Magnetic phase transitions in TbAuIn compound

Magnetic phase transitions in TbAuIn compound

Solid State Communications 136 (2005) 26–31 Magnetic phase transitions in TbAuIn compound Ł. Gondeka,*, A. Szytułab, M. B...

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Solid State Communications 136 (2005) 26–31

Magnetic phase transitions in TbAuIn compound Ł. Gondeka,*, A. Szytułab, M. Bałandac, W. Warkockib, A. Szewczykd, M. Gutowskad a Department of Physics, Cracow Agricultural University, Mickiewicza 21, 31-120 Krako´w, Poland M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krako´w, Poland c H. Niewodniczan´ski Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Krako´w, Poland d Institute of Physics, Polish Academy of Sciences, Lotniko´w 32/46, 02-668 Warszawa, Poland b

Received 28 February 2005; received in revised form 17 June 2005; accepted 20 June 2005 by C. Lacroix Available online 6 July 2005

Abstract Magnetic properties of frustrated antiferromagnet TbAuIn are investigated by AC susceptibility, resistivity as well as specific heat measurements. In temperature dependence of the susceptibility two anomalies are visible, one at 33 K and another at 48 K. According to neutron diffraction studies the Ne´el temperature is 35 K. The second anomaly in the AC susceptibility seems to be attributed to antiferromagnetic cluster-glass state of Tb magnetic moments. The resistivity measurements confirm that TbAuIn exhibits long-range magnetic order below 35 K, moreover they reveal an anomalous behaviour above that temperature. However in the temperature dependence of the specific heat only one anomaly at 30 K is visible. The low temperature behaviour of susceptibility, resistivity and specific heat of the investigated antiferromagnetic material can be described, with a good accuracy, within the spin-wave theory with linear dispersion relation. q 2005 Elsevier Ltd. All rights reserved. PACS: 65.40.Kb; 72.15.Kv; 75.30.Km Keywords: A. Rare earth intermetallic compounds; D. AC susceptibility; D. Resistivity; D. Specific heat

1. Introduction and experimental Recently, a great deal of attention has been paid to investigation of geometrically frustrated hexagonal RTX (R—rare earth, T—d-electron metal, X—p-electron element) compounds of ZrNiAl-type crystal structure [1–4]. Geometrical frustration caused by triangular coordination of rare earth magnetic moments leads to a complex magnetic phase diagram in such class of compounds. According to neutron diffraction as well as to DC magnetic susceptibility studies the TbAuIn compound was proposed to exhibit multiple magnetic transitions in antiferromagnet AFM (35 K) spin-glass SG (58 K) paramagnet PM sequence [5]. TbAuIn compound below * Corresponding author. Tel.: C48 12 632 48 88; fax: C48 12 633 70 86. E-mail address: [email protected] (Ł. Gondek).

0038-1098/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2005.06.026

TNZ35 K exhibits magnetic structure of 1208-type, common in this class of compounds. In this magnetic structure each Tb magnetic moment forms an angle of 1208 with its neighbours [5]. Above TN no magnetic contribution to the neutron diffraction patterns was found [5]. In order to clarify whether the spin-glass phase is present above the Ne´el temperature some additional measurements including AC magnetic susceptibility, resistivity and specific heat were made. The polycrystalline sample was prepared from highpurity terbium (3 N), gold (4 N) and indium (5 N) elements by arc-melting in a purified argon atmosphere. Sample was annealed at 800 8C for 1 week in the evacuated quartz tube. In order to check sample quality X-ray diffraction measurements (Cu Ka radiation) were performed using the Philips PW-3710 apparatus. The crystal structure parameters can be found in Ref. [5]. Magnetic measurements (including AC susceptibility and magnetization in field up to 50 kOe) were made using the Lake Shore 7225

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susceptometer. The resistivity measurements were carried out with standard four contacts technique. Specific heat measurements were performed using quasiadiabatic calorimeter, which was a part of the specific heat option of the Quantum Design PPMS system.

