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Register a new userMagnetic phase diagram of HoFeO$_3$ by neutron diffraction
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Authors
A. K. Ovsianikov
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Neutron diffraction studies of HoFeO$_3$ single crystal were performed under external magnetic fields. The interplay between the external magnetic field, Dzyaloshinsky-Moria antisymmetric exchange and isotropic exchange interactions between Fe and Ho sublattice and inside Fe sublattice provides a rich phase diagram. As the result of the balance of exchange interactions inside crystal and external magnetic field we found 8 different magnetic phases, produced or suppressed by the field.
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We have investigated the temperature evolution of the magnetic structures of HoFeO$_3$ by single crystal neutron diffraction. The three different magnetic structures found as a function of temperature for hfo are described by the magnetic groups Pb$$n$2_1$, Pbn$2_1$ and Pbn$2_1$ and are stable in the temperature ranges $approx$ 600-55~K, 55-37~K and 35$>T>2$~K respectively. In all three the fundamental coupling between the Fe sub-lattices remains the same and only their orientation and the degree of canting away from the ideal axial direction varies. The magnetic polarisation of the Ho sub-lattices in these two higher temperature regions, in which the major components of the Fe moment lie along $x$ and $y$, is very small. The canting of the moments from the axial directions is attributed to the antisymmetric interactions allowed by the crystal symmetry. They include contributions from single ion anisotropy as well as the Dzyaloshinski antisymmetric exchange. In the low temperature phase two further structural transitions are apparent in which the spontaneous magnetisation changes sign with respect to the underlying antiferromagnetic configuration. In this temperature range the antisymmetric exchange energy varies rapidly as the the Ho sub-lattices begin to order. So long as the ordered Ho moments are small the antisymmetric exchange is due only to Fe-Fe interactions, but as the degree of Ho order increases the Fe-Ho interactions take over whilst at the lowest temperatures, when the Ho moments approach saturation the Ho-Ho interactions dominate. The reversals of the spontaneous magnetisation found in this study suggest that in hfo the sums of the Fe-Fe and Ho-Ho antisymmetric interactions have the same sign as one another, but that of the Ho-Fe terms is opposite.
Polarised neutron diffraction measurements have been made on HoFeO$_3$ single crystals magnetised in both the [001] and [100] directions ($Pbnm$ setting). The polarisation dependencies of Bragg reflection intensities were measured both with a high field of H = 9 T parallel to [001] at T = 70 K and with the lower field H = 0.5 T parallel to [100] at T = 5, 15, 25~K. A Fourier projection of magnetization induced parallel to [001], made using the $hk0$ reflections measured in 9~T, indicates that almost all of it is due to alignment of Ho moments. Further analysis of the asymmetries of general reflections in these data showed that although, at 70~K, 9~T applied parallel to [001] hardly perturbs the antiferromagnetic order of the Fe sublattices, it induces significant antiferromagnetic order of the Ho sublattices in the $xmhyphen y$ plane, with the antiferromagnetic components of moment having the same order of magnitude as the induced ferromagnetic ones. Strong intensity asymmetries measured in the low temperature $Gamma_2$ structure with a lower field, 0.5 T $parallel$ [100] allowed the variation of the ordered components of the Ho and Fe moments to be followed. Their absolute orientations, in the 180degree domain stabilised by the field were determined relative to the distorted perovskite structure,. This relationship fixes the sign of the Dzyalshinski-Moriya (D-M) interaction which leads to the weak ferromagnetism. Our results indicate that the combination of strong y-axis anisotropy of the Ho moments and Ho-Fe exchange interactions breaks the centrosymmetry of the structure and could lead to ferroelectric polarization.
By the single crystal inelastic neutron scattering the orthoferrite HoFeO3 was studied. We show that the spin dynamics of the Fe subsystem does not change through the spin-reorientation transitions. The observed spectrum of magnetic excitations was analyzed in the frames of linear spin-wave theory. Within this approach the antiferromagnetic exchange interactions of nearest neighbors and next nearest neighbors were obtained for Fe subsystem. Parameters of Dzyaloshinskii-Moriya interactions at Fe subsystem were refined. The temperature dependence of the gap in Fe spin-wave spectrum indicates the temperature evolution of the anisotropy parameters. The estimations for the values of Fe-Ho and Ho-Ho exchange interaction were made as well.
The magnetic structures and the magnetic phase transitions in the Mn-doped orthoferrite TbFeO$_3$ studied using neutron powder diffraction are reported. Magnetic phase transitions are identified at $T^mathrm{Fe/Mn}_N approx$ 295~K where a paramagnetic-to-antiferromagnetic transition occurs in the Fe/Mn sublattice, $T^mathrm{Fe/Mn}_{SR} approx$ 26~K where a spin-reorientation transition occurs in the Fe/Mn sublattice and $T^mathrm{R}_N approx$ 2~K where Tb-ordering starts to manifest. At 295~K, the magnetic structure of the Fe/Mn sublattice in TbFe$_{0.5}$Mn$_{0.5}$O$_3$ belongs to the irreducible representation $Gamma_4$ ($G_xA_yF_z$ or $Pbnm$). A mixed-domain structure of ($Gamma_1 + Gamma_4$) is found at 250~K which remains stable down to the spin re-orientation transition at $T^mathrm{Fe/Mn}_{SR}approx$ 26~K. Below 26~K and above 250~K, the majority phase ($> 80%$) is that of $Gamma_4$. Below 10~K the high-temperature phase $Gamma_4$ remains stable till 2~K. At 2~K, Tb develops a magnetic moment value of 0.6(2)~$mu_mathrm{B}/$f.u. and orders long-range in $F_z$ compatible with the $Gamma_4$ representation. Our study confirms the magnetic phase transitions reported already in a single crystal of TbFe$_{0.5}$Mn$_{0.5}$O$_3$ and, in addition, reveals the presence of mixed magnetic domains. The ratio of these magnetic domains as a function of temperature is estimated from Rietveld refinement of neutron diffraction data. Indications of short-range magnetic correlations are present in the low-$Q$ region of the neutron diffraction patterns at $T < T^mathrm{Fe/Mn}_{SR}$. These results should motivate further experimental work devoted to measure electric polarization and magnetocapacitance of TbFe$_{0.5}$Mn$_{0.5}$O$_3$.
The magnetic ordering of the hexagonal multiferroic compound YbMnO$_3$ has been studied between 100 K and 1.5 K by combining neutron powder diffraction, $^{170}$Yb Mossbauer spectroscopy and magnetization measurements. The Yb moments of the two crystallographic sites order at two different temperatures, the $4b$ site together with the Mn moments (at $T_N simeq$85 K) and the $2a$ site well below (at 3.5 K). The temperature dependences of the Mn and Yb moments are explained within a molecular field model, showing that the $4b$ and $2a$ sites order via Yb-Mn and Yb-Yb interactions respectively. A simple picture taking into account the local Mn environment of the Rare earth R ($4b$) ion is proposed to couple R and Mn orders in hexagonal RMnO$_3$ manganites. The nature and symmetry of the R-Mn interactions yielding the R order are discussed.
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