ISSN 0021-3640, JETP Letters, 2008, Vol. 87, No. 6, pp. 316–320. © Pleiades Publishing, Ltd., 2008. Original Russian Text © I.A. Garifullin, N.N. Garif ’yanov, R.I. Salikhov, L.R. Tagirov, 2008, published in Pis’ma v Zhurnal Éksperimental’noœ i Teoreticheskoœ Fiziki, 2008, Vol. 87, No. 6, pp. 367–371.
Knight Shift in Superconducting Vanadium I. A. Garifullina, N. N. Garif’yanova, R. I. Salikhova, and L. R. Tagirova, b a Zavoisky
Physical–Technical Institute, Kazan Scientific Center, Russian Academy of Sciences, Sibirskiœ trakt 10/7, Kazan, 420029 Russia e-mail:
[email protected] b Kazan State University, ul. Kremlevskaya 18, Kazan, 420008 Russia Received December 3, 2007; in final form, February 19, 2008
The Knight shift in metallic vanadium in the normal and superconducting states has been measured. In contrast to the previously obtained results, this shift appears to change after the transition to the superconducting state. The behavior of the Knight shift in the superconducting state in vanadium samples doped with iron impurities has been found to be different from that in the “pure” samples. As a possible explanation of the effect, the broadening of the peak of the density of states near the Fermi level due to the scattering of conduction electrons on the iron impurities and the earlier predicted impurity polarization shift of the NMR line are discussed. PACS numbers: 74.25.Nf, 76.60.Cq DOI: 10.1134/S0021364008060106
Recently, the authors of a series of theoretical works [1, 2] on the superconductor/ferromagnet (S/F) layered structures proposed an interesting physical explanation of the spin screening of the magnetic moment of the ferromagnetic (F) layers by a superconductor. Qualitatively, this effect can be explained as follows. The conduction electrons of a thin F layer magnetized in the same direction have the Cooper partners in the superconductor bulk, whose spin is opposite, because the total spin of a singlet Cooper pair should be equal to zero. As a result, the conduction electrons in the superconductor appear to be magnetized to a depth on the order of the coherence length. This magnetization is opposite to that of the conduction electrons in the ferromagnet. More formally, this means that the screening effect is proportional to a decrease in the spin susceptibility of the conduction electrons in the superconducting (S) layer under the superconducting transition. The spin susceptibility of the conduction electrons is, in turn, the physical source of the Knight shift of the nuclear magnetic resonance (NMR) line in metals. Thus, in the NMR, the spin screening effects are expected to manifest themselves in a measure of the decrease in the Knight shift after the transition of the system to the superconducting state. Taking into account the technical limitations of the experimental equipment, we can formulate the main criteria for the choice of a superconducting metal to observe the screening effects: (i) a strong NMR signal; (ii) a sufficiently high superconducting transition temperature in the zero magnetic field, Tc ~ 4–10 K;
(iii) good matching to the ferromagnetic material in the film growth conditions, the quality of the S/F interface and its transparency to electrons; (iv) a considerable decrease in the Knight shift under the superconducting transition. Criteria (i) and (ii) select lead, niobium, and vanadium as suitable superconductors of all of the superconductors where the Knight shift was measured (see, e.g., [3, 4]). Using the results of our studies on the layered S/F structures [5], we can conclude that a combination of lead with ferromagnetic metals of the Fe group has a low interface transparency to electrons, while the Nb– Fe pair [6] has a “dead” layer at the metal–metal interface. On the contrary, the V–Fe pair has a high interface transparency to electrons [7] and the epitaxial growth conditions of the films in any sequence [8]. Therefore, vanadium is the most suitable superconductor according to criteria (i)–(iii). However, Noer and Knight [9] state that the Knight shift in vanadium does not change in the