Double magnetic phase transition in ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ and ${\text{NH}}_4\text{Fe}{\left({\text{HPO}}_4\right)}_2$

Combining neutron diffraction, magnetization measurements up to 330 kOe and specific-heat data, we have studied in detail both the crystal and magnetic structures of triclinic ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ and ${\text{NH}}_4\text{Fe}{\left({\text{HPO}}_4\right)}_2$ compounds. The low symmetry of this structure gives rise to a complex pattern of competing superexchange interactions between the magnetic moments of two types of ${\text{Fe}}^{3+}$ sites (with different site symmetry) that are responsible for the existence of two magnetic phase transitions. Below $T_C=17.82\pm 0.05\text{K}$ ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ orders ferrimagnetically with the magnetic moments lying in the crystallographic plane $ac$. As the temperature is lowered to $T_t=3.52\pm 0.05\text{K}$ the compound undergoes a magnetic phase transition to an equal moment antiphase structure characterized by the propagation vector close to ${\vec{k}}_{\text{AF}}\approx \left(1/16,0,1/16\right)$ and a magnetic moment for the ${\text{Fe}}^{3+}$ ions of $4.8{\mu }_B$ at 1.89 K. In addition, a two-step metamagnetic process is observed in the magnetization measurements at 2 K, where the antiphase ordering is destroyed under a field of only 2 kOe and the compound recovers the high-temperature ferrimagnetic ordering at around 20 kOe. The stability of this ferrimagnetic phase under magnetic field is only broken when the strength of the field reaches values as large as 180 kOe, and the magnetic moments begin to rotate to reach the full-induced ferromagnetic structure. A mean-field model has been used to account for the magnetization process leading to an estimation of the molecular-field coefficient of $-2.86\text{K}$ and the value of the critical magnetic field of 535 kOe to attain the full-induced ferromagnetic phase.

Figure 1

(Color online) Scanning electron microscopy images showing the morphology of ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ and ${\text{NH}}_4\text{Fe}{\left({\text{HPO}}_4\right)}_2$ samples.

Figure 2

(Color online) Observed (points), calculated (solid line) and difference (bottom) neutron-powder-diffraction (D2B) profiles of (a) ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ and (b) ${\text{NH}}_4\text{Fe}{\left({\text{HPO}}_4\right)}_2$. Vertical marks correspond to the position of the allowed Bragg reflections associated with the crystal structure. In both patterns, the strong Bragg reflection near $155°$ is due to aluminium from the cryostat. It is worth noting that the refinement of both patterns (see text) leads to the same crystal structure (see Tables ) for both compounds, the differences observed in the patterns are related to the unlike scattering length for deuterium and hydrogen. The high background in the ${\text{NH}}_4\text{Fe}{\left({\text{HPO}}_4\right)}_2$ compound is due to the high incoherent scattering length of hydrogen.

Figure 3

(Color online) Temperature dependence of the molar magnetic susceptibility, ${\chi }_{\text{M}}$, for ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ measured under a magnetic field of 1 kOe. The field-cooling (heating) data are open circle (square) points. The dashed lines are guides for the eyes. The inset shows a modified Curie-Weiss fit to the inverse molar magnetic susceptibility, ${\chi }_{\text{M}}^{-1}$, according to Eq. (1) (see text).

Figure 4

(Color online) Magnetization isotherms with magnetic field increasing (open circles) or decreasing (solid triangles) for ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ measured up to a field of 90 kOe at selected temperatures 1.89, 10, and 15 K. The inset shows the detail of the low-field magnetization process.

Figure 5

(Color online) High-field magnetization measurements up to 330 kOe at selected temperatures on ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$.

Figure 6

The empty circles represent the heat-capacity experimental data of ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$. $T_t$ is the critical temperature of the AF phase while $T_C$ is the Curie temperature for the ferrimagnetic ordering of the ${\text{Fe}}^{3+}$ magnetic moments. The lattice contribution is represented by the solid line (see text).

