Ising spin ladders of orthopyroxene CoGeO$_3$

Abstract

We present thermodynamic and spectroscopic measurements for an orthopyroxene CoGeO$_3$ with magnetic Co$^{2+}$ ions that form quasi-one-dimensional ladders. We show that non-collinear magnetic order below $T_N$=32 K can be stabilized by a strong local easy-axis anisotropy of $j_\text{eff}=1/2$ moments, which is induced by ligand octahedra distortions. Extraction of a magnetic Hamiltonian from inelastic neutron scattering measurements supports this interpretation and allows us to establish an effective magnetic model. The resulting exchange Hamiltonian justifies CoGeO$_3$ as a realization of an Ising spin ladder compound.

Figures (12)

• Figure 1: Crystal structure of orthorhombic CoGeO$_3$. Magnetic structure redhammer2010a consists of splayed ferromagnetic ladders, which are running along the $c$ axis and are coupled antiferromagnetically.
• Figure 2: CoGeO$_3$ crystal and magnetic structure in the (a) $bc$ plane (Ge atoms not shown) and (b) $ab$ plane. Relevant exchange paths, ranked by the Co-Co distance, are shown.
• Figure 3: Powder-averaged magnetic phase diagram of CoGeO$_3$ constructed from anomalies in bulk measurements. Symbols mark characteristic anomalies observed in $\chi(T)$, $M(H)$, and $C_p(T)$ for a polycrystalline sample. Shaded regions indicate the approximate stability ranges of four antiferromagnetic phases (AFM1–AFM4). Because the data are from a powder, the phase boundaries represent the onset and completion of transitions across different grain orientations rather than orientation-resolved critical fields. The consistent appearance of the same boundaries in three independent probes demonstrates that these anomalies mark real thermodynamic phase transitions in the polycrystalline sample.
• Figure 4: Electronic crystal-field levels from SEQUOIA at $T$=6K, $E_i$=60 meV. One can identify four excitations which correspond to split $j_\text{eff}=3/2$ levels of two inequivalent Co ions.
• Figure 5: One-electron energies for the two inequivalent Co ions, derived from non-magnetic DFT calculations using Wannier projection. They are distinct from crystal-field excitation energies because they neglect correlation effects.