Journal of Magnetism and Magnetic Materials 324 (2012) 173–177
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Probing local magnetic cluster development in (CuZr)93 xAl7Gdx bulk metallic glasses by 27Al NMR M.T. Sandor a,n, X.K. Xi b, J.Q. Wang b, H.Y. Bai b, W.H. Wang b, Y. Wu a a b
Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255, USA Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
a r t i c l e i n f o
Article history: Received 17 May 2011 Received in revised form 31 July 2011 Available online 6 August 2011
We report magnetization properties of (CuZr)93 xAl7Gdx bulk metallic glasses from temperature dependent 27Al nuclear magnetic resonance spectroscopy and magnetic susceptibility measurements. Signiﬁcant non-linear line broadening of 27Al spectra commencing at high temperatures is attributed to the development of a local magnetic susceptibility distribution that prevails over a ﬁnite temperature range. Magnetization measurements conﬁrm the linewidth enhancement due to strong frustrated magnetic short-range order. This study provides insight into the nature of magnetic development and frustration in paramagnetic systems. & 2011 Elsevier B.V. All rights reserved.
Keywords: Bulk metallic glass Nuclear magnetic resonance Knight shift DC susceptibility Magnetic short-range order
1. Introduction Studies of magnetism in metallic glasses have demonstrated overwhelming evidence in support of magnetic inhomogeneities [1–6]. Structural disorder is extremely inﬂuential in metallic glasses, giving rise to frustrated magnetic behaviors such as spinglass, reentrant spin-glass magnetism, and complex cluster-glass states [1–6]. Intrinsic inhomogeneities due to quenched disorder also play a prevalent role in transition-metal oxides such as manganites, [7,8] in the regime of colossal magnetoresistance (CMR), high temperature superconductivity (HTS) observed in cuprates [7,8], and in f-electron systems that have non-Fermi-liquid (NFL) behavior . These non-amorphous systems demonstrate spin-glass characteristics similar to metallic glass, but can also exhibit magnetic Grifﬁths-phase behavior  given by temperature dependent phase-competition, where charge ordering and ferromagnetic ordering in maganites and antiferromagnetism (AFM) and superconductivity (SC) in cuprates compete, due to strong cluster percolation [8–10] within the high temperature paramagnetic regime. Extensive experimental investigations of manganites have even emphasized that magnetic interactions are especially important at high temperatures, where a temperature scale may preside and govern the nature of inhomogenous cluster development well above the Curie temperature . These studies seem to suggest that magnetic frustration, such as cluster formation, is an important
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mechanism inherent to the magnetic development in both intrinsically inhomogenous and amorphous systems. For example, even in the dilute impurity limit for simple magnetic systems, amorphous metallic glass systems such as CuZrGd [4,6] and LaGdAu [5,12] containing S-state ions (L¼0) such as Gd demonstrate extensive cluster development through long-range indirect coupling through the Ruderman–Kittel–Kasuya–Yosida (RKKY)  interactions between localized 4f electron spins. In this work, we explore the local magnetic behaviors using nuclear magnetic resonance (NMR) observation of anomalous magnetic behaviors in (CuZr)93 xAl7Gdx (x¼1, 2) bulk metallic glasses (BMGs) in the temperature range of 77–300 K. NMR is a sensitive and useful tool for probing local magnetic environments. Anomalous linewidth broadening was found and is attributed to strong spatial inhomogeneities in both the hyperﬁne coupling and bulk magnetic susceptibility due to local Gd3 þ ions. Magnetization measurements conﬁrm the existence of these inhomogeneities as frustrated antiferromagnetic (AFM) short-ranged spin clusters that macroscopically retain paramagnetic behavior down to low temperatures.
