Pressure effects on magnetic ground states in cobalt-doped multiferroic ${\mathrm{Mn}}_{1\text{−}x}{\mathrm{Co}}_x{\mathrm{WO}}_4$

Using ambient pressure x-ray and high pressure neutron diffraction, we studied the pressure effect on structural and magnetic properties of multiferroic ${\mathrm{Mn}}_{1\text{−}x}{\mathrm{Co}}_x{\mathrm{WO}}_4$ single crystals ($x=0$, 0.05, 0.135, and $0.17$) and compared it with the effects of doping. Both Co doping and pressure stretch the Mn-Mn chain along the $c$ direction. At high doping level ($x=0.135$ and $0.17$), pressure and Co doping drive the system in a similar way and induce a spin-flop transition for the $x=0.135$ compound. In contrast, magnetic ground states at lower doping level $(x=0$ and $0.05$) are robust against pressure but experience a pronounced change upon Co substitution. As Co introduces both chemical pressure and magnetic anisotropy into the frustrated magnetic system, our results suggest the magnetic anisotropy is the main driving force for the Co induced phase transitions at low doping level, and chemical pressure plays a more significant role at higher Co concentrations.

Figure 1

(a) Crystal structure of ${\mathrm{Mn}}_{1\text{−}x}{\mathrm{Co}}_x{\mathrm{WO}}_4$. The unit cell is denoted by a box in the lower left corner, and the Mn-Mn chain and its characteristic parameters are illustrated. The Co doping dependence of (b) $a,b,c$ and $y\left(\mathrm{Mn}\right)$, (c) chain displacement $d$, and (d) Mn-Mn-Mn angle $\varphi$ are measured at room temperature and ambient pressure. Data in (b) are normalized to the undoped values to present the relative change. In (c) and (d), the pressure effects on the parent compound (blue) were calculated from Ref. [42] and compared with Co doping (black).

Figure 2

Magnetic order parameters of ${\mathrm{Mn}}_x{\mathrm{Co}}_{1\text{−}x}{\mathrm{WO}}_4$ at (a) $x=0$, (b) $x=0.05$, (c) $x=0.135$, and (d) $x=0.17$ at representative pressure $P=0.5$ and $1.5$ GPa. Measurements of AF5 (blue) and AF2 (red) phases were on the ${(-1,0,1)}_{+}$ peak, AF1 (cyan) phase on the ${(0,1,0)}_{+}$ peak, and AF4 (green) phase on the $(-0.5,1,1)$ peak. The onset of transition are marked by vertical dashed lines. (e) Comparison of AF4 transition temperature as a function of Co doping (black) and pressure (blue) with a scale of 0.5 GPa/ (Co%). The circles are the pressure results from $x=0.135$, and squares are from $x=0.17$.

Figure 3

The evolution of various magnetic phases of the $x=0.135$ sample at (a) 0.8 GPa, (b) 1.2 GPa, (c) 1.0 GPa in the warming process, and (d) 1.0 GPa in the cooling process. Panels (a),(b) and panels (c),(d) were measured at CORELLI and HB1A, respectively. For (a) and (b) data are collected near the reciprocal lattice (r.l.u.) vector $\vec{G}=(-1,-1,1)$, which gives magnetic peaks around $(-0.75,-0.5,0.5)$. Data in (c) and (d) are collected near $\vec{G}=(0,0,0)$ with magnetic peaks near $(0.25,0.5,-0.5)$.

Figure 4

The $T-P$ phase diagrams of ${\mathrm{Mn}}_{1\text{−}x}{\mathrm{Co}}_x{\mathrm{WO}}_4$ determined from neutron diffraction. Cyan, magenta, orange, brown, and blue represent AF1-AF5 phases, respectively. The dashed line in panel (c) denotes the lower boundary of AF2 phase.