Home | About | Journals | Submit | Contact Us | Français |

**|**Scientific Reports**|**PMC5379177

Formats

Article sections

Authors

Related links

Sci Rep. 2017; 7: 45814.

Published online 2017 April 4. doi: 10.1038/srep45814

PMCID: PMC5379177

Chunsheng Fang,^{1} Guoxing Li,^{1,}^{2} Jianli Wang,^{a,}^{1,}^{3} W. D. Hutchison,^{4} Q. Y. Ren,^{4} Zhenyan Deng,^{5} Guohong Ma,^{5} Shixue Dou,^{1} S. J. Campbell,^{4} and Zhenxiang Cheng^{b,}^{1}

Received 2016 September 2; Accepted 2017 March 6.

Copyright © 2017, The Author(s)

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

The Tb_{1−x}Y_{x}Mn_{2}Ge_{2} 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 T_{N}^{inter} and from an antiferromagnetic interlayer structure to a collinear ferrimagnetic interlayer structure at T_{C}^{inter}. Compared with the slight change of T_{N}^{inter} (409K, 410K and 417K for x=0, 0.1 and 0.2 respectively), the replacement of Y for Tb leads to a significant decrease in T_{C}^{inter} from 97.5K for x=0 to 74.6K for x=0.2. The variation in T_{C}^{inter} 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 T_{C}^{inter} 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 −ΔS_{max}=9.1Jkg^{−1} K^{−1}, 11.9Jkg^{−1} K^{−1} and 6.3Jkg^{−1} K^{−1} with a field change from 0T to 5T 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 Gd_{5}Si_{2}Ge_{2}^{1}, 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 refrigeration^{2}. A number of materials which exhibit giant magnetic entropy changes at magnetic transitions have been investigated, including MnFeP_{0.45}As_{0.55}^{3}, MnAs_{1−x}Sb_{x}^{4}, Ni-Mn-Sn-based alloys^{5}, Ni-Mn-Ga^{6}^{,7}, and La(Fe,Si)_{13}^{8}. 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 techniques^{9}^{,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 GdLiF_{4}, GdF_{3} and Gd_{3}Ga_{5}O_{12} are used commercially^{11}. As reflected by the increase in exploration of materials which exhibit a large MCE below room temperature^{10}^{,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 RT_{2}X_{2} 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 temperatures^{11}^{,13}^{,14}^{,15}^{,16}. For example, the magnetic entropy values of RNi_{2}Si_{2} (R=Dy, Ho, Er) compounds are 21.3Jkg^{−1} K^{−1}, 21.7Jkg^{−1} K^{−1} and 22.9Jkg^{−1} K^{−1} around 6.5K, 4.5K and 3.5K respectively during a change of magnetic induction intensity from 0–5T^{16}, while the magnetic entropy of ErCr_{2}Si_{2} attained 29.7Jkg^{−1} K^{−1} near the magnetic ordering temperature 4.5K^{17}. The crystal structure of the RT_{2}X_{2} series is body centred tetragonal ThCr_{2}Si_{2}-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 μ_{Tb}=8.8μ_{B} in TbMn_{2}Si_{2} at 5K)^{20} and correspondingly make a large contribution to the magnetocaloric effect^{14}^{,15}^{,17}. Given the sensitivity of the magnetic state in RMn_{2}X_{2} to the intra-planar Mn-Mn spacing^{15}^{,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 behaviour^{25}^{,26}^{,27}. This diversity enables control of the interplay between the R-Mn and Mn-Mn exchange interactions in RMn_{2}X_{2} through external factors such as pressure^{28}, temperature and magnetic field^{29} meaning that such compounds have the potential for competitive performance^{15}^{,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 methods^{19}^{,30}, TbMn_{2}Ge_{2} was reported to be antiferromagnetic below Néel temperature T_{N}=410K with the AFil antiferromagnetic interlayer structure (*i.e.* a collinear antiferromagnetic structure between adjacent Mn planes in a+−+− sequence along the *c*-axis^{22}.) Below T_{C}=100K, TbMn_{2}Ge_{2} exhibits a collinear ferrimagnetic structure in which the Tb moments order ferromagnetically and couple antiferromagnetically with the Mn moment^{23}. Furthermore, in a later study for the Tb_{1−x}Y_{x}Mn_{2}Ge_{2} 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 76K for TbMn_{2}Ge_{2} to almost 0K for Tb_{0.4}Y_{0.6}Mn_{2}Ge_{2}) and magnetovolume effect (the volume effect is V/V=3.2×10^{–3} and 2.7×10^{−3} for x=0 and 0.1 respectively)^{30}. The magnetic phase transitions around T_{C} in the Tb-rich Tb_{1−x}Y_{x}Mn_{2}Ge_{2} compounds were shown to be first order^{30}, 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 Tb_{1−x}Y_{x}Mn_{2}Ge_{2} 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 Tb_{1−x}Y_{x}Mn_{2}Ge_{2} 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 9T physical properties measurement system (PPMS). The magnetic behaviour was investigated over the range from 5K to 340K in a magnetic field 0.01T. Differential scanning calorimetry measurements were performed on differential scanning calorimetry equipment (DSC 204 **F1** Phoenix^{®}) from 340K to 500K. Magnetization-field loops were obtained at temperatures close to the Curie temperature of samples with magnetic fields over the range 0–5T. The heat capacity measurements were performed on a Quantum Design 14T physical properties measurement system scanning from 2K to 250K. The samples were characterized and the structures determined by variable temperatures XRD measurements over the temperature range (12–300K) using a PANAlytical diffractometer with Cu-Kα radiation.