2. Experimental BMG compositions (CuZr)93 xAl7Gdx (x¼1, 2) with good glass forming ability (GFA) were fabricated using conventional copper mold casting . The amorphous nature of these BMGs was conﬁrmed by x-ray diffraction and differential scanning calorimetry (DSC). 27Al NMR experiments were performed in a magnetic ﬁeld of 7.01 T in the temperature range of 77–300 K using an Oxford
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including the narrow 1=2 21=2 central transition, broadened by the second-order quadrupole effect, and wide satellite transitions jmi2jm þ 1i (m a 1=2) broadened by the ﬁrst-order quadrupole interactions. Fig. 1 shows that the narrow central transition broadens signiﬁcantly from 1040 ppm at 300 K to 3600 ppm at 77 K. In addition, the isotropic shift of the central transition also changes with temperature. For metallic systems, the dominant mechanism to the isotropic shift is the Knight shift Kiso . There are two main contributions to Kiso ¼ Ks þKsf . Ks is due to the Fermi contact hyperﬁne interaction associated with the s electrons at the Fermi level and Ksf is due to the transferred hyperﬁne interaction mediated by s f exchange interactions between the localized f-electron spins and the spins of s electrons. Ksf is given by Ahf wfM ðT Þ, where Ahf ¼ zHhf =ðNA mB Þ is the hyperﬁne coupling constant and is generally assumed to be temperature independent . Here Hhf is the hyperﬁne ﬁeld due to local moments, NA is Avogadro’s number, mB is the Bohr magneton, z is the number of Gd ions that are nearest neighbors to Al, and wfM ðTÞ is the bulk magnetic susceptibility due to localized Gd f moments. The nature of magnetic inhomogeneities such as Kondo disorder observed in non-Fermi liquids due to a distribution of magnetic susceptibilities has previously been evaluated using NMR shift and linewidth data . Assuming Ahf and w are not correlated, the Knight shift can be expressed as an average over all distributions of hyperﬁne coupling constants and local magnetic susceptibilities K ¼Ahfw [18,19]. Due to the amorphous nature of these BMGs under study, different local environments at 27Al sites are anticipated to induce a spread in susceptibilities and result in non-linear line broadening. This line broadening can be evaluated by computing the experimental fractional NMR linewidth , which is expressed as
Helium Bath cryostat. NMR spectra were obtained using a Hahnecho pulse sequence 901 t 1801 t detection. Detection of the signiﬁcantly broadened line of 27Al spectra caused by Gd magnetic moments was done using frequency-stepped Fourier-transform methods in the time domain . NMR spectral data for each temperature was acquired by using ﬁve 0.1 MHz frequency steps, where echoes were shifted in the time domain to a common carrier frequency of 78.992 MHz. All the spectra for each frequency step were then obtained through Fourier transform processing and added together to obtain a single spectrum. 27Al Knight shifts were referenced to 1.0 M Al(NO3)3 aqueous solution. Magnetic susceptibility measurements were conducted using a Quantum Design SQUID magnetometer within the temperature range of 1.8–300 K in a magnetic ﬁeld up to 70,000 Oe.
3. Results and analysis 3.1. NMR shift and linewidth Fig. 1 shows 27Al NMR spectra for x ¼2. 27Al is a spin I ¼ 5=2 nucleus and its spectrum consists of ﬁve jmi2jm þ 1i transitions,
k=9Ksf 9 ¼ f½ðdwÞrms =w2 þ ½ðdAhf Þrms =Ahf 2 g
Knight Shift (ppm) Fig. 1. NMR frequency shifted spectra of Cu45.5Zr45.5Al7Gd2 at 300 K and 77 K for comparison. The Gaussian ﬁt dashed lines show the two sources of broadening caused by ﬁrst-order quadrupolar broadening and magnetic broadening due to Gd3 þ moments. The sum of the two contributions is also overlaid.
4 3 2
T = 120 K
where k is the 27Al NMR linewidth. Temperature independent k/9Ks f9 values are expected from magnetically homogenous alloys due to spatially independent local susceptibilities and purely paramagnetic systems. The behavior of line broadening is shown in Figs. 1 and 2(a), which display data for x¼1 of the ratio k/9Ks f9 versus bulk magnetic susceptibility w with temperature as an implicit parameter ranging from 77 to 300 K. A curve ﬁt using two Gaussian functions was implemented to extract the central frequency shift of each spectra, representing the distribution of Kiso, and linewidths caused by magnetic broadening of the central transition and satellite broadening of the ﬁrst-order quadrupolar distribution. The errors derived from both the extraction of the shift and linewidth were used to
0 -50 -100 -150 -200 -250 -300
T = 160 K
0 -75 -150 -225 -300
0.0000 0.0004 0.0008 0.0012 Susceptibility (emu/mole)
0.000 0.001 0.002 0.003 Susceptibility (emu/mole)
0.0006 0.0012 0.0018 0.0024 0.0030 Susceptibility (emu/mole)
Fig. 2. k/Ks f versus w for x¼ 1 (a) and x ¼2 (b) with temperature as an implicit parameter after conduction-electron Knight shift and quadrupolar broadening corrections. The dashed lines are a guide for the eye and indicate pure paramagnetic behavior between Gd ions. The insets show Ks f versus w with temperature as an implicit parameter. The behavior of Ahf is inferred from the slope.
