Magnetic properties of the non-stoichiometric TbCo2Nix alloys

The magnetic and magnetothermal properties of the non-stoichiometric TbCo2Nix (0 ≤ x ≤ 0.2) alloys were studied. It was found that the concentration dependence of the Curie temperature and magnetic moment of the 3d-sublattice have a maximum at x = 0.025. The obtained experimental magnetic properties of the TbCo2Nix alloys were discussed under assumption that the Co magnetic moment in the compounds changes with increasing x. The magnetic entropy change was determined using the temperature dependences of the magnetization and Maxwell’s thermodynamic relation. The obtained results for TbCo2Nix were compared with those for the ErCo2Mnx alloys.


Introduction
It was found recently that ternary RM 2 Mn (R -rare-earth metal, M -3d transition metal Ni, Co) compounds crystallize in the Laves-phase MgCu 2 -type cubic structure in spite of the ratio of the R and M components is 1 to 3. The Mn atoms in Laves-phase structure of the RM 2 Mn compounds partially occupy both the M (16d) and rare earth (8a) sites [1][2][3]. The Curie temperatures T C are considerably higher for the RNi 2 Mn alloys in comparison with T C for corresponding binary RNi 2 and RMn 2 . Later, the structure and magnetic properties of the non-stoichiometric RM 2 Mn x (0 ≤ x ≤ 1.5) compounds with R = Tb, Dy, Gd were studied [4][5][6][7]. It was shown that the MgCu 2 -type structure exists up to the manganese content x = 0.8 for ErCo 2 Mn x and up to x = 1.5 for ErNi 2 Mn x . It was established that T C is a nonmonotonous function of Mn concentration, which has a maximum at x < 1. It was found also that the maximum isothermal entropy change and the adiabatic temperature change remain weakly changed in a wide temperature range in ErCo 2 Mn x . Thus, there is new opportunity to modify magnetic properties of the Laves phase compounds by adding Mn and forming nonstoichiometric RM 2 Mn x compounds.
Up to now the properties of RM 2 M`x -type compounds with M`=Mn were studied only. However, we expect that non-stoichiometric RM 2 M`x compounds with another 3d transition metals can exist. In particularly, such type compounds can forms in case M`=Ni.
In the present paper, we report the results of studies of the structure, magnetic and magnetothermal properties of the non-stoichiometric TbCo 2 Ni x . The obtained results are compared with those for ErCo 2 Mn x which we previously studied.

Experimental details
The ingots of the TbCo 2 Ni x alloys were prepared by induction melting of the constituents in alumina crucibles in argon atmosphere. In order to obtain the equilibrium phase state, the ingots were annealed at 800 о C for 7 days. Structural and magnetic studies were performed at the Centre of Collective Use of the Institute of Metal Physics UB RAS. Room temperature X-ray diffraction patterns were measured for powdered samples with the average particle size 30-50 µm using a DRON-type diffractometer with Cr Kα radiation. The xray diffraction patterns were analysed with the PowderCell 2.4 program. To determine the Curie temperature of the compounds, we measured temperature dependences of ac magnetic susceptibility χ ac and used the position of minimum in the temperature dependences of derivative dχ ac (Т)/dT, which corresponds to the more abrupt decrease in the susceptibility with increasing temperature. The spontaneous magnetization μ s of compounds was determined from the demagnetization curves as magnetization extrapolated to zero internal field. Fig. 1 shows the room temperature X-ray diffraction patterns of TbCo 2 Ni x alloys. All main reflections in the X-ray diffraction patterns are adequately described in terms of the MgCu 2 -type structure ( ); the volume fraction of impurity phases with the PuNi 3 -type structure ( ) does not exceed 8 vol. %. According to X-ray diffraction studies, the single phase non-stoichiometric TbCo 2 Ni x compounds with the cubic Laves-phase structure exist up to critical nickel concentration x = 0.1 [8]. This value is much lower than x = 0.8-1.5 which were observed early for non-stoichiometric RM 2 Mn x compounds. It is known that the stability of the Laves phases is determined by factors such as the relationship of atomic radii of R and M elements and the average number of valence electrons per atom. The chemical bonds in Laves phases are assumed to be mixed metallic-covalence-ionic. Because of this, to analyse the stability of the phases, atomic radii of elements are sometimes used. It is likely that the same factors must affect the concentration boundaries of the existence of the nonstoichiometric compounds. This may be due to that the atomic and ionic radii of Ni are less than those of Mn. And, correspondingly, large difference between Ni and R does not allows to occupy enough amount of R (8a) sites by Ni atoms. Thus, the non-stoichiometric RCo 2 Ni x alloys with cubic MgCu 2 -type Laves phase structure can be obtained in more narrow concentration range than in case of alloying with Mn.

