Magnetic phase transitions in TbRhSn

Magnetic phase transitions in TbRhSn

Journal of Magnetism and Magnetic Materials 261 (2003) 369–376 Magnetic phase transitions in TbRhSn S. Barana,*, M. Ba"andab, P. Fischerc, W. Sikorad...

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Journal of Magnetism and Magnetic Materials 261 (2003) 369–376

Magnetic phase transitions in TbRhSn S. Barana,*, M. Ba"andab, P. Fischerc, W. Sikorad, A. Szytu"aa ! Poland M. Smoluchowski Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow, b ! ! Poland H. Niewodniczanski Institute of Nuclear Physics, ul. Radzikowskiego 152, 31-342 Krakow, c Laboratory for Neutron Scattering, ETH Zurich & Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland d ! Poland Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, al. Mickiewicza 30, 30-059 Krakow, a

Received 6 November 2002

Abstract The magnetic ordering of TbRhSn, crystallizing in the hexagonal ZrNiAl-type structure, has been investigated by high-resolution neutron diffractometry in the temperature range between 1.7 and 23.9 K. Tb in TbRhSn has been found to order magnetically below 19 K. Its magnetic structure corresponds to propagation vector k~ ¼ ½12; 0; 12; and by a new group-theoretical analysis is shown to be based on the two irreducible representations t2 and t4 : This model also explains the change of magnetic ordering at Tt ¼ 11 K: New aspects of bulk magnetic measurements are also reported. Moreover, our results are compared with previously published data. r 2003 Elsevier Science B.V. All rights reserved. PACS: 75.25.+z; 75.30.Kz; 75.50.Ee Keywords: Rare earth compounds; Magnetic structure; Neutron diffraction; Phase transition

1. Introduction The ternary equiatomic rare earth stannides have been attracting researchers’ interest for many years. This is due to the observed variety of their magnetic properties at low temperature [1]. The TbRhSn compound crystallizes in the hexagonal ZrNiAl-type structure [2]. The magnetic susceptibility measurements revealed the presence of an antiferromagnetic ordering below TN ¼ 18:4 K [3]. An additional anomaly was observed at 6.2 K. The paramagnetic Curie temperature was found to be +4 K and the effective magnetic moment was found to be equal to 9:9mB : *Corresponding author. Tel.: +48-12-632-48-88; fax: +4812-633-70-86. E-mail address: [email protected] (S. Baran).

The neutron diffraction studies of TbRhSn are reported in Ref. [4]. A magnetic structure model with magnetic moments forming a triangular configuration was applied to describe magnetic structure below the Ne! el temperature (propagation vector k~ ¼ ½12; 0; 12). No extra magnetic phase transition was detected. The main subject of this publication is to verify the results published in Ref. [4] by means of a highresolution neutron diffractometry.

2. Experiment The sample was obtained by arc melting in argon atmosphere with the use of the respective elements (minimum purity 3N), and was annealed

0304-8853/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-8853(02)01485-3

S. Baran et al. / Journal of Magnetism and Magnetic Materials 261 (2003) 369–376 0.0012

0.00012

χ'

Tt = 10.7 K

χ', χ'' [emu/g]

0.00008 0.0008

0.00004 0.0004

TN = 18.8 K 0.00000

10* χ''

dχ' / dT [emu/gK]

0.0000 -0.00004 4

8

12

16

20

24

28

Temperature [K]

Fig. 1. AC magnetic susceptibility of TbRhSn recorded at f ¼ 110 Hz and H ¼ 1 Oe: w0 is the in-phase (real) while w00 the outof-phase (imaginary) component of magnetic susceptibility.

5

5

35 30

4

Hcr [k Oe]