2. Results and discussion 2.1. AC susceptibility and DC magnetization Temperature dependence of complex AC magnetic susceptibility cACZc 0 Kic 00 , where c 0 is the real and c 00 the imaginary component, was measured at the driving field HACZ5 Oe and a frequency range fZ36–2000 Hz. The real part of magnetic AC susceptibility, presented in Fig. 1(a), shows existence of two anomalies, one at 33 K and another at 48 K. When applying the magnetic field HaZ300 Oe the low temperature anomaly connected with transition into antiferromagnetically ordered phase (AF) at TZTN does not change whereas the second anomaly is shifted to 45 K. The c 00 component presented in Fig. 1(b) shows peak at 47 K which is shifted to 44 K in HaZ300 Oe. Anomaly at TN is hardly visible for c 00 both in ZF and in the field of 300 Oe, nevertheless its position is still at 32 K. The presence of weak c 00 (about 0.01 c 0 ) is natural for a triangular magnetic structure. The inset in the Fig. 1(a) shows the frequency dependence of the temperature Tp of the second c 0 anomaly. Tp is shifting to higher temperatures when the frequency of the driving field is raised (see inset in the Fig. 1(a)). The parameter of the relative Tp variation per decade of frequency aZ(DTp/Tp)/D(log f) is equal to 0.011 that is typical for metallic spin-glass systems [6]. The shift of the second c 0 anomaly with external magnetic field and the above value of a parameter are indicative of the spin-glass character of TbAuIn between AF and the PM state. Above 60 K the real part of cAC obeys the modified Curie–Weiss law with paramagnetic Curie temperature qPZK19 K and effective magnetic moment of 9.68 mB (in good agreement with theoretical value of 9.72 mB for free Tb3C ion). As the sign of the qP is negative the antiferromagnetic interactions are expected to be dominant. In order to get a deeper insight into phase transitions of TbAuIn the non-linear AC susceptibility was measured (Fig. 1(c) and (d)). The non-linear term of the second order c2, corresponding to second harmonic (2 h), is related to the signal detected at the frequency 2f and proportional to c2HAC. The non-linear term of the third order c3, corresponds to the third harmonic (3 h) detected at 3f and 2 proportional to c2 HAC . Two and 3 h were recorded for the fundamental frequency fZ120 Hz. The magnitude of harmonics was less than 0.01% of c 0 . The 2 and 3 h exhibit a double peak at about 50 K, whereas the AF transition is visible only in 3 h. The change of the sign and a jump of 3 h at TN is expected by theory [8]. An anomaly in the 2 h was observed for compounds with spin-glass or cluster-glass


transitions [7]. The divergence of the 3 h at the both sides of spin-glass transition observed in the Fig. 1(d) seems to be in a good agreement with theory [8]. In addition, M(H) measurements were performed at temperatures of 4.2, 15, 29, 41 and 84 K (Fig. 2). There was no irreversibility seen at any of the temperatures. The absence of a hysteresis loop in the proposed spin-glass or cluster-glass state is in a contradiction with expectations. However predominant antiferromagnetic interactions between Tb3C ions must be taken into account. So we propose an antiferromagnetic cluster-glass state to be more likely to exist in the 35–48 K temperature range. Change of slope in the M(H) curves registered at 4.2 and 15 K at 47 kOe is characteristic for anisotropic antiferromagnetic systems. At 29 K the dM(H)/dT curve exhibits a maximum at HZ34 kOe indicating metamagnetic transition. An inset in the Fig. 2 shows temperature dependence of magnetization in external field of 30 kOe. The M(T) curve shows only one broad maximum at 33 K, while at about 50 K only a very weak anomaly can be observed. The diminishing of this anomaly, which is clearly visible in low magnetic fields up to 100 Oe [5], is an evidence of suppression of the cluster-glass state by applying the magnetic field. 2.2. DC resistivity Temperature dependences of electrical resistance of TbAuIn and LaAuIn compounds are shown in Fig. 3(a). For clearance the residual resistivities of 188 and 61 mU cm for TbAuIn and LaAuIn, respectively, were extracted. For TbAuIn the transition into long-range magnetically ordered state is clearly evidenced at temperature of 35 K. At the temperature of about 45 K no significant anomaly was noticed. However the first derivative of resistance shows an increase of its value (departure from the dotted line in Fig. 3(b)) starting from about 70 K down to temperature of 35 K where the AF transition takes place. Resistivity of LaAuIn was analysed using the model of parallel resistors (MPR): rlatt ðTÞ Z

rel–ph ðTÞrsat rel–ph ðTÞ C rsat


where rsat is a temperature independent saturation resistivity. The temperature dependent term of electron–phonon scattering rel–ph is given by:  5 ð q T T x5 dx (2) rph–el Z C Kx x q 0 ð1 K e Þðe K 1Þ where C is a constant and q is considered as a rough approximation of the Debye temperature. The formula (2) was derived taking into account only longitudal phonons, moreover this parameter may be influenced by electron– electron interactions [9]. The best fit of the MPR model to the LaAuIn data were obtained with following parameters:


