7
Exploring the magneto-volume anomalies in Dy 2 Fe 17 with unconventional rhombohedral crystal structure Pablo A ´ lvarez-Alonso a , Pedro Gorria b,, Jose ´ L. Sa ´nchez Llamazares c , Gabriel J. Cuello d , Ine ´s Puente Orench d,e , Jorge Sa ´nchez Marcos f , Gasto ´ n Garbarino g , M. Reiffers h,i , Jesu ´s A. Blanco j a Departamento de Electricidad y Electro ´ nica, Universidad del Paı ´s Vasco, Barrio Sarriena, s/n, 48940 Leioa, Spain b Departamento de Fı ´sica, EPI, Universidad de Oviedo, 33203 Gijo ´ n, Spain c Divisio ´ n de Materiales Avanzados, Instituto Potosino de Investigacio ´ n Cientı ´fica y Tecnolo ´ gica (IPCyT), Camino a la presa San Jose ´ 2055, 78216 San Luis Potosı ´, Mexico d Institute Laue-Langevin, BP 156, 6 rue Jules Horowitz, 38042 Grenoble Cedex 9, France e Instituto de Ciencia de Materiales de Arago ´ n, CSIC–Universidad de Zaragoza, 50009 Zaragoza, Spain f Departamento de Quı ´mica-Fı ´sica, Universidad Auto ´ noma de Madrid, Cantoblanco, 28049 Madrid, Spain g European Synchrotron Radiation Facility (ESRF), BP 220, 6 rue Jules Horowitz, 38043 Grenoble Cedex, France h Faculty of Humanities and Natural Sciences, Presov University, ul. 17. novembra 1, SK-08116 Presov, Slovakia i Institute of Experimental Physics, Watsonova 47, SK-04001 Kos ˇice, Slovakia j Departamento de Fı ´sica, Universidad de Oviedo, Calvo Sotelo, s/n, 33007 Oviedo, Spain Received 6 April 2013; received in revised form 3 September 2013; accepted 18 September 2013 Available online 9 October 2013 Abstract We have synthesized the Dy 2 Fe 17 alloy with an unconventional crystal structure (R 3m space group). Neutron powder thermo-diffrac- tion and X-ray powder diffraction under high pressure (up to 15 GPa) show that the rhombohedral crystal structure is stable. Likewise, the alloy with the usual hexagonal crystal structure (P6 3 /mmc), the rhombohedral variant of Dy 2 Fe 17 compound, exhibits a collinear ferrimagnetic order below the Curie temperature (T C 363 K), with antiparallel mutual alignment of the Dy and Fe sublattices. Addi- tionally, we have observed two distinctive issues related to magneto-volume anomalies: (i) the pressure dependence of the cell volume at room temperature shows the existence of a critical pressure at which the compound is no longer ferrimagnetic; and (ii) the cell volume shows invar-like behaviour in a wide temperature range (2–290 K), with a minimum at T 380 K. The spontaneous volume magneto- striction reaches x S = 1.6 10 2 at 2 K that decreases to zero at T 500 K (1.4 T C ), which is associated with the existence of short- range magnetic correlations. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: X-ray and neutron diffraction; Rare earth/iron alloys; Crystal and magnetic structures; High pressure; Magneto-volume anomalies 1. Introduction R 2 Fe 17 compounds (R = rare earth) have the highest Fe content among the R–Fe series of binary intermetallic com- pounds [1]. Depending on the rare earth element these R 2 Fe 17 alloys exhibit a rich variety of magnetic behaviours (typical ferro-, antiferro- or ferromagnetic, and more com- plex magnetic orderings such as helimagnetism or fan mag- netic structures) [2,3]. Moreover, all of them display large magneto-volume effects related to the strong dependence of the magnetic exchange interaction on the Fe–Fe inter- atomic distances [2,4,5]. In addition, the interstitial R 2 Fe 17 X (X = C, N) families of compounds have attracted 1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.09.034 Corresponding author. Tel.: +34 985102899; fax: +34 985103324. E-mail address: [email protected] (P. Gorria). www.elsevier.com/locate/actamat Available online at www.sciencedirect.com ScienceDirect Acta Materialia 61 (2013) 7931–7937

