Spin-cluster glass state in U(Ga0.95Mn0.05)3
Xie Dong-Hua1, 2, Zhang Wen2, Liu Yi2, Feng Wei2, Zhang Yun2, Tan Shi-Yong2, Zhu Xie-Gang2, Chen Qiu-Yun2, Liu Qin2, Yuan Bing-Kai2, Lai Xin-Chun2, †,
Beijing Institute of Technology, Beijing 100081, China
Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621700, China


† Corresponding author. E-mail: laixinchun@caep.cn

Project supported by the Natural Science Foundation of China Academy of Engineering Physic (Grant No. 2014A0301013) and the National Natural Science Foundation of China (Grant Nos. 11304291 and 11504342).


We report the study of a low temperature cluster glass state in 5% Mn-doped UGa3 heavy fermion compound. This compound transforms from a paramagnetic state to a spin-cluster glass state, which is confirmed by measuring the dc susceptibility and magnetization. The ac susceptibility exhibits a frequency-dependent peak around Tf, which provides direct evidence of the cluster glass state. By analyzing the field-dependent magnetization and frequency-dependent ac susceptibility in detail, we deduce that this compound forms a spin-cluster glass state below Tf.

1. Introduction

The uranium compounds of the UX3 series (X: a group-IIIA or IVA element in the periodic table) present various interesting magnetic behaviors from an enhanced, Pauli-like paramagnetism (UAl3, USi3, and UGe3), through local spin fluctuations (USn3), to a local-moment ordering (UPb3). A great variety of magnetic properties in the UX3 series are commonly attributed to a hybridization effect between the 5f-electron states of uranium and the s, p, d electronic states of neighboring atoms. The antiferromagnetic compound UGa3 (TN = 67 K),[13] crystallizing in the AuCu3 structure, locates a special position at the onset of magnetic order among the UX3 phase. The substitution of the group-IIIA (or group-IVA) element for Ga atoms in UGa3 exhibits interesting magnetic properties through the changes of the hybridization between the uranium 5f electronic states and the conduction electronic states of gallium. For example, with increasing Sn concentration, the f electrons in the UGa3−xSnx system undergo a transition from the itinerant antiferromagnetic state to a typical spin fluctuation state, and finally localize for x ∼ 1.[4] While in UGa3−xGex, the substitution of Ge atoms gradually suppresses the long range magnetic order, and reaches the quantum critical point at x ∼ 0.6, which presents non-Fermi liquid behavior.[5]

Similarly, the hybridization effect would be changed by the substitution of UGa3 in the transition metal for Ga atoms since it not only changes the order degree of the occupied atom, but also prominently changes the exchange interactions through changes of environment (the valence electrons and the U–U distance). This concept motivated us to investigate the properties of Mn-doped UGa3, which present the spin-cluster glass (SCG) state at a low temperature. This compound plays an important role in better understanding the f-electron contributions to the magnetism in uranium compounds.

2. Experiment

Single crystals of U(Ga0.95Mn0.05)3 were grown by the Ga self-flux method.[6,7] The raw materials of U (99.8%), Mn (99.999%), and Ga (99.9999%) were mixed together according to the ratio of U:Mn:Ga = 1:(0.5∼2):10. The feed, placed in an alumina crucible and sealed in an evacuated quartz tube, was heated in a resistance furnace up to 1200 °C, held at this temperature for 24 h and then slowly cooled down to 600 °C at a rate of 1 K/h. Then, the single crystals were separated from the flux by means of centrifuging at 600 °C. The obtained crystals were a cube shape with a maximum dimension of 2 mm× 2 mm× 3 mm.

The actual compositions of the obtained crystals were determined by utilizing energy dispersive x-ray (EDX) microanalysis. All the single crystals prepared by different ratios present the same atomic ratio of U:Ga:Mn, which is 1:2.85:0.15. X-ray diffraction (XRD) was performed on the single crystals and their crushed powder by a diffractometer in a range from 10° to 90°. The frequency-dependent ac susceptibility and low-field magnetization were measured by using a quantum design physical properties measurement system (PPMS). Specific heat experiments were performed in a temperature range of 2 K–200 K on the PPMS using the relaxation method.

3. Results and discussion

Figure 1(a) shows the powder and single crystal XRD patterns for both U(Ga0.95Mn0.05)3 and UGa3 samples, which can be indexed on the basis of AuCu3 type structure (Fig. 1(b)). All the powder diffraction peaks of U(Ga0.95Mn0.05)3 shift to a high angle compared with UGa3 due to the small ionic radius of Mn3+. The calculated lattice parameters of U(Ga0.95Mn0.05)3 and UGa3 are 4.2354 Å and 4.2560 Å, respectively.

