Structural and magnetic properties of Pr5Si3-xGex compounds

Journal of Alloys and Compounds 788 (2019) 468e475

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Structural and magnetic properties of Pr5Si3-xGex compounds Guang Tian a, Honglin Du a, Wenyun Yang a, Changsheng Wang a, Jingzhi Han a, Shunquan Liu a, Jinbo Yang a, b, c, * a

State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, PR China Collaborative Innovation Center of Quantum Matter, Beijing 100871, PR China c Beijing Key Laboratory for Magnetoeletric Materials and Devices, Beijing 100871, PR China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 11 June 2018 Received in revised form 5 December 2018 Accepted 13 February 2019 Available online 14 February 2019

The crystal structures, magnetic properties and electronic structures of pseudo-binary compounds Pr5SixGe3-x were investigated. With the increase of the Ge content, structure of Pr5SixGe3-x gradually changes from the tetragonal Cr5B3-type to the hexagonal Mn5Si3-type. For the compounds with the tetragonal structure, the unit cell volumes as well as the magneto-crystalline anisotropy energy (MAE) increase with the Ge content, leading to the diminishing of the magnetization and the maximum magnetic entropy changes -DSM. As compared to the binary compound Pr5Si3, the intermetallic compounds with Ge doping show broader working temperature span and considerably large relative cooling power (213.9, and 184.8 J kg
1 at DH ¼ 50 kOe for Pr5Si2.5Ge0.5 and Pr5Si2Ge, respectively). For the hexagonal compound Pr5Ge3, a large MAE and an easy magnetization direction close to c axis (polar angle q ~7 ) were calculated, which is related to the macroscopic magnetic transition behavior at low temperature. © 2019 Elsevier B.V. All rights reserved.

Keywords: Magnetocaloric effect First-principles calculations Magnetocrystalline anisotropy energy Second-order magnetic transition

1. Introduction Due to their rich physical characteristics, binary intermetallic compounds (R ¼ rare earth metal, and M is a p-blocking element) have attracted continuous attention during the past few decades [1e5]. Most of the R5M3 (5:3) lanthanide compounds adopt the Mn5Si3etype structure (space group P63/mcm) [3e5], while some of the light rare earth silicides, such as Pr5Si3 and Nd5Si3 crystallize in the tetragonal Cr5B3-type of structure with space group I4/mcm [6,7]. The rare earth elements occupy two inequivalent lattice sites in these compounds, leading to the intrinsically anisotropic magnetic interactions because the nearest neighbors of these rare-earth ions are different. Thereby the compounds always present complex magnetic structures, for example, conical for Tb5Sb3 [8], flat spiral for Tb5Ge3 [9], amplitude sine modulated structure for Ho5Sb3 [10] and Dy5Sb3 [11]. Moreover, contradictory results have been reported for the magnetic behaviors of R5M3, due to their complicated magnetic structures. For instant, Pr5Ge3 was found to have an antiferromagnetic behavior at low temperature and exhibit a field-

* Corresponding author. State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, PR China. E-mail address: [email protected] (J. Yang). https://doi.org/10.1016/j.jallcom.2019.02.172 0925-8388/© 2019 Elsevier B.V. All rights reserved.

induced metamagnetic transition [1], while the presence of competing ferromagnetic and antiferromagnetic interactions was reported by R. Nirmala et al. [12]. The studies of single-crystal Pr5Ge3 by Devang A. Joshi [13], indicated that the magnetic isotherm of the compound along the [0001] direction is typical ferromagnetic, while ferromagnetic correlations set in at around 36 K in Pr5Ge3 in the ab plane followed by an antiferromagnetic transition at 13 K. Besides these investigations of the complicated magnetic structures of R5M3, light rare earth silicide and germanide also have been studied for their magnetocaloric effect (MCE). In our earlier works, a large reversible magnetocaloric effect (-DSM ¼ 11.6 J/kg K at DH ¼ 50 kOe) has been obtained for the light rare earth silicide Pr5Si3 [7], and a maximum magnetic entropy change -DSM of 5.8 J/ kg K at 7 T for Pr5Ge3 also has been observed [12]. It is known that the crystal structures as well as magnetic properties vary with the Si:Ge ratio in pseudobinary mixed silicide-germanide R5(SixGe1
x)4 systems [14,15], Much efforts have been done to investigate the interplay between magnetism and structure in the physical properties of these pseudobinary alloys. However, very few pseudobinary R5(SixGe1
x)3 systems have been explored. In this paper, we have performed an investigation on the crystal structures, magnetic properties and MCE of Pr5SixGe3-x compounds. The density functional theory (DFT) calculations were also

