Magnetic structures of (Gd1-xYx)Mn2Ge2 and (Tb1-xYx)Mn2Ge2 studied by neutron powder diffraction

Magnetic structures and magnetic phase transitions in “naturaly-layered” (Gd1-xYx)Mn2Ge2 and (Tb1-xYx)Mn2Ge2 compounds have been studied by electrical resistivity and neutron powder diffraction experiments. Hot neutrons were used to probe the magnetic structures of Gd-containing materials. The variable R-Mn exchange forces Gd moments to realign from the tetragonal axis into the plane and back to this axis, whereas canted and tripled structures were detected in the series of compounds containing the highly anisotropic Tb-ion.


Introduction
Recent achievements in spintronics require better understanding and classification of antiferro-and ferrimagnetic materials.In the range of hundreds of such materials, tetragonal RT 2 X 2 (R-rare earth or Y, Ttransition metal, X-Ge or Si, ThCr 2 Si 2 -type structure, space group I4/mmm) receives a special interest: superconductivity, mixed valence, Kondo effects have been investigated during last decades.The long-range magnetic order in 3d-sublattice is established only in Mn-containing compounds while in those with Fe, Co and Ni only the rare earth sublattice is magnetic.The magnetic transition in Mn sublattice occurs in RMn 2 T 2 at 350-500K; all compounds with heavy rare earths exhibit the separate transition to ferrimagnetic phase at T less than 100K while for light rare earths the "separate ordering" takes place in a number of cases too, with transition temperatures ranging from 100K to 250K.The manganese atoms form a primitive tetragonal sublattice in the ThCr 2 Si 2 -type structure; the distance between Mn atoms in the layer is approximately half of the distance between the adjacent Mn-layers.This feature leads to a significant spread of the 3d electrons within the layers and this structure could be considered as "naturally layered" in that sense.Consequently, the magnetic structure of such a compound is determined by the interplay of four types of magnetic exchange: Mn-Mn exchange in one particular layer J L Mn-Mn , interlayer exchange J IL Mn-Mn , R-Mn exchange J R-Mn and R-R interaction J R-R .
Magnetic structures of GdMn 2 Ge 2 and TbMn 2 Ge 2 were widely studied by macroscopic as well as microscopic methods.In both compounds the interplanar Mn-Mn exchange has approximately the same value as the R-Mn interaction and the competition between these two types of couplings determines the low temperature properties of these compounds.The Mn-sublattice orders collinearly and antiferromagnetically (AFil structure, here and below we follow the classification given in Ref. [1]) at T N = 363 K in the Gd-based compound and at T N = 414 K in TbMn 2 Ge 2 .Another transition from AFil to collinear ferrimagnetic F structure where the Rsublattice is now aligned antiparallel to the Mnsublattice occurs in both compounds at T C = 95K.This transition is of the first-order type and is accompanied by a significant change of the lattice constants and temperature-dependent resistivity.
The substitution of magnetic rare earth element to non-magnetic Y, La or Lu should, generally, decrease the R-Mn interaction and also the magnetic anisotropy of the R ion.As in-and interlayer interactions between Mn ions depend mostly on Mn-Mn separations, these will be not affected by substitution when the ionic radii of substitutional and replaceable elements are close to each other.Thus, pseudo-ternary (Gd 1-x Y x )Mn 2 Ge 2 and (Tb 1- x Y x )Mn 2 Ge 2 are good objects to investigate magnetic structures and phase transitions caused by the interplay of R-Mn and interlayer Mn-Mn interactions.
Macroscopic properties of (Gd 1-x Y x )Mn 2 Ge 2 were studied in [2,3].Following [2], the collinear lowtemperature phase should be replaced by a canted Fmc structure with increasing of Y-content while the sample with composition (Gd 0.6 Y 0.4 )Mn 2 Ge 2 undergoes two transitions AFil-Fmc-F.According to calculations and experimental data in the ref.[3], the specific canted ferrimagnetic structure with Gd-moment in the c-plane is expected to be a low-temperature phase for compounds with x ~ 0.4.
The (Tb 1-x Y x )Mn 2 Ge 2 system is more complicated with regard to the anisotropy of Tb ions.The magnetisation and X-ray thermal expansion experiments are presented in [4].Following this work, the magnetic structure changes in the consequence AFil-F-Fmc in all diluted compounds.At the same time, the volume effect, characteristic of the first-order type AFil-F transition was seen only in TbMn 2 Ge 2 and (Tb 0.9 Y 0.1 )Mn 2 Ge 2 .
The aim of the current work was to probe directly the magnetic structures in pseudo-ternary systems (Gd 1- x Y x )Mn 2 Ge 2 and (Tb 1-x Y x )Mn 2 Ge 2 .

Experiments
Large 7-8 g polycrystalline samples (Gd 1- x Y x )Mn 2 Ge 2 x = 0,2, 0,4, 0.5, 0.6 and (Tb 1-x Y x )Mn 2 Ge 2 x = 0.1, 0.2, 0.3, 0.4, 0.43, 0.46, 0.50, 0.55, 0.6 were synthesised using the induction melting technique in a quasi-levitation cooper crucible of a special design which provided the minimum contact of the melted elements with the crucible.Preferential Mn evaporation was taken into account; therefore, weights of the components were calculated in accordance to the results of a number of test meltings.After the melting procedure, samples were annealed in dynamic or static vacuum for 7 days.
Magnetisation, ac-susceptibility and resistivity temperature dependencies were measured on synthesized samples for their characterisation.
The neutron diffraction experiments were performed at ILL, Grenoble.Diffractograms for Gdcontained samples were collected at the two-axis diffractometer D4 which is situated at a hot neutron source.The neutron wavelength was set to λ = 0.4972 Ǻ using the Ge monochromator.Diffraction patterns were collected at different temperatures with a counting time of 2 hours per pattern.The background scattering was measured with an empty sample container and the same container filled with highly absorbing enriched 10 B powder.Then the linear combination of both measured backgrounds was subtracted from the measured scattering intensity.Thermodiffractograms for the Tbcontaining series were collected with the high intensity powder diffractometer D1B (dynamic temperature sweep: between 5 -130 K, 2θ range: 10 -90 deg., total counting time: approx.10 hours per sample).

