- Email: [email protected]

F.N. GYGAX, W. RtJEGG, A. SCHENCK, Laboratoryfor High Energy Physics, c/o SIN, CH-5234

H. SCHILLING,

W. STUDER

Villigen, Switzerland

and R. SCHULZE Institute

of Physics,

[email protected] of Maim,

The temperature dependence temperature region between magnetization.

D-6500 Maim,

Fed. Rep. Germany

of the Knight shift of an interstitial muon in paramagnetic nickel has been measured in the 637 and 906 K. The Knight shift has been found to be strictly proportional to the d-spin

In this contribution we present results on the temperature dependence of the Knight shift of a positive muon in paramagnetic nickel in the temperature range 637-906 K. In order to take full advantage of the high stopping rate obtainable from the muon channel at SIN we used the same stroboscopic method, which has recently been applied by us in a new precision determination of the magnetic moment of the positive muon [l, 21. This method is also largely free of systematic errors that are connected with the normally used time differential measurements. The measurements were performed with a single crystal of nickel (purity: 5N), cut to a sphere. An external field of 7.38 kG was applied parallel to the easy axis of magnetization. The external field was measured and stabilized by proton NMR to a precision of 1 ppm, the combined statistical and systematical errors in the determination of the precession frequency from the stroboscopic signal amounted to 22 to 90 ppm. The low temperature results for the Knight shift constant K are shown in fig. 1, where log( 1/K) is plotted against log(T - T,), T, = 632.5 K. fig. 2 shows the high temperature data, where K is plotted versus the bulk susceptibility (taken from ref. [3]). The Knight shift is generally negative, like the hyperfine field in ferromagnetic nickel. This hyperfine field is primarily due to the different densities of df and d&-electrons at the muon position, a consequence of the different radial parts of the nickel 3d-electron wave functions [4]. In order to compare the Knight shift with the hyperfine field one can “normalize” the Knight shift with the magnetization: for the field shift per magnetization unit we deduce from fig. 2: AK/$

Journal of Magnetism

Ax = 0.172 -+ 0.005.

and Magnetic

Materials

15- 18 (1980)

In the ferromagnetic pression is: B,,/!j

case

the corresponding

n M = 0.157 + 0.002.

ex-

(2)

The almost equal values strongly support the assumption, that the mechanism, which is responsible for the hyperfine field is the same that causes the Knight shift in the paramagnetic state (in the ferromagnetic case the Knight shift is positive and therefore of different origin [5]). This leads us to the conclusion that the local magnetization at an interstitial site (as seen by a muon) only depends

5

6

-10 05

8 10 12 15

20 25 30 LC 50 60

10

15

80 100ATk 2

lagIT-Tcl

Fig. I. Low temperature (T > T,) Knight shift results, the lines correspond to functions (T - T,)T. From these measurements we deduce a critical exponent of y o 1.28. Bulk suscep tibihty measurements gives an experimental value of y = 1.35

(1)

1191- 1192 aNorth Holland

f 0.02.

1191

1192

F. N. Gygax et al./Muon

r -L F

/ ~JP i4

l/x

47

t

r

amagnetic origin could not be found within present accuracy, In the low temperature region (near ‘TJ deviations of the temperature dependence of susceptibility from a Curie-Weiss law can be scribed with a critical exponent, y, using following function:

-+

2000

Knight shift in nickel

y, ( s;'u/

-10 t20 ppm ,,,I.,,,

>,I

01

ILL__ 02

; J

m+7-

Fig. 2. High temperature (T > T,) Knight shift plotted against bulk susceptibility. The Knight shift is everywhere proportional to the susceptibility. A temperature independent contribution is smaller than (- 10 2 20) ppm.

on the polarization of the d-moments, i.e. is completely independent of the mechanism that causes the polarization (exchange field or external field). From fig. 2 we can also see, that the high temperature Knight shift follows a Curie-Weiss law, i.e. is strongly proportional to the bulk susceptibility. A temperature independent contri bution to the Knight shift of s-, orbital- and di-

= (T -

r,,’

the the the dethe

(3)

with an experimental value of 1.35 -+ 0.02 for y. As can be seen from fig. 1. the Knight shift follows the same law, with a critical exponent of y z 1.28, in good agreement with the above value. To our knowledge this is the first determination of the critical exponent by Knight shift measurements in nickel. In conclusion it has been shown, that the hyperfine field of the interstitial positive muon in paraand ferromagnetic nickel is everywhere strictly proportional to the d-spin magnetization. References [I] M. Camani,

[2]

[3] [4] [5]

F. N. Gygax, E. Klempt, W. Ruegg, A. Schenck, H. Schilling, R. Schulze and H. Wolf, Phys. Rev. Lett. 42 (1979) 679. M. Camani, F. N. Gygax, E. Klempt, W. Riiegg, A. Schenck, H. Schilling, R. Schulze and H. Wolf, Phys. Lett. 77B (1978) 326. S. Arajs and R. V. Calvin, J. Phys. Chem. Solids 24 (1963) 1233. K. G. Petzinger and R. Munjal, Phys. Rev. B15 (1977) 1560. M. Camani, F. N. Gygax, W. Ruegg, A. Schenck and H. Schilling, Hyperfine Interactions 6 (1979) 8 1.