Spin reorientation behaviour and dielectric properties of Fe-doped h-HoMnO₃

The end compounds of the series HoMn_1−x Fe_x O₃ possess contrasting crystallographic structures. The parent compound HoMnO₃, under ambient conditions, crystallizes in hexagonal phase with the space group P6₃ cm (SG No. 185) [19] whereas the compound HoFeO₃ adopts a GdFeO₃ type distorted perovskite structure with the space group Pnma (SG No. 62) [43]. The coordination chemistry of the cations Ho³⁺, Mn³⁺ and Fe³⁺ in both the structural phases are significantly different. In the case of hexagonal compounds (P6₃ cm) the transition metal occupies the Wyckoff position (6c) and is five-fold coordinated by the oxygen anions. The Mn/Fe–O₅ trigonal bipyramids are arranged in a layered structure forming a two dimensional Mn/Fe–O–Mn/Fe array in the a–b plane. These layers are separated by Ho³⁺ ions which are seven fold coordinated and occupy the (4b) and (2a) Wycoff positions. On the other hand in the orthorhombic perovskite phase the transition metal cation is six fold coordinated by the oxygen ions in an octahedral geometry whereas the rare earth ions are twelve coordinated. In this case the Mn/Fe–O–Mn/Fe interactions exist both along the a–b and the a–c axis thereby leading to both inter and intra layer exchange interactions. A gradual transition from the hexagonal to the orthorhombic phase is observed as the dopant concentration is increased.

Figure 1 shows the (a) x-ray and (b) neutron diffraction patterns at 300 K for three samples x = 0.01, 0.10 and 0.25. A single phase hexagonal model (P6₃ cm) was found to fit the data of the parent compound h-HoMnO₃, whose lattice parameter and volume were found to be in agreement with the earlier reports [44]. For higher doping concentrations (x = 0.05 and 0.10), Bragg reflections (112) and (031) corresponding to the orthorhombic phase were observed. Therefore, we chose a two phase model with both hexagonal and orthorhombic phases for the refinement of the structure in these samples. The results of the refinement at 300 K are summarized in table 1. With increase in the dopant concentration to 25% a complete transformation to the orthorhombic phase was observed. Figure 2 shows the increase in the concentration of the orthorhombic phase as a function of dopant concentration (x), obtained from the Rietveld analysis of the neutron diffraction data. As compared to other trivalent dopants on the Mn site such as Cr³⁺ [38] or Co³⁺ [45], Fe³⁺ maintains the stability of the hexagonal structure up to a higher degree of dopant concentration. This is probably due to the similar ionic sizes of the Mn³⁺ and the Fe³⁺ ions in the five coordination (0.58 Å) and the six-fold coordination states (0.645 Å). However, as compared to YFe_1−x Mn_x O₃ [32], the transformation to the orthorhombic phase was found to be much faster.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Figure 3 shows the Raman spectra of all the doped samples recorded in the range 85 cm⁻¹ ⩽ $\bar{\nu }$ ⩽ 750 cm⁻¹ at T = 300 K. The difference in phonon modes observed for x ⩽ 0.1 compounds, and x = 0.25 compound corroborates the complete structural transition of the hexagonal phase to the orthorhombic phase in case of the x = 0.25 compound observed from the analysis of the neutron diffraction pattern. The identification of the Raman active modes in the case of hexagonal and orthorhombic compounds was carried out in accordance with references [46, 47] respectively. We could not identify any peaks corresponding to the modes of the orthorhombic phase in the compounds with x ⩽ 0.1, due to very small orthorhomobic phase fraction in these compounds as obtained from neutron diffraction.