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conducted on the pseudobinary compounds in order to gain additional understanding of the bonding and magnetic properties in these phases, which has not been investigated before. It is found that the structures of Pr5SixGe3-x compounds vary with the increase of Ge content because of the changing of the ion radius ratio. Moreover, the magneto-crystalline anisotropy energies (MAEs) of these pseudo-binary alloys deduced from the spin-orbit coupling increase with the Ge content, which are responsible for the changes of the magnetic properties as well as the magnetocaloric effects of Pr5SixGe3-x compounds. 2. Experimental and calculation details The polycrystalline Pr5Si3-xGex (x ¼ 0.5, 1.0, 1.5, 2.0, 3.0) samples were prepared by arc melting of high purity raw materials, in a water-cooled copper crucible under a protective argon atmosphere. Approximately 5 wt% excess Pr was added during melting. Each sample was turned over and remelted five times to improve the homogeneity. The ingots were then sealed in an argon-filled quartz tube and subsequently annealed at 1050  C for 7 days. Powder Xray diffraction (XRD) measurements were conducted by using X'pert Pro MPD diffractometer (Cu Ka radiation) and the XRD patterns were refined with the Rietveld method. The magnetic measurements were carried out using the magnetic property measurement system (MPMS-7, manufactured by Quantum Design Inc.). The electronic calculations were carried out using the densityfunctional theory (DFT) method [16] as implemented in the Vienna ab initio simulation package VASP within a plane wave basis set [17,18]. Projector augmented wave (PAW) potentials were used [19]. G-centered (4, 4, 4) k-point grids were used to sample the first Brillouin zone for reciprocal space integration, and the energy cutoff of the plane wave basis was set to 400 eV to ensure that the total energies are converged within 10
5 eV. For the total energy calculations, atomic positions and lattice parameters were relaxed to ensure that the structural parameters and cell energies were fully converged, and the ionic convergence criterion was set to 10
3 eV/Å. 3. Results and discussion Fig. 1 shows the powder X-ray diffraction patterns of Pr5Si3-xGex (x ¼ 0.5, 1.0, 1.5, 2.0, 3.0) compounds. It can be seen that the samples with x ¼ 2.0 and 3.0 show a dominant phase of the Mn5Si3etype structure (space group P63/mcm), while the samples with lower Ge contents (x ¼ 0.5, 1.0) crystallize in the tetragonal Cr5B3-type of structure with space group I4/mcm. While the Pr5Si1.5Ge1.5 compound contains the tetragonal Cr5B3-type structure as the major phase together with a significant amounts of the hexagonal phase. Based on the Rietveld refinement of the XRD patterns, the unit cell parameters of Pr5Si3-xGex compounds were determined and listed in Table 1. For both of the phases, the unit cell volumes increase with decreasing Si content, in agreement with the smaller size of Si as compared to Ge. It can also be found that the replacing of Si atoms by larger Ge atoms leads to the gradual structural transition in the pseudobinary Pr5Si3-xGex system. Since the doping of Ge in the silicides has little effect on the valence electron number, the observed structural transitions are likely driven by the changing of the ion radius ratio. The average anion radius increases with the Ge content in Pr5Si3-xGex, leading to the decrease of the cationanion radius ratio (rPr/rSi,Ge), thereby the compounds tend to adopt the hexagonal structure. This also appears in the 5:3 binary rareearth metal silicides, and most of RE5Si3 compounds (RE ¼ Sm, Gd, Dy, Tb, Ho, Er) crystallize in Mn5Si3etype structure [1e5],