Fig. 1. (a) Room temperature XRD patterns of the powder of UGa3 and U(Ga0.95Mn0.05)3 single crystals after grinding. The inset shows the XRD pattern of the corresponding single crystal, showing mainly the c-axis orientation featured with very sharp peaks. (b) Schematic diagram of UGa3 unit cell.

The values of the dc susceptibility χ (χ = M/H) of U(Ga0.95Mn0.05)3 measured in the zero-field-cooled (ZFC) and field-cooled (FC) modes under various applied magnetic fields are shown in Fig. 2. At low fields (e.g., 100 Oe, 1 Oe = 79.5775 A·m−1), the magnetic susceptibility exhibits a sharp increase below 60 K, and an irreversibility behavior is manifested by the bifurcation between the χZFC(T) and χFC(T) curves below 41.7 K. Those phenomena, together with results of ac susceptibility, suggest the formation of the SCG state in the U(Ga0.95Mn0.05)3 sample below Tir. By increasing the magnetic fields, the cusp in the χZFC(T) curve at Ta loses its intensity and broadens, and both Ta and Tir shift to a lower temperature. These phenomena are typical of spin glass behaviors. In canonical spin glass (SG) systems, the cusp in χZFC(T) is governed by SG dynamic transition and the magnetic irreversibility generally starts at the temperature slightly lower than Ta.[8,9] The obvious difference between Tir and Ta in U(Ga0.95Mn0.05)3 suggests the existence of short-range interactional clusters with different sizes. When the system is cooled down from the high temperature in a zero or nonzero field, magnetic moments of the different size spin clusters in U(Ga0.95Mn0.05)3 may be frozen in the directions energetically favored by the strong Ruderman–Kittel–Kasuya–Yosida (RKKY) action or by the external field. There would be a competition between the RKKY action and the external field acting on the spin moment. The RKKY action is predominant at T < Ta and the external field is predominant at T > Ta. Thus, the broad cusp at Ta marks a crossover region where the RKKY action energy and the energy caused by the external field are comparable to each other.

Fig. 2. DC susceptibility χ (χ = M/H) data for U(Ga0.95Mn0.05)3 measured in the FC (closed symbols) mode and the ZFC (open symbols) mode in various magnetic fields. Ta is denoted by the temperature where χZFC(T) reaches a maximum and Tir is the temperature where χFC(T) and χZFC(T) start to separate from each other. Tm is defined as the temperature where the susceptibility sharply increases. The inset displays the temperature dependence of the inverse molar magnetic susceptibility.

Above 60 K, the reciprocal susceptibility curve can be well fitted by the Curie–Weiss law χ = C/(Tθp) (inset of Fig. 2), where C is the Curie constant and θp is the paramagnetic Curie temperature. From this fit, the effective magnetic moment and the paramagnetic Curie temperature are determined to be μeff = 1.54μB/U, and θp = 43.7 K, respectively. The obtained μeff value is much smaller than that of a free U ion with f2 (μeff ∼ 3.58μB/U) or f3 (μeff ∼ 3.62μB/U) electronic configuration, suggesting the itinerant behavior of 5f electrons and/or Kondo effect in this compound. The positive sign of θp suggests that the ferromagnetic exchange interaction is dominant.

Figure 3(a) shows the dc isothermal magnetizations for U(Ga0.95Mn0.05)3 at various temperatures. The dependence of magnetization on the applied magnetic field at 80 K presents a characteristic linear behavior of the paramagnetic state. However, the magnetization below 60 K exhibits a sharp jump at very low field (H < 500 Oe) followed by a monotonic increase in the high field range without reaching saturation up to 9 T, which provides strong evidence of the existence of the SCG state. By increasing the applied field, the frozen net moment part tends to be saturated, whereas the cluster glass part increases linearly and results in the unsaturation of magnetization. In addition, the small magnetic hysteresis loop (S-type curve) below 60 K shown in Fig. 3(b) also indicates the existence of a frozen net moment in the U(Ga0.95Mn0.05)3 sample.

Fig. 3. (a) Magnetizations up to 9 T and (b) the hysteresis curves measured at various temperatures for U(Ga0.95Mn0.05)3 single crystal.

