Magnetoelastic coupling forbidden by time-reversal symmetry: Spin-direction-dependent magnetoelastic coupling on MnO, CoO, and NiO

Abstract

In the Landau free energy, which is a powerful tool for describing the physical properties and phase transitions in condensed-matter physics, it has been generally believed that time-reversal symmetry allows only even-power polynomials in the magnetic moment when magnetic transition happens. Although no experimental evidence supports it, this symmetry constraint is very strict in theory. On the other hand, MnO, CoO, and NiO have been extensively studied for several decades since these materials are used to test advance experimental and theoretical methods. However, their precise spin directions and phase-transition mechanism have remained as a long-standing problem until now. To resolve these issues, we used the cutting-edge time-of-flight neutron powder diffractometer (SuperHRPD) at the Japan Proton Accelerator Research Complex (J-PARC) to study the spin-direction-dependent magnetoelastic coupling in MnO, CoO, and NiO. We also constructed a group-subgroup structure relation from $Fm\ensuremath{-}3m$ to $C2/m$ with exchange striction and a type of magnetostriction (dipolar and roto magnetostriction). These unified viewpoints and the high-resolution neutron powder diffractometer enable us to construct an order-parameter vector diagram. The order-parameter vector diagram reveals distinguished order-parameter coupling and phase-transition characters by different ${\mathrm{\ensuremath{\Gamma}}}_{1}^{+}({A}_{g})$ and ${\mathrm{\ensuremath{\Gamma}}}_{2}^{+}({B}_{g})$ spin direction. Moreover, the experiment results show clearly that the ${\mathrm{CoO}}_{6}$ octahedral distortion and the Co magnetic moment couple through a magnetoelastic coupling ${\ensuremath{\epsilon}}_{\text{oct}}\ensuremath{\sim}{M}^{3}$, which is forbidden by time-reversal symmetry but allowed by the more general magnetic symmetry---the so-called rotation-time-reversal symmetry in the double antisymmetry space group. Rotation-time-reversal symmetry allows the coupling of odd-power polynomials in the spin vector and odd-power ones in the roto vector when both spin- and roto-axial vectors belong to the same irreducible representation in Landau free energy. Here, we show experimental evidence that the magnetic order parameter and static structural order parameter belong to the same irreducible representation in the materials. Experimental discovery of general magnetic symmetry opens a way to find the physics forbidden by time-reversal symmetry in condensed matter physics.