Fig. 1. Schematic representation of powder X-ray diffraction patterns of Pr5Si3-xGex (x ¼ 0.5, 1.0, 1.5, 2.0, 3.0) samples. Positions of the Bragg peaks for the tetragonal and hexagonal phase are marked by solid circles (in red) and hollow triangles (in black), respectively. The samples with x ¼ 2.0 and 3.0 show a dominant phase of the Mn5Si3etype structure (space group P63/mcm), while the samples with lower Ge contents (x ¼ 0.5, 1.0) crystallize in the tetragonal Cr5B3-type of structure with space group I4/mcm. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

however, the silicides with RE ¼ Nd and Pr [6,7], in which the cation radii are relative larger, adopt the tetragonal Cr5B3-type of structure. It is worth mentioning that only 28.1 wt% Mn5Si3etype phase exist in Pr5Si1.5Ge1.5 compound, while slight impurity of Cr5B3-type phase can still be detected in samples Pr5SiGe2 and Pr5Ge3, indicating that the tetragonal structure is more stable in the pseudobinary Pr5Si3-xGex system. Furthermore, as shown in Fig. 1, only the Bragg peaks (123) of Cr5B3-type phase can be detected in the XRD patterns for Pr5SiGe2 and Pr5Ge3, and therefore it is most unlikely to accurately determine the phase ratio of the impurity in these compounds by using Rietveld refinement. We consider that the ionic radius ratio of Pr and Ge should be closed to the critical value of the radius ratio to form the Mn5Si3-type phase. Accordingly, once a few Ge atoms being replaced by Si, the effective cation-anion radius ratio increases, resulting in the formation of some Cr5B3type phase. The refined atomic parameters of the two-phase compound Pr5Si1.5Ge1.5 are listed in Table 2, to clarify the site preference of Si/ Ge atoms in both tetragonal and hexagonal phase. It is noticed that all the Si atoms tend to enter into the Cr5B3-phase. Moreover, in the tetragonal structure, the larger Ge atoms preferentially occupy atomic sites 4a (0, 0, 1/4), which have noticeably larger bond distances with Pr. The optimized crystal structure parameters of Pr5Si3, Pr5Si2Ge and Pr5Ge3 using the total energy minimization were listed in Table 1. In the calculations of Pr5Si2Ge, considering the site preference of Ge in the tetragonal phase, all of four Si atoms at crystal site 4a were replaced by Ge with the stoichiometric ratio of Si and Ge to be 2:1. The deviations on the calculated equilibrium lattice constants are typical for the DFT calculations. Moreover, as mentioned in the introduction part, different from the ferromagnetic materials with tetragonal Cr5B3-type phase, Pr5Ge3 was

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Table 1 The crystallographic parameters of Pr5SixGe3-x alloys. It is found from the Rietveld refinement that there are 28.1 wt% Mn5Si3etype phase and 71.9 wt% Cr5B3-type phase in the Pr5Si1.5Ge1.5 sample. x

3.0 2.5 2.0 1.5 1.0 0

Space group

I4/mcm I4/mcm I4/mcm I4/mcm P63/mcm P63/mcm P63/mcm

Experimental

Calculated

a(Å)

c(Å)

V(Å3)

a(Å)

c(Å)

7.8089(6) [7] 7.8245(6) 7.8387(8) 7.8498(5) 8.7538(6) 8.7729(4) 8.8081(3)

13.7510(13) [7] 13.789(1) 13.812(1) 13.805(1) 6.6888(6) 6.6979(3) 6.7023(3)

838.5211 [7] 844.2321 848.7026 850.6876 443.8885 446.4315 450.3184

7.7279

12.7448

7.7848

12.8002

8.9073

6.2199

Table 2 The atom parameters of the Cr5B3-type and Mn5Si3-type phase in Pr5Si1.5Ge1.5 compound. Phase type

Atom

Wyck.position

Occupancy

x

y

z

Cr5B3-type

Pr1 Pr2 Si1 Si2 Ge1 Ge2 Pr1 Pr2 Ge1 Si

16l 4c 4a 8h 4a 8h 4d 6g 6g 6g

1 1 0.2(1) 0.73(7) 0.8(1) 0.27(7) 1 1 1 0

0.6748(3) 0 0 0.135(1) 0 0.135(1) 0.3333 0.2378(6) 0.605(1) 0.605(1)

