Optical signatures of spin symmetries in unconventional magnets

TL;DR

This work shows that in magnets with weak spin-orbit coupling, spin-group symmetries, not just magnetic point groups, govern the dominant spin and charge photoresponse, particularly for the quadratic shift current. A minimal double-exchange model demonstrates how spin symmetries constrain the shift-conductivity tensor $\sigma^{abc}$, and a stringent ab initio study of Mn$_5$Si$_3$ reveals that only the noncoplanar p-wave spin structure satisfies these spin-symmetry requirements, while the coplanar configuration is strongly suppressed. The authors provide a practical photogalvanic protocol to identify the spin configuration of Mn$_5$Si$_3$: measure the shift current (or related transport signals) under controlled polarization and photon energy, where the noncoplanar structure yields markedly larger signals with distinct angular dependences. The findings generalize to other light-element magnets and all orders of the electric field response, offering a new route to classify unconventional magnets and to design materials with enhanced photoconductive responses.

Abstract

The concept of spin symmetries has gained renewed interest as a valuable tool for classifying unconventional magnetic phases, including altermagnets and recently identified p-wave magnets. In this work, we show that in compounds with weak spin-orbit coupling, the dominant spin and charge photoresponse is determined by spin group rather than the conventional magnetic group symmetry. As a concrete realization we consider the nonlinear shift photocurrent in Mn$_5$Si$_3$, a material that features the two possible classes of unconventional p-wave magnetism in the form of two competing spin structures, a coplanar and non-coplanar one. While both are predicted to generate shift currents based on magnetic symmetry considerations, only the non-coplanar configuration survives the spin symmetry requirements. This is numerically confirmed by our $\textit{ab-initio}$ calculations, providing a protocol to experimentally identify the spin configuration of this promising material in photogalvanic or transport measurements.

Figures (9)

• Figure 1: a) Schematic illustration of d.c. photocurrent generated on a rectangular lattice with noncollinear spin arrangement respecting $\mathcal{T}\boldsymbol{\tau}_m$ symmetry with $\boldsymbol{\tau}_m = (a,2a)$. The spin symmetry $[E||M_{x}|\bm{0}]$ has been highlighted (see text). b) Spin polarized bands of the model for different values of $|\mathbf{m}|$ displaying $\mathcal{T}-$symmetry. c) Charge shift photoconductivity spectra for different values of $|\mathbf{m}|$. A $\times10^{3}$ factor has been applied to the $|\mathbf{m}|=0.13\mu_{B}$ curve for visibility purposes. d) Evolution of the value of $\sigma^{yxx}$ for the peaks at $\omega \approx 1.4$ eV and $\omega \approx 1.9$ eV as a function of $|\mathbf{m}|$. For reference, we have included maximum shift photoconductivity of TaAs and BaTiO from Refs. osterhoudt2019 and PhysRevB.101.045104. e) Spin shift photoconductivity spectra for $m=0.75\mu_{B}$, clearly fulfilling the predictions of spin symmetries.
• Figure 2: Left panel: Lattice (a) and Fermi surface at $k_y =0$ (b, c) of the non-coplanar structure for spin projections $S_{x}$ and $S_y$. Right panel: same as left panel but for coplanar structure. In d), the plane of magnetization in $yz$ is displayed. Spin projection $S_z$ not shown in neither panel; it is finite for the non-coplanar structure and virtually zero (like $S_y$) in the coplanar one.
• Figure 3: a) Top and bottom: shift photoconductivity of the non-coplanar and coplanar structures of Mn$_5$Si$_3$, respectively. b) D.c. photocurrent $J^{x}$ at $\hbar\omega=0.15$ eV as a function of polarization angle in the two structures.
• Figure S1: Charge shift photoconductivity spectrum of the model described in the main text for $m=2\mu_B$.
• Figure S2: Spin shift photoconductivity spectrum of the model described in the main text for $m=0.75\mu_B$.