Magnetic field induced phase transitions in disordered altermagnets

In altermagnets (AM), flipping spins can be compensated by a rotation, similar to antiferromagnets, where this is accomplished by a translation or by inversion. Even though AM are states of homogeneous order, their symmetry requires that, in sharp contrast to ferromagnets, there is no direct bilinear coupling to a homogeneous magnetic field. However, since many altermagnets display piezomagnetism, a trilinear coupling with magnetic field and strain is generally allowed. This is the case for externally applied, for dynamic, and for random strain. Consequently, in the presence of random strain, a magnetic field behaves as an effective random field conjugate to the AM order parameter, providing a rare realization of a tunable random-field Ising model. Here, we solve the corresponding transverse-field Ising model in the presence of random longitudinal fields via mean-field to gain insight into the impact of a magnetic field on the AM phase diagram. We find two competing effects enabled by an increasing magnetic field: an increasing random-field disorder, which suppresses long-range AM order, and an enhanced coupling to elastic fluctuations, which favors AM order. We discuss the outcome of this competition and determine its fingerprints in various experimentally-accessible quantities, such as the magnetic susceptibility, the elastocaloric effect, the shear modulus, and the AM order parameter.