Magnetic field-temperature phase diagrams of multiferroic $({\mathrm{Ni}}_{0.9}{\mathrm{Co}}_{0.1}{)}_3{\mathrm{V}}_2{\mathrm{O}}_8$

We present macroscopic and neutron diffraction data on multiferroic lightly Co doped ${\mathrm{Ni}}_3{\mathrm{V}}_2{\mathrm{O}}_8$. The magnetic $H-T$ phase diagrams have been derived from magnetization and electric polarization measurements with field directions parallel to the principal crystallographic axes. While the phase diagram for $H\parallel b$ is very similar to that of the parent compound ${\mathrm{Ni}}_3{\mathrm{V}}_2{\mathrm{O}}_8$ for the commonly involved phases, the zero-field phases in ${\left({\mathrm{Ni}}_{0.9}{\mathrm{Co}}_{0.1}\right)}_3{\mathrm{V}}_2{\mathrm{O}}_8$ show a stronger instability for applied magnetic fields along the $a$ or $c$ axis. Neutron single-crystal diffraction revealed the magnetic structure of the field-induced phase for $H\parallel c$ with a collinear spin alignment along the $a$ and $b$ axes for the two magnetically inequivalent sites. A pronounced irreversibility has been observed for the transition between the zero-field spin cycloid and the field-induced phase, which is manifested in a propagation vector change from $\mathbf{q}=\left(\mathrm{0.322\; 0\; 0}\right)$ to $\mathbf{q}=\left(\mathrm{0.306\; 0\; 0}\right)$, with slight modifications of the magnetic structure after reentering the zero-field phase. The reentrant phase is characterized by a significantly larger $b$ component of the cross-tie site spin, therefore showing remanent features of the high-field phase. For $H\parallel a$ the magnetization data reveal anomalies, one of which was proved to reflect a field-induced transition from the cycloidally to the sinusoidally modulated magnetic structure.

Figure 1

Magnetic phase transitions in ${\left({\text{Ni}}_{1-x}{\text{Co}}_x\right)}_3{\text{V}}_2{\text{O}}_8$ for $x=0$, 0.07, and 0.10. The transition temperatures were taken from Refs. [11, 20].

Figure 2

Real part of the ac magnetic susceptibility as a function of temperature for superimposed dc magnetic fields applied along the $a$ (top panel), $b$ (middle panel), and $c$ axes (bottom panel). All data shown were recorded on warming up after a zero-field-cooling procedure.

Figure 3

Real part of the ac magnetic susceptibility at different temperatures for dc magnetic fields applied along the principle crystallographic directions. Solid (open) circles represent data measured with increasing (decreasing) field. The inset in the bottom panel shows the magnetization as a function of applied field at different temperatures.

Figure 4

(a) Magnetic field ramps clearly showing a hysteresis at the LTI-$C$ transition. The extent of the hysteresis is reduced towards the HTI phase. (b) Field-dependent imaginary part of the magnetic susceptibility clearly indicating magnetic losses at the field-induced transitions. The inset shows the temperature-dependent susceptibility revealing that a field-treated sample (open symbols) behaves differently than a non-field-treated sample (solid symbols) in the temperature region corresponding to the LTI phase.

Figure 5

Electric polarization as a function of magnetic field at fixed temperatures (left column) and as a function of temperature at fixed magnetic field (right column) with $H\parallel a$ (top row) and $H\parallel c$ (bottom row). Solid (open) symbols represent data measured with increasing (decreasing) field. In the bottom left panel circles represent a field sweep after ZFC, while triangles show data recorded after field cooling.

Figure 6

Magnetic $H-T$ phase diagrams of ${\left({\text{Ni}}_{0.9}{\text{Co}}_{0.1}\right)}_3{\text{V}}_2{\text{O}}_8$ for magnetic fields along the principal crystallographic axes. Red dots were obtained from the anomalies in the $\chi \left(H\right)$ curves, while the blue dots emerge from the anomalies in $\chi \left(T\right)$. Green dots represent the phase transitions observed by neutron diffraction. Light blue dots were obtained from $P_b\left(H\right)$ measurements, and magenta dots were obtained from $P_b\left(T\right)$. Open symbols denote the $C\to \text{LTI}$ phase transition in decreasing magnetic field. For $H\parallel c$ the $C$ phase in parentheses refers to the fact that weak commensurate reflections coexist within the LTI and HTI phases after a field treatment.

Figure 7

Left ordinate: Integrated intensities as a function of the applied magnetic field along the $a$ axis (solid circles). With increasing field the incommensurate reflections are weakened, while the evolution seems to reveal two kinks at 3 and 8 T. The kink at 8 T has a clear origin (i.e., the transition to the sinusoidal state accompanied by a disappearance of the $b$ component of the spine spin), while the kink at 3 T [only clearly observable for the ($-0.68,1,-1$) reflection but not for ($-0.68,1,0$)] has no such clear physical origin. We may speculate that it reflects the onset of the cycloidal $b$ component suppression which is already evident at 4 T (see Table 1). Right ordinate: The refined ratio between the imaginary $b$ and the real $a$ components of the spine spins from full data collections at different field values revealing a similar evolution with magnetic field (the solid line is a guide to the eye). The inset shows the field dependence of the commensurate antiferromagnetic (130) reflection representative for the $C$ phase.

Figure 8

Integrated intensities of incommensurate (blue symbols, left ordinate) and commensurate (green symbols, right ordinate) magnetic reflections as a function of the applied magnetic field along the $c$ axis. Data recorded with increasing ($\mathbf{q}={\mathbf{q}}_0$) and decreasing ($\mathbf{q}={\mathbf{q}}_H$) field are represented by circles and triangles, respectively. In the top panel the solid and dashed lines are guides to the eye, while the inset shows the field evolution of a nuclear reflection. The data show a clear hysteretic behavior at $T=1.5$ K, which is reduced for $T=4.5$ K and absent for $T=7$ K. The inset in the bottom panel shows a $q$ scan along the $a^{*}$ direction before the first application of the external field, clearly illustrating the absence of the (110) reflection.

Figure 9

The $q$ scans along the $a^{*}$ direction across the (110)+${\mathbf{q}}_0$ and (150)+${\mathbf{q}}_H$ magnetic satellites at $H=0$ T before and after applying a magnetic field along the $c$ axis. The shift in the position clearly shows a smaller incommensurability for the field-treated state.

Figure 10

Visualization of the magnetic structures of the (a) cycloidally modulated LTI phase, (b) the sinusoidally modulated HTI, and the (c) commensurate $C$ phase. Note that the cross-tie spins (orange) are overscaled by a factor of 5 with respect to the spine spins (yellow) in (a) and (b).