Zoom In Zoom Out Reset image size

Figure 4(a) shows the variation of lattice parameters and the volume of the hexagonal phase as a function of Fe content. Both the lattice parameters a and c were found to increase linearly with increase in dopant concentration, which is in contrast to the cases of YbMn_1−x Fe_x O₃ [48] and LuMn_1−x Fe_x O₃ [49] where the a axis decreases and the c axis increases with increase in Fe concentration. A similar increasing trend of the a and c axis is observed for YMn_1−x Fe_x O₃ [32] until the development of the orthorhombic phase from where the a and c lattice parameters start decreasing. The relative change in the c-axis (0.3%) was found to be larger than the change in the a-axis (0.1%), thereby increasing the c/a ratio. An associated change [50] in the T_N with c/a was not observed due to a only a small relative change (0.01) with increase in dopant concentration. Due to the absence of Jahn–Teller effect in the hexagonal system, these changes must be associated with orbital effects induced due to doping of Fe³⁺ions. Figure 4(b) shows the temperature evolution of volume for x = 0.01 sample where a monotonous increase is observed with increasing temperature. The solid line shows fit to the volume via Debye model, using Grüneisen approximation [51]. In this approximation the temperature dependence of volume is given as V(T) = [γU(T)/B₀ + V₀], where γ, B₀ and V₀ are Grüneisen parameter, bulk modulus and volume at T = 0 K. In the Debye model, internal energy U(T) is given by $U\left(T\right)=9N{k}_{\mathrm{B}}T{\left(\frac{T}{{\theta }_{\mathrm{D}}}\right)}^{3}{\int }_{0}^{\frac{{\theta }_{\mathrm{D}}}{T}}\frac{{x}^{3}}{{\mathrm{e}}^{x}-1}\enspace \mathrm{d}x$, where N is the number of atoms in the unit cell, k_B is the Boltzmann constant, and θ_D is the Debye temperature. It is clearly seen from the fit that the volume does not exhibit any anomaly in the vicinity of either T_N or T_SR. In the inset to figure 4(b) we have shown the temperature variation (7 K ⩽ T ⩽ 150 K) of specific heat measured for the x = 0.01 sample in fields of 0 and 2 T. Even though the volume does not exhibit a significant anomaly at either T_N or T_SR, a clear lambda type anomaly is observed in the specific heat data at T_N, in corroboration with the dielectric data. This clearly indicates that the magnetic ordering couples with the lattice though the changes are not apparent in the temperature evolution of volume. However, in contrast to the report on YMnO₃ [52], no broadening of the anomaly at T_N was observed in C(T) in an applied field of 2 T.

Zoom In Zoom Out Reset image size

In figure 5 we show the temperature dependence of magnetization for compounds of the series HoMn_1−x Fe_x O₃ (0.01 ⩽ x ⩽ 0.25). Unlike in Fe doped YMnO₃ compounds [32], the magnetization curves do not reveal the presence of any anomaly at the T_N or the T_SR, and appear to be paramagnetic down to the lowest temperature. This behaviour arises due to the large paramagnetic moment of the Ho³⁺ ions (=10.6 μ_B) which masks the magnetic ordering of the Mn/Fe ions. The paramagnetic susceptibility data was fitted to the (C–W) law, given by χ = C/(T − θ_CW), where C and θ_CW are the Curie constant and C–W temperature respectively. The susceptibility data was found to follow the C–W law in the temperature range (∼140–300 K) for x = 0.01–0.10 hexagonal samples as shown in the inset to figure 5. The susceptibility data for x = 0.25 was found to deviate from the C–W behaviour at ∼30 K, which is associated with the development of short range order observed in the neutron diffraction pattern in this compound. Using the Curie constant values, we calculated the value of effective paramagnetic moment (μ_eff) by using the equation, $C=\frac{N{\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}^{2}{\mu }_{\mathrm{B}}^{2}}{3{k}_{\mathrm{B}}}$. The theoretical value of the effective paramagnetic moment can be calculated, by assuming Mn, Fe and Ho in the trivalent state, by using the expression ${\mu }_{\mathrm{e}\mathrm{ff}}^{\mathrm{c}\mathrm{a}\mathrm{l}}=\sqrt{{\mu }_{\mathrm{e}\mathrm{ff}}^{2}\left(\mathrm{H}{\mathrm{o}}^{3+}\right)+x{\mu }_{\mathrm{e}\mathrm{ff}}^{2}\left(\mathrm{M}{\mathrm{n}}^{3+}\right)+\left(1-x\right){\mu }_{\mathrm{e}\mathrm{ff}}^{2}\left(\mathrm{F}{\mathrm{e}}^{3+}\right)}$, where μ_eff for Mn³⁺ (S = 2), Fe³⁺ (S = 5/2) and Ho³⁺ are 4.89 μ_B, 5.9 μ_B and 10.6 μ_B respectively. The experimental and the theoretical value of μ_eff for x = (0.01, 0.1, 0.25) were found to be (11.26, 11.21, 11.11) μ_B and (11.68, 11.70, 11.79) μ_B respectively. We note that the experimentally obtained moment values are in agreement with the calculated values for trivalent state of Ho, Fe and Mn.