0.1748(3) 0 0 0.635(1) 0 0.635(1) 0.6667 0 0 0

0.1472(2) 0 1/4 0 1/4 0 0 1/4 1/4 1/4

Mn5Si3-type

considered to exhibit an antiferromagnetic ordering at low tem
el temperature is below 20 K according to perature, and the Ne some earlier reports (12 K in Ref.1 and 18 K in Ref. 12). Therefore, two solutions were considered for Pr5Ge3 compound during the DFT investigations: one with a ferromagnetic arrangement of Pr (4d) and Pr (6g) sublattices and another with an antiferromagnetic one. It is found from the calculations that the ferromagnetic structure is preferred for Pr5Ge3. The density of states (DOS) for Pr5Si3, Pr5Ge3 and Pr5Si2Ge are plotted in Fig. 2. The energy scales in all cases are presented with the corresponding Fermi levels as the reference. The DOS curves for Pr5Si3 and Pr5Si2Ge have common features, which arise from the fundamental Cr5B3-type structure for both, but also show some distinct differences. It can be seen from Fig. 2 (b) that the contribution of 2p states of Ge (at 4a crystal site) below the Fermi level are obviously larger for Pr5Si2Ge as compared to the 2p states of Si (at 4a crystal site) in Pr5Si3, indicating that the p-f interaction was strengthened as Ge doped in Pr5Si3 compound. The valance states near the Fermi level have mainly Ge-p character while Ge-s states appear approximately 7 eV below the Fermi level. Above about
3 eV, the DOS curves consist of a strong mixture of main group valence p-orbitals with 6s and 4f orbitals of Pr. Although the interaction of p-state (4a site) with Pr-f electron are enhanced due to the substitution of Ge for Si, the hybridizations between the pstates of Si at 16l site and the 4f states are weakened resulted from the relatively larger distance to Pr atoms, which will lead to an increase of the magnetic moments in these compounds. As mentioned above, R5M3 compounds typically have complicated magnetic structures despite their relatively simple formula, due to the different near-neighbor environment associated with the two sites of rare earth elements. Therefore, the noncollinear arrangement of the spin moments in Pr5Si3, Pr5Ge3 and Pr5Si2Ge were calculated, and the in-plane as well as out-plane magnetic moments are listed in Table 3. It is suggested that the magnetic moments of two nonequivalent types of Pr atoms in Cr5B3-type structure tend to align parallel along the c axis. However, the magnetic moments of Pr-4d and Pr-6g in Mn5Si3-type structure are calculated to be both misaligned from the c axis by 8.12 .

Furthermore, we have calculated the MAEs of Pr5Si3-xGex (x ¼ 0, 1.0, 3.0) compounds caused only by the spin-orbital (SO) interaction. The MAE is defined as the difference between two selfconsistently calculated total energies for two different magnetic field directions, K ¼ E(q)
E(001), in which q is the polar angle of the Cartesian coordinate system where the c axis coincides with the z axis. The calculated results of magneto-crystalline anisotropy energy K as a function of the polar angle q in Pr5Si3, Pr5Ge3 and Pr5Si2Ge are presented in Fig. 3. It is shown that very large MAEs were found in all the compounds, and the easy magnetization directions of the alloys with tetragonal Cr5B3-type structure are along the c direction, while the minimal energy of Pr5Ge3 is at around 7 from the c-axis. In addition, the MAE in Pr5Si3 is not as large as that in the Ge-doping compound. It also should be noticed that the maximum in the total energy are both at q ~63 for Pr5Si3 and Pr5Si2Ge, which may lead to the loss of magnetization at a small applied field, as there is even a considerable barrier for the moments aligned nearly in-plane change to the easy axis. The zero-field-cooled (ZFC) and field-cooled (FC) magnetization curves of Pr5Si3-xGex (x ¼ 0.5, 1.0, 2.0, 3.0) compounds in a magnetic field of 50 Oe are depicted in Fig. 4. The samples with x ¼ 0.5 and 1.0 adopting the Cr5B3-type of structure show typical ferromagnetic properties and their Curie temperatures TC are 53.1 K and 56 K, respectively, corresponding to the minimum in the dM/dT curve. The ZFC and FC curves of these two compounds are reversible around TC, a characteristic of the second-order magnetic transition (SOMT), while a large difference can be seen in the low temperature range below TC. This phenomenon has also been observed in other Pr-silicides [20]. The maximal points in the ZFC M-T curves of Pr5Si3xGex are considered to be caused by the thermal activation of domain wall movement, consequently leading to the increase of the net magnetization [7]. The high magneto-crystalline anisotropy energy, which is the origin of the presence of narrow walls, is originated from the crystal field interaction of moments that contains an orbital contribution and the spin-orbital coupling in these compounds. At low temperature, the thermal energy is too low to overcome the energy barrier for moving the narrow walls. Therefore there is no an appreciable net magnetization in the ZFC curve