superconducting transition. We experimentally showed that this is not the case and the Knight shift in pure vanadium changes in the transition to the superconducting state as in pure niobium [10], which has a similar electron structure. Introducing a small (0.5– 1.5 at %) amount of Fe impurity, we obtained additional evidence of the presence of the spin contribution made by the conduction electrons to the Knight shift of the NMR line for vanadium. Since the penetration depth of the magnetic field in vanadium is small, λ 500 Å, and, accordingly, a few nuclei are involved in the resonance, and the NMR measurements are a serious problem. To solve this problem, we built a supersensitive NMR spectrometer operating in the continuous mode. This NMR spec-
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trometer was based on a Robinson generator (see, e.g., [11]). Field-effect transistors capable of operating at low temperatures made it possible to immerse the generator into liquid helium immediately near the samplecontaining coil. Therefore, we sharply reduced the thermal noise and excluded losses in the line connecting the coil to the generator. Since the gyromagnetic ratios for the Cu and V nuclei are close, the resonant coil was winded with a high-purity silver wire rather than with a copper wire. At liquid-helium temperatures, this circuit had a high Q factor that also considerably increased the NMR spectrometer sensitivity. The generator output was connected to a synchronous detector with digital signal processing. The source of the dc magnetic field in the spectrometer was the magnetic system of an ER-418 EPR spectrometer (Brooker Company), which included the field sweep and stabilization by the Hall unit. The precision measurements of the magnetic field were performed by a Sh1-1 gaussmeter whose NMR sensor was in a strictly fixed position. The measurement error of the magnetic field including its inhomogeneity in the operating range (4 × 10–5 Oe/cm) did not exceed 0.2 Oe. The sample was prepared from 99.99%-pure vanadium rolled through steel rolls to a thickness of 50 µm. Each rolling procedure was followed by annealing at about 1000°C in a vacuum of about 10–5 Torr. The ratio RRR = R(300 K)/R0 of electric resistance at room temperature, R(300 K), to the residual electric resistance near the superconducting transition temperature, R0, appeared to be about 20. With the given phonon contribution to the resistivity of vanadium, ρphon (300 K) = 18.2 µΩ cm, we determined the residual resistivity ρ0 1 µΩ cm. Following Lazar et al. [5] and using the Pippard relations [12], we established the relation ρ0l = 2.5 × 10–6 µΩ cm2 between the mean-free path l of the conduction electrons and the residual electric resistance of vanadium. For our samples, this gives l = 250 Å. The BCS coherence length for vanadium is ξ0 = 440 Å. The relation between l and ξ0 implies that the superconducting properties of our samples are closer to the “dirty” limit (l ξ0) than to the “clean” limit (l ξ0). The same purity vanadium and 99.99% purity iron were used to prepare the Fe-doped vanadium samples. The VFe alloys were prepared in an arc furnace filled with ultrapure argon (99.999%). Three types of samples containing 0.5, 1.0, and 1.5 at % Fe were prepared. After fusion, the alloy balls were rolled and subjected to intermediate and final annealings as in the case of the pure vanadium samples. The temperature Tc was measured according to the variation of the ac magnetic susceptibility of the samples. It appeared that Tc is suppressed by the Fe impurity at a rate of 0.7 K/at % Fe. The upper critical field Hc2 was determined according to the dc resistance variation. The NMR measurements were performed on 51V nuclei in the temperature range of 1.4–4.2 K. Since the JETP LETTERS
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Fig. 1. NMR spectra of pure V samples in the normal (T = 4.2 K) and superconducting (T = 2.2 and 1.4 K) states in the external magnetic field perpendicular to the sample plane. The dashed lines mark the fitting results (see the main text).
