Pressure-induced incommensurate antiferromagnetic order in a ferromagnetic $B$-site ordered double-perovskite ${\mathrm{Lu}}_2{\mathrm{NiMnO}}_6$

We have investigated the pressure effect on magnetic ordering of the ferromagnetic double perovskite ${\mathrm{Lu}}_2{\mathrm{NiMnO}}_6$ by magnetization, ac magnetic susceptibility, and neutron diffraction experiments up to 8.0 GPa in order to understand the ferromagnetic-to-antiferromagnetic phase transition by substitution of the $A$ sites in $A_2{\mathrm{NiMnO}}_6$ from rare-earth to indium or scandium ions. Strong ferromagnetic spin correlation seen in the susceptibility at low pressure is significantly suppressed by increasing pressure. In a neutron diffraction experiment, the magnetic Bragg reflections associated with ferromagnetic ordering disappear above 4.5 GPa. For the high-pressure region above 4.5 GPa, an antiferromagnetic ordering with long-period incommensurate modulation appears, which is coexistent with ferromagnetic short-range order. From mean-field calculations, we infer that pressure modification of the delicate balance of the competing next-nearest-neighbor exchange interactions between Ni and Ni, or Mn and Mn, plays an important role in the phase transition from ferromagnetic to antiferromagnetic ordering in $A_2{\mathrm{NiMnO}}_6$.

Figure 1

Magnetic phase diagram of $A_2{\mathrm{NiMnO}}_6$ as functions of temperature and ionic radius. The phase-transition temperature points are taken from previous papers [17, 18, 19]. The hatched area denotes the phase boundary between ferromagnetic (FM) and antiferromagnetic (AFM) phases. The inset shows the ionic radius dependence of bond angles, Ni-O1-Mn, Ni-O2-Mn, and Ni-O3-Mn.

Figure 2

Temperature dependences of (a) dc magnetization and (b) the real part of magnetic susceptibility for typical pressures in ${\mathrm{Lu}}_2{\mathrm{NiMnO}}_6$. The insets in (a) and (b) show the magnetic field variation of the magnetization at $T=2.0$ K and the magnification for the high-pressure data, respectively.

Figure 3

Temperature vs pressure magnetic phase diagram for ${\mathrm{Lu}}_2{\mathrm{NiMnO}}_6$. Triangle, circle, and square symbols denote the magnetic phase transitions determined by the dc magnetization, ac magnetic susceptibility, and neutron diffraction experiments, respectively.

Figure 4

Temperature dependence of neutron diffraction profiles at ambient pressure in ${\mathrm{Lu}}_2{\mathrm{NiMnO}}_6$. The data are subtracted by those measured at $T=80$ K. Arrows denote the positions of magnetic Bragg reflections.

Figure 5

(a) Result of the Rietveld refinement for the data at $T=4.2$ K and ambient pressure. The experimental data are subtracted by those at $T=80$ K. Circles and thick and thin lines denote the observed data, calculated data, and the difference between the data, respectively. The vertical bars are the symmetry-allowed magnetic Bragg positions. (b) Illustration of the determined magnetic structure at ambient pressure in ${\mathrm{Lu}}_2{\mathrm{NiMnO}}_6$.

Figure 6

Temperature dependence of neutron diffraction profiles. The data are subtracted by the data at $T=80$ K and $P=6.0$ GPa. The arrow indicates the position of the antiferromagnetic signal, which is described in the main text.

Figure 7

The neutron diffraction profiles at $T=4.2$ K and $P=1$ bar, $P=4.5$ GPa, and $P=6.0$ GPa, which are subtracted by the data at 50, 25, and 20 K, respectively. The inset shows the magnification of the data around $Q\sim 0.17{\AA }^{-1}$ at $T=4.2$ K and $P=6.0$ GPa.

Figure 8

Illustration of the exchange interaction paths bonding two spins of atoms, (1)Mn1(0,1/2,0), (2)Ni1(1/2,0,0), (3)Mn2(1/2,0,1/2), and (4)Ni2(0,1/2,1/2).

Figure 9

(a) Magnetic phase diagram representing the stability of different states in the case when $J_1=J_2=J_3=1.0, J_4^{\mathrm{Ni}}=J_4^{\mathrm{Mn}}=J_4, J_5^{\mathrm{Ni}}=J_5^{\mathrm{Mn}}=-1.0$, and $J_6^{\mathrm{Ni}}=J_6^{\mathrm{Mn}}=J_6^{\prime \mathrm{Ni}}=J_6^{\prime \mathrm{Mn}}=J_6$. The color scale denotes an incommensurability in the propagation vectors, $\mathit{k}=(k_x,0,0)$ and $\mathit{k}=(k_y,0,0)$. (b) Dispersion relations for the eigenvalues of the exchange matrix, Eq. (1), for the sets of $J$-parameters indicated by the filled circles in (b), along directions connecting special points, $D=(\frac{1}{2},\frac{1}{2},0), \mathrm{\Gamma }=(0,0,0)$, and $B=(\frac{1}{2},0,0)$, in the first Brillouin zone of the $P{2}_1/n$ space group. (c) and (d) Magnetic phase diagrams for the other cases with $J_5=-0.5$ in (c) and $J_5=-2.0$ in (d) and the other $J$-parameters are the same as (a).