{\\mathcal{PT}}}}}\\)-symmetric antiferromagnet. Fig.\u20094c, d<\/a> show the profiles of \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) for the two adjacent devices #1 and #2, respectively, after cooling from room temperature without applying any field or current. Notably, the positions of the sharp peaks and dips of \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) are reversed between #1 and #2, apart from the relatively large background component in #2. This clearly indicates that the sign of \u03f5r and \u03f52D, i.e. the domain of antiferromagnetic order, differs between the two devices, even within the same micro-fabricated crystal (inset to Fig.\u20094c, d<\/a>).<\/p>\n

Fig. 4: Electric-magnetic control of the nonpolar \\({{{{\\mathcal{PT}}}}}\\)-symmetric antiferromagnetic order.\"figure<\/a><\/p>\n

a SEM image of the neighbouring devices. The interlayer resistivity in device #1 was measured between terminals 2\u20133, while in device #2, it was measured between terminals 1\u20132. b Schematic showing the direction of the electric current (I) along [001] and the magnetic field (B) along [110] for domain poling. c, d\u00a0\u03c6 dependence of \\({\\rho }_{zz}^{2\\omega }(\\phi )\\) in devices #1 (c) and #2 (d) at 1.5\u2009K and 12\u2009T for Iz\u2009=\u2009200\u2009\u03bcA before domain poling. e, f\u00a0Corresponding \\({\\rho }_{zz}^{2\\omega }(\\phi )\\) profiles for devices #1 (e) and #2 (f) after domain poling by current-field cooling, showing an inversion of the peak and dip positions in device #1. The insets illustrate the domain of antiferromagnetic order in the Mn-Bi layers of each device.<\/p>\n

To align the domains, we employed a poling procedure conducted above TN. Symmetry analysis predicts that the domains of \\({{{{\\mathcal{PT}}}}}\\)-symmetric antiferromagnetic order in this nonpolar system can be aligned by applying an electric current and a magnetic field orthogonal to each other, as illustrated in Fig.\u20094b<\/a> (see discussions below)48<\/a>. To achieve this experimentally, we applied a current of 1 mA (jz\u00a0~3\u2009\u00d7\u2009108A\/m2) along [001] and a field of 18 T along [110] at 305\u2009K (>TN), and then cooled the sample to 4.2\u2009K. After poling, we repeated the AMR measurements at 1.5\u2009K and 12\u2009T. In device #1, the peak and dip of \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) are inverted compared to the previous measurement without poling (Fig.\u20094e<\/a>). On the other hand, in device #2, the magnitude of the peak and dip of \\({\\rho }_{zz}^{2\\omega }(\\varphi )\\) is enhanced while keeping their positions (Fig.\u20094f<\/a>). These results indicate that the antiferromagnetic domains in both devices were aligned to the original domain in device #2 through the poling procedure, thereby demonstrating electric-magnetic manipulation of the nonpolar \\({{{{\\mathcal{PT}}}}}\\)-symmetric antiferromagnetic order. We note that the gradual background component in device #2 does not change before and after the poling, suggesting that it may arise from pinned domains and\/or other extrinsic effects.<\/p>\n

We next discuss the mechanisms underlying this control of antiferromagnetic domains in the present material. Recently, several current-driven domain control methods have been developed for metallic antiferromagnets, although their variety remains limited49<\/a>,50<\/a>. For \\({{{{\\mathcal{T}}}}}\\) odd antiferromagnets with spin-split bands3<\/a>, conventional control mechanisms, similar to those in ferromagnets, can be employed. Examples include spin-orbit torque switching at the interfaces of artificial heterostructures12<\/a>,13<\/a>,14<\/a>. In contrast, the control mechanisms for \\({{{{\\mathcal{PT}}}}}\\) -symmetric antiferromagnets with spin-degenerate bands are significantly more intricate. In the polar systems, such as CuMnAs15<\/a>,27<\/a> and Mn2Au51<\/a>, current-induced switching was achieved via the sublattice-dependent spin-momentum locking52<\/a>,53<\/a>. However, in nonpolar systems like SrMnBi2, the absence of polarity (p-wave) in momentum space prevents the domain switching using current alone. Instead, the higher-order f-wave polarity in momentum space can be utilised. To this end, we have applied an in-plane field, effectively rendering the system polar and enabling current-induced switching. This combined electric and magnetic manipulation of \\({{{{\\mathcal{PT}}}}}\\) -symmetric antiferromagnetic domains provides a novel protocol distinct from those employed for \\({{{{\\mathcal{T}}}}}\\) -odd or polar antiferromagnets currently under active investigation.<\/p>\n

For \\({{{{\\mathcal{PT}}}}}\\)-symmetric antiferromagnets, a variety of nonlinear conduction phenomena, classified by the dependence on the relaxation time, were theoretically predicted23<\/a>. In this context, our study focuses on the Drude component to provide direct evidence of current-induced electronic nematicity, manifested as nonlinear interlayer conduction along the high-symmetry c\u2212axis under a magnetic field. In addition, SrMnBi2 is also predicted to exhibit other types of nonlinear in-plane conduction along the ab plane, such as the (zero-field) nonlinear Hall effect arising from the quantum geometric component27<\/a>,28<\/a>,29<\/a>. Exploring in-plane nonlinear responses may thus represent an important direction for future research in nonpolar \\({{{{\\mathcal{PT}}}}}\\)-symmetric antiferromagnets.<\/p>\n

To conclude, we report the observation of current-induced electronic nematicity in the nonpolar \\({{{{\\mathcal{PT}}}}}\\)-symmetric antiferromagnet SrMnBi2 by measuring the nonreciprocal angular magnetoresistance (AMR) effect. The breaking of the original four-fold rotoinversion symmetry is detectable via the valley degrees of freedom of Dirac fermions in the Bi square net, which is adjacent to the Mn-Bi tetrahedral layer exhibiting \\({{{{\\mathcal{PT}}}}}\\)-symmetric antiferromagnetic order. By employing a phenomenological model of the AMR effect attributed to elliptic Dirac valleys, we quantitatively reproduce the two-fold nonreciprocal AMR signal, demonstrating the current-induced lifting of the valley degeneracy. The layered structure incorporating a Dirac fermion layer in this material offers a novel platform for the electrical control of valleys by the \\({{{{\\mathcal{PT}}}}}\\)-symmetric antiferromagnetic order. Our findings may pave the way for developing unconventional spintronic and valleytronic devices, thereby broadening the scope of antiferromagnetic spintronics.<\/p>\n","protected":false},"excerpt":{"rendered":"To achieve high current density without significant current heating effects, we fabricated micro-devices (Fig.\u20092a) capable of reaching a…\n","protected":false},"author":2,"featured_media":223409,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[5927,1928,7940,1929,111,139,69,393,147,3304,42065],"class_list":{"0":"post-223408","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-electronic-properties-and-materials","9":"tag-humanities-and-social-sciences","10":"tag-magnetic-properties-and-materials","11":"tag-multidisciplinary","12":"tag-new-zealand","13":"tag-newzealand","14":"tag-nz","15":"tag-physics","16":"tag-science","17":"tag-spintronics","18":"tag-topological-insulators"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/posts\/223408","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/comments?post=223408"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/posts\/223408\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/media\/223409"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/media?parent=223408"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/categories?post=223408"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/tags?post=223408"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}