M.T. Sandor et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 173–177
calculate the error bars as seen in Fig. 2. Here Ks f was obtained by subtracting the Fermi-contact shift Ks of 342 ppm for x¼1 and 330 ppm for x¼2 as determined from the y-intercept of Kiso plotted against w. This value agrees with the shift value observed in the x¼0 sample. Second-order quadrupolar broadening of the central transition was also corrected for by subtracting the linewidth observed in x¼0. The pseudo-contact interaction strength was also considered, which results in a dipolar coupling interaction between the thermally averaged magnetic moment of unpaired electrons of a paramagnetic ion and the nucleus . This results in a pseudo-contact shift, which can be calculated from the distances between the electronic and nuclear spins . The pseudo contact shifts were found to be negligible, giving at most a shift of 4.8 and 9.5 ppm for x¼1 and 2 at 77 K. Fig. 2(a) shows that values of k/9Ks f9 remain constant at high temperatures, as expected for purely paramagnetic behavior. Near 120 K the ratio k/9Ks f9 commences proportionally to w as temperature is lowered. This signiﬁes the onset of a magnetic phase-like transition and supports the existence of a magnetic susceptibility distribution in this temperature regime. In addition, a distribution of Ahf is reﬂected in the large constant offset of 3.5 and is anticipated in amorphous systems. Fig. 2(b) displays k/9Ks f9 versus w for x¼2 and demonstrates a similar NMR linewidth enhancement occurring at a higher temperature of 160 K with a corresponding non-zero distribution of Ahf denoted by an offset of 7.75. Anomalies span a wider temperature range for x¼2, which may be due to the twofold increase in the number of magnetic moments. The proportionality between k/9Ks f9 and w conﬁrms that the linewidth dependence on temperature is signiﬁcantly stronger than paramagnetic effects caused by RKKY coupling between individual Gd spins and host Al nuclei . In general, the distribution of susceptibilities and Ahf for this alloy system is not entirely unexpected since the spatially disordered nature of these BMGs is anticipated to give rise to a distribution in the magnetic environments due to ﬂuctuations of local interatomic distances and atomic coordination . Interestingly, k/9Ks f9 is observed to saturate near 77 K for both compositions and suggests that a magnetic susceptibility distribution develops only over a narrow temperature range between 1601 and 771 and 1201 and 771 for x¼1 and 2, respectively. The nature of these susceptibility distributions is further elaborated upon through magnetization experiments in the discussion below. The temperature dependence of the hyperﬁne coupling constant Ahf at Al sites due to local f moments of Gd is also explored in the insets of Fig. 2(a) and (b), where Ks f is plotted against w and shows that Ahf is negative as evidenced in the slope. The error bars for the distribution of Ks f at each temperature are also shown as determined from ﬁtting the spectra and varies between 3 and 15 ppm. A linear ﬁt was applied, yielding a transferred hyperﬁne ﬁeld of zHhf ¼ 1.2 kOe for x¼1 and zHhf ¼ 0.6 kOe for x¼ 2. A stronger hyperﬁne coupling for x¼1 may be due to a larger distribution of local Gd moments in the vicinity of Al. A distribution in Ahf and w mentioned previously would suggest that these couplings might have various strengths in temperature and space. The linear behavior demonstrated in both x¼1 and x¼2 shows that Ahf is temperature independent and is not the source of non-linear NMR linewidth broadening in the temperature range of 77–300 K.
1000 500 0 0
200 150 Temperature (K)
Fig. 3. Magnetic susceptibility w 1 versus T for Cu46Zr46Al7Gd1 and Cu45.5 Zr45.5Al7Gd2 at 10,000 Oe. The dashed lines are linear interpolations of the susceptibility at high temperatures, giving paramagnetic Curie temperatures of ( 30 71) K for x¼ 1 and ( 57 1) K for x ¼2. The inset contains preliminary ﬁts (black solid) at low temperatures to test the possibility of the ‘‘Grifﬁths phase’’. Fits to w1 ðT ÞpðTT0 Þ1l yield l values of 0.52 and 0.33 for x ¼1 and x ¼2, respectively, and do not meet the criteria of the Grifﬁths magnetization scaling law, where 0o l o 1 is predicted.