Exploring the magneto-volume anomalies in Dy2Fe17 with unconventional rhombohedral crystal structure

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Available online at www.sciencedirect.com

www.elsevier.com/locate/actamat

ScienceDirect

Acta Materialia 61 (2013) 7931–7937

Exploring the magneto-volume anomalies in Dy2Fe17

with unconventional rhombohedral crystal structure

Pablo Alvarez-Alonso a, Pedro Gorria b,⇑, Jose L. Sanchez Llamazares c, Gabriel J. Cuello d,Ines Puente Orench d,e, Jorge Sanchez Marcos f, Gaston Garbarino g, M. Reiffers h,i,

Jesus A. Blanco j

a Departamento de Electricidad y Electronica, Universidad del Paıs Vasco, Barrio Sarriena, s/n, 48940 Leioa, Spainb Departamento de Fısica, EPI, Universidad de Oviedo, 33203 Gijon, Spain

c Division de Materiales Avanzados, Instituto Potosino de Investigacion Cientıfica y Tecnologica (IPCyT), Camino a la presa San Jose 2055,

78216 San Luis Potosı, Mexicod Institute Laue-Langevin, BP 156, 6 rue Jules Horowitz, 38042 Grenoble Cedex 9, France

e Instituto de Ciencia de Materiales de Aragon, CSIC–Universidad de Zaragoza, 50009 Zaragoza, Spainf Departamento de Quımica-Fısica, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid, Spain

g European Synchrotron Radiation Facility (ESRF), BP 220, 6 rue Jules Horowitz, 38043 Grenoble Cedex, Franceh Faculty of Humanities and Natural Sciences, Presov University, ul. 17. novembra 1, SK-08116 Presov, Slovakia

i Institute of Experimental Physics, Watsonova 47, SK-04001 Kosice, Slovakiaj Departamento de Fısica, Universidad de Oviedo, Calvo Sotelo, s/n, 33007 Oviedo, Spain

Received 6 April 2013; received in revised form 3 September 2013; accepted 18 September 2013Available online 9 October 2013

Abstract

We have synthesized the Dy2Fe17 alloy with an unconventional crystal structure (R3m space group). Neutron powder thermo-diffrac-tion and X-ray powder diffraction under high pressure (up to 15 GPa) show that the rhombohedral crystal structure is stable. Likewise,the alloy with the usual hexagonal crystal structure (P63/mmc), the rhombohedral variant of Dy2Fe17 compound, exhibits a collinearferrimagnetic order below the Curie temperature (TC � 363 K), with antiparallel mutual alignment of the Dy and Fe sublattices. Addi-tionally, we have observed two distinctive issues related to magneto-volume anomalies: (i) the pressure dependence of the cell volume atroom temperature shows the existence of a critical pressure at which the compound is no longer ferrimagnetic; and (ii) the cell volumeshows invar-like behaviour in a wide temperature range (2–290 K), with a minimum at T � 380 K. The spontaneous volume magneto-striction reaches xS = 1.6 � 10�2 at 2 K that decreases to zero at T � 500 K (�1.4 TC), which is associated with the existence of short-range magnetic correlations.� 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: X-ray and neutron diffraction; Rare earth/iron alloys; Crystal and magnetic structures; High pressure; Magneto-volume anomalies

1. Introduction

R2Fe17 compounds (R = rare earth) have the highest Fecontent among the R–Fe series of binary intermetallic com-pounds [1]. Depending on the rare earth element these

1359-6454/$36.00 � 2013 Acta Materialia Inc. Published by Elsevier Ltd. All

http://dx.doi.org/10.1016/j.actamat.2013.09.034

⇑ Corresponding author. Tel.: +34 985102899; fax: +34 985103324.E-mail address: [email protected] (P. Gorria).