Results and discussion
Figure 1 shows the thermal dependence of the electrical resistivity ρ(T) for synthesized samples of both series.As can be seen from these dependencies, the low temperature behaviour of studied samples is significantly different.One first order transition likely from AFil to F structures accompanied by jump-like decrease in resistivity could be seen in Gd 0.8 Y 0.2 Mn 2 Ge 2 and in Tbseries with x ≤ 0.3.Gd 0.6 Y 0.4 Mn 2 Ge 2 sample shows two consequent magnetic transitions, which is in agreement with the data from the Ref. [2].Only one phase transition is detected for Tb-based compounds, however, the ρ(T) dependence for 0.4 ≤ x ≤ 0.46 is different from those for 0.5 ≤ x ≤ 0.55.Samples with yttrium content of 60% show no transitions and should stay in AFil phase down to lowest temperatures.The interpretation of hot-source diffractograms obtained for (Gd 1-x Y x )Mn 2 Ge 2 series is complicated as the short wavelength of the hot neutrons leads to overlapping of reflections.Nevertheless, several conclusions about the magnetic structure could be drawn from the analysis of the first diffraction peaks and the differences of diffraction patterns for different temperatures.
The diffraction patterns for Gd 0.2 Y 0.8 Mn 2 Ge 2 are similar to those of non-diluted GdMn 2 Ge 2 where collinear F low temperature phase was confirmed [5].
Two magnetic transitions are expected for Gd 0.6 Y 0.4 Mn 2 Ge 2 [2,3].Neglecting the thermal expansion in this temperature and angle range, the differences between diffraction patterns are caused only by different magnetic contributions.The difference plots are shown in the Fig. 2. One can see that the (001) magnetic reflection, characteristic of the Fmc phase is not observed at any temperature.At the same time, the magnetic contribution to the (002) peak related to the inplane magnetic component is strongly temperature dependent: it increases down to 34 K before it decreases again when cooling to the base temperature of 4 K.Then, comparing the high-temperature AFil phase and the low-temperature phase, there is no change in (002) intensity.Thus, our hot source diffraction experiments give the following scenario, which is different from both [2] and [3].Gd ions order within the tetragonal basis plane first at T ~ 47 K.The negative R-Mn interaction force the Mn moments to rearrange from antiparallel AFil orientation into the tetragonal basis plane too (T' phase in the ref.[3] ).The second magnetic transition directs Gd and Mn moments back to the c-axis and the resulting structure is collinear F.
The Neutron data for the sample with composition Gd 0.5 Y 0.5 Mn 2 Ge 2 show only one magnetic transition from AFil to T' magnetic phases.
Figure 3 shows diffraction angle-temperatureintensity 3D-plots for selected compounds of (Tb 1- x Y x )Mn 2 Ge 2 .The collinear ferrimagnetic F low temperature phase is confirmed for compounds with high terbium content.The low temperature phase for samples with Tb-content 0.4 ≤ x ≤ 0.46 must be different from F following our ρ(T) experiments.Diffraction data show the presence of intense (0,0,2n+1) peaks, which are the indication of antiferromagnetic component in adirection, below the Curie temperature.The Rietveld analyse clearly proves the canted Fmc low temperature phase for these concentrations.
As Tb content decreases the diffraction patterns change again.The low temperature plot for Tb 0.5 Y 0.5 Mn 2 Ge 2 and Tb 0.55 Y 0.45 Mn 2 Ge 2 reveals magnetic peaks of (h,k,l/3)-type together with (0,0,2n+1) reflections, characteristic of Fmc structure.The magnetic state is then a mixture of the Fmc phase and the "triplet" collinear phase, whose magnetic cell is three time larger in the tetragonal direction.One third of Mn ions ordered antiparallel to another 2/3 in this cell, then one third of Tb ions, located between different Mn orientations, are non-magnetic.This magnetic structure has been previously observed in DyMn 2 Ge 2 and TbMn 2 Si 2 and could be interpreted using additional interlayer J IL-3 Mn-Mn term [6,7].This long-periodic magnetic structure creates a band gap in the first Brillouin zone in tetragonal direction, explaining the significant increase of electrical resistivity in comparison to antiferromagnetic AFil phase.
As a summary, magnetic structures, realized in RMn 2 Ge 2 with tuneable R-Mn exchange were directly probed in this work.Results of neutron diffraction experiments found to be in good agreement with bulk measurements and partly in agreement with theory expectations.Although the hot neutron diffraction data could not be used for quantitative refinements, it was possible to use the information to select between relatively simple magnetic structures.Thus, we demonstrated that variable R-Mn exchange leads Gd moments to realign from the tetragonal axis into the plane and back to this axis in low-anisotropic Gd-series.In contrast, high-anisotropic Tb holds itself to the c-axis and forces reorientation of Mn moments.Ab-initio calculations with known CEF-parameters for rare earth ions could provide the quantitative data on magnetic structures and phase transitions in these series.

Fig. 2 .
Fig. 2. Hot neutron diffraction patterns for Gd 0.6 Y 0.4 Mn 2 Ge 2 for different temperatures (left) and their difference plots (right).Bragg indexes are indicated above.