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Sci Rep. 2017; 7: 45814.
Published online 2017 April 4. doi:  10.1038/srep45814
PMCID: PMC5379177

New insight into magneto-structural phase transitions in layered TbMn2Ge2-based compounds


The Tb1−xYxMn2Ge2 series (x = 0, 0.1, 0.2) compounds are found to exhibit two magnetic phase transitions with decreasing temperature: from the paramagnetic state to the antiferromagnetic interlayer state at TNinter and from an antiferromagnetic interlayer structure to a collinear ferrimagnetic interlayer structure at TCinter. Compared with the slight change of TNinter (409 K, 410 K and 417 K for x = 0, 0.1 and 0.2 respectively), the replacement of Y for Tb leads to a significant decrease in TCinter from 97.5 K for x = 0 to 74.6 K for x = 0.2. The variation in TCinter can be ascribed to the combination of two effects: (1) chemical pressure and (2) magnetic dilution effect by Y substitution for Tb. Besides, a strong anisotropic magnet-volume effect has been detected around TCinter in all compounds with Δa/a = 0.125%, 0.124% and 0.130% for x = 0, 0.1 and 0.2, respectively while no obvious effect is detected along the c-axis. The maximum magnetic entropy change were found to be −ΔSmax = 9.1 J kg−1 K−1, 11.9 J kg−1 K−1 and 6.3 J kg−1 K−1 with a field change from 0 T to 5 T for x = 0, 0.1, 0.2 respectively.

Since the discovery in 1997 of a giant magnetocaloric effect (GMCE) originating from a discontinuous first order magnetic transition in Gd5Si2Ge21, room-temperature magnetic refrigeration based on the magnetocaloric effect (MCE) has attracted significant attention due to its energy efficiency and environment friendly in comparison with conventional gas compression-expansion refrigeration2. A number of materials which exhibit giant magnetic entropy changes at magnetic transitions have been investigated, including MnFeP0.45As0.553, MnAs1−xSbx4, Ni-Mn-Sn-based alloys5, Ni-Mn-Ga6,7, and La(Fe,Si)138. The key features of these systems are the temperature- and magnetic field-induced first-order magneto-structural or magneto-elastic phase transitions. Given these promising developments, magnetic materials which exhibit a large magnetocaloric effect have been studied extensively, both experimentally and theoretically, over the past two decades with the overall aim of increasing the efficiency of magnetic refrigeration techniques9,10. While a key focus is exploration of materials that exhibit a pronounced magnetocaloric effect at room temperature, materials that operate in the low temperature region are also useful in meeting the cooling requirements for fields such as gas liquefaction or attaining millikelvin for experimental research facilities. However, so far only a few materials such as GdLiF4, GdF3 and Gd3Ga5O12 are used commercially11. As reflected by the increase in exploration of materials which exhibit a large MCE below room temperature10,11,12,13, the search for materials which exhibit large magnetocaloric effects over temperature ranges relevant for hydrogen and natural gas liquefaction are also important for exploring potential applications.