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 package^{31} 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 T_{c} for each sample (the transition temperatures were determined as the point where the value of dM/dT is minimum). Similar behaviours for TbMn_{2}Ge_{2} were also determined by Morellon *et al*.^{23} for which an anomaly in the thermal expansion along the *a*-axis was found near T_{c}. The discontinuity in the *a* lattice parameter around T_{c} 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 Pr_{0.5}Y_{0.5}Mn_{2}Ge_{2}^{15} (i.e. PrMn_{2}Ge_{2} diluted by Y), but different from NdMn_{2}Ge_{0.4}Si_{1.6}^{32}, NdMn_{1.9}Ti_{0.1}Si_{2}^{33} and NdMn_{1.7}Cr_{0.3}Si_{2}^{34}^{,35} (where Mn diluted with transition metal Ti or Ge diluted by Si) for which the lattice parameter *a* decreases with increasing temperature around T_{C} while the lattice parameter *c* expands. In order to derive the magneto-volume effect below T_{C}, we have calculated the contribution from lattice vibration using the Debye model:

Temperature dependence of the lattice constants a, c and unit cell volume: (**a**) TbMn_{2}Ge_{2}, (**b**) Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and (**c**) Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2}. The dashed lines show the phonon contribution to the lattice expansion as evaluated from the Gruneisen relation.

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

where k_{B} 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 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 TbMn_{2}Ge_{2}, Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} 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 T_{C}=94K, T_{C}=83K and T_{C}=70K 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 ω_{s} (=ΔV_{m}/V) at 5K determined as: TbMn_{2}Ge_{2} - ω_{s}=4.1×10^{−3}; Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} - ω_{s}=3.2×10^{−3} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} - ω_{s}=5.8×10^{−3}.

The magnetisation of the three samples have been measured in a field of B=0.01T over the temperature range 5–340K. As in Fig. 2(a,b and c) the TbMn_{2}Ge_{2}, Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} samples were respectively measured on warming from 5K in three states: after cooling in zero field (ZFC heating) and after cooling and heating in a field of B=0.01T (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 T_{C}^{inter} 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 TbMn_{2}Ge_{2}^{23}. Of the three samples, TbMn_{2}Ge_{2} has the highest T_{C}^{inter}(warm)=97.5K and T_{C}^{inter}(cool)=93.0K transitions respectively as determined from the FC heating and cooling M-T curves, while the values for Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} are derived to be T_{C}^{inter}(warm)=87.5K and T_{C}^{inter}(cool)=81.8K with the values for Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} being T_{C}^{inter}(warm)=74.6K and T_{C}^{inter} cool)=66.0K (normally the transition temperature during the FC process is chosen as the Curie temperature T_{c}). As expected, the higher the level of doping of non-magnetic Y atoms in Tb_{1−x}Y_{x}Mn_{2}Ge_{2}, the lower the magnetic phase transition temperature^{30}.