Zoom In Zoom Out Reset image size

Figure 6 shows magnetization measured as a function of applied external field at 5 K. The absence of hysteresis in M(H) curves indicates the absence of ferromagnetic component, however a small hysteresis curve is observed for x = 0.25. A decrease in the value of magnetic moment at 5 T with increase in the Fe ion concentration is observed. In inset (a) to figure 6 we show variation of magnetization with temperature measured up to 1.5 K for x = 0 sample. A clear decrease in the value M at ∼4 K marks the ordering of Ho ions in an antiferromagnetic configuration, discussed later. In inset (b) to figure 6 we show M(H) measured for x = 0 sample at 1.5 K. In contrast to the measurements on single crystals [26], we did not observe a jump in value of magnetization at 1 T or 2.5 T, however the value of magnetization was found to saturate at ∼5 T to 8 μ_B which is nearly the value of magnetic moment of the Ho³⁺ ions indicating a possible field induced reorientation of Ho spins.

Zoom In Zoom Out Reset image size

A section of the neutron diffraction pattern of HoMnO₃ at few selected temperatures is shown in figure 7. Similar magnetic ordering associated with the hexagonal phase was observed in the samples, x = 0.01, 0.05, 0.10, as well. The appearance of the superlattice reflection (011) at 65 K, below the T_N (∼72 K) of the sample, originates due a 2D ordering of the Mn moments in the a-b plane. On further lowering of temperature to 35 K the (011) reflection loses intensity while the superlattice reflection (010) gains intensity. A significant increase in the intensity of the reflection (102) is also observed at this juncture. The change in the relative intensities of the (011) and (010) reflection indicates the 90° reorientation of Mn³⁺ spins in the a–b plane and change in the magnetic symmetry of the compound. Along with the reorientation of Mn spins, moment on the Ho1(2a) sites, aligned along the c-axis, is also observed at 35 K. Below T = 15 K, the (011) reflection again gains intensity and an additional superlattice reflection (201) is observed in the raw data. These new peaks correspond to the ordering of the Ho2 ions located at the (4b) site, oriented parallel to the c-axis. These observations are corroborated by the modelling of the magnetic structure as described below.

Zoom In Zoom Out Reset image size

Following the classification given by Bertaut [53–55], there are six possible magnetic configurations (Γ₁–Γ₆) for the space group P6₃ cm with the propagation vector $\overrightarrow {k}=0$ for both the Mn atom, which occupies the (6c) site, and the Ho1 and Ho2 atoms, which occupy the (2a) and 4b sites, respectively. Description of the representation analysis for h-RMnO₃ can be found in ref [54]. Among these configurations for the Mn ion, (Γ₁, Γ₃) and (Γ₂, Γ₄) are homometric and cannot be distinguished using neutron diffraction. But, as was discussed earlier, the magnetic ordering of h-HoMnO₃ has been established, using various techniques [19–22], below T_N as Γ₄ (P6₃'c'm) and below T_SR as Γ₃ (P6₃'cm') along with the ordering of Ho³⁺ spins, located at the (2a) site, parallel to the c-axis. Thus we carried out the refinement in accordance with the magnetic structure reported in the literature [19] and found to be in agreement with it. The basis vectors corresponding to the various irreducible representations were obtained using SARAH programme [56].