Some RT2X2 compounds (R = rare earth, T = transition metal, and X = Si or Ge) have been found to exhibit large MCE values with small hysteresis losses near their low magnetic transition temperatures11,13,14,15,16. For example, the magnetic entropy values of RNi2Si2 (R = Dy, Ho, Er) compounds are 21.3 J kg−1 K−1, 21.7 J kg−1 K−1 and 22.9 J kg−1 K−1 around 6.5 K, 4.5 K and 3.5 K respectively during a change of magnetic induction intensity from 0–5 T16, while the magnetic entropy of ErCr2Si2 attained 29.7 J kg−1 K−1 near the magnetic ordering temperature 4.5 K17. The crystal structure of the RT2X2 series is body centred tetragonal ThCr2Si2-type (with space group I4/mmm)15,18,19, with the sequence -R-X-T-X-R- atomic layers stacked along the c-axis. The rare earth elements typically exhibit large magnetic moment (for example μTb = 8.8 μB in TbMn2Si2 at 5 K)20 and correspondingly make a large contribution to the magnetocaloric effect14,15,17. Given the sensitivity of the magnetic state in RMn2X2 to the intra-planar Mn-Mn spacing15,19,21,22,23,24, compounds in this series are found to display a rich variety of interesting phenomena, including superconductivity, magnetism, mixed valence, heavy fermions, and Kondo behaviour25,26,27. This diversity enables control of the interplay between the R-Mn and Mn-Mn exchange interactions in RMn2X2 through external factors such as pressure28, temperature and magnetic field29 meaning that such compounds have the potential for competitive performance15,19,24. The notations used in this paper to describe the magnetic structure type and critical transition temperatures are defined by Venturini et al.22 Using standard magnetic methods19,30, TbMn2Ge2 was reported to be antiferromagnetic below Néel temperature TN = 410 K with the AFil antiferromagnetic interlayer structure (i.e. a collinear antiferromagnetic structure between adjacent Mn planes in a +  + − sequence along the c-axis22.) Below TC = 100 K, TbMn2Ge2 exhibits a collinear ferrimagnetic structure in which the Tb moments order ferromagnetically and couple antiferromagnetically with the Mn moment23. Furthermore, in a later study for the Tb1−xYxMn2Ge2 series (x = 0–0.4), it was reported that the replacement of Y for Tb leads to significant modifications of both the Curie temperature (from 76 K for TbMn2Ge2 to almost 0 K for Tb0.4Y0.6Mn2Ge2) and magnetovolume effect (the volume effect is [increment]V/V = 3.2 × 10–3 and 2.7 × 10−3 for x = 0 and 0.1 respectively)30. The magnetic phase transitions around TC in the Tb-rich Tb1−xYxMn2Ge2 compounds were shown to be first order30, offering scope for large magnetocaloric effects around the region of their Curie temperatures.

Here we present a systematic study of the magnetic transition from antiferromagnetism to ferromagnetism in a series of Tb1−xYxMn2Ge2 samples (x = 0, 0.1, 0.2) using a combination of methods including variable temperature x-ray diffraction (XRD), specific heat, differential scanning calorimetry (DSC) and magnetization measurements. The overall aim is to understand fully the influence of Y substitution for Tb on magnetocaloric effects and search for novel magnetocaloric materials that may be suitable for operation over the hydrogen and natural gas liquefaction temperature ranges.


The polycrystalline Tb1−xYxMn2Ge2 samples with x = 0, 0.1, 0.2 were prepared by arc melting constituent elements of 99.9% purity under argon atmosphere. For improved crystallization and chemical homogeneity, the samples were annealed in vacuum-sealed quartz tube at 850 °C for 7 days after arc melting. The dc magnetic measurements were performed using a Quantum Design 9 T physical properties measurement system (PPMS). The magnetic behaviour was investigated over the range from 5 K to 340 K in a magnetic field 0.01 T. Differential scanning calorimetry measurements were performed on differential scanning calorimetry equipment (DSC 204 F1 Phoenix®) from 340 K to 500 K. Magnetization-field loops were obtained at temperatures close to the Curie temperature of samples with magnetic fields over the range 0–5 T. The heat capacity measurements were performed on a Quantum Design 14 T physical properties measurement system scanning from 2 K to 250 K. The samples were characterized and the structures determined by variable temperatures XRD measurements over the temperature range (12–300 K) using a PANAlytical diffractometer with Cu-Kα radiation.