Temperature dependence of magnetization on ZFC heating, FC cooling and FC heating processes under a field of B=0.01T: (**a**) TbMn_{2}Ge_{2}, (**b**) Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and (**c**) Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2}. (**d**) the differential scanning calorimetry curves **...**

Differential scanning calorimetry measurements have been carried out on the Tb_{1−x}Y_{x}Mn_{2}Ge_{2} samples over the temperature range 300–500K (Fig. 2(d)) in order to investigate the paramagnetic to antiferromagnetic transition^{10}^{,23} at T_{N}^{inter}. As revealed by the DSC results in Fig. 2(d), the T_{N}^{inter} transition temperatures are found to increase slightly with increasing Y concentration - T_{N}^{inter}=409K, T_{N}^{inter}=410K and T_{N}^{inter}=417K 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 T_{N}^{inter} 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 PrMn_{2}Ge_{2−x}Si_{x} system^{36} 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 TbMn_{2}Ge_{2}, Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} under various external magnetic fields are presented in Fig 3(a,b and c) respectively. As expected the ferromagnetic transition temperature T_{C}^{inter} is shifted to higher temperature with increase in applied magnetic field. For example, the transition temperatures are T_{C}^{inter}=101.8K, T_{C}^{inter}=92K and T_{C}^{inter}=76K for TbMn_{2}Ge_{2}, Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} respectively in an external magnetic field of B=1T, while the transition temperatures are shifted to T_{C}^{inter}=107K, T_{C}^{inter}=98.2K and T_{C}^{inter}=81K respectively in a field of B=5T. The field dependence of the magnetic transition temperatures are summarized in Fig. 3(d). The values of dT_{c}/dB (obtained on linear fitting of the experimental data in Fig. 3(d) along with a summary of experimental data determined for Tb_{1−x}Y_{x}Mn_{2}Ge_{2} (x=0, 0.1, 0.2) in this investigation, are provided in Table 1.

As noted above, the effect of replacing the magnetic rare earth Tb with the nonmagnetic ion Y in Tb_{1−x}Y_{x}Mn_{2}Ge_{2} is to weaken the exchange interaction between magnetic ions due to the dilution effect. The magnetic behaviour of Y-doped Tb_{1−x}Y_{x}Mn_{2}Ge_{2} will also be modified as a result of chemical pressure due to differences in the atomic radii of the Tb(1.80Å) and Y(1.78Å) 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 T_{C} by chemical pressure was calculated as follows. The chemical pressure Δp was calculated^{20}^{,22}^{,33} according to the Murnaghan equation below:

where V_{0}, B_{0} and are the volume, the bulk modulus and its first derivative of TbMn_{2}Ge_{2} 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 RMn_{2}Ge_{2} system, we assume that the values of B_{0} and for PrMn_{2}Ge_{2} (B_{0}=38.0Gpa, =19.5 as derived from our synchrotron data under external pressure^{37}) can be applied to TbMn_{2}Ge_{2} at room temperature. Given that the doped materials Tb_{1−x}Y_{x}Mn_{2}Ge_{2} (x=0.1, 0.2) retain the ThCr_{2}Si_{2}-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 TbMn_{2}Ge_{2} (dT_{c}/dP=−2.9K/kbar)^{38}, the values of ΔT_{C} can be deduced by the relationship:

where Δp is the calculated chemical pressure. The calculated values of ΔT_{C} for Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} are ΔT_{C=}1.94K and ΔT_{C}=8.7K respectively. As noted above (see also Fig. 1, Figs 2 and and3.)3.) the effect of replacing Tb atoms with Y atoms in Tb_{1−x}Y_{x}Mn_{2}Ge_{2} 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 dT_{c}/dp can be derived using the Clausius-Clapeyron thermodynamic relation as follows:^{15}