Figure 4 displays the in-phase and the out-of-phase components of the ac susceptibility for U(Ga0.95Mn0.05)3 at various frequencies f = ω/2π. Both and curves exhibit the characteristic pronounced maxima whose amplitudes and positions strongly depend on the applied magnetic field frequency. These features further confirm an SG state in U(Ga0.95Mn0.05)3 below Tf. Here, Tf is defined as the temperature corresponding to the peak position in the curve. The frequency shift rate δTf = ΔTf/(TfΔ lg ω) = 0.019 for U(Ga0.95Mn0.05)3 falls in a range between canonical spin glasses (e.g., δTf ∼ 0.005 for CuMn alloy)[10] and non-interacting ideal superparamagnetic systems (δTf ∼ 0.1).[11] This value is comparable to those of a nonmagnetic atom-disorder SG system, such as U2PdSi3 (δTf = 0.020),[12,13] URh2Ge2 (δTf = 0.025),[14] and U2AuGa3 (δTf = 0.01).[15]

Fig. 4. In-phase and out-of-phase components of the ac susceptibility versus temperature in an applied ac field of 10 Oe at various frequencies for U(Ga0.95Mn0.05)3.

The dynamical parameter, relaxation time τ, follows the conventional power-law divergence of critical slowing down,[8,9]

where τ is the dynamical fluctuation time corresponding to the measured frequency (τ = 1/(2πf)), τ0 is the spin flipping time of the relaxing entity, z is the dynamic scaling exponent, ν is the critical exponent, Tf corresponds to the peak in the curve at a given measuring frequency, and TSG represents the infinitely slow cooling dc (equilibrium) value of Tf (f → 0). The value of TSG is obtained by extrapolating the plot of Tf versus f to f = 0, which gives TSG = 40.9 K. We rewrite Eq. (1) as

The ln–ln plot of relaxation time τ versus [(TfTSG)/TSG] is shown in Fig. 5(a). The solid line in Fig. 5(a) represents the best fitting result of Eq. (2). The slope and intercept of the plot yield = 4.6(2) and τ0 = 1.5× 10−10 s. Many experimental results give the typical value of between 4 and 12 for various spin glass systems,[16] while is usually around 2 for conventional phase transitions.[9] Moreover, the value of τ0 is much larger than that of canonical spin glass (10−13 s),[9,16] which means a slow spin flip process in U(Ga0.95Mn0.05)3 caused by the strongly interacting clusters rather than individual spins. Hence, Tf ≈ 41.7 K (the maximum in at 11 Hz) can be defined as a cluster spin freezing temperature below which the clusters will be randomly frozen.

Fig. 5. (a) Relaxation time of freezing temperature plotted as ln(τ) versus ln [TfTSG]/TSG]. The solid line represents the fit to the power-law divergence. (b) The frequency dependence of freezing temperature plotted as Tf versus 100/ln(ω0/ω). The solid line represents the fit to Vogel–Fulcher law.

The frequency dependence of freezing temperature Tf can be obtained using the empirical Vogel–Fulcher law:[1620]

where ω0 is the characteristic attempt frequency, T0 is the Vogel–Fulcher temperature (representing the inter-cluster interaction strength), and Ea is the average activation energy, and kB is the Boltzmann constant. We rewrite Eq. (3) as

A plot of Tf versus 100/[ln(ω0/ω)] is shown in Fig. 5(b). The solid line in Fig. 5(b) represents the fit to Eq. (4). Here, we have used the value of attempt frequency ω0 = 1/τ0. The determination of characteristic time constant τ0 = 1.5× 10−10 s, has been discussed before. The slope and intercept of the plot yield T0 = 380 K and Ea/kB ≈ 68.5 K (Ea ≈ 1.7 kBTf) for our U(Ga0.95Mn0.05)3 sample. The nonzero value of T, arising from the interaction between spins, suggests a cluster spin-glass behavior in the U(Ga0.95Mn0.05)3 compounds. Furthermore, the result that T0 is very close to Tf suggests that the RKKY interaction is relatively strong in the compound. According to the Tholence criterion, δTTh = (TfT)/Tf, we obtain δTTh = 0.088 for U(Ga0.95Mn0.05)3, which is comparable to that of the RKKY spin-glass system (e.g., δTTh = 0.07 for CuMn system).[19] Therefore, these phenomena indicate that U(Ga0.95Mn0.05)3 has an RKKY spinglass behavior, similar to PrRhSn3.[21]

Figure 6 shows the temperature dependences of the specific heat for U(Ga0.95Mn0.05)3 and UGa3 below 200 K. A λ -type anomaly for UGa3 is found to be at 67 K corresponding to the antiferromagnetic transition. However, no anomaly was observed in specific heat of U(Ga0.95Mn0.05)3 around Tf. This indicates that no long-range magnetic order exists in this SCG system. The specific-heats of U(Ga0.95Mn0.05)3 and UGa3 in a temperature range of 2 K–10 K follow the Cp(T) = γT + βT 3 as shown in the plot of Cp/T versus T2 (see the inset of Fig. 6). By fitting the experimental data, the electron specific heat coefficient γ of U(Ga0.95Mn0.05)3 is obtained to be 90 mJ/mol·K−2, which indicates that its electron effective mass is much larger than that of UGa3. The enhancement of electron effective mass for U(Ga0.95Mn0.05)3 is caused by the spin-cluster glass state resulting from the presence of atomic disorder, as for other nonmagnetic atom-disorder spin glass compounds Ce2CuGe3[22] and Ce2CuSi3.[23]