Results and Discussion

Structural behaviour

The room temperature x-ray diffraction study shows that all samples are single phase and that patterns can be indexed with a space group of I4/mmm as expected. The Rietveld refinements have been carried out using the FullProf package31 with the main results shown in Fig. 1(a,b and c) for x = 0, 0.1 and 0.2 respectively. It can be seen from Fig. 1. that the variations of lattice parameters of a and c with temperature display strong anisotropy: the lattice parameter c (red solid circle) increases monotonically with increasing temperature while a pronounced discontinuity is observed in the a lattice parameter (black solid square) around the Curie temperature Tc for each sample (the transition temperatures were determined as the point where the value of dM/dT is minimum). Similar behaviours for TbMn2Ge2 were also determined by Morellon et al.23 for which an anomaly in the thermal expansion along the a-axis was found near Tc. The discontinuity in the a lattice parameter around Tc leads to the associated decrease in the unit cell volume for all samples as also evident in Fig. 1. These behaviours are very similar to the behaviour reported for Pr0.5Y0.5Mn2Ge215 (i.e. PrMn2Ge2 diluted by Y), but different from NdMn2Ge0.4Si1.632, NdMn1.9Ti0.1Si233 and NdMn1.7Cr0.3Si234,35 (where Mn diluted with transition metal Ti or Ge diluted by Si) for which the lattice parameter a decreases with increasing temperature around TC while the lattice parameter c expands. In order to derive the magneto-volume effect below TC, we have calculated the contribution from lattice vibration using the Debye model:

Figure 1
Temperature dependence of the lattice constants a, c and unit cell volume: (a) TbMn2Ge2, (b) Tb0.9Y0.1Mn2Ge2 and (c) Tb0.8Y0.2Mn2Ge2. The dashed lines show the phonon contribution to the lattice expansion as evaluated from the Gruneisen relation.
An external file that holds a picture, illustration, etc.
Object name is srep45814-m1.jpg

where β is the volume thermal expansion coefficient of the parameter state, k is the compressibility, γ is the Gruneisen constant and Cv is the specific heat at constant volume caused by lattice vibrations. Cv was derived from the Debye theory of the specific heat using the value of the Debye temperature θD (as derived from our specific heat measurements for each of the samples as described below for the three compositions):

An external file that holds a picture, illustration, etc.
Object name is srep45814-m2.jpg

where kB is the Boltzmann constant and N is the number of the atoms. The thermal expansion for the hypothetical paramagnetic state is derived on integrating Eq. (2) with respect to temperature. The parameter An external file that holds a picture, illustration, etc.
Object name is srep45814-m3.jpg was adjusted to obtain the best least-squares fitting to the successive data points of the observed thermal expansion curve well above the magnetic ordering temperature (based on the fact that the magnetic contribution in the antiferromagnetic region to total thermal expansion can be ignored for these types of compounds)32.

The temperature dependence of the unit cell volumes based on Debye theory for the TbMn2Ge2, Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2 samples are shown by the dashed lines in Fig. 1(a,b and c) with pronounced magneto-volume effects evident below their magnetic transition temperatures TC = 94 K, TC = 83 K and TC = 70 K respectively. The discontinuous nature of the changes in a lattice parameter and unit cell volume V at the Curie temperatures as shown in Fig. 1, are consistent with the first order nature of these transitions as discussed fully below. The changes in the lattice parameter a are Δa/a = 0.125%, Δa/a = 0.124% and Δa/a = 0.130% for x = 0, 0.1 and 0.2 respectively with spontaneous volume magnetostriction ωs (=ΔVm/V) at 5 K determined as: TbMn2Ge2 - ωs = 4.1 × 10−3; Tb0.9Y0.1Mn2Ge2 - ωs = 3.2 × 10−3 and Tb0.8Y0.2Mn2Ge2 - ωs = 5.8 × 10−3.