R2Fe17 alloys exhibit a rich variety of magnetic behaviours(typical ferro-, antiferro- or ferromagnetic, and more com-plex magnetic orderings such as helimagnetism or fan mag-netic structures) [2,3]. Moreover, all of them display largemagneto-volume effects related to the strong dependenceof the magnetic exchange interaction on the Fe–Fe inter-atomic distances [2,4,5]. In addition, the interstitialR2Fe17X (X = C, N) families of compounds have attracted

rights reserved.

7932 P. Alvarez-Alonso et al. / Acta Materialia 61 (2013) 7931–7937

considerable attention because some of them are suitablefor being used as permanent magnets [6]. The interest inthese R2Fe17 intermetallics has been renewed due to themagneto-caloric properties shown by ferromagnetic Pr2

Fe17 and Nd2Fe17 compounds near room temperature [5,7].Two different crystal structures are found for R2Fe17

compounds [1]: (i) the Th2Zn17-type crystal structure(rhombohedral R3m space group), with a single R crystal-lographic site (6c) and four non-equivalent positions forthe Fe atoms (6c, 9d, 18f, 18h); and (ii) the Th2Ni17-typecrystal structure (hexagonal P63/mmc space group), withtwo R sites (2b, 2c) and four Fe sites (4f, 6g, 12j, 12k). Inthis R2Fe17 series the rhombohedral crystal structure isfound for R = Ce, Pr, Nd and Sm; the Gd2Fe17 and Tb2-

Fe17 compounds can crystallize in both crystal structuresdepending on the heat treatments [8–10], and the rest ofthe stable compounds (R = Dy, Er, Tm and Lu) showuniquely the hexagonal one. Sometimes the properties ofan intermetallic compound crystallizing in different struc-tures show differences in the magnetic properties due tothe anisotropy, such is the case of Tb2Co7 alloy, where astrong influence of symmetry element 1/m (mirror planeperpendicular to the main axis, present in the hexagonalvariant and absent in rhombohedral one) has been reported[11].

In particular, all the reported studies for the Dy2Fe17

alloy show exclusively the hexagonal phase [12], exhibitingcollinear ferrimagnetic ordering with all the magneticmoments lying in the basal plane, but opposite directionsbetween the Fe and Dy sublattices, and with a Curie tem-perature TC � 370 K [13–15]. However, it is possible tochange the structure type from Th2Ni17 to Th2Zn17 by add-ing either interstitial or substitutional C, Si, Al, Mn or Gaatoms [16,17], or alloying rare earths as RxR

01�xFe17

(R, R0 = rare earths) pseudobinary compounds [18,19].The addition of such elements provokes drastic changesof the Curie temperature, i.e. up to TC = 557 K (down toTC = 232 K) for the Ga(Mn)-substituted Dy2Fe14Ga3

(Dy2Fe12Mn5) rhombohedral compound [20,21].In this paper we report on the crystal and magnetic

structures and the magnetic properties, as well as the mag-neto-volume anomalies of the Dy2Fe17 compound withunconventional rhombohedral crystal structure by meansof neutron and X-ray powder diffraction experimentsunder different environments (temperature and high-pres-sure) and magnetization measurements.

2. Experimental methods and data analysis

Pieces of commercial (Goodfellow) Fe and Dy metalswere used (Fe 99.9% and Dy 99.98% rare-earth contentpurity [22]) for preparing Dy2Fe17 as-cast pellets by arcmelting. Ingots were re-melted three times to ensure goodstarting homogeneity. An excess of 5% of Dy was addedto compensate for the evaporation losses of this elementduring melting. As-cast alloys were wrapped in tantalumfoil and sealed under vacuum in a quartz ampoule and

annealed for 1 week at 1373 K. After annealing, the sam-ples were quenched in water.