Results and discussion
The lattice parameter of the Ni-containing compounds are virtually independent of x (Fig. 2). Such behavior caused by two opposite factors. It is known that the atoms of the alloying element (Ni or Mn) occupy both the R (8a) and the M (16d) sites. The partial substitution of the R atoms by Ni or Mn at the 8a sites leads to decrease the lattice parameter. On the other hand, the substitution of the Co atoms at the 16d sites by a 3d element with a larger ionic or metallic radius leads to increasing of the lattice parameter. Two opposite tendencies lead to a weak concentration change of the lattice parameter for RM 2 M`x.  As can be seen in Fig. 3, concentration dependence of the Curie temperature increases sharply at small Ni concentrations and has maximum at T = 233 K. With further increasing the Ni content, the concentration dependence of the T C decreases. The Curie temperature of ErCo 2 Mn x compounds monotonically increases and reaches maximum value 212 K at manganese concentration x = 0.6 [6].
The spontaneous magnetic moments µ s decreases with increasing x both for TbCo 2 Ni x and for ErCo 2 Mn x as result of antiparallel ordering of magnetic moments of heavy rare-earth ions and 3d-transition atoms (Fig. 4). Fig. 5 shows the concentration dependence of the magnetic moment of 3d-sublattice of ErCo 2 Mn x and TbCo 2 Ni x compounds. We calculated magnetic moment of 3d-sublattice µ 3d in assumption that the R and 3d magnetic moments have collinear antiparallel alignment: where µ s -spontaneous magnetic moment of the compounds, µ R -magnetic moment of the rare-earth ion. The maximum µ 3d value is 1.38 µ B for TbCo 2 Ni 0.025 compound and 1.5 µ B for ErCo 2 Mn 0.6 compound. It is seen that character of the µ 3d (x) concentration dependencies both for ErCo 2 Mn x and for TbCo 2 Ni x is very similar to those for Curie temperatures.
The µ 3d (x) dependence has maximum for TbCo 2 Ni x and is monotonous for ErCo 2 Mn x . Our analysis of magnetic moments shows that the increase in the Curie temperature of the compounds is mainly due to changes in the band structure. It is possible, that alloying with Mn and Ni increase the Co magnetic moment due to the additional splitting of the 3d band. This, in turn, leads to an increase in the R-Ni (Mn), Co-Ni (Mn) exchange interaction.
We measured temperature dependences of magnetization M(T) in magnetic field H 1 = 1 T. It allows us to determine temperature variation of the magnetic entropy change ΔS m (T) in TbCo 2 Ni x compounds for magnetic field change µ 0 ΔH = H 1 -0 = 1 T using well known Maxwell`s thermodynamic relation: (2) Fig. 6 shows the temperature dependences of entropy change for ErCo 2 Mn x and TbCo 2 Ni x compounds. Maximum isothermal entropy change is -1.1 J kg -1 K -1 for TbCo 2 Ni 0.025 and -1.15 J kg -1 K -1 for ErCo 2 Mn 0.2 for the magnetic field change 1 T. These values are close to those observed, for the binary TbCo 2 -based compounds.
The magnitudes of ΔS m (T) decrease with increasing M` concentration because of decreasing the spontaneous magnetic moment of compounds. The behaviour of the ΔS m (T) curves strongly differs. For TbCo 2 Ni x , ΔS m (T) curves have maximum near T C whereas, for ErCo 2 Mn x maxima are observed at temperatures which are much lower than T C . Such difference arises because ΔS m (T) shape depends on shape of temperature dependence of resultant magnetization which reflects a non-Brillouin behavior of the resultant magnetization of the ferrimagnetically ordered R and M(M`) magnetic sublattices.

Conclusion
We studied the effect of Ni alloying on the structure, magnetic and magnetothermal properties of TbCo 2 Ni x alloys. It was established that single-phase nonstoichiometric compounds with the cubic MgCu 2 -type structure are formed at the Ni content x ≤ 0.1.
We found that concentration dependences of the Curie temperature and magnetic moment of 3d-sublattice have maximum at Ni content x = 0.025. Our analysis shows that all these changes are associated with changes in the Co magnetic moment which can arise from changes of compounds electron band structure.
Using magnetization measurements, we estimated the magnetocaloric effect in the ErCo 2 Mn x and TbCo 2 Ni x compounds. The maximum values of the ΔS m of TbCo 2 Ni x compounds are sufficiently close for all nickel concentrations.