In figure 8 we show the magnetic structure of the parent compound HoMnO₃ both below and above T_SR, obtained using Rietveld refinement. Here we point out that equivalent fit to the data of 2 K could be obtained using (i) P6₃ cm (Γ₁) ordering of the Mn³⁺ ions along with AFM ordering of the Ho2 ions ((4b) position) [55] and (ii) P6₃'cm'(Γ₃) ordering of Mn³⁺ ions with ferromagnetic coupling of Ho1 and Ho2 within the planes, and which are coupled antiferromagnetically between the planes, as shown from polarimetry studies [19]. We have chosen the latter model as the ground state magnetic structure for reasons discussed later. The values of the Mn site moment were found to be ∼3 μ_B which is lower than 4 μ_B expected for fully ordered Mn³⁺ spins. The lower value of Mn³⁺ moment originates from the effect of frustration in layered systems. The values obtained in the case of Ho at both the sites are also lower than the expected value of 10 μ_B. The Brillioun function dependence indicates that the temperature has to be lowered further to achieve the saturation.

Zoom In Zoom Out Reset image size

Figures 9(a) and 9(b) show the temperature evolution of magnetic moments for the x = 0.01 and x = 0.1 compounds respectively. At the T_SR, along with the reorientation of Mn spins, a simultaneous increase in the magnetic moment of the Ho1 ions located at the (2a) site is observed. This observation falls in accordance with the symmetry consideration of the P6₃'c'm (Γ₄) and P6₃'cm' (Γ₃) ordering of the Mn ions as the former does not allow moments on the Ho1 site while the latter does [19]. An inconsistency exists in literature regarding which Ho site orders at T_SR, (2a) [18] or (4b) [19, 27]. In powder neutron diffraction pattern, ordering of the Ho ions at both the (2a) and the (4b) sites, parallel to the c-axis, contributes to the same superlattice Bragg reflections (011) and (201). We obtained equivalent fits of the neutron data on considering Ho moments on the (2a) or the (4b) sites, however a final model was chosen based on the results reported by neutron polarimetry study [19].

Zoom In Zoom Out Reset image size

The ordering of the Ho1 sites may be induced by the reorientation of Mn spins in the a–b plane via the anisotropic superexchange between the 3d and 4f ions [16, 57]. With further decrease in temperature moments at Ho2 sites order at 10 K, coupled antiferromagnetically inter-plane with Ho1 ions, and ferromagnetically in intra-plane. In contrast to YMn_1−x Fe_x O₃ [32], we did not observe a mixed phase of Γ₃ and Γ₄ structures at any temperature. Following the molecular field analysis by Fabreges et al [27] for the case of YbMnO₃, we find the temperature variation of variation of moment of the Mn site could be described by the Brillioun function,

$$\begin{equation*}{m}_{\mathrm{M}\mathrm{n}}\left(T\right)={m}_{\mathrm{s}\mathrm{a}\mathrm{t}}{B}_{2}\left[\frac{\left(g{\mu }_{B}S{\lambda }_{0}{m}_{\mathrm{M}\mathrm{n}}\left(T\right)\right)}{{k}_{\mathrm{B}}T}\right]\end{equation*}$$

and the variation of the Ho moment as,

$$\begin{equation*}{m}_{\mathrm{H}\mathrm{o}}\left(T\right)=\frac{1}{2}{g}_{\mathrm{H}\mathrm{o}}{\mu }_{\mathrm{B}}\enspace \mathrm{tanh}\left[\frac{\left({g}_{\mathrm{H}\mathrm{o}}{\mu }_{\mathrm{B}}{\lambda }_{1}{m}_{\mathrm{M}\mathrm{n}}\left(T\right)\right)}{2{k}_{\mathrm{B}}T}\right],\end{equation*}$$

