Anisotropic magnon transport in an antiferromagnetic trilayer heterostructure: is BiFeO$_3$ an altermagnet?

Abstract

Magnons provide a route to ultra-fast transport and non-destructive readout of spin-based information transfer. Here, we report magnon transport and its emergent anisotropic nature in BiFeO$_3$ layers confined between ultrathin layers of the antiferromagnet LaFeO$_3$. Due to the confined state, BiFeO$_3$ serves as an efficient magnon transmission channel as well as a magnetoelectric knob by which to control the stack by means of an electric field. We discuss the mechanism of the anisotropic spin transport based on the interaction between the antiferromagnetic order and the electric field. This allows us to manipulate and amplify the spin transport in such a confined geometry. Furthermore, lower crystal symmetric and suppression of the spin cycloid in ultrathin BiFeO$_3$ stabilizes a non-trivial antiferromagnetic state exhibiting symmetry-protected spin-split bands that provide the non-trivial sign inversion of the spin current, which is a characteristic of an altermagnet. This work provides an understanding of the anisotropic spin transport in complex antiferromagnetic heterostructures where ferroelectricity and altermagnetism coexist, paving the way for a new route to realize electric-field control of a novel state of magnetism.

Figures (5)

• Figure 1: (a) Device schematic to measure the non-local inverse spin Hall effect (ISHE) voltage generated by antiferromagnetic magnons excited through the SHE (black arrows on the right Pt electrode). Light shaded, wavy arrow, in the BFO middle layer represents the magnon flow direction. $\varphi$ is the angle between the long axis of the Pt wire and $[010]$, $s$ is the spacing between the metal wires, which is $\sim$1.5 $\mu$m unless otherwise specified. Bottom right is the top-view of the device imaged by the scanning electron microscopy, scale bar is 1$\mu$m. (b) Ferroelectric pulsed polarization measured for various devices under the PUND scheme. PUND: positive-up-negative-down, is a standard protocol to record the switched ferroelectric polarization under short electrical pulses (4$\mu$s) and eliminates parasitic contributions to the charge response from resistive leakage and dielectric responses. (c) $V_{ISHE}$ hysteresis measured from the devices with various in-plane angles with respect to the substrate, shown in (a). The hysteresis measured at various angles has been centered with respect to the $0\degree$ data to facilitate comparison.
• Figure 1: Possible altermagnetism contribution to the observed sign inversion in the spin transport. Brillouin zone schematic of spin polarization corresponding to 45$\degree$$I-III$ (a-c) and 135$\degree$$II-IV$ (d-f). The green shaded planes in (a, d) represent the mirror-time-reversal symmetry of Cc' magnetic space group. When the ferroelectric polarization switches from I-III or II-IV, the magnetic orders are mirrored, represetned by yellow shaded planes in (b, e). The differential in (c) and (f) show the altermagnetism contribution to $\Delta V_{ISHE}$.
• Figure 2: The differential voltage ($\Delta V_{ISHE}$) as a function of the angle ($\varphi$) with respect to the substrate edge $[100]$. The Pt wires are parallel to $[010]$ and the electric field is applied along $\varphi$ to measure the polarization and spin transport hysteresis. The data in red have been recorded in the pristine state when the electric field was not applied. The pristine state measurements were simply conducted by swapping the source and drain connections (Supplementary Figure 5 SM). (b) $\Delta V_{ISHE}$ as a function of injected current in two devices of $\varphi=45\degree$ and $\varphi=135\degree$ in the LFO/BFO/LFO trilayer. The sign of the $\Delta V_{ISHE}$ gets reversed when the injected current direction is opposite. The hysteresis in the left and right panels is of opposite polarity due to two opposite currents used in the source Pt wire. Similarly, in the orthogonal devices ($\varphi=45\degree$ or $\varphi=135\degree$), the corresponding hysteresis also shows opposite polarities. The hystereses shown here were measured at a 2mA supply DC.
• Figure 3: Description of the anisotropy and sign inversion:(a) Representation of the rhombohedral R3c structure of BFO, illustrating its relationship to the ideal cubic perovskite lattice. The threefold symmetry axis along the pseudocubic [111] direction is marked by a red arrow. (b) A view along the $[111]$ direction. The $c_m$-glide planes are highlighted with dotted black lines. (c) Top view of the four possible situations of the devices at angles of 0$\degree$, 45$\degree$, 90$\degree$, and 135$\degree$ being under consideration under poled conditions. $\alpha$ is the tilt due to the non-centrosymmetric $R3c$, $l$ and $m$ are the antiferromagnetic and canted moment of BFO. $I, II, III$ and $IV$ correspond to the four 4-quadrants that provide access to explain four device angles and connected symmetries.
• Figure 4: Anisotropic magnons and emergence of altermagnetism in BiFeO$_3$(BFO). (a) Plane view of the $(001)_{\mathrm{pc}}$ Brillouin zone cross-section. Two considered $k$-point paths connecting S and S$_1$ points lie at the boundary of the Brillouin zone and are related via the $(1\bar{1}0)_{\mathrm{pc}}$ mirror plane. Calculated Kohn-Sham band structure of BFO along the two k-point paths shown in panels (b) and (c). Red and blue lines indicate the spin-up and spin-down bands, respectively. (d) First Brillouin zone of the rhombohedral unit cell of $R3c$ bulk BFO with overlapped red and blue spin density bands. Point $X$ corresponds to a $(1\bar{1}0)_{\mathrm{pc}}$ mirror image of $Q$. The corresponding mirror plane containing $P$, $Z$ and $P_1$ points is shown as a gray polygon with light blue edges. Solid blue line passing through $S$, $X$, $S_1$ and $Q$ highlights the boundary of the $(001)_{\mathrm{pc}}$ plane cross-section of the Brillouin zone. (e), (f) The differential spin texture in the band structure corresponds to the devices patterned at $\varphi=$ 45$\degree$ and $\varphi=$ 135$\degree$, respectively. Dark/light color contrast represents the high and low signal, generating the hysteresis between the two polar states.