Energy-dispersive X-ray spectroscopy (EDS) was usedto determine the average elemental chemical compositionof the alloy using a JEOL model JSM-6100 scanning elec-tron microscope. Several X-ray and neutron powder dif-fractometers with different wavelengths were used toensure that our conclusions are applicable to both the sur-face and the bulk. Room temperature X-ray powder dif-fraction patterns were collected on the Seifert (Cu Ka

radiation, k = 1.5418 A and Mo Ka radiation,k = 0.7107 A) and PANalytical’s X’Pert PRO (Cu Ka radi-ation) diffractometers. The neutron powder diffractionexperiments were carried out at the Institut Laue-Langevin(Grenoble, France). High-resolution neutron powder dif-fraction patterns were collected on the D2B (k = 1.59 A)instrument at T = 2 K and T = 400 K (above TC of thealloy), while a neutron thermo-diffraction experimentbetween 2 and 620 K was performed on the high-fluxD1B powder diffractometer (k = 2.52 A). We used a dou-ble-walled vanadium cylinder sample holder to reduce neu-tron absorption. The room temperature X-ray powderdiffraction patterns under hydrostatic pressure were mea-sured on the ID27 (k = 0.3738 A) beamline at ESRF (Gre-noble, France). The Dy2Fe17 polycrystalline powders werepressurized in a diamond anvil cell. Raw experimental datawere integrated using the FIT2D program to obtain one-dimensional diffraction patterns [23]. Analysis of the dif-fraction data based on both the Le Bail and Rietveld anal-ysis of the full profile was performed using the FullProfsuite package [24].

The magnetic measurements were performed with aQuantum Design SQUID magnetometer in the 2–390 Ktemperature range. The temperature dependence of themagnetization, M(T), was measured under a low appliedmagnetic field, l0H, of 5 mT. The isothermal magnetiza-tion curve as a function of the applied magnetic field,M(l0H), was measured at T = 2 K up to a maximumapplied magnetic field of 5 T.

3. Results and discussion

3.1. Crystal and magnetic structure analysis

The EDS analysis confirmed that the stoichiometry ofthe compound is 2:17, with an experimental uncertaintylower than 1%. In consonance with the EDS spectrum,we satisfactorily indexed the Bragg reflections for the roomtemperature X-ray powder diffraction patterns (see Fig. 1aand b) based on a rhombohedral Th2Zn17-type crystalstructure. Attempts to fit the patterns using the hexagonalTh2Ni17-type crystal structure led to unsatisfactory results(see Fig. 1c).

The analysis of the high-resolution neutron powder dif-fraction patterns gives similar results. The patterns col-lected on D2B at two different temperatures (2 and400 K) are depicted in Fig. 2 together with the corresponding

0

5000

10000(a)Cu K

0

150

300

1.5 2 2.5 3 3.5 4

Inte

nsit

y (c

ount

s)

d (Å)

(b)Mo K

0

5000

10000

2 2.25 2.5In

tens

ity

(cou

nts)

d (Å)

(c)

Cu K

Fig. 1. Observed (dots) and calculated (solid line) conventional X-raypowder diffraction patterns collected at room temperature with Cu (a) andMo (b) radiation, respectively. The vertical bars indicate the position ofthe Bragg diffraction reflections; the first row corresponds to therhombohedral Th2Zn17-type crystal structure, and the second row to aa-Fe impurity. The observed-calculated difference is depicted at thebottom of each figure. (c) Fit of the central region of the pattern (Curadiation) to the hexagonal Th2Ni17-type structure.

0

200

400 T = 400 K

Inte

nsit

y (c

ount

s)

0

200

400

1 2 3 4 5

d (Å)

T = 2 K

Fig. 2. Observed (dots) and calculated (solid line) high-resolution neutronpowder diffraction patterns collected at T = 400 K and T = 2 K. Thevertical bars indicate the position of the Bragg reflections; the upper rowscorrespond to Dy2Fe17 (nuclear and magnetic reflections in the case ofT = 2 K), and those at the bottom are related to a a-Fe impurity (nuclearand magnetic reflections). The observed–calculated difference is depictedat the bottom of each figure.

P. Alvarez-Alonso et al. / Acta Materialia 61 (2013) 7931–7937 7933

Rietveld fit. The crystallographic information was obtainedfrom the Rietveld refinement of the high-resolution neu-

tron powder diffraction pattern collected at T = 400 K,because the compound is in the paramagnetic state at thistemperature (see below for details about the determinationof the Curie temperature). As starting values, we used thosefor the atomic positions found from the fit of the X-raypowder diffraction patterns.