at 800 C for one week. X-ray diffraction (CuKa radiation) confirmed that the sample crystallizes in the ZrNiAl-type structure. The determined lattice parameters were in reasonable agreement with the data published previously [2,4]. AC magnetic susceptibility wAC ¼ w0  iw00 ; where w0 is the in-phase (real) and w00 the out-ofphase (imaginary) component, was measured by means of the Lake Shore 7225 susceptometer with the frequency of the driving field of 110 Hz and the amplitude of 1 Oe. Magnetization curves MðHÞ at several selected temperatures in applied magnetic field up to 56 kOe were measured with the DC option of the same instrument using the extraction method. Isothermal magnetization curves were recorded for zero-field-cooled (ZFC) samples. Neutron diffraction patterns were recorded in the high-intensity mode on the high-resolution diffractometer HRPT [5] at the Swiss spallation neutron source SINQ of Paul Scherrer Institute at Villigen, Switzerland. The incident neutron wave( Under He gas atmosphere the length was 1.8857 A. powder sample of TbRhSn was enclosed in a cylindrical V container of 5 mm diameter, filled to about 15 mm. The data were collected at several temperatures between 1.7 and 23.9 K, using an ILL-type cryostat. The neutron diffraction data were analyzed with the use of the Rietveld program FULLPROF [6].

Magnetization [µB]

370

4 25 20

3

3

15 0

5

2

T [K]

10

2.3 K 3.2 K 5.0 K 5.9 K 7.0 K 8.3 K 8.9 K 12.7 K 19.4 K

15

1

0

2

1

0 0

10

20

30

40

50

Magn. Field [kOe]

3. Bulk magnetic data The temperature dependence of the AC susceptibility is presented in Fig. 1. The data show a flat maximum for w0 and a very weak imaginary component w00 (less than 1% of w0 ) present in the ordered state. From the temperature derivative of w0 one can determine two characteristic temperatures of the investigated compound. The transition from the paramagnetic to the antiferromagnetic state occurs at TN ¼ 18:8 K; where dw0 =dT ¼ 0: The temperature Tt ¼ 10:7 K of the distinct change in the w0 slope may be due to some reorientation of the magnetic moments in connection with the anisotropy change. The out-of-phase component, which disappears at TN ; suggests a presence of some uncompensated moment in the

Fig. 2. Magnetization of TbRhSn per one Tb ion at several temperatures between 2.3 and 19.4 K. The inset shows the temperature dependence of critical magnetic field.

entirely antiferromagnetic structure. However, its value is probably too small to be detected by other methods. The temperature dependence of the reciprocal magnetic susceptibility of TbRhSn is linear above 60 K. The fit to the experimental data yielded the paramagnetic Curie temperature yp ¼ 31 K and the effective magnetic moment meff ¼ 9:62 mB : The value of meff is close to the free Tbþ3 ion value (9:72 mB ). Magnetization curves recorded at several temperatures are presented in Fig. 2. In the applied

S. Baran et al. / Journal of Magnetism and Magnetic Materials 261 (2003) 369–376

field the compound undergoes a metamagnetic-like transition, best seen for the lowest temperatures. The critical fields, determined from the susceptibility maxima and given in the inset, are high (33 kOe at T ¼ 2:3 K) but decrease with the rise of temperature. Above T ¼ 13 K no anomaly is seen. At the highest accessible field the magnetization (the magnetic moment per one Tb-ion) is less than half of its saturation value gJ½JðJ þ 1Þ1=2 ¼ 9:72 mB :

4. Crystal structure Previous X-ray [2] and neutron diffraction studies [4] revealed that the title compound exhibits the hexagonal ZrNiAl-type crystal structure (space group P6% 2m) with atoms at the following sites: 3 Tb atoms at 3(g) site: xTb ; 0; 12 0; xTb ; 12 x% Tb ; x% Tb ; 12; 3 Sn atoms at 3(f) site: xSn ; 0; 0 0; xSn ; 0 x% Sn ; x% Sn ; 0; 2 Rh atoms at 2(c) site: 1 2 2 1 3; 3; 0 3; 3; 0; 1 Rh atom at 1(b) site: 0; 0; 12: The high-resolution diffractometry allowed to determine the lattice parameters very precisely at temperatures below 25 K. The values of the refined lattice and positional parameters obtained from the neutron data collected above the ordering temperature are listed in Table 1. The neutron diffraction pattern of TbRhSn at 23.9 K is shown in Fig. 3. The peaks originating from an unidentified impurity were found within 2y range from 46 to 50 : This region was excluded from the refinement.