Fig. 6. Temperature dependences of the specific heat C(T) for U(Ga0.95Mn0.05)3 and UGa3. Inset shows C/T versus T2 plot.

It is generally accepted that both randomness and frustration of magnetic moments are essential to produce the spin glass state.[9] As for U(Ga0.95Mn0.05)3, the magnetic U atoms form a fully periodic lattice, the 3d half-filled Mn atom and non-magnetic Ga atom randomly occupy the ligand site. The disorders of Mn and Ga atoms in the lattice can destroy the long-range magnetic correlation between U atoms and introduce individual spins or spin clusters with net magnetic moments by the local RKKY interaction. In addition, the Mn atom may have a local magnetic moment which has not been completely screened by the conduction electrons in this compound. Within one layer, U atoms and Mn atoms may form triangles of the nearest neighbors and no single configuration of the spins is extraordinarily favored. Therefore, the combination of the site randomness of Ga/Mn ions and frustration of magnetic moments resulting from the competing ferromagnetic and antiferromagnetic interactions between U ions easily leads to the randomly distributed spin-clusters in U(Ga0.95Mn0.05)3.

4. Conclusions

The ac and dc magnetic susceptibilities, isothermal magnetization, and specific-heat data of U(Ga0.95Mn0.05)3 single crystal provide conclusive evidence of SCG behavior below the characteristic freezing temperature Tf = 41.7 K. Irreversible magnetism behaviors in ZFC and FC, and a frequency-dependent anomaly in the ac susceptibility reveal a spin-glass behavior with a freezing temperature Tf. The sharp increase in dc susceptibility, a small jump at the very small field in the isothermal magnetization below Tm and no anomaly in the specific heat support the presence of clusters with frozen moments. We deem that the disorders of Mn and Ga atoms in the crystal lattice and frustration of magnetic moments lead to the random distribution of spin-clusters below Tf.

1Dervenagas PKaczorowski DBourdarot FBurlet PCzopnik ALander G H 1999 Physica 269 368
2Kaczorowski DKlamut P WCzopnik AJezowski A1998J. Magn. Magn. Mater.177–18141
3Kaczorowski DHauser RCzopnik A1997Physica B230–23235
4Kaczorowski DTroć RBadurski DBöhm AShlyk LSteglich F 1993 Phys. Rev. 48 16425
5Gofrky KKaczorowski D2003Acta Physica Polonica B34
6Xie D HLai X CChen Q YZhang Y ZXu Q YLuo L Z2014Rare Metal Mater. Eng.43646
7Schoenes JBarkow UBroschwitz MOppeneer P MKaczorowski DCzopnik A 2000 Phys. Rev. 61 7415
8Binder KYoung A 1986 Rev. Mod. Phys. 58 801
9Mydosh J A1993J. Bio. Phys.19310
10Mydosh J A1996J. Magn. Magn. Mater.157–158606
11Dormann JBessais LFiorani D 1988 J. Phys. C: Solid State Phys. 21 2015
12Li D XShiokawa YHaga YYamamoto EOnuki Y2002J. Phys. Soc. Jpn.7418
13Li D XNimori SShiokawa YHaga YYamamoto EOnuki Y 2003 Phys. Rev. 68 172405
14Süllow SNieuwenhuys G JMenovsky A AMydosh J AMentink S A MMason T EBuyers W J L 1997 Phys. Rev. Lett. 78 354
15Li D XYamamura TNimori SYubuta KShiokawa Y 2005 Appl. Phys. Lett. 87 142505
16Souletie JTholence J L 1985 Phys. Rev. 32 516
17Fulcher G I 1925 J. Am. Ceram. Soc. 8 789
18Vogel H 1925 J. Am. Ceram. Soc. 8 339
19Tholence J L 1984 Physica 126 157
20Tholence J L 1993 Solid State Commun. 88 917
21Anand V KAdroja D THillier A D 2012 Phys. Rev. 85 014418
22Tien CFeng C HWur C SLu J J 2000 Phys. Rev. 61 12151
23Hwang J SLin K JTien C 1996 Solid State Commun. 100 169