Table 1 summarizes the cell parameters (a comparisonwith reported data for the hexagonal Dy2Fe17 compoundis included), and Table 2 the Dy and Fe atomic coordinates(labels correspond to those used in the International Tablesfor Crystallography [25]). Furthermore, we investigated thetemperature dependence of the crystal structure by meansof an in situ neutron thermo-diffraction experiment inorder to check whether a structural transition to theconventional Th2Ni17-type hexagonal structure occurs inDy2Fe17; neither traces of the hexagonal variant norchanges in the crystal structure were detected.

The transition from the magnetic ordered to the para-magnetic state occurs at TC = 363 ± 2 K and it has beendetermined from the thermo-magnetization measurementsunder a low applied magnetic field (see inset of Fig. 3).The value of TC is close to that reported for the hexagonalcompound, TC = 370–380 K (see Table 1) [20,26]. Similardifferences between the Curie temperatures have beenobserved for other 2:17 compounds exhibiting both crystal-line variants [9,27,28].

The magnetic structure of the Dy2Fe17 compound wasdetermined from the neutron powder diffraction patternscollected at T = 2 K. Although no new peaks weredetected, the intensity of several peaks largely increasedwith respect to those in the paramagnetic state (see theregion for d < 2 A in Fig. 2), which results in a propagationvector k = (0, 0,0). The magnetic moments of both atomicspecies lie on the basal plane, being those of the Dy-sublat-tice antiparallel to the Fe moments, giving rise to a collin-ear ferrimagnetic structure.

The refinement of the magnetic structure was conductedconstraining the Fe magnetic moments of the four differentcrystallographic sites to have the same magnitude. The esti-mated Dy magnetic moment [10.1(1) lB] is close to themaximum attainable value (10 lB) for the Dy3+ free ion(i.e. 10 lB) predicted using Hund’s rules, whereas the Femagnetic moments [lFe = 2.0(1) lB] are similar to thoseof other R2Fe17 compounds [10,29]. We calculated the totalmagnetic moment of Dy2Fe17 subtracting the contributionof both sublattices due to the ferrimagnetic character of thecompound [30]:

lTotalDy2Fe17

¼ lTotalFe � lTotal

Dy ¼X17

i¼1

lFei�X2

i¼1

lDyið1Þ

The total magnetic moment at T = 2 K is 13.8(2) lB/f.u.[equivalent to MS = 60.4(2) A m2 kg�1], which is somewhatlower than the values reported for the hexagonal com-pound (see Table 1). To estimate the value for the low tem-perature spontaneous magnetization, MS, of thecompound, we used an approach-to-saturation law [31]

Table 1Comparative data of the unit cell parameters and volume at T = 400 K, Curie temperature and the total magnetic moment of each sublattice and of themagnetic unit cell at 2 K, together with the spontaneous magnetostriction at 2 K corresponding to the hexagonal and the rhombohedral variants ofDy2Fe17.

Crystal Structure Ref. a (A) c (A) V (A3) TC (K) lDy (lB) lFe (lB) lTOT (lB/f.u.) xS

Rhombohedral This work 8.496(1) 12.412(1) 775.83(1) 363(2) 10.1(1) 2.0(1) 13.8(2) 1.6(1)�10�2

Hexagonal [45] 8.455** 8.325** 515.4** 370 16.7 1.22 � 10�2

Hexagonal [12] 8.438 8.296 511.5 380 9.9 2.1 15.9Hexagonal [20] 8.483 8.251 514.2 370 14.1Hexagonal [21,47] 8.46 8.33 516.3 370(4) 10* 2.2(1) 16.6(1)Hexagonal [26] 8.461(1) 8.306(1) 515.02(1) 375(4)Hexagonal [48] 8.467 8.312 516.05 371 16.0Hexagonal [49,50] 8.455 8.309 514.4 370 10* 2.14 16.38Hexagonal [51] 8.464 8.307 515.4 395 10* 2.2 17.1Hexagonal [52] 8.51(5) 8.33(5) 522.4

Magnetic R-factor: 5.0.* Value estimated by the authors (i.e. not measured).** At T = 300 K.

