# Velocity-determined anisotropic behaviors of RKKY interaction in 8-\textit{Pmmn} borophene

## TL;DR

This paper investigates how the anisotropic and tilted velocities of Dirac fermions in 8-Pmmn borophene influence the long-range RKKY interaction, revealing velocity-dependent anisotropic behaviors with potential spintronic applications.

## Contribution

It provides an analytical demonstration that the RKKY interaction's anisotropy in 8-Pmmn borophene is velocity-determined and independent of the Fermi level, highlighting tunability through velocity engineering.

## Key findings

- RKKY interaction anisotropy is velocity-dependent.
- The anisotropic behaviors are independent of the Fermi level.
- Velocity engineering can tune the RKKY interaction.

## Abstract

As a new two-dimensional Dirac material, 8-\textit{Pmmn} borophene hosts novel anisotropic and tilted massless Dirac fermions (MDFs) and has attracted increasing interest. However, the potential application of 8-\textit{Pmmn} borophene in spin fields has not been explored. Here, we study the long-range RKKY interaction mediated by anisotropic and tilted MDFs in magnetically-doped 8-\textit{Pmmn} borophene. To this aim, we carefully analyze the unique real-space propagation of anisotropic and tilted MDFs with noncolinear momenta and group velocities. As a result, we analytically demonstrate the anisotropic behaviors of long-range RKKY interaction, which have no dependence on the Fermi level but are velocity-determined, i.e., the anisotropy degrees of oscillation period and envelop amplitude are determined by the anisotropic and tilted velocities. The velocity-determined RKKY interaction favors to fully determine the characteristic velocities of anisotropic and tilted MDFs through its measurement, and has high tunability by engineering velocities shedding light on the application of 8-\textit{Pmmn} borophene in spin fields.