The values of the change in the unit cell volume ΔV_{m} he change in moment Δμ during magnetic phase transition around T_{C} and dT_{c}/dB for each sample were taken from the present experimental results listed in Table.1. The derived results are dT/dp=−3.03K/kbar, −2.84K/kbar and −3.07K/kbar for TbMn_{2}Ge_{2}, Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2}, respectively. These calculated values are in general accord with the value of dT_{c}/dp=−2.9K/kbar for TbMn_{2}Ge_{2}^{38}, deviating by ~4.5%, ~2.1% and ~5.9% for the x=0.0. 0.1, 0.2 samples respectively.

Graphs of the magnetization as a function of applied field are shown for TbMn_{2}Ge_{2}, Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2}, and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} at temperatures around T_{C}^{inter} in Fig. 4(a,b and c) respectively. It can be seen that with increasing temperature beyond T_{C}^{inter}, 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 TbMn_{2}Ge_{2} is indicated by arrows in Fig. 4(a) as a typical example. This behaviour indicates that the region of ferromagnetic ordering in Tb_{1−x}Y_{x}Mn_{2}Ge_{2} can be shifted to higher temperatures by a stronger applied magnetic field.

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 M^{2} versus B/M (Fig. 5). As can be seen in Fig. 5(a,b and c), negative slopes are detected in the M^{2} versus B/M graphs for the TbMn_{2}Ge_{2} and Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} samples thus indicating that the antiferromagnetic to ferromagnetic processes are first order^{39}. However, Some papers^{40}^{,41} reported that for compounds near the critical point (from first order to second order magnetic phase transition) such as DyCo_{2}, this criterion of Arrott plots do not always work properly. It is also noted that the negative slopes for Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} around the antiferromagnetic to ferromagnetic transition was reduced compared with those for the TbMn_{2}Ge_{2} and Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} 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 T_{C}^{inter} has been detected (Fig. 1).

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

The calculated temperature dependent magnetic entropy changes for the Tb_{1−x}Y_{x}Mn_{2}Ge_{2} samples with x=0, 0.1 and 0.2 for both increasing field and decreasing field processes between field changes of ΔB=0–1T and ΔB=0–5T are shown in Fig. 6(a,b and c) respectively with the maximum values ΔS_{max} shown as a function of applied field in the insets of Fig. 6. With a field change of ΔB=0–5T, the value of −ΔS_{max} are 9.1J/kgK, 11.9J/kgK and 6.3J/kgK for TbMn_{2}Ge_{2}, Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} respectively, demonstrating that the entropy change for Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} is the largest of the three samples. As it is clear from Fig. 4, while TbMn_{2}Ge_{2} has the highest fraction of magnetic rare earth element and largest saturation magnetization (42.5 Am^{2}/kg at 84K), its large hysteresis loss (7.40J/kg) leads to reduction in the magnetic entropy change. By comparison, with the lowest concentration of magnetic rare earth Tb, the Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} sample displays the lowest saturation magnetization (only 32.5 Am^{2}/kg even at 55K) and the smallest hysteresis loss 5.21J/kg), while as shown in Fig. 4(b), Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} with medium concentration of Tb has a relatively large saturation magnetization of 38.0 Am^{2}/Kg at 84K and small hysteresis loss (5.36J/kg). The refrigerant capacity (RCP), defined as the product of −ΔS_{max} and the full width at half maximum of the −ΔS_{max} curve, for the three samples are: 93.3J/kg, 102.9J/kg, 62.4J/kg for TbMn_{2}Ge_{2}, Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} respectively, with a field change of ΔB=0–5T. The MCE value of Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} is comparable to those of other materials for a field change of ΔB=0–5T including: GdCoAl, −ΔS_{max}(T)=10.4J/kgK at 100K^{34}, TbCoAl, −ΔS_{max}(T)=10.5J/kgK at 70 K^{34} and GdMn_{2}Ge_{2}, −ΔS_{max}(T)=1.2J/kgK at 95K^{28}, all of which, in common with Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2}, importantly exhibit negligible field and thermal hysteresis losses.