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Fig. 3. The magnetic-crystal anisotropy K of Pr5Ge3 (a) and Pr5Si3-xGex (x ¼ 0, 1.0) (b) as a function of the polar angle q. Fig. 2. The total densities of states (a) calculated for Pr5Si3-xGex (x ¼ 0, 1.0, and 3.0) and the partial densities (b) of p states of Si/Ge and f states of Pr. The values of the DOS are in units of states eV
1/(atom spin).

in low temperature region [21]. While the FC curves were obtained at low temperature and a field of 50 Oe, the moments were aligned to the field direction before the measurements and no magnetization decrease were found at low temperature. For Pr5Ge3 compound, an antiferromagnetic-like transition is observed around 22.2 K in the M-T curve, as shown in Fig. 4(a). However, considering the calculated results of noncollinear magnetic structure for Pr5Ge3 in this work and the ferromagnetic behavior of single-crystalline Pr5Ge3 along the c-axis below 13 K [13], it is reasonable to consider the phase change around 22 K to be

a ferromagnetic (FM) to paramagnetic (PM) phase transition for polycrystalline Pr5Ge3. Accordingly, the relatively small magnetization of the compound in a field of 50 Oe is mainly caused by the large magneto-crystalline anisotropy energy arising from crystal field interaction and spin-orbital coupling, as interpreted above. For the compound Pr5Si2Ge, there are two local minima in the dM/dT curve, corresponding to the magnetic transition temperatures of the hexagonal phase (T1) and the slight impurity tetragonal phase (T2), respectively, as shown in inset (i) of Fig. 4. For compounds Pr5Si3-xGex, instead of any direct magnetic coupling between the nearest Pr-Pr atoms, because of large interatomic distances, the local spins interact with each other via the conduction electrons. According to the RKKY approximation, the magnetic ordering temperature of rare earth based ferromagnetic

Table 3 Magnetic moments carried by Pr atoms in Pr5Si3, Pr5Si2Ge, and Pr5Ge3. The magnetic moments of Pr-4d and Pr-6g in Mn5Si3-type structure are calculated to be both misaligned from the c axis by 8.12 . m4c x ðmB =PrÞ

m4c z ðmB =PrÞ

m16l x ðmB =PrÞ

m16l z ðmB =PrÞ 2.233 2.247

Cr5B3-type

Pr5Si3 Pr5Si2Ge

0.002 0.100

2.247 2.279

0.004 0.095

Mn5Si3-type

Pr5Ge3

m4d x ðmB =PrÞ 0.337

m4d z ðmB =PrÞ 2.362

mx ðmB =PrÞ 0.315

6g

6g

mz ðmB =PrÞ 2.208

472

G. Tian et al. / Journal of Alloys and Compounds 788 (2019) 468e475

Fig. 4. Temperature dependence of the ZFC and FC magnetization of Pr5SiGe2,(a), Pr5Ge3 (a), Pr5Si2.5Ge0.5 (b), and Pr5Si2Ge (b), under a magnetic field of 50 Oe. The inset (i) represents the dM/dT curve for Pr5SiGe2.

materials can be calculated as follows [22],

TC ¼

X   3pn2 2 J sf ðg
1Þ2 JðJ þ 1Þ F 2kF Rij kEF isj

(1)

where n is the average number of conduction electrons per atom, k is Boltzmann's constant, EF and kF represent the Fermi energy and Fermi wave vector of the s-conduction electrons, Jsf is the s-f exchange integral, and F(2kFRij) is a spherical oscillating function of Rij,

FðxÞ ¼

x cos x
sin x x4

(2)

According to Callaway [23], the effective exchange interaction is long range, and decrease with R
3 (R is the interatomic distance of magnetic atoms). Table 4 lists the nearest neighboring inter-atomic distances for Pr atoms at different crystal sites in compounds Pr5Si3, Pr5Si2.5Ge0.5, and Pr5Si2Ge, which were calculated based on the Rietveld refinement results. The average interatomic distance R of Pr5Si3, Pr5Si2.5Ge0.5, and Pr5Si2Ge are calculated to be 3.472, 3.486,

