Magnetic Anisotropy and Orbital Ordering in Ca$_2$RuO$_4$

TL;DR

This study uses resonant elastic x-ray scattering to investigate magnetic and orbital states in Ca$_2$RuO$_4$, revealing a c-axis canting of magnetic moments and challenging existing orbital ordering models.

Contribution

It provides new experimental insights into magnetic moment orientation and questions the traditional orbital ordering picture in Ca$_2$RuO$_4$.

Findings

Detected a c-axis canting of magnetic moments (~0.1 m_b)

Found no evidence of symmetry breaking at the orbital ordering temperature

Observed no change in orbital pattern across the antiferromagnetic transition

Abstract

We review the magnetic and orbital ordered states in \cro{} by performing Resonant Elastic X-ray Scattering (REXS) at the Ru L$_{2,3}$-edges. In principle, the point symmetry at Ru sites does not constrain the direction of the magnetic moment below $T_N$. However early measurements reported the ordered moment entirely along the $\vec{b}$ orthorhombic axis. Taking advantage of the large resonant enhancement of the magnetic scattering close to the Ru L$_2$ and L$_3$ absorption edges, we monitored the azimuthal, thermal and energy dependence of the REXS intensity and find that a canting ($m_c \simeq 0.1 m_b$) along the $\vec{c}$-orthorhombic axis is present. No signal was found for $m_a$ despite this component also being allowed by symmetry. Such findings are interpreted by a microscopic model Hamiltonian, and pose new constraints on the parameters describing the model. Using the same technique we reviewed the accepted orbital ordering picture. We detected no symmetry breaking associated with the signal increase at the "so-called" orbital ordering temperature ($\simeq 260$ K). We did not find any changes of the orbital pattern even through the antiferromagnetic transition, suggesting that, if any, only a complex rearrangement of the orbitals, not directly measurable using linearly polarized light, can take place.