Table 2Atomic coordinates for each crystallographic site obtained from therefinement of the high-resolution neutron powder diffraction collected atT = 400 K.

Atomic site x y z

Dy-6c 0.000 0.000 0.343(1)Fe-6c 0.000 0.000 0.098(1)Fe-9d 0.500 0.000 0.500Fe-18f 0.292(1) 0.000 0.000Fe-18h 0.167(1) 0.334(2) 0.489(1)

The reliability factors of the refinement were as follows: Rp = 5.2,Rwp = 6.7, Rexp = 5.4, Bragg R-factor RB = 3.9, and RF = 2.5.

0

20

40

60

0 1 2 3 4 5

M (

Am

2 kg-1

)

0H (T)

T = 2 K

0

1

2

3

200 300 400

M (

A m

2 kg-1

)

T (K)

0H = 5 mT

TC

= 363 K

Fig. 3. Magnetic field dependence of the magnetization measured atT = 2 K. Inset: temperature dependence of the low-magnetic fieldmagnetization.

7934 P. Alvarez-Alonso et al. / Acta Materialia 61 (2013) 7931–7937

to fit the high-magnetic-field region of the M(H) curvemeasured at T = 2 K (see Fig. 3), using the followingequation:

M ¼ MS 1� b

H 2

� �þ v0H ð2Þ

From the fit, we obtained a value of MS = 61.7(2)A m2 kg�1 [14.1(2) lB/f.u.], in good agreement with thevalue found from neutron diffraction. For the hexagonalphase an MS value of over 66.1 A m2 kg�1 (15.1 lB/f.u.)has been reported (see Table 2). Note that the M(l0H)curve presents a considerable slope even under appliedmagnetic field values above 5 T, thus indicating that thesample is far from being magnetically saturated. A similartrend has also been observed in the hexagonal Dy2Fe17,which at low temperature (T = 4.2 K) is in an unsaturatedstate until l0H > 35 T [30]. This finding is a clear signatureof the existence of strong magneto-volume anomalies,which are also present in other R2Fe17 compounds[2,4,10,29].

3.2. Magneto-volume anomalies

We estimated the pressure dependence of the crystal cellparameters and the unit cell volume from the synchrotron-light powder diffraction patterns collected under highhydrostatic pressure. Fig. 4a and b shows the X-ray pow-der diffraction patterns at 0 and 15 GPa, respectively.Upon increasing pressure, the diffraction peaks shift con-tinuously to higher angles, indicating the pressure-inducedcontraction of the cell parameters. The observed peaks at15 GPa belong to the rhombohedral Th2Zn17-type crystalstructure, pointing out the absence of any structural phasetransition. In Fig. 4c we show the normalized (to the valueat P = 0) unit cell parameters of Dy2Fe17 as a function ofthe applied hydrostatic pressure: both lattice parametersdecrease unceasingly, the lattice contraction being slightlyanisotropic (the difference between both a(P) and c(P)curves is well above experimental uncertainty); similaranisotropic behaviour in the pressure and temperaturedependence of the cell parameters has been reported inthe case of Lu2Fe17 compound [32].

As occurs with hexagonal R2Fe17 compounds (includingDy2Fe17) we could expect the rhombohedral Dy2Fe17 to

Fig. 4. Observed (dots) and calculated (solid line) X-ray powder diffraction patterns for Dy2Fe17 collected at P = 0 GPa (a) and P = 15 GPa (b). Theobserved–calculated difference is depicted at the bottom of each figure. (c) Pressure dependence of the cell parameters normalized to the value obtained atP = 0 GPa of Dy2Fe17 at room temperature. (d) Least-squares fit of the P(V) curve using the Birch– Murnaghan equation of state.