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 Mn_{3}GaN (S_{bar}=22.3J/K kg)^{42} and Ni–Mn–In magnetic superelastic alloys (S_{bar}=27.7J/K kg)^{43}. Based on the fact that all these three Tb_{1−x}Y_{x}Mn_{2}Ge_{2} samples exhibit strong magnetovolume effect around magnetic phase transition, we have calculated the barocaloric effect using the Clausius_Clapeyron relation^{43}. The barocaloric effects entropy change S_{bar}, have been derived to be S_{bar}=9.6J/kgK, 13.5J/kgK and 13.2J/kgK for TbMn_{2}Ge_{2},Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} 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.

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

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

where C_{ph}, C_{el} and C_{m} are the lattice, electronic, and magnetic contributions respectively^{44}. In the absence of a magnetic phase transition, the heat capacity can be described as:

where γ and β are the electronic and phonon heat capacity coefficients, respectively. For the specific heat of TbMn_{2}Ge_{2} at low temperatures T≤1K, well away from the magnetic transition, as shown in Fig. 7(b), a fit to the graph of C_{p}/T versus T^{2} leads to γ=(65.2±0.95)mJ/molK^{2}, β=(4.53±0.156)×10^{−4}J/molK^{4}. The electronic density of states N(E_{F}) at the Fermi surface can be calculated by the formula:^{44}

where k_{B} is the Boltzmann constant. For the TbMn_{2}Ge_{2} compound, the value of N(E_{F}) is derived to be (5.54±0.08) state/eV atom. Likewise, the Debye temperature θ_{D} can also be obtained by:

where R is the universal gas constant and the number of atoms n=5^{45}. The Debye temperature for TbMn_{2}Ge_{2} was determined as θ_{D}=278±3K.

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

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 −ΔS_{M=}2.6J/kgK for TbMn_{2}Ge_{2} (field change of ΔB=2T), which is smaller than the value (−ΔS_{M}=5.9J/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, −ΔT_{ad} (shown as inset of Fig. 7(c) can be evaluated from −ΔS_{M} (T, B) and the heat capacity data.

The equivalent heat capacity parameters for Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} are shown in Figs 8 and and9,9, respectively. The Debye temperatures were found to increase from 281K for TbMn_{2}Ge_{2} to 344K for Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and 354K for Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2}; with the increases understood in terms of the differences in their molecular mass^{31}. The adiabatic temperature changes near the Curie temperature are found to decrease from −ΔT_{ad}=2.6K for TbMn_{2}Ge_{2}, to −ΔT_{ad}=2.3K for Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and 1.8K for Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2}.

The electron density at the Fermi surface is found to decrease from 5.54 state/eV atom for TbMn_{2}Ge_{2} to 2.18 state/eV atom and 3.06 state/eV atom for Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} and Tb_{0.8}Y_{0.2}Mn_{2}Ge_{2} 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 θ_{D} 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 La_{1−x}Y_{x}Mn_{2}Si_{2} 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=1.0^{49}. Moreover, it is also noted that the electron density at the Fermi level for TbMn_{2}Si_{2}^{29} was reported to be 2.38 states/eV atom, which is close to the values reported here for Tb_{1−x}Y_{x}Mn_{2}Ge_{2} samples.

In conclusion, we have carried out a detailed investigation around the region of the magnetic transitions of compounds in the Tb_{1−x}Y_{x}Mn_{2}Ge_{2} 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 T_{N}^{inter} and T_{C}^{inter} for each of the three samples. The antiferromagnetic transition at T_{N}^{inter} is shown to increase slightly with increase in the Y concentration, while the ferromagnetic transition at T_{C}^{inter} drops significantly. The mechanism of reduction of T_{C} 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 Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} is found to exhibit very good magnetocaloric performance around T_{C}^{inter} (−ΔS=11.9Jkg^{−1} K^{−1} and RCP=102.9Jkg^{−1} for a field change of ΔB=0–5T) with a small hysteresis loss of 5.36J/kg. This behaviour reflects the potential suitability of Tb_{0.9}Y_{0.1}Mn_{2}Ge_{2} for operation as a magnetic refrigerant below the nature gas liquefaction temperature. The Debye temperature and the density of states N(E_{F}) at the Fermi level have been determined and analyzed from the heat capacity.