Magnetic phase transition

The magnetisation of the three samples have been measured in a field of B = 0.01 T over the temperature range 5–340 K. As in Fig. 2(a,b and c) the TbMn2Ge2, Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2 samples were respectively measured on warming from 5 K in three states: after cooling in zero field (ZFC heating) and after cooling and heating in a field of B = 0.01 T (FC cooling and FC heating). As is evident from the magnetization versus temperature curves of Fig. 2(a,b and c), there is an abrupt change in magnetisation at the Curie temperature TCinter that marks the magnetic phase transition from a collinear antiferromagnetism (AFil)22 at higher temperature to a collinear ferrimagnetic structure along the c axis at lower temperature according to the neutron diffraction study on TbMn2Ge223. Of the three samples, TbMn2Ge2 has the highest TCinter(warm) = 97.5 K and TCinter(cool) = 93.0 K transitions respectively as determined from the FC heating and cooling M-T curves, while the values for Tb0.9Y0.1Mn2Ge2 are derived to be TCinter(warm) = 87.5 K and TCinter(cool) = 81.8 K with the values for Tb0.8Y0.2Mn2Ge2 being TCinter(warm) = 74.6 K and TCinter cool) = 66.0 K (normally the transition temperature during the FC process is chosen as the Curie temperature Tc). As expected, the higher the level of doping of non-magnetic Y atoms in Tb1−xYxMn2Ge2, the lower the magnetic phase transition temperature30.

Figure 2
Temperature dependence of magnetization on ZFC heating, FC cooling and FC heating processes under a field of B = 0.01 T: (a) TbMn2Ge2, (b) Tb0.9Y0.1Mn2Ge2 and (c) Tb0.8Y0.2Mn2Ge2. (d) the differential scanning calorimetry curves ...

Differential scanning calorimetry measurements have been carried out on the Tb1−xYxMn2Ge2 samples over the temperature range 300–500 K (Fig. 2(d)) in order to investigate the paramagnetic to antiferromagnetic transition10,23 at TNinter. As revealed by the DSC results in Fig. 2(d), the TNinter transition temperatures are found to increase slightly with increasing Y concentration - TNinter = 409 K, TNinter = 410 K and TNinter = 417 K for x = 0.0, 0.1 and 0.2 respectively. Compared with the reduction in ferromagnetic transition temperature on replacement of Tb atoms by Y atoms, the paramagnetic to antiferromagnetic transition temperatures are found to exhibit a slight increase (Fig. 2). The increase in TNinter values is due to enhancement of the Mn-Mn exchange interaction as a result of the slight reduction of Mn-Mn distance. This behaviour is similar to the PrMn2Ge2−xSix system36 in which the paramagnetic to antiferromagnetic transition temperatures are found to increase slightly while the antiferromagnetic to ferromagnetic transition temperatures decrease on replacing Ge with Si.

The temperature dependences of magnetization for TbMn2Ge2, Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2 under various external magnetic fields are presented in Fig 3(a,b and c) respectively. As expected the ferromagnetic transition temperature TCinter is shifted to higher temperature with increase in applied magnetic field. For example, the transition temperatures are TCinter = 101.8 K, TCinter = 92 K and TCinter = 76 K for TbMn2Ge2, Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2 respectively in an external magnetic field of B = 1 T, while the transition temperatures are shifted to TCinter = 107 K, TCinter = 98.2 K and TCinter = 81 K respectively in a field of B = 5 T. The field dependence of the magnetic transition temperatures are summarized in Fig. 3(d). The values of dTc/dB (obtained on linear fitting of the experimental data in Fig. 3(d) along with a summary of experimental data determined for Tb1−xYxMn2Ge2 (x = 0, 0.1, 0.2) in this investigation, are provided in Table 1.

Figure 3
The magnetisation versus temperature curves during cooling under various magnetic field (B = 1–5 T).
Table 1
Experimental data for the three Tb1−xYxMn2Ge2 samples (x = 0, 0.1 and 0.2).