where the molecular field constant λ₀ and λ₁ represent the Mn/Fe–Mn/Fe and Ho–Mn/Fe exchange, respectively. A fit using these expressions to the thermal evolution of magnetic moments is shown in figures 9(a) and (b). The variation of the Mn moment is well described by the Brilliuon function with the value of λ₀ = 56.5 T μ_B ⁻¹. This value is large as compared to the values of 10.2 T μ_B ⁻¹ [32] and 19 T μ_B ⁻¹ [27] obtained for the cases of YMn_1−x Fe_x O₃ and YbMn_1−x Fe_x O₃. The variation of the Ho1 (2a) moment is described well by the above expression with λ₁ = 4 T μ_B ⁻¹. However, its variation cannot be extrapolated, beyond ∼35 K (T_SR), to the T_N. Unlike in the case of YbMnO₃, where the moment is predominantly on Yb2 (4b) site, we observe moment on Ho1 (2a) site. The temperature variation of the moments on Ho1 and Ho2 sites are similar to the observations of Brown and Chatterji [19].

As against the increase of magnetic moment, expected with increase in the concentration of Fe³⁺ ions in the system, a lower value moment was observed in the doped samples, as shown in table 2. Further we did not find any long range magnetic ordering in the fully orthorhombic x = 0.25 sample down to the temperature of 1.5 K. However, a large broad hump is observed at the position where the superlattice reflection of G-type AFM ordering would have appeared. Figure 10 shows the diffraction pattern at 2 K and 300 K for x = 0.25. The increase in intensity at lower angles in the neutron diffraction data starts to develop from 35 K. The 1/χ(T) behaviour too is found to deviate from linearity at about this temperature as shown in the inset to figure 10. This suggests a magnetic short range ordering in this compound. The scattering intensity due a 3D short range spin–spin correlation can be expressed by a Lorentzian function as [58],

$$\begin{equation*}{I}_{hkl}\left(Q\right)=A/\left[{\left(Q-{Q}_{\mathrm{C}}\right)}^{2}+{k}^{2}\right].\end{equation*}$$

Where A is a proportionality constant, k is the inverse of the 3D magnetic correlation length and Q_C is the length of the scattering vector at which the peak of I(Q) occurs. A fit using this expression, to the background subtracted curve, is found to give an unphysical correlation length of 1 Å. However for higher doping concentration, x ⩾ 0.4, a magnetic order of the G_XG_Z type (Γ₁ + Γ₄) was found to set in the orthorhombic phase, whose results are reported in another study [59].

