Antiferromagnet with an antisymmetry center in an external static magnetic field as a left-handed medium

Using the example of a tetragonal easy-axis antiferromagnet with a 4 _z ⁻2 _x ⁺ I ⁻ structure, the conditions have been determined under which both the negative refraction effect and the negative phase velocity effect are simultaneously possible in an external field orthogonal to the easy axis. The results are extended to multiferroics with the uniform magnetoelectric effect and to centrosymmetric magnets.