Y doping in Tb1−xYxMn2Ge2 - Chemical pressure effect

As noted above, the effect of replacing the magnetic rare earth Tb with the nonmagnetic ion Y in Tb1−xYxMn2Ge2 is to weaken the exchange interaction between magnetic ions due to the dilution effect. The magnetic behaviour of Y-doped Tb1−xYxMn2Ge2 will also be modified as a result of chemical pressure due to differences in the atomic radii of the Tb(1.80 Å) and Y(1.78 Å) ions and resultant changes in lattice parameters. In order to separate these two contributions - dilution effect and pressure effect - and their influence on the variation in magnetic transition temperature, the decrease of TC by chemical pressure was calculated as follows. The chemical pressure Δp was calculated20,22,33 according to the Murnaghan equation below:

An external file that holds a picture, illustration, etc.
Object name is srep45814-m4.jpg

where V0, B0 and An external file that holds a picture, illustration, etc.
Object name is srep45814-m5.jpg are the volume, the bulk modulus and its first derivative of TbMn2Ge2 and V is the volume of the unit cell at room temperature of the Y doped samples. Here, due to the similarity of crystal structure for the RMn2Ge2 system, we assume that the values of B0 and An external file that holds a picture, illustration, etc.
Object name is srep45814-m6.jpg for PrMn2Ge2 (B0 = 38.0 Gpa, An external file that holds a picture, illustration, etc.
Object name is srep45814-m7.jpg = 19.5 as derived from our synchrotron data under external pressure37) can be applied to TbMn2Ge2 at room temperature. Given that the doped materials Tb1−xYxMn2Ge2 (x = 0.1, 0.2) retain the ThCr2Si2-type tetragonal structure, the chemical pressure Δp caused by doping can be assumed to have the same effect as mechanical pressure. According to previous findings that describe the pressure effect on the magnetic properties of TbMn2Ge2 (dTc/dP = −2.9 K/kbar)38, the values of ΔTC can be deduced by the relationship:

An external file that holds a picture, illustration, etc.
Object name is srep45814-m8.jpg

where Δp is the calculated chemical pressure. The calculated values of ΔTC for Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2 are ΔTC = 1.94 K and ΔTC = 8.7 K respectively. As noted above (see also Fig. 1, Figs 2 and and3.)3.) the effect of replacing Tb atoms with Y atoms in Tb1−xYxMn2Ge2 also contributes to the decrease in the Curie temperature. It can therefore be concluded that chemical pressure accounts for ~17.3% and ~32.2% of the decrease in transition temperatures for x = 0.1 and 0.2 respectively. In addition, the value of dTc/dp can be derived using the Clausius-Clapeyron thermodynamic relation as follows:15

An external file that holds a picture, illustration, etc.
Object name is srep45814-m9.jpg

The values of the change in the unit cell volume ΔVm he change in moment Δμ during magnetic phase transition around TC and dTc/dB for each sample were taken from the present experimental results listed in Table.1. The derived results are dT/dp = −3.03 K/kbar, −2.84 K/kbar and −3.07 K/kbar for TbMn2Ge2, Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2, respectively. These calculated values are in general accord with the value of dTc/dp = −2.9 K/kbar for TbMn2Ge238, deviating by ~4.5%, ~2.1% and ~5.9% for the x = 0.0. 0.1, 0.2 samples respectively.

Magnetocaloric effect

Graphs of the magnetization as a function of applied field are shown for TbMn2Ge2, Tb0.9Y0.1Mn2Ge2, and Tb0.8Y0.2Mn2Ge2 at temperatures around TCinter in Fig. 4(a,b and c) respectively. It can be seen that with increasing temperature beyond TCinter, a field-induced metamagnetic phase transition from the antiferromagnetic state to the ferromagnetic state at certain temperatures has been detected. The region of the metamagnetic phase transition for TbMn2Ge2 is indicated by arrows in Fig. 4(a) as a typical example. This behaviour indicates that the region of ferromagnetic ordering in Tb1−xYxMn2Ge2 can be shifted to higher temperatures by a stronger applied magnetic field.

Figure 4
Curves of isothermal magnetization versus magnetic field at temperatures around Tc.

