Emergent 1/3 magnetization plateaus in pyroxene ${\mathrm{CoGeO}}_3$

Despite the absence of an apparent triangular pattern in the crystal structure, we observe unusually well-pronounced 1/3 magnetization plateaus in the quasi-one-dimensional Ising spin chain compound ${\mathrm{CoGeO}}_3$ which belongs to the class of pyroxene minerals. We succeeded in uncovering the detailed microscopic spin structure of the 1/3 magnetization plateau phase by means of neutron diffraction. We observed changes of the initial antiferromagnetic zero-field spin structure that resemble a regular formation of antiferromagnetic “domain wall boundaries,” resulting in a kind of modulated magnetic structure with a 1/3-integer propagation vector. The net ferromagnetic moment emerges at these “domain walls” whereas two thirds of all antiferromagnetic chain alignments can be still preserved. We propose a microscopic model on the basis of an anisotropic frustrated square lattice to explain the observations.

Figure 1

Crystal structure of ${\mathrm{CoGeO}}_3$ (from the $c$ direction); a chain running along the $c$ axis is shown on the right. Green: Co1; dark yellow: Co2; blue: Oxygen; gray: Ge. The high-temperature polymorph of ${\mathrm{CoGeO}}_3$ has a monoclinic crystal structure with space group $C2/c$ [$a=9.6623\left(2\right)$ Å, $b=8.9928\left(2\right)$ Å, $c=5.16980\left(10\right)$ Å, $\beta =101.2785{\left(10\right)}^{\circ }$] [30].

Figure 2

Phase diagram: (a) Magnetization $M\left(H\right)$ of ${\mathrm{CoGeO}}_3$ for $H\parallel c$. (Data obtained by ramping up to 9 T and down to 0 T after virgin zero-field cooling from 200 K down.) Pronounced 1/3 magnetization plateaus can be seen. Inset: The magnetization for $H\perp c$ at 5 K as a function of (increasing and decreasing) magnetic field which is linear in $H$ and unsaturated up to 9 T. (b) Real part of the ac susceptibility as a function of applied magnetic field (ac frequency: 100 Hz; ac field: 10 Oe). (c) The magnetization for various fields $H\parallel c$. The shift of the order temperature with magnetic field can be seen. At $\sim 8$ T the order is completely suppressed and the system enters the field-polarized (FP) regime. At intermediate fields the occurrence of the 1/3 magnetization plateau becomes visible. (d) Field dependence of dielectric constant $\varepsilon$ at $T=10$ K (${\mu }_{0}H$ was scanned in the range of $-9$ and 9 T with a rate of 30 Oe/s). Inset: Temperature dependence of $\varepsilon$ and the corresponding dielectric loss $tan\delta$ in zero field. (e) Specific heat $C_p\left(T\right)$ of ${\mathrm{CoGeO}}_3$ measured for different external fields ($H=0$–9 T) along the $c$ axis. (f) Magnetic phase diagram of ${\mathrm{CoGeO}}_3$ for $H\parallel c$. (Lines are guide to the eyes.)

Figure 3

Neutron scattering intensity maps within the $HK0$ scattering plane measured at (a) 0 T and (b) 6.5 T using an area detector.

Figure 4

(a) Neutron scans across the magnetic peak positions in the $K$ direction. (b) A detailed magnetic field dependence (for a ZFC process).

Figure 5

Neutron refinement results for the zero-field phase: Calculated structure factor ${\left|F\right|}_{\text{cal}}^2$ against the observed structure factor ${\left|F\right|}_{\text{obs}}^2$ for (a) the nuclear structure and (b) the magnetic structure refinement at 0 T. The corresponding magnetic structure is shown in (c) in a view from the $b$ direction, and in (d) for a different perspective. (e) Local coordination of the two Co sites; green: Co1; dark yellow: Co2; blue: oxygen.

Figure 6

Neutron refinement results for the 1/3 magnetization plateau phase: (a) Calculated structure factor ${\left|F\right|}_{\text{cal}}^2$ against the observed structure factor ${\left|F\right|}_{\text{obs}}^2$ for the magnetic structure refinement at 6.5 T. (b) Zero-field magnetic structure. The purple lines indicate the AFM unit cell. (c) The magnetic structure at 6.5 T with an $a\times 3b\times c$ magnetic unit cell (black lines). The light blue lines indicate planes of ferromagnetically aligned Co chains. The dashed purple lines indicate regions where the spins are aligned as in the zero-field magnetic unit cell.

Figure 7

Calculated energies for an anisotropic frustrated square lattice with one diagonal exchange interaction. The 1/2 $M_S$ phase is never stable. For a ratio of the values of AFM NN- and NNN-exchange interactions around 3 the expected phase diagram resembles the one shown in Fig. 2. The inset visualizes the underlying model of a frustrated square lattice with diagonal exchange.