371

5. Magnetic structure There are three terbium ions in elementary unit cell. These ions occupy the 3(g) sites and are located at the following positions: Tb1 ion at 0:5936; 0; 12 Tb2 ion at 0:4064; 0:4064; 12 Tb3 ion at 0; 0:5936; 12 The neutron diffractogram of TbRhSn recorded at 1.7 K is shown in Fig. 4. All magnetic reflections could be indexed by assuming an antiferromagnetic order described by a propagation vector k~ ¼ ½12; 0; 12: The best fits were obtained for two magnetic structure models with all magnetic moments within the basal plane. In the first model, magnetic moments on ions Tb1 and Tb2 are of the same magnitude while the magnetic moment on ion Tb3 is smaller. The projection of this magnetic structure on the basal plane is shown in Fig. 5. In the second model all magnetic moments are of the same magnitude (the orientations of magnetic moments remain the same as for the first model). The parameters of the magnetic structure of TbRhSn at 1.7 K are summarized in Table 2. The relative intensities of magnetic peaks in the neutron diffraction pattern of TbRhSn depend on temperature. It is clearly seen in Fig. 6 (for instance when the intensities of magnetic peaks at 2y ¼ 16:6 and 20:4 are compared). The change in the relative magnetic intensities is due to the relative change of the magnetic moments located at different positions. Fig. 7 shows the temperature dependence of the magnetic moments located at different positions (the data originate from refinements with the use of the first magnetic structure model). The temperature of the transition between two different magnetic structures can be estimated to be equal to Tt ¼ 11 K:

Table 1 Structural parameters of TbRhSn and residuals for profile and integrated intensities from refinement, based on the data recorded at 23.9 K ( a (A)

( c (A)

c=a

( ) V (A

xTb

xSn

w2

RBragg (%)

7.5344(2)

3.7791(1)

0.50158(2)

185.79(1)

0.5936(4)

0.2614(4)

2.70

5.64

3

S. Baran et al. / Journal of Magnetism and Magnetic Materials 261 (2003) 369–376

372

8000

Yobs. Ycal. Yobs.-Ycal.

6000

Counts

4000

2000

0

|

|

|

|

|

| |

| |

| |

|

| |

| |

70

80 90 2θ [deg.]

|| ||

|| ||

| ||

|| |

||| |||

| |||

120

130

140

||

-2000 10

20

30

40

50

60

100

110

150

160

Fig. 3. Neutron diffraction pattern of paramagnetic TbRhSn at 23.9 K together with Rietveld fit and difference plot. Vertical ticks indicate the positions of nuclear reflections.

8000

Yobs. Ycal. Yobs.-Ycal.

Counts

6000

4000

2000

0

| |

|

| | |

| |

| | |

| | | | | | | | | | | | | || || || || |

| | | | | | | | || || || || || || || || | | |

| | || | || || | | | | | | || || || || ||

| || || | ||| ||

|||

|| ||| |||

-2000 10

20

30

40

50

60

70

80 90 2θ [deg.]

100

110

120

130

140

150

160

Fig. 4. Neutron diffraction pattern of antiferromagnetic TbRhSn at 1.7 K together with Rietveld fit (the first model — see main text for details) and difference plot. Vertical ticks indicate the positions of nuclear and magnetic reflections, respectively.

6. Symmetry analysis It is from the theory of group and representations that there follows the idea that the magnetic ~fk~L g structure, as an axial vector function S localized on the set of equivalent positions of a given space group, may be presented as a linear ~ fk~L g of the combination of the basic vectors (BV) C n;l

irreducible representations (IRs) of this space group ~fk~L g ¼ S

lk~ j X ln X X

~

~

fk L g ~ fk L g Cn;l C n;l ;

L¼1 n¼1 l¼1

where L labels the arms of the star for a given propagation vector k~L ; n labels the IRs, l labels

S. Baran et al. / Journal of Magnetism and Magnetic Materials 261 (2003) 369–376

373

20000 1.7 K

8.9 K

b 15000

10.0 K

11.1 K

Fig. 5. Magnetic structure of TbRhSn at 1.7 K (the first model — see main text for details). The adjacent (0 0 1) planes are coupled antiferromagnetically.

Counts

a

12.2 K 10000 13.9 K

Table 2 Parameters of the magnetic structure of TbRhSn at 1.7 K Magnetic structure model Propagation vector m1 ; m2 ðmB Þ m3 ðmB Þ f1 n (deg) f2 n (deg) f3 n (deg) w2 Rmagn (%) n

First

Second ½12; 0; 12

9.09(8) 6.64(19)

15.0 K

5000

8.32(4) 8.32(4) 180 60 60

5.54 9.80

18.9 K

23.9 K 0

5.64 8.69

f is an angle between the a-axis and the magnetic moment.