and 3.499 Å, respectively, suggesting that the interatomic distances of Pr atoms in Pr5Si3-xGex compounds increase gradually as the Ge content increases. Therefore, the composition dependence of the Curie temperature in Pr5Si3-xGex system could not be explained simply by the difference of effective exchange interaction determined by the average interatomic distances of magnetic Pr atoms, which have also been observed in the Pr5Si4-xGex compounds [15]. For these compounds, the positive correlation of Tc with the Ge content can be caused by the increasing of MAE, as described in the DFT calculation part. The larger magneto-crystalline anisotropy not only leads to smaller saturation magnetic moments, but also has a negative effect on the disordered arrangement of magnetic moments as temperature rises, which could lead to a higher Tc. The isothermal magnetization curves (M-H) ranging from 38 to 68 K and 41e71 K were measured for the samples with x ¼ 0.5 and 1.0, respectively, and are shown in Fig. 5 (a) and (b). The temperature intervals between the isotherms are 3 K and the magnetic field varies between zero and 50 kOe. For the samples Pr5Si2.5Ge0.5 and Pr5Si2Ge, it can be seen that the magnetic behaviors are of typical ferromagnetic below 53 and 56 K, respectively. However, the magnetization is not fully saturated at 50 kOe. The calculated saturation magnetic moments of 1.39 mB and 1.30 mB per Pr atom for Pr5Si2.5Ge0.5 and Pr5Si2Ge were obtained by the extrapolation of high-field data to the origin at temperatures just below TC, far below the corresponding value of 2.21 mB from the DFT calculation for Pr5Si2Ge and the value of 3.65 mB of free Pr ion. The difference of the results between the static calculations and experimental magnetic properties is due to the large domain wall energy arising from magneto-crystal anisotropy, which can make the magnetization of different domains aligning along applied field harder. To further study the magnetic phase transition of Pr5Si2.5Ge0.5 and Pr5Si2Ge, the Arrott plots (M2 versus H/M) [24] are depicted in Fig. 5 (c) and (d), deduced from the M-H isotherms. Along with determining the critical temperature for the phase transition, Arrott plots also employed to analyze the nature of a phase transition. The presence of inflection points (S-shaped curve) or negative slopes in Arrott plots represents the negative contribution of some higher order terms in the Landau free energy expansion, which is indication of a first-order phase transition (FOMT). On the contrary, the positive slope and linear behavior near Tc often mean that the phase transition is a SOMT [25,26]. Fig. 5 (c) and (d) clearly reveals the occurrence of the second-order FM to PM phase transition near Tc ¼ 53 and 56 K for Pr5Si2.5Ge0.5 and Pr5Si2Ge, respectively. It can also be seen from Fig. 5 (a) and (b) that the MeH isotherms around TC with increasing and decreasing field are nearly identical, which also confirms the second order nature of the phase transitions near the magnetic ordering temperature. As shown in Fig. 4, different from the hexagonal compounds, Pr5Si3-xGex (x ¼ 0.5, 1.0) compounds with pure Cr5B3-type phase have relatively high magnetization at low temperature, and the changes of the magnetization are rather sharp near their Curie temperature, indicating that large magnetic entropy changes could be observed near the phase transition temperature, as detected in Pr5Si3 [7]. Therefore, the magnetocaloric effects of compounds Pr5Si3-xGex (x ¼ 0.5, 1.0) have been investigated in this paper. The isothermal entropy change, due to the change of the applied magnetic field from an initial value H ¼ 0 to a final value H was calculated from the isothermal magnetization curves by means of the following formula [27].

ðH 

DSM ðT; HÞ ¼ SM ðT; HÞ
SM ðT; 0Þ ¼ 0

vM vT

 H0

dH0

(3)

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Table 4 The nearest-neighbor inter-atomic distances (Å) in Pr5Si3-xGex (x ¼ 0, 0.5, and 1.0), Pr atoms that occupy Wyckoff positions 16l and 4c are denoted by Pr1 and Pr2, respectively. Pr5Si3

Pr5Si2.5Ge0.5

Pr5Si2Ge

atom

Near-neighbourgh

distance(Å)

atom

Near-neighbourgh

distance(Å)

atom

Near-neighbourgh

distance(Å)