below 150 K, in agreement with the onset temperature of the NMR linewidth enhancement and suggests they have a common origin. Deviations from the Curie–Weiss behavior from high temperature extrapolations of the data yield the Curie–Weiss temperatures of ( 30 71) K for x ¼1 and ( 571) K for x¼2, demonstrating anti-ferromagnetic short-range order. The Curie constants obtained from the extrapolated ﬁt yield an effective moment of 9.9mB for x ¼1 and 10.0mB for x ¼2. These values of effective moment are much larger than 7.94mB for localized Gd þ 3 ions. An enhancement of the effective moment could originate from the effect of 5d conduction electron polarization  . The low temperature behavior of the magnetic susceptibility suggests a broad range of inter-cluster interactions centered on T¼0 K, which is largely reminiscent of spin-glass or cluster-glass behavior observed in YAlGd, ZrCuGd, LaGdAu, and MgGdZn amorphous systems [5,25]. The importance of short-range clusters in the high temperature paramagnetic regime is emphasized by larger effective moments for x¼1 and x ¼2 and strongly suggests the presence of short-ranged magnetic correlations as seen in the Grifﬁths systems, including randomly doped manganites and heavy-fermion alloys [7,10,26]. The Grifﬁths phase is characterized by an onset temperature caused by singularities, which gives rise to a non-analytical susceptibility . Preliminary ﬁts to the low temperature susceptibility data in the ‘‘Grifﬁth’s phase’’ are shown in the inset of Fig. 3 and demonstrate that local magnetic characteristics in these BMGs are not in agreement with the Grifﬁths scaling behavior characterized by w1 ðT ÞpðTT0 Þ1l ; the expected l value for the Grifﬁths phase is 0 o l o1 whereas the ﬁttings yield l values of 0.52 and 0.33 for x ¼1 and x¼2, respectively.
3.2. Magnetic susceptibility 3.3. Isothermal magnetization Additional insight into the nature of magnetic linewidth broadening can be gained through magnetization experiments. Molar susceptibility measurements taken at 10,000 Oe are shown in Fig. 3 for x¼1 and x ¼2. The inverse of magnetic susceptibility approaches the origin at T¼0, indicating the absence of longrange magnetic ordering in these systems. Further inspection reveals deviations from the conventional Curie–Weiss behavior,
Further investigations of the magnetic behavior were also obtained through isothermal magnetization M(H) shown in Fig. 4(a) and (b) for x¼1 and x¼ 2 from H¼0 to 70,000 Oe at 300 K, 80 K, and 2 K. A Brillouin function with a corresponding magnetic moment of 7mB is also included for comparison. Although NMR observations in Fig. 2(a) and (b) demonstrate the
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x x==11 x x==11 x x==22 x x==22
µB/ Gd at.
µB/ Gd at.
x=1 x=2 Brillouin - 7µB
4 3 2
40000 H (Oe)
40000 H (Oe)
Fig. 4. (a) Magnetization isotherms for x ¼1 and x¼ 2 at 80 K and 300 K for ﬁelds up to 70,000 Oe show paramagnetic behavior and (b) magnetization isotherms for x¼ 1 and 2 at 2 K are compared to a Brillouin function with a magnetic moment gJ ¼7mB. Direct comparison shows the presence of strong non-Brillouin behavior at 2 K for both x¼ 1 and 2.
8.1 x=1 x=2
8.0 7.9 Μ (μB/ Gd at.)
development local magnetic susceptibility inhomogeneities at high temperatures, inspection of Fig. 4(a) reveals that isotherms at 80 K and 300 K exhibit purely paramagnetic behavior. Fig. 4(b) also shows that the magnetization does not reach saturation even at the maximum applied ﬁeld at 2 K and displays non-Brillouin behavior most possibly due to frustrated RKKY magnetic correlations as also observed in amorphous spin-glass systems [12,27]. Random magnetic anisotropies are not expected to play an important role in suppressing the magnetization due to a non-existent orbital angular momentum (J ¼S, L¼0). However, local anisotropies due to the magnetic exchange coupling mediated between f electrons and conduction electrons might be signiﬁcant. A comparison to RKKY theory for spin-glass for the dilute impurity limit can be made using the relationship for reduced magnetization  given by M ¼1 (2/3)V0n(2Jþ1)/ (gmBH) and is valid for V0n bgmB and gmB HbkBT, where n is the impurity number density and V0 is the amplitude of the RKKY interaction strength. Fig. 5 shows the saturation moment for x¼1 and 2 as obtained from a linear extrapolation of M versus H 1 at high ﬁelds (60–70 kOe) and 2 K. For x ¼1 the saturation moment of 7.9mB is larger than the nominally expected value of 7.0mB for Gd3 þ and may be attributed to magnetic short-range order, as implied by high temperature molar susceptibility ﬁts given in Fig. 3, or conduction electron polarization as seen in Gd–La and Gd–Y alloys [27,29]. The relevance of evaluating isothermal magnetization data in this way was further veriﬁed using the y-intercept of M versus H 1 and normalizing by mBJ, which shows that the intercept is 1.12 and 1.16 for x¼1 and 