operating frequencies are somewhat different for different samples, to visually compare the resonance line positions, all of the data were recalculated to a single radio frequency, in our case, to ν = 6115.8 kHz. In the dc magnetic field perpendicular to the film plane and the pure V samples in the normal state, the asymmetric NMR line is observed (Fig. 1, T = 4.2 K). The character of the asymmetry directly indicates that the sample thickness is comparable to the skin-layer depth, which is estimated as 50 µm at the operating frequency. The resonance line shape was quite accurately described by a combination of the dispersion and absorption Gaussian curves. This fitting made it possible to determine the resonance line position with an absolute error lower than 0.3 Oe. The resonance line width (the peak-topeak distance of the absorption line derivative) was found to be ∆H = 16.9 Oe. The Knight shift in the normal state equal to the ratio of the NMR line shift (δH = 31.4 Oe) with respect to its position in an insulator, 5464.4 Oe (51V in Figs. 1–3), to the resonant field H0 = 5433.0 Oe appeared to be equal to 0.58 ± 0.01%. It is in complete agreement with the previously measured value [9]. In the superconducting state (T = 2.24 and 1.4 K in Fig. 1), as the temperature is decreased, the resonance line is shifted to higher magnetic fields and is broadened approximately up to 23 Oe at T = 1.4 K. In this case, owing to the decrease in the signal-to-noise ratio and the necessity of including the drift of the baseline in the superconducting state, the error in the Knight shift measurement is almost doubled. If the dc magnetic field is parallel to the sample surface in the normal state, the spectrum observed is similar to that observed in the above case of the perpendicular orientation (T = 4.2 K in Fig. 2). The resonance signal intensity in the superconducting state appears to be somewhat lower than that in the perpendicular orienta-
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Fig. 2. NMR spectra of pure V samples in the normal (T = 4.2 K) and superconducting (T = 2.35 K) states in the external magnetic field parallel to the sample plane. The dashed lines mark the fitting results (see the main text).
tion and the line shift to higher magnetic fields occurs much faster. The signal amplitude below 2 K decreases drastically so that the line becomes unobservable. The character of the ∆H variation remains unchanged. In the vanadium samples doped with 1 at % of Fe, the NMR line behaves similarly; however, the shift of the resonance signal from the 51V nuclei to higher magnetic fields in the superconducting state is noticeably smaller. The evolution of the NMR spectrum from this sample for the parallel orientation is shown in Fig. 3. The table presents the Knight shift values in “pure” samples and the samples doped with 1 at % of Fe at various temperatures. We now discuss the results obtained. To date, the most detailed analysis of the NMR results in type II superconductors in the mixed state was performed by Knight shifts Kexp in pure V and 1-at %-Fe-doped V in normal (N) and superconducting (S) states at various temperatures
V (N) V (S) V0.99Fe0.01 (N) V0.99Fe0.01 (S)
T, K
Kexp, %
4.2
0.58 ± 0.01
2.6
0.51 ± 0.02
2.35
0.51 ± 0.02
2.2
0.52 ± 0.02
4.2
0.62 ± 0.02
2.5
0.56 ± 0.02
2.4
0.54 ± 0.02
2.3
0.54 ± 0.02
Fig. 3. NMR spectra of the V0.99Fe0.01 alloy samples in the normal (T = 4.2 K) and superconducting (T = 2.5 and 1.4 K) states in the external magnetic field parallel to the sample plane. The dashed lines mark the fitting results (see the main text).
Rossier and MacLaughlin [10]. We will follow them in discussing our results. It is known that the portion of nuclei in the Abrikosov vortex lattice is greatest at the saddle point Hs. According to [13], for the triangular vortex lattice, H v – H c = 1.46 ( H – B )
(1)
H s – H c = 0.12 ( H – B ).
(2)
and Here, Hv and Hc are the field at the vortex center and the minimum field in the vortex lattice, respectively, and H – B = –4πM. It follows from these relations that H v – H s = 1.34 ( H – B ).
(3)
In the case of the parallel orientation of the sample, the field Hv at the vortex center appears to be equal to the external magnetic field He due to the zero demagnetization factor in this orientation. Thus, the true magnetic field in this sample orientation is H 0 = H s = H e + 1.34 × 4πM.