Figure 7

(Color online) (a) Magnetic field dependence of specific heat for the ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ between 1.8 and 40 K. $T_t$ is the critical temperature of the AF phase while $T_C$ is the Curie temperature for the ferrimagnetic ordering of the ${\text{Fe}}^{3+}$ magnetic moments. (b) Magnetic field dependence of the magnetic entropy, $\Delta S_{theo}=R\text{ln}\left(2S+1\right)=1.79R$ is the expected value for a $S=5/2$ spin state.

Figure 8

(Color online) The $H\text{−}T$ magnetic phase diagram of ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ based on the magnetization and specific-heat data. PM, FI, and AF are the paramagnetic, ferrimagnetic, and antiferromagnetic phases, respectively.

Figure 9

(Color online) Powder neutron-diffraction patterns for ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ collected on (D1B). Observed (points) and calculated (solid line) values at 4 and 1.89 K. Bragg reflection positions are represented by vertical bars. The first (second) row of Bragg diffraction reflections corresponds to the nuclear (magnetic) peaks. The observed-calculated difference is depicted at the bottom of each pattern. In the pattern measured at 1.89 K within the AF phase the notation ${\left(hkl\right)}^{\pm }$ corresponds to magnetic reflections of type $\left(h+k_x,k,l+k_z\right)$ with $k_x=1/16$ and $k_z=1/16$ (see text).

Figure 10

(Color online) Observed (points) and calculated (solid line) powder-neutron-diffraction patterns collected on D2B for ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ (a) at 12 K, (b) at 2 K and for ${\text{NH}}_4\text{Fe}{\left({\text{HPO}}_4\right)}_2$ (c) at 12 K, (d) at 2 K. Bragg reflection positions are represented by vertical bars. The first (second) row of Bragg diffraction reflections corresponds to the nuclear (magnetic) peaks. The observed-calculated difference is depicted at the bottom of each pattern. Within the experimental uncertainty the refinement of the magnetic diffraction patterns leads to propose the same magnetic structure for ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ and ${\text{NH}}_4\text{Fe}{\left({\text{HPO}}_4\right)}_2$ samples (see text and Table ).

Figure 11

(Color online) Representation of the magnetic moments of Fe1 and Fe2 ions within a unit cell for the ferrimagnetic ordering (see text).

Figure 12

(Color online) Temperature dependence of the Fe relative magnetic moment, ${\mu }_{\text{Fe}}$, ${\mu }_{\text{Fe}}\left(T\right)/{\mu }_{\text{Fe}}\left(T=3.8\text{K}\right)$ obtained from neutron-diffraction data experiments on D1B compared with the Brillouin function, $S=5/2$ (see text).

Figure 13

(Color online) Intensity contour map of neutron-diffraction pattern of ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ collected at different temperatures from 2.5 K up to 4 K. Note the disappearance of Bragg magnetic peaks associated with the ferrimagnetic structure and the onset of the peaks related to the AF structure (see text). The magnetic peaks appearing below 3.5 K corresponding to the magnetic structure of the AF phase are those labeled in Fig. 9.

Figure 14

(Color online) Schematic representation of the antiferromagnetic antiphase magnetic structure of ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$ obtained from neutron diffraction at 1.89 K (see text).

Figure 15

(Color online) Polyhedral representation of the crystal structure of ${\text{ND}}_4\text{Fe}{\left({\text{DPO}}_4\right)}_2$. The solid lines indicate the superexchange pathways between iron cations, the grey spheres are P atoms and the orange octahedra are ${\text{FeO}}_6$ units.

Figure 16

(Color online) Calculated field dependence of the free energy of the initial $\left(E_{\text{FI}}\right)$, intermediate $\left(E\right)$, and final $\left(E_{\text{FM}}\right)$ states, angles ($\theta$ and $\phi$), and magnetization $\left(M\right)$ together with the experimental magnetization curve at 4 K (○).