Ferro-spinetic Altermagnets from Electronic Correlations

TL;DR

This work establishes ferro-spinetic polarization as the spin analogue of ferroelectricity in altermagnets, showing that electronic correlations generate a switchable edge-localized spin accumulation in a fully compensated antiferromagnetic insulator without net magnetization. A many-body chiral symmetry forbids charge polarization while permitting $P_s$, and quantum Monte Carlo confirms robust LRO and edge spin texture tied to lattice symmetry. Breaking the chiral symmetry unlocks a perpendicular ferroelectric polarization $P_c$, yielding mutually perpendicular, switchable spin- and charge-polarized responses; symmetry dictates the allowed directions of these polarizations. Mn-based metal-organic frameworks, especially Mn-MOFs, emerge as realistic platforms, with first-principles results supporting the predicted ferro-spinetic and orthogonal ferroelectric responses, offering a route to experimental verification and potential spintronic applications.

Abstract

Altermagnets are fully compensated collinear antiferromagnets that lack the combined time-reversal and translation symmetry. Here we show that their symmetry allows for a switchable ferro-spinetic polarization - the spin analogue of ferroelectricity - in a direction dictated by the lattice symmetry. We demonstrate this effect first in its purest form in an interacting altermagnetic fermion model, in which a many-body chiral symmetry forbids any charge polarization. Our quantum Monte Carlo simulations reveal edge-localized, reversible spin accumulations fully consistent with this symmetry locking. Breaking the chiral symmetry releases the charge sector: a ferroelectric polarization emerges orthogonal to the ferro-spinetic one, yielding mutually perpendicular switchable spin- and charge-polarized responses. We identify Mn-based metal-organic frameworks as realistic hosts for this effect, offering a practical route for experimental verification.

Figures (9)

• Figure 1: Interacting model of fermions in Eq. \ref{['model']} and schematic of the local moment structure and ferro-spinetic (ferroelectric) polarization $P_s$ ($P_c$) in the altermagnetic insulating state. The unit cell contains four fermionic sites (A, B, C, D) and the fermions are subject to $t$, $t' (\equiv t_1+\delta t_1/2)$, $t"(\equiv t_1-\delta t_1/2)$ hopping integrals and a repulsive, onsite Hubbard $U$ interaction. The lattice vectors are $\mathbf{a}_1=(1,0)$ and $\mathbf{a}_2=(0,1)$.
• Figure 2: Correlation ratio $R^{S}$ for the AFM order as a function of $U$ [(a), with $\delta t_1=0$] and $\delta t_1$ [(b), with $U=5$] for different lattice sizes $L$. In the shaded regions, $R^{S}$ increases with increasing $L$, indicating the presence of long-range AFM order (LRO). Outside these regions, $R^{S}$ decreases with $L$, signaling the absence of long-range AFM order and a transition to a valence-bond solid (VBS) phase.
• Figure 3: Real-space distribution of magnetization $m_z(i)$, from which the spin polarization is evaluated as $P_s=\sum_{i} i m^z(i)$. Panel (a) shows results for the $\parallel x+y$ geometry, with periodic boundaries along the $\mathbf{a}_2 - \mathbf{a}_1$ direction and open boundaries along the $\mathbf{a}_2 + \mathbf{a}_1$ direction. Panel (b) corresponds to the $\parallel x-y$ geometry, where the boundary conditions are reversed. These results correspond to a case where chiral symmetry is preserved. Here, a finite $\delta t_1$ breaks inversion symmetry. The charge polarization $P_c$ is obtained analogously by replacing $m_z(i)$ with the charge distribution.
• Figure 4: Real-space distribution of magnetization $m_z(i)$, along with the polarization quantities $P_s$ and $P_c$, for the same conditions and geometry as in Fig. \ref{['fig:Polarization']}, but in a case where chiral symmetry is broken. Here, a finite $\eta$ breaks chiral symmetry.
• Figure 5: Ferro-spinetic and altermagnetic properties of [C$_2$H$_5$NH$_3$]Mn[(HCOO)$_3$] (Mn-MOF). (a) Crystal and magnetic structures. The building blocks are ethylammonium (C$_2$H$_5$NH$_3^+$), divalent Mn$^{2+}$ ions, and carboxylate (HCOO$^-$). The spin ($P_s$) and charge ($P_c$) polarization directions are indicated in (b). With screw-rotation ($\overline{2}_{001}$) and glide-mirror ($\overline{m}_{010}$) symmetries, $P_s$ and $P_c$ are aligned along the $y$ and $z$ axes, respectively. (c) $P_s$, illustrating the effect of inversion symmetry ($I$). The sign of $P_s$ reverses when only the structural configuration is inverted, while keeping the direction of the Néel order $(N)$ fixed, confirming the transformation property of $P_s$ under inversion symmetry. Consistently, $P_s = 0$ along directions such as the $x/y$ axes.