**How to cite this article:** Fang, C. *et al*. New insight into magneto-structural phase transitions in layered TbMn_{2}Ge_{2}-based compounds. *Sci. Rep.*
**7**, 45814; doi: 10.1038/srep45814 (2017).

**Publisher's note:** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

- Pecharsky V. K. & Gschneidner K. A.
Giant Magnetocaloric Effect in Gd
_{5}(Si_{2}Ge_{2}). Physical Review Letters 78, 4494 (1997). - Gschneidner Jr K. A., Pecharsky V. K. & Tsokol A. O.
Recent developments in magnetocaloric materials. Reports on Progress in Physics
68, 1479–1539 (2005); Gschneidner Jr, K. A. and Pecharsky, V. K. Thirty years of near room temperature magnetic cooling: Where we are today and future prospects.
*International Journal of Refrigeration***31**, 945–961 (2008); Shen, B. G. et al. ., Recent Progress in Exploring Magnetocaloric Materials.*Advanced Materials***21,**4545–4564 (2009). - Tegus O., Brück E., Buschow K. H. J. & de Boer F. R. Transition-metal-based magnetic refrigerants for room-temperature applications. Nature 415, 150–152 (2002). [PubMed]
- Wada H. & Tanabe Y.
Giant magnetocaloric effect of MnAs
_{1−x}Sb_{x}. Applied Physics Letters 79, 3302 (2001). - Krenke T. et al. . A. Inverse magnetocaloric effect in ferromagnetic Ni–Mn–Sn alloys. Nature materials 4, 450– 454 (2005). [PubMed]
- Hu F. X., Shen B. G.
Sun J. R. & Wu G. H.
Large magnetic entropy change in a Heusler alloy Ni
_{52.6}Mn_{23.1}Ga_{24.3}single crystal, Physical Review B 64, 132412 (2001). - Pasquale M.
et al. . Magnetostructural transition and magnetocaloric effect in Ni
_{55}Mn_{20}Ga_{25}single crystals. Physical Review B 72, 094435 (2005). - Zhang X. X.
et al. . Magnetic entropy change in Fe-based compound LaFe
_{10.6}Si_{2.4}. Applied Physics Letters 77, 3072 (2000); Hu, F.X. et al. ., Influence of negative lattice expansion and metamagnetic transition on magnetic entropy change in the compound LaFe_{11.4}Si_{1.6}.*Applied Physics Letters***78,**3675 (2001). - Casanova F.
et al. . Effect of a magnetic field on the magnetostructural phase transition in Gd
_{5}(Si_{x}Ge_{1−x})_{4}. Physical Review B 69, 104416 (2004). - von Ranke et al. . Magnetocaloric effect in the RNi
_{5}(R=Pr, Nd, Gd, Tb, Dy, Ho, Er) series. Physical Review B 70, 134428 (2004). - Zeng R., Dou S. X., Wang J. L. & Campbell S. J.
Large magnetocaloric effect in re-entrant ferromagnet PrMn
_{1.4}Fe_{0.6}Ge_{2}. Journal of Alloys and Compounds 509, L119–L123 (2011). - Wang L. C. et al. . Low-temperature large magnetocaloric effect in the antiferromagnetic CeSi compound. Journal of Alloys and Compounds 587, 10–13 (2014).
- Maji B., Ray M. K., Suresh K. G. & Banerjee S.
Large exchange bias and magnetocaloric effect in TbMn
_{2}Si_{2}. Journal of Applied Physics 116, 213913 (2014). - Samanta T., Das I. & Banerjee S.
Giant magnetocaloric effect in antiferromagnetic ErRu
_{2}Si_{2}compound. Applied Physics Letters 91, 152506 (2007). - Wang J. L. et al. . Driving Magnetostructural Transitions in Layered Intermetallic Compounds. Physical Review Letters 110, 217211 (2013). [PubMed]
- Zuo W. L., Hu F. X., Rong S. J. & Shen B. G.
Low-field large reversible magnetocaloric effect in the RNi