The nature of the magnetic transitions (first order or second order) was analysed using Arrott plots with the magnetisation expressed in the usual way as graphs of M2 versus B/M (Fig. 5). As can be seen in Fig. 5(a,b and c), negative slopes are detected in the M2 versus B/M graphs for the TbMn2Ge2 and Tb0.9Y0.1Mn2Ge2 samples thus indicating that the antiferromagnetic to ferromagnetic processes are first order39. However, Some papers40,41 reported that for compounds near the critical point (from first order to second order magnetic phase transition) such as DyCo2, this criterion of Arrott plots do not always work properly. It is also noted that the negative slopes for Tb0.8Y0.2Mn2Ge2 around the antiferromagnetic to ferromagnetic transition was reduced compared with those for the TbMn2Ge2 and Tb0.9Y0.1Mn2Ge2 samples. However, the first order transition characters of all the three samples can be confirmed from our variable temperatures crystal structure analyses above, where strong magneto-elastic coupling around TCinter has been detected (Fig. 1).

Figure 5
Arrott plots: isotherms graphs of M2 versus B/M for decreasing magnetic fields at temperatures around Tc.

The magnetic entropy changes ΔSM for all samples have been determined from the isothermal magnetization curves of Fig. 4(a,b and c), by using the standard Maxwell relationship:

An external file that holds a picture, illustration, etc.
Object name is srep45814-m10.jpg

The calculated temperature dependent magnetic entropy changes for the Tb1−xYxMn2Ge2 samples with x = 0, 0.1 and 0.2 for both increasing field and decreasing field processes between field changes of ΔB = 0–1 T and ΔB = 0–5 T are shown in Fig. 6(a,b and c) respectively with the maximum values ΔSmax shown as a function of applied field in the insets of Fig. 6. With a field change of ΔB = 0–5 T, the value of −ΔSmax are 9.1 J/kgK, 11.9 J/kgK and 6.3 J/kgK for TbMn2Ge2, Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2 respectively, demonstrating that the entropy change for Tb0.9Y0.1Mn2Ge2 is the largest of the three samples. As it is clear from Fig. 4, while TbMn2Ge2 has the highest fraction of magnetic rare earth element and largest saturation magnetization (42.5 Am2/kg at 84 K), its large hysteresis loss (7.40 J/kg) leads to reduction in the magnetic entropy change. By comparison, with the lowest concentration of magnetic rare earth Tb, the Tb0.8Y0.2Mn2Ge2 sample displays the lowest saturation magnetization (only 32.5 Am2/kg even at 55 K) and the smallest hysteresis loss 5.21 J/kg), while as shown in Fig. 4(b), Tb0.9Y0.1Mn2Ge2 with medium concentration of Tb has a relatively large saturation magnetization of 38.0 Am2/Kg at 84 K and small hysteresis loss (5.36 J/kg). The refrigerant capacity (RCP), defined as the product of −ΔSmax and the full width at half maximum of the −ΔSmax curve, for the three samples are: 93.3 J/kg, 102.9 J/kg, 62.4 J/kg for TbMn2Ge2, Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2 respectively, with a field change of ΔB = 0–5 T. The MCE value of Tb0.9Y0.1Mn2Ge2 is comparable to those of other materials for a field change of ΔB = 0–5 T including: GdCoAl, −ΔSmax(T) = 10.4 J/kgK at 100 K34, TbCoAl, −ΔSmax(T) = 10.5 J/kgK at 70 K34 and GdMn2Ge2, −ΔSmax(T) = 1.2 J/kgK at 95 K28, all of which, in common with Tb0.9Y0.1Mn2Ge2, importantly exhibit negligible field and thermal hysteresis losses.

Figure 6
The magnetic entropy changes around the ferromagnetic transition temperatures for applied magnetic fields from 1–5T.