8.42

8.46

8.50

12.34

12.38

12.42

a c

a (Å

)c

(Å)

757

761

765

769

773

0 200 400 600

V (

Å3 )

Temperature (K)

Fig. 5. Temperature dependence of the experimental a and c cellparameters. The solid lines correspond to the extrapolation of a(T) andc(T) from the paramagnetic region down to low temperature. At thebottom of the figure the temperature dependence of the experimental unitcell volume, V(T), is displayed. The solid line corresponds to the non-magnetic contribution to the volume (see text for details).

P. Alvarez-Alonso et al. / Acta Materialia 61 (2013) 7931–7937 7935

exhibit similar magneto-volume anomalies in the ferrimag-netic state [29]. One such anomaly is the negative pressuredependence of the Curie temperature [33], because underhydrostatic pressure the magnetic order is destabilized, giv-ing rise to a significant decrease in the Curie temperature(dTC/dP � �40 K GPa�1 for Invar compounds, such asR2Fe17, Fe65Ni35 or FeZrB metallic glasses) [33–37]. There-fore, the cell volume variation under pressure is larger inthe ferrimagnetic phase than in the paramagnetic one[32]. Insomuch as the patterns were collected at room tem-perature (i.e. below TC at P = 0), we expect that the criticalpressure, PC, at which TC(PC) is just below RT, must be�3–4 GPa. Thus, we separate the cell volume vs. pressuredata (plotted in Fig. 4d) in two different regions [35,36]and fitted to a third-order Birch–Murnaghan equation ofstate (with dB/dP = 4) [38,39] to estimate the bulk moduluscorresponding to the paramagnetic state, BPM, and to theferrimagnetic phase, BFIM. We observe a cut-off of thosecurves resulting from better refinements in the immediacyof P = 4 GPa; the estimated values for the bulk modulusare BPM = 116 ± 2 GPa and BFIM = 99 ± 2 GPa, similarto those reported in other R2Fe17 compounds [40].

Fig. 5 shows the temperature dependence of the cellparameters, a(T) and c(T), together with that of the unitcell volume, V(T).

Complementary to that found in the room temperatureX-ray diffraction experiments under hydrostatic pressure,we also observe magneto-volume anomalies in the temper-ature dependence of the cell parameters: (i) a continuousand moderate decrease of the crystalline cell along thec-axis on heating from 2 up to 380 K; (ii) a slight increaseof the basal-plane cell parameters up to T = 300 K

Fig. 6. Normalized spontaneous magnetostriction, xS=x�S, as a functionof the normalized temperature, T/TC, compared with behaviour of thesquare of the normalized Fe sublattice magnetic moment, (lFe)

2/(l�Fe)2.

The coincidence of both curves up to T/TC � 0.8 suggests that bothnormalized magnitudes follow a similar dependence (see text for details).

7936 P. Alvarez-Alonso et al. / Acta Materialia 61 (2013) 7931–7937

followed by a small diminution; and (iii) a minimum ofboth a and c parameters in the immediacy of the Curie tem-perature. These anomalies give rise to an Invar-like behav-iour of the unit cell volume up to T � 300 K, due to thecompensation of the moderate contraction along the c-axiswith the small increase in the basal-plane parameters, andto a minimum near TC, as both parameters also have aminimum. However, for T P 500 K (�1.4 TC) the cellparameters display Gruneisen-like behaviour. Likewise, inthe rest of the R2Fe17 family [10,29], the strong dependenceof magnetic exchange coupling on the interatomic Fe–Fedistances are at the origin of those magneto-volume anom-alies in the Dy2Fe17 compound [4,32,41].

