  It was recently discovered that, depending on their symmetries, collinear
antiferromagnets may break spin degeneracy in momentum space, even in absence
of spin-orbit coupling. Such systems, dubbed altermagnets, have electronic
bands with a spin-momentum texture set mainly by the combined crystal-magnetic
symmetry. This discovery motivates the question which novel physical properties
derive from altermagnetic order. Here we show that one consequence of
altermagnetic order is a fluctuation-driven piezomagnetic response. Using the
checkerboard Heisenberg hamiltonian as a prototypical localized moment
altermagnet, we determine its fluctuation induced piezomagnetic coefficient
considering temperature induced transversal spin fluctuations. We establish in
addition that magnetic fluctuations induce an anisotropic thermal spin
conductivity.