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Fig. 2. Isothermal magnetization versus magnetic field at 4.2, 15, 29, 41 and 84 K. Inset shows temperature dependence of magnetization in magnetic field of 30 kOe.

rsatZ166 mU cm; CZ74.85 mU cm and qZ157 K. A magnetic part of TbAuIn resistivity rMagn was estimated as extraction of LaAuIn data from TbAuIn experimental points. The detailed inspection of rMagn at low temperatures will be given later. 2.3. Specific heat In Fig. 4 temperature dependence of specific heat is given. A broad l peak in CP(T) is visible at 30 K, this peak is connected with AF transition. No additional anomaly is visible in the vicinity of 45 K. The inset in the Fig. 4 shows influence of external magnetic field of 10 and 30 kOe on the position as well as on the magnitude of the l peak. In fact there is only a slightly difference between anomalies registered in zero field and in 10 kOe. In higher magnetic fields the peak’s position changes to 29 K. A lowering of its magnitude is observed as well. Such behaviour is typical of AF transition. In order to extract magnetic contribution, the specific heat data were analysed using formula: CphCel Z

9nR 1 K aD T

T qD

3 ð

qD T 0

x4 ex dx C gT ðe K 1Þ2 x


where R—gas constant; n—number of ions per formula unit. Estimated parameters are as follow: Debye temperature qDZ198 K, Sommerfeld coefficient gZ16 mJ/mol K2 and anharmonic coefficient aDZ8!10K5 KK1. Anharmonic correction was required as at the room temperature specific Fig. 1. Real (a) and imaginary (b) part of AC magnetic susceptibility of TbAuIn compound in magnetic field of 300 Oe and zero field. Second (c) and third (d) harmonics recorded at zero field. Inset in the part (a) shows frequency dependence (in a log f scale) of the temperature of the second c 0 anomaly.

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Fig. 5. Temperature dependence of the magnetic part of the specific heat of TbAuIn. The solid line represents calculated Schottky contribution. The inset shows CF splitting of the ground multiplet. Fig. 3. Temperature dependence of: (a) TbAuIn and LaAuIn resistivity (residual resistivities were extracted); (b) derivative dr/dT for TbAuIn. The solid line in the part (a) represents parallel resistors model fit (see text for details). The dotted line in the part (b) is the linear fit of dr/dT taken in the 100–260 K temperature range.

heat values exceeded the Dulong-Petit limit. The relatively low values of g are typical for such compounds [10]. In order to check whether estimation of qD is reliable additional measurements of isostructural non-magnetic LaAuIn compound were performed. The obtained value of qDZ203 K for LaAuIn compound was rescaled using formula given in Ref. [11]. The rescaled value of qDZ198.8 K for TbAuIn is in a good agreement with our estimation. The magnetic contribution to the specific heat CMagn was calculated as the difference between the measured specific

Fig. 4. Specific heat of TbAuIn compound versus temperature. Inset in the shows evolution of the peak in specific heat at external magnetic fields.

heat and the CphCel contribution, estimated using Eq. (3). The magnetic part of specific heat is shown in Fig. 5. The Schottky contribution was fitted using the standard expression: 0 1 E E !2 P P13 2 K Ti K Ti R @ 13 iZ1 Ei e iZ1 Ei e A CSchottky Z 2 P13 KEi K P13 KEi T iZ1 e T iZ1 e T


The corresponding energies of crystal field (CF) splitted ground multiplet are 0 K (quasi-doublet); 65; 121; 189; 200 K (doublet); 218; 224; 232; 240; 260 and 275 K (see inset in Fig. 5). The total splitting of the ground multiplet is similar to TbNi5 compound crystallizing in hexagonal CaCu5-type structure (P6/mmm) Ð[12]. Using formula Smagn ðTÞZ 0T ðCmagn ðT 0 ÞÞ=ðT 0 ÞdT 0 the temperature dependence of magnetic entropy was calculated

Fig. 6. Temperature dependence of the magnetic entropy on a log-T scale.


