Competing magnetic interactions and spin-glass-like behavior in PrCoRuSi2

Journal of Alloys and Compounds 374 (2004) 93–96

Competing magnetic interactions and spin-glass-like behavior in PrCoRuSi2 D.X. Li a,∗ , S. Nimori b , Y. Shiokawa a b

a Institute for Materials Research, Tohoku University, Oarai, Ibaraki 311-1313, Japan Tsukuba Magnet Laboratory, National Research Institute for Materials Science, 3-13 Sakura, Tsukuba 305-0003, Japan

Abstract The results of dc magnetization, ac susceptibility, magnetic relaxation, specific heat and electrical resistivity measurements on PrCoRuSi2 , an amalgamation of the ferromagnetic compound PrRu2 Si2 and the antiferromagnetic compound PrCo2 Si2 crystallizing in the same tetragonal ThCr2 Si2 -type structure, are reported. The data for this sample reveal spin-glass-like anomalies at the temperature T0 = 15 K where long-range magnetic ordering sets in. Below T0 , the observed irreversible magnetism, the long-time magnetic relaxation effect as well as the evident upward-shift of the peak temperature of ac susceptibility with increasing frequency are considered to originate, at least partly, from spin-glass-like magnetic frustration due to the competing magnetic interactions. © 2003 Elsevier B.V. All rights reserved. Keywords: PrCoRuSi2 ; Magnetic susceptibility; Magnetic anisotropy; Spin-glass

1. Introduction The ternary intermetallic compounds RT2 X2 (R = rareearth metal or U, T = transition metal, and X = Ge, Si) have been studied intensively during the last two decades. These compounds show various kinds of magnetic order and interesting features in their magnetic behavior. Recently, spin-glass (SG) behavior was found in two 1:2:2 systems, say, in URh2 Ge2 [1] and in PrAu2 Si2 [2,3]. It is generally accepted that frustration and disorder are necessary to achieve a SG state. Since URh2 Ge2 and PrAu2 Si2 crystallize in the ThCr2 Si2 or the CaBe2 Ge2 type structure with a perfect periodic atomic arrangement, the SG behavior of them is unforeseen and calls for further studies. We are interested in the mechanism of this unusual magnetic feature, and try to obtain much experimental information on SG behavior in some pseudo-1:2:2 systems. The early studies revealed that praseodymium compound PrCo2 Si2 is an antiferromagnet with complex spin structure [4–6], and PrRu2 Si2 is a ferromagnet with magnetic moment parallel to the c-axis [7,8]. It is naturally considered that competing magnetic interactions, necessary for SG state, may be introduced in an amalgamation of these two compounds. We have prepared ∗

Corresponding author. E-mail address: [email protected] (D.X. Li).

0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.11.073

a polycrystalline sample of PrCoRuSi2 and have studied its magnetic properties by dc magnetization, ac susceptibility, magnetic relaxation, specific heat and electrical resistivity measurements. The results are presented in this report.

2. Experimental details The polycrystalline sample of PrCoRuSi2 was prepared by melting appropriate amounts of the constituent elements in an arc furnace under purified argon atmosphere. The sample was than wrapped into tantalum foil and annealed in evacuated silica tube at 800 ◦ C for one week. X-ray powder diffraction was performed at room temperature with Cu K␣ radiation. The diffraction lines can be indexed based on a tetragonal ThCr2 Si2 -type structure model (space group I4/mmm) with Pr atoms on 2a sites, Si atoms on 4e sites and Co and Ru atoms statistically distributed over the 4d sites. The samples used in the experiments are small pieces cut from the annealed buttons. The ac susceptibility, dc magnetization and magnetic relaxation were measured using a quantum design superconducting quantum interference device (SQUID) magnetometer. The adiabatic heat pulse method was employed for specific heat measurements. The electrical resistivity measurement was performed using a standard four-terminal dc method.