~

17.0 K

fk L g the dimensions of a given IR and Cn;l are the coefficients which have to be found experimen~ fk~L g follows form the theory of tally. The form of C n;l group and representations. We used the program ~ fk~L g : MODY [7] for calculating C n;l In case of the space group G ¼ P6% 2m and the propagation vector k~ ¼ ½12; 0; 12 the Gðk~Þ group is a subgroup of G: The positions 3ðgÞ; in the relation to the Gðk~Þ; split into two independent orbits. The positions Tb1 and Tb2 belong to the first orbit while the position Tb3 belongs to the second orbit. This means that the magnetic structure on these two different orbits may order independently. In the decomposition of the magnetic representation for the positions of the first orbit, the one-dimensional IRs t1 ; t2 ; t3 and t4 are present (IRs are labeled according to Kovalev [8]). IRs t1 and t3 appear once while t2 and t4 appear twice.

10

20

30

40 2θ [deg.]

50

60

70

Fig. 6. The temperature dependence of the TbRhSn neutron diffraction pattern. Note the slight change towards higher scattering angles of the first magnetic Bragg peak at 11.1 and 12.2 K.

In the decomposition of the magnetic representation for the positions of the second orbit, the IRs t2 ; t3 and t4 are present (all of them appear once). The BV are given in Table 3. The magnetic structure for which the best fit to the experimental data was obtained (see Section 5) may be described with a model structure which is a linear combination of BVs of two IRs (t2 "t02 "t4 "t04 ). For the first orbit the mixing coefficients follow the relation C2 ¼ C4 ¼ ~ðTb1 þ ~ C20 ¼ C40 : Then S t Þ ¼ ½2C2 ; 0; 0expðik~ ~ðTb2 þ ~ ~ t Þ and S t Þ ¼ ½0; 2C2 ; 0expðik~ ~ t Þ; where ~ t is a lattice translation. For the second orbit a linear combination of the BV of the same IRs (t2 "t4 ) is required. The mixing coefficients follow ~ðTb3 þ ~ the relation C* 2 ¼ C* 4 : Then S tÞ ¼ ½2C* 2 ; 2C* 2 ; 0expðik~ ~ t Þ: In this case all Cn and C* n are real, positive numbers.

S. Baran et al. / Journal of Magnetism and Magnetic Materials 261 (2003) 369–376

374

10

µ1,2 µ3

Magnetic moment [µΒ]

8

6

4

2

0

0

2

4

6

8 10 12 Temperature [K]

14

16

18

20

Fig. 7. Temperature dependence of the magnetic Tb moments of TbRhSn located at different positions. The values were obtained from Rietveld refinement. Table 3 BV of the IR-s for the first and second orbit IR

t1 t2 t02 t3 t4 t04

First orbit

Second orbit

Tb1

Tb2

Tb3

[0,0,1] [1,0,0] [0,1,0] [0,0,1] [1,0,0] [0,1,0]

[0,0,1] [1,1,0] [0,1,0] [0,0,1] [1,1,0] [0,1,0]

— [0,1,0] [0,0,1] [2,1,0]

The similar fit (Rmagn ¼ 8:80%) was obtained for the magnetic structure model which involved the BV of only one representation (t2 "t02 in case of the first orbit and t2 in case of the second orbit). The magnetic moments at temperature T ¼ 1:7 K were equal to 10:09ð4Þ mB for the moments on the first orbit and to 0:05ð5Þ mB for the moments on the second orbit. This magnetic structure model was rejected due to non-physical values of the magnetic moments.