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(Fig. 6). The magnetic entropy is related to the w angular momentum degrees of freedom using expression SmagnZ R ln(w). For Tb ion the total angular momentum J is equal to 6 and consequently the expected value of w is (2JC1)Z13. At the AF transition point the Smagn reaches 90% of value R ln(2) expected for quasi-doublet ground state. Apart from the small splitting of the lowest quasi-dublet, the presence of short-range correlations of Tb magnetic moments above TN can be responsible for such lowering of the magnetic entropy. At the room temperature the entropy reaches 95% of R ln(13). 2.4. Low temperature thermodynamic properties—AF magnons evidence A closer inspection of temperature dependences of magnetic susceptibility, resistivity and specific heat connected with AF transition anomaly leads to a conclusion that they fulfill dependences predicted for antiferromagnetic magnons (AFM) with linear dispersion relation 32(k)ZD2C Dk2 with energy gap D. Magnetic susceptibility at sufficient low temperatures for anisotropic antiferromagnet is given within spin-wave theory [13] by: D

cjj Z 3BD3=2 T 1=2 eK T


D 3 3 ct Z A K BD1=2 T 3=2 eK T 2 2


where A and B are constants, D—gap in AFM dispersion relation. For powder sample the susceptibility may be easily calculated as: cZ

pffiffiffiffiffiffiffi D  1 c C 2ct Z A C B DT eK T ðD K TÞ 3 jj


Formula (6) was fitted to the low temperature part of susceptibility (Fig. 7(a)). The refined parameters are: AZ 74.2!10K3 [emu/mol], BZ65.1!10K5 [emu/mol K2] and DZ63.9 K. The A parameter is proportional to 1/b, where b is the anisotropy constant. In case of AFM magnetic part of the resistivity can be written as [14]: rffiffiffiffi     T KD 3 T 2 T 2 rMagn Z bD2 (7) e T 1C C D 2 D 15 D This formula was fitted to the low temperature part of magnetic resistivity (Fig. 7(b)). The constant factor b was found to be 22.0!10K5 [mU cm KK2] and the DZ 64.7 K. The spin-wave theory predicts temperature dependence of specific heat at temperatures below the Ne´el point [13]. The relevant expression is given by: 1


CTran Z aT K 2 eK T


Fig. 7. Low temperature dependences of susceptibility (a), resistivity (b) and specific heat (c) below the Ne´el temperature. In all cases D represents the energy gap in dispersion of AF spinwaves.

The resulting fit is presented in the Fig. 7(c). The refinement parameters are: aZ407 [J/mol K1/2] and the DZ58.3 K. Thus, one can state that the D values obtained from fitting the theoretical dependences of various thermodynamic functions, derived in frames of the magnons theory for

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antiferromagnetic materials, to the low temperature experimental data are in a very good agreement.

3. Summary Concluding, it is clear that magnetic transition at about 35 K evidenced by AC magnetic susceptibility, resistance as well as specific heat measurements corresponds to antiferromagnetic ordering of Tb magnetic moments. The transition at about 50 K seems to be of magnetic disorder– disorder origin according to the resistance data, however no additional anomaly in CP(T) was evidenced. Strong influence of the external magnetic field and driving field frequency on the position as well as on the magnitude of the AC susceptibility anomaly at about 50 K seems to be an indication of an AF cluster-glass—paramagnet phase transition. The temperature dependences of cAC higher harmonics support the existence of glassy magnetic state above the Ne´el point; moreover reported earlier diffuse neutron scattering above the TN for TbAuIn compound makes the existence of AF cluster-glass probable [5]. Low temperature dependences of magnetic susceptibility, resistivity and specific heat obey scaling expected for antiferromagnetic magnons with linear dispersion relation. The value of the D gap in the magnon energy spectrum derived from our refinements is (62G4) K.


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