2, respectively, implying a small correction to the reduced magnetization expression. In addition to the high quality of ﬁt from linear extrapolation, these results strongly suggest the relevance of RKKY interaction with spin-glass-like characteristics in this BMG system. The saturation behavior for x ¼2 yields a similarly large moment of 8.1mB. Interestingly, a ﬁeld much greater than 70,000 Oe is necessary to obtain saturation at 2 K and strongly suggests the importance of frustration such as spin-glass behavior in CuZrGd alloy systems  although past studies of similar BMG systems and recent AC susceptibility measurements conﬁrm that x¼ 1 and 2 remain paramagnetic up to 2 K [25,30] . The slope determined from the linear ﬁt gives V0 ¼3 10 38 and 2.3 10 38 erg cm3 for x ¼1 and x¼ 2, respectively. For a free electron the Fermi energies are estimated to be EF ¼9.34 eV and 9.40 eV and pﬃﬃﬃthe exchange integral Js f can be determined from 2 Jsf ¼ V0 32 2EF k3F =½92 JðJ þ 1Þ [4,31], giving 9Js f9¼0.15 eV and 0.13 eV for x¼1 and x ¼2, respectively. This interaction strength is comparable to those of amorphous alloys such as LaAuGd [12,32], but is 3–4 times larger than the interaction strength
7.8 7.7 7.6 7.5 7.4 7.3 7.2 0.0
H-1 (Oe-1 x 10-5) Fig. 5. Linear extrapolation of M versus H 1 at high ﬁelds (60–70 kOe) results in a large saturation moment of 7.9mB and 8.1mB for x¼ 1 and 2, respectively.
determined in CuZrGd  with considerably higher Gd concentration and (La, Gd)Al  alloy systems containing comparable Gd content. It is interesting to note that less Gd content (x¼ 1) yields a slightly stronger interaction strength, which is consistent with the NMR (insets in Fig. 2(a) and (b)) and susceptibility measurements (Fig. 3(a) and (b)).
4. Discussion In general, NMR and magnetization measurements both conﬁrm the development and the importance of AF short-range order of x ¼1 and 2 commencing at high temperatures near 150 K. This is supported by temperature independent hyperﬁne couplings Ahf for x ¼1 and x ¼2, which show that the source of broadening is due to the local magnetic susceptibility distribution at high temperatures. Non-linear linewidth broadening shown in Fig. 2(a) and (b) clearly proves that this distribution is prominent at high temperatures, evolves over a narrow temperature range (40–801), and stops development near 77 K. Furthermore, the non-Brillouin isothermal magnetization behavior at low temperatures seems to suggest that the AF cluster development in both x¼1 and 2 is magnetically frustrated. The intra-cluster interaction strength for x ¼1 and 2, as determined by the exchange integral
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9Js f9, shows that this frustration is quite strong as it is considerably higher than other Gd-bearing amorphous systems [4,31] showing long-range spin-glass behavior. The arrested development behavior of magnetic clusters for x ¼1 and 2 is quite different from the magnetic cluster formation observed in intrinsically inhomogenous systems such as manganites  and NFLs  in the Grifﬁths phase , where short-range order shows tremendous development and also beginning similarly at high temperatures near 150 K over a broad temperature range up until the long-range ordering temperature. This may explain the deviation of the low temperature susceptibility ﬁt from the theoretical scaling predicted for the Grifﬁths phase shown in the inset of Fig. 3. The development of AF cluster frustration at such high temperatures has not been demonstrated previously in these Gd-bearing ZrCuAl BMG systems and further demonstrates the importance of preliminary magnetic development that can occur in paramagnetic systems. The current NMR and magnetization results and past studies of ZrCuGd amorphous systems strongly indicate that further addition of Gd would eventually drive the system from frustrated AF short-range to long-range FM order [4,25]. Although these studies provide some interesting insight into the nature and limits of frustrated short-range order in dilute magnetic amorphous systems more extensive magnetization measurements, in addition to transport and mSR measurements, are clearly necessary to fully understand the magnetic behavior, which is especially important at high and at low temperatures.
5. Conclusions In conclusion, we utilized temperature dependent 27Al NMR spectroscopy and magnetization measurements to explore the local magnetism in (CuZr)46.5 xAl7Gdx (x ¼1, 2) BMGs with high GFA. For the ﬁrst time, it was observed that strong spectral linewidth enhancement emerges at high temperatures arising from a distribution of the local susceptibility that spans a narrow temperature range. Magnetization experiments conﬁrm that while the local susceptibility is inhomogenous and gives rise to strong AF short-range frustration these amorphous systems on average remain paramagnetic.
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