High field knight shift and hyperfine anisotropy for 57Fe in bcc iron

H I G H FIELD K N I G H T S H I F T AND H Y P E R F I N E A N I S O T R O P Y F O R S7Fe IN BCC IRON* A. OPPELT, N. K A P L A N Institut fur Festkorperphysik, Technische Hochschule Darmstadt, D-6100 Darmstadt, Fed. Rep. Germany

D. F E K E T E and N. KAPLAN** Racah Institute, Hebrew University, Jerusalem, Israel

N M R of 57Fe (natural abundance) was studied in single crystal spheres of bcc iron in the range 0 < H 0 < 20 kG. Anisotropy of Hht, commensurate with the crystal, was observed in the range 5 < H o < 7.5 kG. The anisotropy disappeared for H o > 8 kG. A tenfold improvement in accuracy over previously reported attempts enabled a derivation of the sign and magnitude of the high field Knight shift in fcc iron, K = (78 ___ 15) × 10 -4. A n essentially model-independent delineation of the electronic contributions to X yields Xw = 143 x 10 -6 emu tool - l , Xd = 162 × 10 - 6 emu mol - I . Results are compared with predictions in the framework of two-band models of itinerant electron ferromagnetism.

1. Introduction High field Knight shift, K, and hyperfine anisotropy, a, in saturated single domain samples of 3d metal, ferromagnets provide valuable information concerning the nature of magnetism in these systems [1, 2]. The most serious attempt to elucidate the above properties in iron was reported a few years ago [1]. The Mrssbauer technique utilized in the attempt, enabled only the derivation of an upper limit, e~luivalent to K = (15 _ 100) × 10 -4. No a value was reported for iron. In the present publication we report the first successful determination of K and a, obtained by employing a somewhat unconventional nmr scheme.

2. Experimental Following similar considerations to those discussed previously for other ferromagnetic systems [2, 3], a polished spherical sample was prepared from a single crystal of bcc iron with a natural abundance of 57Fe. To achieve practical measuring times, we decided to use the Fast Fourier Transform Technique (FFT). The required rf irradiation across the whole 57Fe line profile was obtained by a spin-echo sequence. The amplitudes of the two rf pulses, at a frequency f0, were adjusted to obtain

an effective rotating field H ~ tf , ~ 3.5 k G at the 57Fe nuclei. Pulse widths of about 1 /ts were utilized. Under such conditions, 57Fe nuclei in a range of 0.5 M H z around fo were excited. The nuisance of "ringing", usually encountered with metallic single crystals, was avoided by using large separation, z = 800-1500 /~s, between the two rf pulses. All data were taken at 4.2 K. Examples of resulting echo signals are shown in fig. 1. The traces shown required averaging of 2 × 104 echos. To our surprise, however, the spin - e c h o sequence could be repeated at a rate of 100 s - l with no apparent T 1 saturation effects. Using F F T algorithm, the echos were transformed into absorption profiles as shown in fig. 2. The half width of these profiles, 8 ~ 20 kHz or 8H ~ 150 G, is the narrowest observed so far for 57Fe in domains of iron, enabling determination of the resonance frequency f0 with an accuracy of _+4 kHz ( + 30 G).

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*Supported in part by the SFB Darmstadt/Frankfurt. **Also: Institut fiir Festk~rperphysik, Technische Hochschule Darmstadt, D-6100 Darmstadt, FRG.

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Journal of Magnetism and Magnetic Materials 15-18 (1980) 660-662 ©North Holland

A. Oppelt et al./ High field Knight shift in bcc iron :~l

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Results

Values of f, as a function of the angle 0 between the magnetizing field H o and the [100] direction in the (110) plane, were measured for several H 0 values (fig. 3). Hyperfine anisotropy, commensurate with the crystal symmetry, is clearly visible for H 0 values below and around (4¢rM)/3 46,640 (a)

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Fig. 4. 57Fe hyperfine frequency in an iron sphere as function of the magnitude of the magnetizating field. --7288 G. For reference, the cubic anisotropy energy of bcc iron is also included in fig. 3. A plot of f versus the magnitude of H 0 in the range 0 - 2 0 kG is s h o w n in fig. 4. A linear fit was determined in the region H 0 ~> 9 kG, yielding f = fo - Vaf 11o with fo = (47 650 _+ 10) kHz and Yaf = (138.64.4- 0.10) Hz G -1. The "high field" shift, K - - ('/at - ~,57)/~/57, is calculated using "r57 = (137.56 _ 0.10) Hz G -z [4], and we find K = (78 +_. 1(3) × 10 -4. Thus, for the first time both the sign and the magnitude of the intrinsic Knight shift in ferromagnetic iron are determined. 4. Discussion

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Fig. 3. (a) S7Fe hyperfine frequency in an iron sphere as function of the direction of the magnetizing field. (b) Crystalline an/sotropy energy in bcc iron.

From fig. 3 it is apparent that the observed hyperfine anisotropy is connected with the transition from a multidomain system to a single domain sample. In particular, the variation of the functional form of the anisotropy (compare the 7.3 k G curve with the 6.0 kG curve) indicates that the phenomenon is related to the detailed variation of the demagnetizing field throughout the transition. In principle, one also expects to find intrinsic hyperfine anisotropy in the single domain region of cubic iron. Such anisotropy, attributed to the transfered hyperfine mechanism induced by magnetostriction, has been previously reported for the cubic insulating ferromagnet EuO [5]. However, with the

662

A. Oppelt et al./ High fieM Knight shift in bcc iron

present accuracy only an u p p e r limit, a(SVFe)------AHhf/Hhf < 0.3 × 10 -3, can be derived for bcc iron, c o m p a r e d with ct = 1.2 × 10 -3 for E u O [5]. Perhaps the m o s t rewarding consequence of the present study is related to K. As s h o w n previously [2], it is possible to delineate the various contributions to the bulk susceptibility X in a ferromagnetic metal by combining high field K n i g h t shift a n d susceptibility results. One m a y thus separate between the orbital contribution X~v and the spin contribution Xa. T h e latter in particular is a convenient quantity, as it is readily c o m p a r a b l e with the prediction of the rigid t w o - b a n d model of itinerant ferromagnetism. U s i n g bulk X values for iron [1], and following a procedure similar to the one outlined in ref. [2], an essential model independent derivation of Xw and Xd of iron is possible. We find X~, -~ 143 × 10 - 6 e m u mol - l a n d Xd = 162 × 10 -6 emu tool-~. The value of X~ is larger than the previous guesses [1], b u t no "first princi-

pie" calculation is yet available for X~ in any of the 3d metals. Our value of Xd verifies nicely the rigid t w o - b a n d model calculation for fcc iron [7].

References [1] S. Foner, A. J. Freeman, N. A. Blum, R. B. Frankel, E. J. McNiff and H. C. Praddaude, Phys. Rev. 181 (1969) 863. [2] D. Fekete, A. Grayevski, D. Shalti¢l, U. Goebel, E. Dormann and N. Kaplan, Phys. Rev. Lett. 36 (1976) 1566. [3] D. Fekete, A. Grayevski, N. Kaplan and E. Walker, Solid State Commun. 17 (1975) 573. [4] P. R. Locher and S. Geschwind, Phys. Rev. 139 (1965) A991. [5] D. Fekete, N. Kaplan and T. B. Reed, Solid State Commun. 15 (1974) 1827. [6] E. P. Wohlfarth, J. App. Phys. 41 (1970) 1205. [7] S. Wakoh and J. Yamashita, J. Phys. Soc. Japan 21 (1966) 1712; R.A. Tawil and J. Callaway, Phys. Rev. B7 (1973) 4242.