7. Discussion The splitting of the 3ðgÞ position into two independent orbits allows the different tempera-

ture dependences of the magnetic moments located on different orbits. In fact, this is the case of TbRhSn (see Fig. 7). The description of the magnetic structure model that involves the BV of two different IRs suggests that the interactions between the magnetic ions are not simple exchange interactions (not only the second order in the Landau free energy [9]). Some results of our magnetic measurements differ from those presented in Ref. [3]. It is worthwhile to note that we performed our magnetic susceptibility measurements in a very low magnetic field (1 Oe) while the data from Ref. [3] were recorded in the field of 1 kOe. Such a high magnetic field can induce some extra effects in the sample. This is probably the reason for the differences that were observed. The transition temperature deduced from our susceptibility data Tt ¼ 10:7 K (in Ref. [3] Tt ¼ 6:2 K) is close to the value found from neutron diffraction (Tt ¼ 11 K). The paramagnetic Curie temperature yp ¼ 31 K is negative which is characteristic of an aniferromagnetic ordering (in Ref. [3] yp ¼ þ4 K). These facts testify to a good quality of our magnetic data. A representation theory analysis for isostructural TbNiAl compound, in case of propagation vector k~ ¼ ½12; 0; 12; is presented in Ref. [10]. The

S. Baran et al. / Journal of Magnetism and Magnetic Materials 261 (2003) 369–376

375

7.537 3.779

7.536 3.778 c [Å]

3

a [Å]

Volume [Å ]

185.80

185.76

7.535

3.777 185.72

0

5 10 15 20 25 Temperature [K]

3.776 7.534

0

2

4

6

8

10 12 14 16 Temperature [K]

18

20

22

24

Fig. 8. The temperature dependence of the a lattice parameter ( ), the c lattice parameter (~) and the unit cell volume (\) of TbRhSn.

magnetic structure models proposed in this paper differ from the models that follow our symmetry analysis. Nevertheless, when we applied Ref. [10]suggested magnetic structure models to our diffraction data, collected at 1.7 K, the smallest value of Rmagn factor that we obtained was Rmagn ¼ 16:03%: This value was significantly larger than the values that were obtained for our models (Rmagn ¼ 9:80% in case of the first model or Rmagn ¼ 8:69% in case of the second model). The different magnetic structure model was proposed in Ref. [4]. In this model all magnetic moments lie in the basal plane and form 180 ; 60 and 60 angles with the a-axis for Tb1 ; Tb2 and Tb3 ; respectively. For this magnetic structure model we found Rmagn ¼ 20:48%: The knowledge of precise values of the lattice constants may be exploited to study the magnetostriction effect. Fig. 8 presents the temperature dependence of lattice parameters and unit cell volume below 25 K. The a lattice parameter decreases with the increase of temperature while the c lattice parameter increases. The unit cell volume shows a jump at the transition temperature Tt ¼ 11 K and another (smaller) change at the Ne! el temperature.

It is worth while to note that isostructural TbPdAl undergoes a first-order phase transition at about 100 K (the transition temperature depends on whether the sample is being cooled or heated) [11]. This transition is asociated with a small jump in volume. In contrast with TbRhSn, the lattice parameter a increases while the lattice parameter c decreases with increasing temperature. The two phases coexist in the temperature range of about 20 K. The transition temperature is significantly above the Ne! el temperature which is equal to 43 K for TbPdAl. It is difficult to ascertain whether the phase transition observed at Tt ¼ 11 K in TbRhSn has the same nature as the phase transition at 100 K in TbPdAl. The magnetic structure model with two different values of magnetic moments at different atom positions seems to be exotic. However, such a model was proposed for isostructural TbNiAl [12].

Acknowledgements S. Baran thanks PSI for kind hospitality during the time of performing the neutron diffraction experiment.

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[7] W. Sikora, in: Proceedings of the SSPCM, Zajaczkowo, ‘ Poland, 1–7 September 1994, p. 484. [8] O.V. Kovalev, in: H.T. Stokes, D.M. Hatch (Eds.), Representations of the Crystallographic Space Groups, Gordon and Breach, Switzerland, Australia, Belgium, France, 1993. [9] Yu.A. Izyumov, V.N. Syromyatnikov, Phase Transitions and Crystal Symmetry, Kluwer Academic Publishers, Dordrecht, 1990. [10] P. Javorsk!y, P. Burlet, V. Sechovsk!y, A.V. Andreev, J. Brown, P. Svoboda, J. Magn. Magn. Mater. 166 (1997) 133. . [11] A. Donni, H. Kitazawa, P. Fischer, F. Fauth, J. Alloys Compounds 289 (1999) 11. [12] H. Maletta, V. Sechovsky, J. Alloys Compounds 207/208 (1994) 254.