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3. Results and discussion The temperature dependence of dc magnetization M of PrCoRuSi2 was measured in the zero-field cooling (ZFC) mode and in the field-cooling (FC) mode in various applied fields (H). For the sake of convenience, hereafter we call M/H dc susceptibility and note it as χ (=M/H). Fig. 1 shows a plot of dc susceptibility (χZFC ) versus tempera−1 ture (T) and also a plot of χZFC versus T for PrCoRuSi2 in the temperature range of 1.8–300 K taken at H = 0.01 T. Above 25 K the observed susceptibility could be nicely fitted (dashed line in Fig. 1) using a modified Curie–Weiss law, χ = χ0 + C/(T − θp ), with the effective magnetic moment µeff = (8C)−1/2 = 3.47µB /Pr, which is very close to that expected for free ion Pr+3 in the Hund’s rule ground state indicating the 4f electrons are almost localized within the Pr atoms. The paramagnetic Curie temperature θ p is found to be 7.8 K, the positive sign suggests the presence of dominant ferromagnetic correlations. At low temperatures, a large peak is observed at T0 = 15 K indicating the occurrence of a magnetic phase transition at this temperature. This behavior can be seen clearly in Fig. 2 with an expanded scale, where we compare the temperature variations of the FC and the ZFC susceptibilities. In a field of 0.001 T, both χFC (T) and χZFC (T) show a rapid increase with decreasing T starting at about 18 K due to impending magnetic order in this compound. As T is further lowed, χZFC goes through a maximum at T0 = 15 K and decreases slowly down to a field dependent temperature T1 (=7.5 K for H = 0.001 T) where a shoulder appears. The χFC (T) curve bifurcates from the χZFC (T) curve at temperature Tir = 18 K (>T0 ). Note that with increasing H, T1 and Tir shift to low temperatures and almost no change can be observed for T0 up to 0.5 T (for the sake of clarity, positions of T0 , T1 and Tir are marked only in the curve of H = 0.001 T in Fig. 2). This irreversibility between FC and ZFC dc susceptibility is a characteristic feature of SG’s and

1.2

6 5

H=0.01 T 4

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3

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0.0

0

50

100

150

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300

−1

4

0.8

χ ZFC (10 g/emu)

1.0

−3

χZFC (10 emu/g)

PrCoRuSi2

0

T(K) Fig. 1. Zero-field-cooled dc susceptibility (χZFC = MZFC /H) and recip−1 ) as a function of temperature for PrCoRuSi2 in rocal susceptibility (χZFC a magnetic field of 0.01 T. The dashed line represents the fitting result using a modified Curie–Weiss law.

Fig. 2. Difference between FC (䊊) and ZFC (䊉) dc susceptibilities of PrCoRuSi2 in various magnetic fields. T0 and T1 show the peak and the shoulder temperature in ZFC dc susceptibility curve, respectively, and Tir represents the temperature where FC and ZFC susceptibility curves separate from each other.

long-range-ferromagnetically ordered systems with strong magnetic anisotropy. In order to confirm whether the large peak in χZFC (T) curve at T0 is due to long-range magnetic ordering, specific heat C (for 1.7 K
D.X. Li et al. / Journal of Alloys and Compounds 374 (2004) 93–96

C/T(J K-2mole-1)

10 0.20

C (J K−1 mole−1)

8

0.15

PrCoRuSi2

0.10

6 0.05 0

5

10

15

T0

T2(K2)

4 2

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T0

3

ρ (10 µΩ cm)

PrCoRuSi2 1.22

1.21

(b) 1.20

0

5

10

15

20

25

30

T (K) Fig. 3. Temperature dependences of specific heat (a) and electrical resistivity (b) of PrCoRuSi2 up to 30 K. The inset shows the plot of C/T vs. T2 .

range 0.1 ≤ v ≤ 1000 Hz, in order to explore the possible  , of ac susceptiSG effects. The data of the real part, χac bility taken in zero dc magnetic field are shown in Fig. 4 between 5 and 25 K. For v = 0.1 Hz, there is a distinct peak  curve at about 15.1 K and the peak position moves in χac towards a high temperature, say, from 15.1 to about 15.7 K as v is increased from 0.1 to 1000 Hz. Such a significant fre peak position strongly suggests quency dependence of χac the formation of SG-like state in the PrCoRuSi2 sample at about T0 . The initial frequency shift calculated as δT0 = 1.4 T0

PrCoRuSi2

χ'ac (10

−3

emu/g)

1.2

0.1Hz 1Hz 10Hz 100Hz 1000Hz

1.0 0.8 0.6 T0 (K)

15.6

0.4 0.2

15.4 15.2

100/ln(ν0 /ν ) 3.2

5

10

3.6

15

4.0

4.4

20

25

T (K)  ) of the ac susceptibility of PrCoRuSi vs. Fig. 4. Real component (χac 2 temperature at various frequencies. The inset shows the plot of T0 vs. 1/ln(v0 /v) for this sample with v0 = 1013 Hz, and the solid line represents the fit to the Vogel–Fulcher law.

