Piezomagnetic effect in 5$d$ transition metal oxides Y${}_2$Ir${}_2$O${}_7$ and Cd${}_2$Os${}_2$O${}_7$ with all-in/all-out magnetic order

We investigated the piezomagnetic effect in pyrochlore-type oxides Y${}_2$Ir${}_2$O${}_7$ and Cd${}_2$Os${}_2$O${}_7$, which show a non-coplanar magnetic structure called the all-in/all-out antiferromagnetic order at low temperatures. The all-in/all-out magnetic order can be viewed as a ferroic order of the $xyz$-type magnetic octupoles. We observed a linear development of magnetization with applying stress for both materials. We then estimated the powder-averaged piezomagnetic tensor at 50 K to be $Q=5.74\times {10}^{-6}$ ${\mu }_{\text{B}}$/Ir$\cdot$MPa for Y${}_2$Ir${}_2$O${}_7$, and $Q=3.49\times {10}^{-7}$ ${\mu }_{\text{B}}$/Os$\cdot$MPa for Cd${}_2$Os${}_2$O${}_7$. We discuss the microscopic mechanism of the piezomagnetic effect in terms of the stress-induced modification of the g-tensor anisotropy and Dzyaloshinskii-Moriya (D-M) interactions. This work paves the way for the further development of piezomagnetic materials using a strategy based on magnetic multipoles.