Elastic counterpart of the RKKY interaction in insulating altermagnets

The presence of local magnetic moments can lead to emergent physical effects in condensed-matter systems. In metals, local moments interact through the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, whose long-range oscillatory form arises from gapless particle-hole excitations around a sharp Fermi surface. Such behavior is absent in insulators, as they lack analogous gapless modes. In this talk, we show that in materials with combined broken time-reversal and rotational symmetries, gapless elastic strain modes can serve as counterparts to the particle-hole pairs in metals. Through the piezomagnetic coupling between magnetization and strain, elastic fluctuations mediate a long-range spin-spin exchange — an elastic RKKY interaction. We show that, in a d-wave altermagnetic phase, the elastic compatibility relations force the exchange to oscillate in sign even in insulators without a Fermi surface. To understand the effects of this interaction, we study a two-dimensional tetragonal lattice of local spins that do not contribute to the primary altermagnetic order parameter, but that do interact through the elastic RKKY exchange. Our Monte Carlo simulations reveal that the local spins order into a low-temperature ferromagnetic or antiferromagnetic phase. We find that the lattice incompressibility not only tunes the magnetic phase from ferromagnetic to antiferromagnetic but it also changes the universality class of the transition from mean-field to two-dimensional Ising criticality.