Pr1

1 2 2 1 2 4 2 8

3.003 3.096 3.220 3.313 3.512 3.098 3.438 3.512

Pr1

1 2 2 1 2 4 2 8

2.981 3.144 3.219 3.290 3.536 3.072 3.447 3.536

Pr1

1 2 2 1 2 4 2 8

3.036 3.118 3.228 3.310 3.547 3.100 3.453 3.547

Pr2

Si2 Si2 Si1 Pr1 Pr2 Si2 Si1 Pr1

Pr2

Si2 Si2 Si1 Pr1 Pr2 Si2 Si1 Pr1

Pr2

Si2 Si2 Si1 Pr1 Pr2 Si2 Si1 Pr1

Fig. 5. The isothermal magnetization curves for Pr5Si2.5Ge0.5 (a) and Pr5Si2Ge (b) measured on field increase (solid squares, in black) and field decrease (solid triangles, in red), and the Arrott plots (M2 vs. H/M) of Pr5Si2.5Ge0.5 (c) and Pr5Si2Ge (d) with the temperature step of 3 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

which can be obtained from the well-known Maxwell relation. Using the magnetization data obtained at discrete values of the field and temperature, the calculations of DSM can be evaluated by the following expression [28] as a numerical approximation of Eq. (3).


DSM ¼

X i

1 ðMiþ1
Mi ÞDHi Tiþ1
Ti

(4)

where Mi is the magnetization at temperature Ti. The calculated results are plotted in Fig. 6. The maximum values of the magnetic entropy changes -DSM at DH ¼ 50 kOe are 9.3 and 7.7 J kg
1 K
1 for

Pr5Si2.5Ge0.5 and Pr5Si2Ge, respectively. Although the maximal values of -DSM for Ge doped Pr5Si3-xGex (x ¼ 0.5, 1.0) alloys are not as large as that of Pr5Si3 (11.6 J kg
1 K
1 at DH ¼ 50 kOe) [7], the temperature spans are rather broader. From the views of the potential prospect for applications in magnetic refrigeration, the temperature range in which the magnetic refrigerant materials can operate should also be considered. Furthermore, the relative cooling power (RCP), which represents the heat transferred between the cold and hot reservoirs in the ideal refrigeration cycle, is popularly used to describe the potential suitability of materials as working substance in magnetic refrigeration. According to the Wood and Potter method [29], the value of

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Fig. 6. Magnetic entropy change as a function of temperature for different applied magnetic fields in Pr5Si3-xGex (x ¼ 0.5, 1.0).

RCP can be calculated from the numerical equation, as follows

RCPðSÞ ¼ jDSM jMAX  dTFWHM

(5)

where dTFWHM is the full width at half maximum of the DSM -T curve. For Pr5Si2.5Ge0.5 and Pr5Si2Ge, the DSM spans in a wide temperature range and the dTFWHM approaches to 23 K and 24 K for the magnetic field changes of 50 kOe, respectively, much larger than that of Pr5Si3 (13 K, Ref. 7). Consequently, the RCP values for Pr5Si2.5Ge0.5 and Pr5Si2Ge are 213.9 J kg
1 and 184.8 J kg
1, are found to be higher than that of Pr5Si3 (162.4 J kg
1 at DH ¼ 50 kOe). As already mentioned above, the magnetization and maximum values of magnetic entropy changes decrease with the increase of Ge content in Cr5B3-type compounds Pr5Si3-xGex, while the dTFWHM increases with the doping of Ge. This could be caused by the appearance of larger MAE together with large domain wall energy in the compounds with more Ge content. On the one hand, the crystal field effect and the strong SO coupling may lead to smaller saturation magnetic moments of the magnetic ions and bulk polycrystalline, as demonstrated above, resulting in lower maximum values of entropy changes. On the other hand, the larger magneto-crystalline anisotropy can also have a negative effect on the disordered arrangement of magnetic moments as temperature rises, which could lead to a high Tc and broader working temperature span.

4. Conclusion We have investigated the structural and magnetic properties of the Pr5Si3-xGex alloys as function of composition of Si and Ge. With the increase of Ge content, the structures of Pr5SixGe3-x compounds varies from the tetragonal Cr5B3-type to the hexagonal Mn5Si3-type of structure, and the magnetic ordering temperatures accompanied with lattice parameters of the Cr5B3-type compounds increase as well. Large magnetic entropy changes -DSM are observed in the typical ferromagnetic compounds Pr5SixGe3-x (x ¼ 2.5, 2.0), which are accompanied with a second-ordered magnetic transition from the ferromagnetic to paramagnetic state. For a magnetic field change of 50 kOe, the maximum values of -DSM for them are 9.3 and 7.7 J kg
1 K
1, and the relative cooling power reach to 213.9 and 184.8 J kg
1, respectively. This indicates that the proper substitution of Ge for Si can not only adjust the Curie temperature of Pr5Si3, but also broaden the working temperature span of magnetic

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