_{2}Si_{2}(R=Dy, Ho, Er) compounds. Journal of Magnetism and Magnetic Materials 344, 96–100 (2013). - Li L.
et al. . Low-field giant reversible magnetocaloric effect in intermetallic compound ErCr
_{2}Si_{2}. Scripta Materialia 67, 237–240 (2012). - Ban Z. & Sikirica M.
The crystal structure of ternary silicides ThM
_{2}Si_{2}(M=Cr, Mn, Fe, Co, Ni and Cu) Acta Crystallographica 18, 594–599 (1965). - Purwanto S.
et al. . The effects of dilution on the competing exchange state in (Tb, Y)Mn
_{2}X_{2}(X=Ge, Si). Physica B. 213,214, 318–320 (1995). - Granovsky , S. A.
et al. . The magnetic structures and the magnetic phase diagram of the TbMn
_{2}(Ge, Si)_{2}system. Physica B 391, 79–87 (2007). - Brabers J. H. V. J.
et al. . Strong Mn-Mn distance dependence of the Mn interlayer coupling in SmMn
_{2}Ge_{2}-related compounds and its role in magnetic phase transitions. Physical Review B 50, 16410 (1994). [PubMed] - Venturini G., Welter R., Ressouche E. & Malaman B.
Neutron diffraction study of Nd
_{0.35}La_{0.65}Mn_{2}Si_{2}: A SmMn_{2}Ge_{2}-like magnetic behaviour compound. Journal of Magnetism and Magnetic Materials 150, 197 (1995). - Morellon L., Algarabel P. A., Ibarra M. R. & Ritter C.
Magnetic structures and magnetic phase diagram of Nd
_{x}Tb_{1−x}Mn_{2}Ge_{2}. Physical Review B 55, 12363 (1997). - Purwanto S., Oihashi M., Yamauchi H., Onodem H. & Yamaguchr Y. Prosiding PertemuanI lmiah Sains Materi 1410 (1997).
- Ott H. R. & Fisk Z. Handbook on the Physics and Chemistry of the Actinides, (ed. Freeman A. J. & Lander G. H.) 85 (1987).
- Szytula A. & Leciejewicz J. Handbook on the Physics and Chemistry of Rare Earths (ed. Gscheidner Jr K. A. & Eyring L.) 133 (1989).
- Kolmakova N. P., Sidorenko A. A. & Levitin R. Z.
Features of the magnetic properties of rare-earth intermetallides RMn
_{2}Ge_{2}. Low Temperature Physics 28, 653 (2002). - Kumar P.
et al. . Pressure-induced changes in the magnetic and magnetocaloric properties of RMn
_{2}Ge_{2}(R=Sm, Gd). Physical Review B 77, 224427 (2008). - Li G. X.
et al. . Large entropy change accompanying two successive magnetic phase transitions in TbMn
_{2}Si_{2}for magnetic refrigeration. Applied Physics Letters 106, 182405 (2015); Li, L. W. et al. . Giant reversible magnetocaloric effect in ErMn_{2}Si_{2}compound with a second order magnetic phase transition. Applied Physics Letters**100,**152403 (2012). - Dubenko I. S., Gaidukova I. Y., Granovsky S. A., Inoue K. & Markosyan A. S.
Magnetic phase transitions in (Tb,Y) Mn
_{2}M2 (M=Ge and Si) Systems. Journal of Applied Physics 93, 10 (2003). - McCusker ,. L. B. et al. . Rietveld refinement guidelines. Journal of Applied Crystallography 32, 36–50 (1999).
- Wang J. L.
et al. . Magnetocaloric effect in layered NdMn
_{2}Ge_{0.4}Si_{1.6}. Applied Physics Letters 98, 232509 (2011). - Md Din
et al. . Magnetic properties and magnetocaloric effect of NdMn
_{2−x}Ti_{x}Si_{2}compounds. Journal of Physics D: Applied Physics 46**(44)**, 1–11 (2013). - Md Din
et al. . Magnetic phase transitions and entropy change in layered NdMn
_{1.7}Cr_{0.3}Si_{2}. Applied Physics Letters 104, 042401 (2014). - Matsunami D., Fujita A., Takenaka K. & Kano M.