Moreover, it is well accepted that first-order phase transitions are accompanied by a latent heat and the barocaloric effect can be expected. In fact giant barocaloric effect has been found in several systems recently including Mn3GaN ([increment]Sbar = 22.3 J/K kg)42 and Ni–Mn–In magnetic superelastic alloys ([increment]Sbar = 27.7 J/K kg)43. Based on the fact that all these three Tb1−xYxMn2Ge2 samples exhibit strong magnetovolume effect around magnetic phase transition, we have calculated the barocaloric effect using the Clausius_Clapeyron relation43. The barocaloric effects entropy change [increment]Sbar, have been derived to be [increment]Sbar = 9.6 J/kgK, 13.5 J/kgK and 13.2 J/kgK for TbMn2Ge2,Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2 respectively. These barocaloric values indicate that these materials can be considered as a potential candidate for mechanocaloric effects over the hydrogen and natural gas liquefaction temperature ranges.

Heat Capacity

The heat capacity of TbMn2Ge2 over the temperature range 2–250 K is shown in Fig. 7(a). The sharp peak in the heat capacity near the Curie temperature of TbMn2Ge2 on both zero magnetic field and a field of 2 T reflects the first order character of the magnetic phase transition. The peak in specific heat shifts from ~98 K to 102.6 K for magnetic fields of 0 T and 2 T respectively; this behaviour corresponds well to the values of the Curie temperature of TbMn2Ge2 - 97.5 K (B = 0 T) to 103 K (B = 2 T) - obtained for the magnetization measurements (Fig. 3(d)).

Figure 7
The specific heat capacity relative parameters for TbMn2Ge2.

The heat capacity C(T) of a metallic magnetic material includes contributions from phonons, electrons and magnons and can be described as follows:

An external file that holds a picture, illustration, etc.
Object name is srep45814-m11.jpg

where Cph, Cel and Cm are the lattice, electronic, and magnetic contributions respectively44. In the absence of a magnetic phase transition, the heat capacity can be described as:

An external file that holds a picture, illustration, etc.
Object name is srep45814-m12.jpg

where γ and β are the electronic and phonon heat capacity coefficients, respectively. For the specific heat of TbMn2Ge2 at low temperatures T  1 K, well away from the magnetic transition, as shown in Fig. 7(b), a fit to the graph of Cp/T versus T2 leads to γ = (65.2 ± 0.95)mJ/molK2, β = (4.53 ± 0.156) × 10−4 J/molK4. The electronic density of states N(EF) at the Fermi surface can be calculated by the formula:44

An external file that holds a picture, illustration, etc.
Object name is srep45814-m13.jpg

where kB is the Boltzmann constant. For the TbMn2Ge2 compound, the value of N(EF) is derived to be (5.54 ± 0.08) state/eV atom. Likewise, the Debye temperature θD can also be obtained by:

An external file that holds a picture, illustration, etc.
Object name is srep45814-m14.jpg

where R is the universal gas constant and the number of atoms n = 545. The Debye temperature for TbMn2Ge2 was determined as θD = 278 ± 3 K.

The magnetic entropy change, −ΔSM (T, B) can also be derived from measurements of the in-field heat capacity using the expression thermodynamic relations below:46

An external file that holds a picture, illustration, etc.
Object name is srep45814-m15.jpg

where C(T, B) and C(T, 0) are the values of the heat capacity measured in field B and zero field, respectively. The maximum of magnetic entropy change has been derived to be −ΔSM = 2.6 J/kgK for TbMn2Ge2 (field change of ΔB = 2 T), which is smaller than the value (−ΔSM = 5.9 J/kgK) deduced from the isothermal magnetization curves. This behaviour may be due to the fact that a straightforward numerical integration using Maxwell equation based on magnetization curves is not applicable in the phase-separated state as described in ref. 47,48. The corresponding adiabatic temperature change, −ΔTad (shown as inset of Fig. 7(c) can be evaluated from −ΔSM (T, B) and the heat capacity data.