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T0 /(T0  log v) is δT0 = 0.010. This value is comparable to ␦Tf , the frequency shift of freezing temperature, known for canonical SG’s [9], e.g., AuFe: 0.010, PdMn: 0.013, and typical concentrated SG systems, e.g., URh2 Ge2 : 0.025 [1] and U2 AuSi3 : 0.015 [10]. In addition, the frequency shift of the ac susceptibility peak can well be described by the Vogel–Fulcher law [9,11], v = v0 exp[−Ea /kB (T0 − Ta )], with three fitting parameters—characteristic frequency v0 , activation energy Ea (kB is the Boltzmann constant) and Vogel-Fulcher temperature Ta . As shown in the inset of Fig. 4, a linear variation of T0 with 1/ln(v0 /v) is observed, where v0 is 1013 Hz typically taken in the SG systems [12]. This behavior is also typical of SG materials. The observed thermomagnetic irreversibility and frequency-dependent ac susceptibility indicate the nonequilibrium characters of the low-temperature magnetic state. Thermodynamically, such a nonequilibrium state directly relates to slow relaxation. For studying the magnetic relaxation behavior of PrCoRuSi2 , the isothermal remanent magnetization MIRM was measured as a function of time t at 2 and 5 K. The sample was first ZFC from 150 K to the desired temperature, then a magnetic field of 0.2 T was applied for 5 min and MIRM was measured immediately after the field was switched off. The results (not shown here) reveal that the decay of MIRM (t) at 2 and 5 K is remarkably slow and can be fitted very well using a logarithmic function, MIRM (t) = M0 − S ln(1 + t/t0 ). Where M0 is the initial zero-field magnetization, and S the magnetic viscosity. The parameter t0 depends on the measuring conditions and has only limited physical relevance [13]. Such a logarithmic relaxation behavior of remanent magnetization MIRM has also be observed in Gd2−x Yx PdSi3 (x = 0, 0.4, 1.0 and 1.6) [13] and in R2 PdSi3 (R = Nd, Tb and Dy) [14]. It should be emphasized that long-time magnetic relaxation is a characteristic feature for both SG [9,11] and ferromagnet with high magnetic anisotropy [15]. This effect in PrCoRuSi2 seems to have its origin in both SG-like spin freezing and domain-wall pinning. Summarizing the ac susceptibility, dc magnetization, magnetic relaxation, specific heat and electrical resistivity measurements, it is concluded that PrCoRuSi2 shows the SG-like anomalies at the temperature (∼15 K) where a long-range magnetic ordering sets in, suggesting the existence of competing magnetic interactions. Although PrCoRuSi2 is a crystallographically ordered substance, all the Co and Ru atoms seem to distribute statistically over the 4d sites of the ThCr2 Si2 -type structure. Such a non-magnetic atom disorder structure could vary the electronic environment around the Pr atoms and introduce the statistical distribution of RKKY interactions (competing ferro- and antiferromagnetic interactions) necessary for the SG-like state. It is interesting to compare the present case of PrCoRuSi2 with other 1:2:2 compounds. As stated in the introduction, SG behavior has been observed for URh2 Ge2 and PrAu2 Si2 . To explain the necessary disorder in the URh2 Ge2 , Süllow et al. [1] proposed a mixture of two

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possible crystallographic structures, say, the ThCr2 Si2 -type and the CaBe2 Ge2 -type structures, leading to a random distribution of Rh and Ge atoms. For PrAu2 Si2 , Krimmel et al. [2,3] determined a modest disorder between Au and Si with approximately 10% of these ions, and if this level of disorder is sufficient to introduce SG state in this system, the local environment must play an important role even in the case of dominant RKKY-type interactions between well-localized spins. A further comparison with some non-magnetic atom disorder 2:1:3 compounds, crystallizing in the AlB2 -type crystal structure, is also intriguing. For instance, a long-range (or extended short-range) magnetic phase transition occurs in Nd2 AgIn3 [16], Nd2 PtSi3 [17] and U2 RhSi3 [18] accompanied with SG (or SG-like) anomalies. It is considered that random distribution of the non-magnetic atoms both in the 1:2:2 and in the 2:1:3 compounds, is responsible for the competing magnetic interactions, which lead to the frustrated type magnetic ordering at low temperature with complex spin structure.

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