Zoom In Zoom Out Reset image size

Figure 11 shows a section of the diffraction pattern at selected temperatures for x = 0.1 sample. The existence of the (010) reflection characteristic of the Γ₃ phase is observed up to 55 K. Above this temperature the (011) reflection gains in intensity while the (010) is suppressed, indicating a transition from Γ₃ to Γ₄ phase at 55 K in x = 0.1 sample. A clear signature of increase in T_SR is observed with doping of Fe, as shown in figure 12. The origin of T_SR in hexagonal manganites has been attributed primarily to the onset of Ho ordering and therefore to the Ho–Mn interaction [35]. Earlier results have also shown that perturbations like external pressure [41] and magnetic field [39, 40] lead to lowering of T_SR. However T_SR can either be increased or decreased with doping different ions such as Ga [60], Er [36], Y [37] and Cr [38]. In earlier works [41, 61], the variation of T_SR with pressure has been correlated with the suppression of the c-axis. In our case, the c-axis expands for the doped compounds. This weakens the interlayer coupling between Ho and Mn and therefore, plausibly shifts the T_SR to higher temperatures in doped compounds. In figure 12, the variation of the T_SR, ${T}_{\mathrm{N}}^{\mathrm{M}\mathrm{n}}$, ${T}_{\mathrm{N}}^{\mathrm{H}\mathrm{o}}$ with composition is summarized. In the hexagonal rich end while the T_N of Mn and Ho do not vary within the error bar, the T_SR clearly increases with composition.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Figure 13 shows the temperature variation of dielectric constant (ε) (for clarity only 10 kHz is shown, behaviour is same at all other frequencies). A distinct fall in the value of ε' is observed for the doped compounds x = 0.05 and 0.10 at their Néel temperature (T_N), which is similar to that observed in the parent compound h-HoMnO₃ [62]. In contrast to the dielectric measurements on single crystals of HoMnO₃ [41, 63], we did not observe a sharp anomaly at the spin reorientation temperature of the compounds, where the Mn³⁺ spins reorient in-plane by π/2, from the P6₃'c'm (Γ₄) to the P6₃'cm'(Γ₃) magnetic structure. However a small hump in the dielectric data was found to be present at the T_SR for x = 0.05 sample. The jump in the dielectric constant at T_SR has been ascribed to the intermediate magnetic phase between Γ₄ and Γ₃ type of orderings, P6₃', whose physical properties are susceptible to external perturbation [31, 64].However due to symmetry constraints [65], a direct coupling between the magnetic moments and the electric polarization is allowed only when the Mn moments tilt out of plane with a component along the c-axis [63]. In our neutron diffraction experiments, although we observe the in-plane rotation of the Mn spins, we do not find any signature of magnetic moment along the c-axis. This might be possibly due to a very small value (< 0.1 μ_B) of moment along the c-axis which is beyond the resolution of our Neutron diffraction instrument.

Zoom In Zoom Out Reset image size

In the absence of external electric and magnetic fields, the anomaly in dielectric constant at T_N is most likely driven by isostructural phase transitions associated with the displacement of the Mn ions present in system. Indeed such a case is observed in YMnO₃ and LuMnO₃ which exhibit exceptionally large motion of the Mn ion from its x ∼ 1/3 position at T_N [66, 67]. An alternative explanation for the observed variation of ε based on the 'pinning' between the domain walls of the AFM and the FE phases also exists in literature [64, 68].

The lattice contribution to the dielectric constant can be modelled by using the expression $\varepsilon \left(T\right)={\varepsilon }_{0}+\frac{C}{\mathrm{exp}\left(\frac{\hslash {\omega }_{0}}{{k}_{\mathrm{B}}T}\right)-1}$, where ε₀ is the value of dielectric constant at 0 K, ω₀ is the fitted frequency of the polar mode and the C is a constant [69, 70]. Inset to figure 14 shows the fit carried out for the x = 0.1 sample in the vicinity of T_N. By subtracting the lattice contribution from the experimental data we obtain Δε which represents the magnetic contribution to the dielectric constant below T_N. The expansion of free energy from the Landau's theory [69], can be given as,

$$\begin{equation*}F=F+\frac{{a}_{1}}{2}{L}^{2}+\frac{{a}_{2}}{2}{L}^{4}+\frac{{b}_{1}}{2}{P}^{2}+\frac{{c}_{1}}{2}{P}^{2}{L}^{2}+\frac{{c}_{2}}{2}{P}^{2}{H}^{2}-EP.\end{equation*}$$

Where E, H, P and L are the electric field, magnetic field, polarization and anti-ferromagnetic vector, respectively. Using this relation, it has been shown in the case of YMn_1−x Fe_x O₃ [32] that the dielectric permittivity below T_N varies linearly with the square of the anti-ferromagnetic vector L, which is equal to the magnetic moment (M) below T_N. Figure 14 shows a plot of Δε(ε(T) − ε(0)) vs M², where the values of M at various temperatures have been obtained by extrapolating the fitted curve shown in figure 9. A linear correlation between the two order parameters shows the coupling between lattice and magnetism in the frustrated antiferromagnetic system of HoMn_1−x Fe_x O₃ in absence of any external field.

Zoom In Zoom Out Reset image size