(4)
In the geometry of our experiment, the demagnetizing factor in the parallel and perpendicular sample orientations is equal to zero and –4πM, respectively. Therefore, we can determine the 4πM value as the difference between the resonant fields in the perpendicular and parallel sample orientations with respect to the external magnetic field. This means that the true resonant field in the superconducting state is Hs = 5436 Oe, and the Knight shift in the superconducting state for the sample of “pure” vanadium at T = 2.2 K appears to be equal to 0.52 ± 0.02%. This result contradicts the previous data from [9], where it was stated that the Knight shift does not change at the superconducting transition. AccordJETP LETTERS
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ing to the calculations [14], the magnetic susceptibility χ(T) and Knight shift K(T) of vanadium in the normal state can be written as χ ( T ) = χ s + χ orb + χ d ( T )
(5)
K ( T ) = K s + K d–sp + K d–orb ,
(6)
and
where χs and χd(T) are the spin susceptibilities of the s and d bands, respectively; and χorb is the orbital susceptibility of the degenerate d band. The shifts Ks and Kd−sp associated with the s and d bands, respectively, vanish in the superconducting state. Hence, the shift K = Korb should be observed in the superconducting state; it appeared to be about 0.5%. We now discuss the NMR data for the V1 – xFex alloys. The Knight shift in the normal state appears to be equal to 0.62 ± 0.02 (see the table). In the transition to the superconducting state at all temperatures, the shift appears to be somewhat higher than that in the “pure” samples. We assume that, first of all, iron and vanadium at concentrations on the order of 1% are in a nonmagnetic state as follows from the experiment [15]. The introduction of this amount of a nonmagnetic impurity to a normal metal hardly changes its properties significantly. However, in vanadium, as well as in niobium and intermetallic compounds with the A15 structure, some physical parameters are determined by the presence of a narrow peak of the density of states near the Fermi level. Owing to the introduction of impurities, this narrow peak is smeared and the density of states of conduction electrons at the Fermi level decreases [16]. Naturally, Tc and the static susceptibility of the d band also decreases. The latter circumstance reduces the contribution Kd–sp to the Knight shift given by Eq. (6). This means that the Knight shift in the normal state should increase because this contribution is negative. It is seen from the table that a slight increase in the Knight shift is experimentally observed. In the superconducting transition, we may expect that the spin contribution to the Knight shift vanishes, i.e., that the Knight shift decreases to ~0.5% as in pure vanadium. Actually, the resulting Knight shift in the superconducting state is somewhat larger. In view of this circumstance, we cannot exclude that the nonmagnetic behavior of the Fe impurity in V is only spurious and it is actually magnetic. In this case, as Tagirov and Khalliulin predicted [17], the polarization shift of the NMR line should be observed in the superconducting state. The physics of this phenomenon differs only slightly from that proposed for the layered S/F systems [1]: the localized moment polarizes the spins of the surrounding conduction electrons due to the exchange sd interaction. The polarization sign depends on the sign of the exchange integral Jsd (this JETP LETTERS
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polarization mediates the Ruderman–Kittel–Kasuya– Yosida interaction between the localized impurity moments in normal nonmagnetic metals). In the superconducting phase, a cloud of polarized conduction electrons near the localized moment induces the constantsign polarization of the opposite sign at a distance on the order of the coherence length to provide the zero total response of the singlet condensate at T = 0 [18]. Since the average distance between the impurity moments at concentrations on the order of 1 at % is much shorter than the superconductor coherence length, the “superconducting” polarization is almost uniform in space. The resultant Knight shift is expressed as follows: K = K { 1 – δχ ( T ) ( 1 + α ) }, S
N
(7)
where α = cJsdχi/gegiβ2 and χi = g i β2S(S + 1)/3kT is the susceptibility of the localized spins. The impurity polarization contribution (∝α) to the Knight shift depends on the sign of Jsd. Our data imply that the integral Jsd of the exchange interaction between the localized moment of iron and the conduction electron spins is negative (α < 0, hence Jsd < 0). This indicates that Fe in V is a Kondo impurity. Since the standard measurements of magnetization reveal the nonmagnetic behavior of the samples, we can conclude that the Kondo temperature TK of this system is sufficiently high. In this case, because the conduction electrons screen the impurity magnetic moment, the Fe impurity seems to be nonmagnetic as observed in the experiment [15]. We are sincerely grateful to the referee for his constructive and invaluable contribution to the final version of our paper. This work was supported by the Russian Foundation for Basic Research [project nos. (experiment) 05-02-17198 and (theory) 07-02-00963] and by the Deutsche Forschungsgemeinschaft (German Research Foundation, grant no. SFB 491). 2
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Translated by E. Perova
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