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Geometry induced net spin polarization of $d$-wave altermagnets

Abhiram Soori

TL;DR

This paper shows that altermagnets, which have spin-split bands without net magnetization, can develop a net spin polarization purely from geometric constraints in finite rectangular samples. By counting occupied states with a spin-resolved, anisotropic Fermi contour, the authors demonstrate that $L_x eq L_y$ yields $N_ eq N_downdown$, while the symmetric square case and the thermodynamic limit restore balance. They connect this finite-size polarization to transport: in the tunneling regime, the ratio of spin to charge conductance $G^s/G$ exhibits square-like patterns in sample dimensions, and FM--AM--FM junctions show an asymmetry in magnetoresistance under Zeeman-field reversal, both serving as experimental probes. The work highlights geometry as a control knob for spin polarization in altermagnets and points to mesoscopic devices as a practical platform for geometry-driven spintronic functionality.

Abstract

Altermagnets exhibit spin-split electronic band structures despite having zero net magnetization, making them attractive for field-free spintronic applications. In this work, we show that a finite rectangular altermagnetic sample can acquire a net spin polarization purely due to its geometry. This effect arises from the interplay between the anisotropic, spin-resolved Fermi contours of an altermagnet and the discrete sampling of momentum space imposed by unequal sample dimensions. By explicitly counting occupied states, we demonstrate that rectangular samples with $L_x \neq L_y$ host a finite spin polarization, which vanishes in the symmetric limit $L_x=L_y$ and in the thermodynamic limit. We further show that this geometry-induced spin polarization can be directly probed in transport measurements. In the tunneling regime, the ratio of spin to charge conductance exhibits characteristic square-like patterns as a function of sample dimensions, faithfully reflecting the underlying spin polarization. In addition, transport across ferromagnet--altermagnet--ferromagnet junctions reveals an asymmetric magnetoresistance with respect to reversal of the Zeeman field, providing an independent transport signature of the finite spin polarization. Our results establish geometry as an effective control parameter for spin polarization in altermagnets and suggest a viable route for exploiting finite-size effects in mesoscopic altermagnetic spintronic devices.

Geometry induced net spin polarization of $d$-wave altermagnets

TL;DR

This paper shows that altermagnets, which have spin-split bands without net magnetization, can develop a net spin polarization purely from geometric constraints in finite rectangular samples. By counting occupied states with a spin-resolved, anisotropic Fermi contour, the authors demonstrate that yields , while the symmetric square case and the thermodynamic limit restore balance. They connect this finite-size polarization to transport: in the tunneling regime, the ratio of spin to charge conductance exhibits square-like patterns in sample dimensions, and FM--AM--FM junctions show an asymmetry in magnetoresistance under Zeeman-field reversal, both serving as experimental probes. The work highlights geometry as a control knob for spin polarization in altermagnets and points to mesoscopic devices as a practical platform for geometry-driven spintronic functionality.

Abstract

Altermagnets exhibit spin-split electronic band structures despite having zero net magnetization, making them attractive for field-free spintronic applications. In this work, we show that a finite rectangular altermagnetic sample can acquire a net spin polarization purely due to its geometry. This effect arises from the interplay between the anisotropic, spin-resolved Fermi contours of an altermagnet and the discrete sampling of momentum space imposed by unequal sample dimensions. By explicitly counting occupied states, we demonstrate that rectangular samples with host a finite spin polarization, which vanishes in the symmetric limit and in the thermodynamic limit. We further show that this geometry-induced spin polarization can be directly probed in transport measurements. In the tunneling regime, the ratio of spin to charge conductance exhibits characteristic square-like patterns as a function of sample dimensions, faithfully reflecting the underlying spin polarization. In addition, transport across ferromagnet--altermagnet--ferromagnet junctions reveals an asymmetric magnetoresistance with respect to reversal of the Zeeman field, providing an independent transport signature of the finite spin polarization. Our results establish geometry as an effective control parameter for spin polarization in altermagnets and suggest a viable route for exploiting finite-size effects in mesoscopic altermagnetic spintronic devices.
Paper Structure (4 sections, 5 equations, 4 figures)

This paper contains 4 sections, 5 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Spin polarization of a two-dimensional rectangular AM
  3. Transport probe of geometry-induced spin polarization
  4. Summary and conclusions

Figures (4)

  • Figure 1: Normalized spin polarization $(N_\uparrow-N_\downarrow)/(N_\uparrow+N_\downarrow)$ versus $(L_x,L_y)$ for $t_J=0.8t$ and $E_F=0.6t$. The samples with $L_x\neq L_y$ exhibit nonzero spin polarization.
  • Figure 2: A thin rectangular slab of AM connected to NM electrodes with rectangular cross-section of same size. The dimensions of the AM slab is $L_x\times L_y \times d$. The NM leads are extended along $z$-direction and have same cross sectional dimensions as that of AM.
  • Figure 3: The ratio of spin conductance to charge conductance (both in dimensionless units) across AM versus the system size $(L_x,L_y)$ for $t_n=0.2t$, $t_J=0.8t$, and $d=5a$.
  • Figure 4: Magnetoresistance of the FM-AM-FM setup. (a) MR versus Zeeman energy $b$ for different system sizes. (b) MR versus $L_0$ for system with size $L_0\times5L_0$ for $b=0.5t$. Other parameters are same as in Fig. \ref{['fig:GsG']}.