Giant barocaloric effect enhanced by the frustration of the antiferromagnetic phase in Mn
_{3}GaN. Nature Material 14, 73–78 (2015). [PubMed] - Wang J. L. et al. . Phase gap in pseudoternary R1−yRyMn2X2−xXx compounds. Physical Review B 87, 104401 (2013).
- Kennedy S. J., Wang J. L., Campbell S. J., Hofmann M. & Dou S. X.
Pressure induced magneto-structural phase transitions in layered RMn
_{2}X_{2}compounds. Journal of Physics 115, 172617 (2014). - Morellon , L., Arnold Z., Kamarad J., Ibarra M. R. & Algarabel P. A.
The magnetic phase transitions and related volume changes in (Nd
_{1−x}Tb_{x})Mn_{2}Ge_{2}compounds. Journal of Magnetism and Magnetic Materials 177, 1085–1086 (1998). - Ray M. K., Bagani K. & Banerjee S.
Effect of excess Ni on martensitic transition, exchange bias and inverse magnetocaloric effect in Ni
_{2+x}Mn_{1.4−x}Sn_{0.6}alloy. Journal of Alloys and Compounds 600, 55–59 (2014). - Parra-Borderias M., Bartolome F., Herrero-Albillos J. & Garcia L. M. Detailed discrimination of the order of magnetic transitions and magnetocaloric effect in pure and pseudobinary Co Laves phases. Journal of Alloys and Compounds 481, 48 (2009).
- Bonilla C. M. et al. . A new criterion to distinguish the order of magnetic transitions by means of magnetic measurements. Journal of Applied Physics 107, 09E–131 (2010).
- Mañosa L. et al. . Giant solid-state barocaloric effect in the Ni-Mn-In magnetic shape memory alloy. Nature Mater 9, 478–481 (2010). [PubMed]
- Matsunami D., Fujita A., Takenaka K. & Kano M.
Giant barocaloric effect enhanced by the frustration of the antiferromagnetic phase in Mn
_{3}GaN. Nature Material 14, 73–78 (2015). [PubMed] - Bouvier M., Lethuillier P. & Schmitt D. Specific heat in some gadolinium compounds. I. Experimental. Physical Review B 43, 13137 (1991). [PubMed]
- Emre B., Dincer I. & Elerman Y.
Analysis of heat capacity and magnetothermal properties of the La
_{0.775}Gd_{0.225}Mn_{2}Si_{2}compound. Intermetallics 31, 16–20 (2012). - Nirmala , R., Morozkin A. V. & Malik S. K.
Magnetism and heat capacity of Dy
_{5}Si_{2}Ge_{2}. Physical Review B 75, 094419 (2007). - Liu G. J. et al. . Determination of the entropy changes in the compounds with a first-order magnetic Transition. Applied Physics Letters 90, 032507 (2007).
- Caron L. et al. . On the determination of the magnetic entropy change in materials with first-order transitions. Journal of Magnetism and Magnetic Materials 321, 3559–3566 (2009).
- Gerasimov E. G., Gaviko V. S. & Kanomat T.
Heat capacity of La
_{1−x}Y_{x}Mn_{2}Si_{2}La_{1−x}Y_{x}Mn_{2}Si_{2}compounds. Journal of Magnetism and Magnetic Materials 310, e563–e565 (2007).

Articles from Scientific Reports are provided here courtesy of **Nature Publishing Group**

PubMed Central Canada is a service of the Canadian Institutes of Health Research (CIHR) working in partnership with the National Research Council's national science library in cooperation with the National Center for Biotechnology Information at the U.S. National Library of Medicine(NCBI/NLM). It includes content provided to the PubMed Central International archive by participating publishers. |