The solid lines in Fig. 5 represent the non-magnetic con-tribution to the cell parameters and to the unit cell volumeobtained through the extrapolation of the experimentala(T), c(T) and V(T) curves, from the high temperature(T > 500 K) paramagnetic region down to low temperature,using the Gruneisen relation [42–44]. With the aim of esti-mating the non-magnetic contribution we used the valueof the bulk modulus BPM = 116 ± 2 GPa obtained fromthe fit of the pressure dependence of the unit cell volumein the paramagnetic region. The value for the Debye tem-perature (HD = 450 K) has been taken from literature,where similar values for all the R2Fe17 compounds areassumed [45,46]. The Gruneisen parameter, C = 1.9, andthe non-magnetic volume at zero-temperature,V0 = 759.5 A3, result from the fit of the V(T) curve in theparamagnetic zone. The value of C is similar to thosereported for several R2Fe17 compounds [29]. The relativedifference between the experimental and the extrapolated(non-magnetic) values for the cell parameters and the unitcell volume (see Fig. 5) defines the linear (ka and kc) and vol-ume (xS) spontaneous magnetostriction. At low tempera-ture the linear and volume spontaneous magnetostrictionare positive, because the experimental values of the unit cellparameters are larger than those extrapolated (non-mag-netic) using the Gruneisen relation, and their correspondingmaxima ðkmax

a ¼ 0:5� 10�2; kmaxc ¼ 0:7� 10�2;xmax

S ¼1:6� 10�2Þ occur at T = 2 K. These results are�30% largerthan those already reported for the hexagonal Dy2Fe17

phase (xS = 1.22 � 10�3) [45]. In Fig. 6, we plot both xS

and the square of the total magnetic moment of the Fe sub-lattice (lFe)

2 (which has been taken from the reported datafor Er2Fe17 [29]) normalized to their respective values at 2 K(x�S and l�Fe, referred in the figure to xS=x�S and (lFe)

2/(l�Fe)

2, respectively) as a function of T/TC.Up to T/TC � 0.8, xS=x�S follows almost the same trend

as the square of the Fe sublattice total magnetic moment(red solid line in Fig. 6). Therefore, the spontaneous mag-netostriction is almost completely determined by thebehaviour of the Fe magnetic moment. However, due tothe existence of short-range magnetic correlations thespontaneous volume magnetostriction does not vanish atTC, but falls down to zero values at �1.4 TC

(T � 500 K). This comportment is analogous to thatrecently observed in the hexagonal Er2Fe17 alloy [29].

4. Summary

In the present investigations, combining neutronthermo-diffraction and X-ray diffraction under high pres-sure the magneto-volume anomalies of rhombohedral Dy2-

Fe17 have been explored. From the experimental results thevalues of the bulk modulus in the paramagnetic(116 ± 2 GPa) and ferrimagnetic (99 ± 2 GPa) states, andthe magnitude of the spontaneous magnetostriction(1.6 � 10�2 extrapolated at T = 0 K) have been estimated.We show that the unconventional rhombohedral Th2Zn17-type variant of the binary Dy2Fe17 intermetallic compoundis stable without any crystalline structural change over thewhole temperature (up to 620 K) and pressure (up to15 GPa) ranges investigated. The magnetic structure ofthe rhombohedral Dy2Fe17 is ferrimagnetic with two ferro-magnetic sublattices, one of the rare earth with magneticmoments antiparallel to those of the Fe sublattice, and witha Curie temperature (TC = 363 K) slightly lower than thatof the hexagonal phase.

Acknowledgements

Financial support from Spanish MICINN (projectMAT2011-27573-C04) and Mexican CONACYT (projectCB-2010-01-156932) is acknowledged. J.L. SanchezLlamazares also acknowledges the support received fromLaboratorio Nacional de Investigaciones en Nanocienciasy Nanotecnologıa (LINAN, IPICyT). M. Reiffers acknowl-edges the VEGA 2/0070/12 contract. The CEX Nanofluidas the Centre of Excellence SAS, the structural EXTREM26220120005, NANOFLUID 26220120021 and the SCTsat the University of Oviedo are also acknowledged. Wethank ILL and CRG-D1B as well as ESRF for allocatingneutron and synchrotron beamtime, respectively. The USSteel Kosice, s.r.o, sponsored the liquid nitrogen for themagnetic measurements.

P. Alvarez-Alonso et al. / Acta Materialia 61 (2013) 7931–7937 7937

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