We investigate the Friedel oscillations of the local density of states (LDOS) induced by a single impurity with both a spin-independent potential and an exchange coupling to the electrons in altermagnets and unconventional 𝑝-wave magnets. We identify features that make the Friedel oscillations and magnetization distinct from other materials with nontrivial spin texture such as Rashba metals. Because time-reversal symmetry is broken in altermagnets, both magnetic and nonmagnetic impurities lead to local magnetization with the spatial pattern that reflects the symmetry of the altermagnetic splitting. The period of the corresponding oscillations provides an alternative way to quantify the altermagnetic spin splitting and the shape of the altermagnetic bands. The LDOS pattern in 𝑝-wave magnets, which respect combined time-reversal and translation symmetries, is rich. It reveals anisotropy related directly to the spin splitting, but surprisingly also features LDOS oscillations with a doubled period in the proximity of the impurity. The latter effect is also observed in a Rashba metal with an exchange field and originates from the interplay of propagating and evanescent waves. The obtained results are instrumental for investigating altermagnets and unconventional 𝑝-wave magnets via tunneling probes.

中文翻译：

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互交磁体和 p 波磁体中杂质诱导的 Friedel 振荡


我们研究了由单个杂质引起的局部态密度 （LDOS） 的弗里德尔振荡，该杂质具有与自旋无关的电位以及与交替磁体和非常规 p 波磁体中电子的交换耦合。我们确定了使 Friedel 振荡和磁化与其他具有非平凡自旋纹理的材料（如 Rashba 金属）不同的特征。由于互通磁体中的时间反转对称性被打破，磁性和非磁性杂质都会导致局部磁化，其空间模式反映了互通磁分裂的对称性。相应振荡的周期提供了一种量化交替磁自旋分裂和交替磁带形状的替代方法。p 波磁体中的 LDOS 模式非常丰富，它尊重组合的时间反转和平移对称性。它揭示了与自旋分裂直接相关的各向异性，但令人惊讶的是，它还具有 LDOS 振荡，在杂质附近具有加倍的周期。后一种效应在具有交换场的 Rashba 金属中也观察到，它源于传播波和消逝波的相互作用。获得的结果有助于通过隧道探测研究交替磁体和非常规 p 波磁体。