The equivalent heat capacity parameters for Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2 are shown in Figs 8 and and9,9, respectively. The Debye temperatures were found to increase from 281 K for TbMn2Ge2 to 344 K for Tb0.9Y0.1Mn2Ge2 and 354 K for Tb0.8Y0.2Mn2Ge2; with the increases understood in terms of the differences in their molecular mass31. The adiabatic temperature changes near the Curie temperature are found to decrease from −ΔTad = 2.6 K for TbMn2Ge2, to −ΔTad = 2.3 K for Tb0.9Y0.1Mn2Ge2 and 1.8 K for Tb0.8Y0.2Mn2Ge2.

Figure 8
The specific heat capacity relative parameters for Tb0.9Y0.1Mn2Ge2.
Figure 9
The specific heat capacity relative parameters for Tb0.8Y0.2Mn2Ge2.

The electron density at the Fermi surface is found to decrease from 5.54 state/eV atom for TbMn2Ge2 to 2.18 state/eV atom and 3.06 state/eV atom for Tb0.9Y0.1Mn2Ge2 and Tb0.8Y0.2Mn2Ge2 respectively. All the fitting results including electronic heat capacity coefficient γ, phonon heat capacity coefficient β, electronic density of states N(EF) and Debye temperature θD are summarized in Table 2. The modification of the electron density at the Fermi surface may be related to the difference of electronic configuration of Y and Tb as well as the unit cell size variation. The latter may lead to the variation in the degree of hybridization of Mn 3d states with p states of Ge with decreasing interatomic distances for Y doped samples. Similar behaviour has been found in the La1−xYxMn2Si2 system where the electron density is derived to be 2.83 states/eV atom for x = 0, 2.51 states/eV atom for x = 0.25, 2.54 states/eV atom for x = 0.3 and 1.47 states/eV atom for x = 1.049. Moreover, it is also noted that the electron density at the Fermi level for TbMn2Si229 was reported to be 2.38 states/eV atom, which is close to the values reported here for Tb1−xYxMn2Ge2 samples.

Table 2
Calculated heat capacity parameters for Tb1−xYxMn2Ge2 (x = 0, 0.1, 0.2).


In conclusion, we have carried out a detailed investigation around the region of the magnetic transitions of compounds in the Tb1−xYxMn2Ge2 series (x = 0, 0.1, 0.2) by variable temperature x-ray diffraction, heat capacity, differential scanning calorimetry and magnetic measurements. Two magnetic phase transitions occur at TNinter and TCinter for each of the three samples. The antiferromagnetic transition at TNinter is shown to increase slightly with increase in the Y concentration, while the ferromagnetic transition at TCinter drops significantly. The mechanism of reduction of TC due to the substitution of Y for Tb has been analysed and chemical pressure is found to play a significant role. Moreover, the entropy change of Tb0.9Y0.1Mn2Ge2 is found to exhibit very good magnetocaloric performance around TCinter (−ΔS = 11.9 J kg−1 K−1 and RCP = 102.9 J kg−1 for a field change of ΔB = 0–5 T) with a small hysteresis loss of 5.36 J/kg. This behaviour reflects the potential suitability of Tb0.9Y0.1Mn2Ge2 for operation as a magnetic refrigerant below the nature gas liquefaction temperature. The Debye temperature and the density of states N(EF) at the Fermi level have been determined and analyzed from the heat capacity.

Additional Information

How to cite this article: Fang, C. et al. New insight into magneto-structural phase transitions in layered TbMn2Ge2-based compounds. Sci. Rep. 7, 45814; doi: 10.1038/srep45814 (2017).

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Z. X. Cheng thanks the Australia Research Council for Future Fellowship (FT0990391). This work was supported in part by Australia Research Council Discovery Grant No. DP110102386. The authors thank Dr. T. Silver for his contribution to English expression.


The authors declare no competing financial interests.

Author Contributions J.L. Wang and Z.X. Cheng designed the project. C.S. Fang, G. X Li, J.L. Wang, W.D. Hutchison, Z.X. Cheng and Q.Y. Ren carried out the experimental work. C.S. Fang, J.L. Wang, Z.X. Cheng and S.J. Campbell wrote the paper. All the authors interpreted and discussed the work.


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