Induced magnetic fields at Gd nuclei in GdFe2 and Gd

Volume 27A, number 4

INDUCED

PHYSICS LETTERS

MAGNETIC B.

FIELDS

AT

1 July 1968

Gd NUCLEI

IN GdFe 2 AND

Gd *

PERSSON **, H. B L U M B E R G *** and M. BENT

California Institute of TechnolosY, Pasadena, CaUfornia, USA Received 20 May 1968

Large magnetic fields at the site of the Gd nucleus are found to be induced by the application of external magnetic fields on GdFe2 and Gd metal.

Th e m a g n e t i c h y p e r f i n e interacti~ms ~n t ~ r r i m a g n e t i c G d F e 2 and f e r r o m a g n e t i c Gd m e t a l / t a r e b e e n studied at 4.2°K and 1.8°K by m e a n s of r e c o i l l e s s resm'xance a b s o r p t i o n of the 89 keV g a m m a r a y s f r o m t h e 2 + s t a t e in 156Gd. T h e cubic L a v e s p h a s e s YbA12, YAI~ as well a s A1 w e r e u s e d a s h o s t s f o r the 156E~ s o u r c e s . T h e a b s o r b e r s c o n s i s t e d o f fine p o w d e r of G d F e 2 or Gd d i s p e r s e d in wax. A s m a l l quadrupole i n t e r action is e n c o u n t e r e d in Gd m e t a l , but none in the cubic L a v e s p h a s e G d F e 2. T h e p o l y c r y s t a U i n e a b s o r b e r s w e r e u s e d d e m a g n e t i z e d as well as m a g n e t i z e d in the d i r e c t i o n of the g a m m a - r a y b e a m s by f i e l d s ~< 56 kOe f r o m a s u p e r c o n d u c t i n g coil. Th e h y p e r f i n e s p l i t t i n g s in the a b s o r b e r s e x hibit a s t r o n g d e p e n d e n c e on the e x t e r n a l l y a p plied f i e l d s . In o r d e r to i n v e s t i g a t e p o s s i b l e e f f e c t s f r o m the s t r a y f i e l d a t the s o u r c e , m e a s u r e m e n t s w e r e p e r f o r m e d with the s o u r c e e x p o s e d to d i f f e r e n t s t r a y f i e l d s . I d e n t i c a l s p e c t r a w e r e obtained f o r the v a r i o u s s o u r c e s and f o r different source positions. The velocity spectra h a v e been l e a s t - s q u a r e s fitted to s u p e r p o s i t i o n s of L o r e n t z i a n s c o n s t r a i n e d by the r e l e v a n t h y p e r fine i n t e r a c t i o n . Additional c o n s t r a i n t s such as equal widths and i s o m e r shifts f o r the whole s e t of s p e c t r a obtained f o r a p a r t i c u l a r a b s o r b e r and s o u r c e did not signHicanfly a f f e c t the evaluation of the m a g n e t i c h y p e r f i n e s p l i t t i n g s . T h e m a g n e t i c f i e l d s at the n u c l e a r s i t e s , d e m o n s t r a t e d in fig. 1, w e r e d e r i v e d f r o m the m e s s * This work was performed under the auspieces of the U. S.Atomic Energy Commission. Prepared u n d e r Contract AT(04-3)-63 for the San Francisco Operations Office, U.S.Atomic Energy Commission. ** On leave from the University of Lund, Sweden. *** On leave from the Institute flir Strahlen- und Kernphysik of the University of Bonn, Germany.

J

~rll:= v~de v 2

eoo

J

~/

/

D

f 2

4oo' SYMBOL

2oo

SOURCE MATRIX ~b~ z

0.54 ~

¢ •

-"-,YAI z -"AI

-"096 Hit Q54 ~ -.-.-

vn

g

STRAY FfELD

o •

E 4.2 1.8 42 42 18 4.2

0 I

/

"g II( "K eK ~K eK

r f

/

0

/

-200 1

i 0

f

I 2O

i

I 4O

a 60

Fig. 1. Magnetic hyperfine splitting an~i magnetic field, Hnuc, at Gd in GdFe 2 and Gd metal plotted as function o f the externally applied field, Hext, corrected for the average demagnetizing field ' /:-aem ~ v (~ 2 kOe for GdFe 2 and ~ 7 kOe for Gd). Dashed lines correspond to the v ). relation Hnu c = Hhf + (1 +c) (Hext -/~dem u r e d m a g n e t i c s p l i t t i n g s of the 2 + s t a t e of 156Gd with the u s e of t h e NMR v a l u e of Hhf = 430 * 5 kOe [1] f o r the h y p e r f i n e f i e l d at Gd in GdFe2, which h as been m e a s u r e d at 4.2°K in t h e a b s e n c e of any e x t e r n a l l y applied field. Combining this NMR v a l u e with t h e p r e s e n t m e a s u r e m e n t s , which w e r e p e r f o r m e d u n d er i d e n t i c a l conditions, one obtains f r o m the sp l i t t i n g in G d F e 2 a v a l u e of 189

V o l u m e 27A, n u m b e r 4

P H Y SIC S LET T E R S

0.393 • 0.007 for the g - f a c t o r of the 2+ state in 156Gd and f r o m the splitting in Gd m e t a l a value of -305 + 18 kOe for the hyperfine field in Gd metal. The l a t t e r field is in good a g r e e m e n t with the value of -300 ± 23 kOe d e t e r m i n e d in a r e c e n t independent Mt}ssbauer e x p e r i m e n t [2]. The v a r i o u s s o u r c e s for the hyperfine field in Gd m e t a l have r e c e n t l y been s u m m a r i z e d by Httfn e r [3]. The m a j o r c o n t r i b u t i o n s a r e due to core p o l a r i z a t i o n (-340 * 20 kOe), conduction e l e c t r o n p o l a r i z a t i o n by ionic 4f e l e c t r o n s (+240 ± 50 kOe), and neighbor effects (-200~-60 kOe). With the a n t i p a r a l l e l spin a r r a n g e m e n t in GdFe 2 one may expect a positive c o n t r i b u t i o n f r o m the neighbor effects. The total positive c o n t r i b u t i o n f r o m conduction e l e c t r o n s , t h e r e f o r e , supposedly o v e r c o m p e n s a t e s the n e g a t i v e c o r e c o n t r i b u t i o n giving r i s e to a l a r g e positive hyperfine field in G d F e 2. Fig. 1 d e m o n s t r a t e s the induction of l a r g e positive fields at Gd in both GdFe 2 and Gd metal by the e x t e r n a l l y applied magnetic fields. The t e m p e r a t u r e independence of the induced fields s e e m s to exclude the p r e s e n c e of a s i z e a b l e

EXACT

1 J u l y 1968

c r y s t a l l i n e field splitting due to spin o r b i t i n t e r action. Magnetization data [4] suggests that the n e t spin of Cad and t h e r e f o r e also the core p o l a r i zation contribution to the hyperfine field is not influenced by the application of an external m a g netic field. The l a r g e induced fields t h e r e f o r e a r e p r e s u m a b l y due to an i n c r e a s e d conduction e l e c t r o n p o l a r i z a t i o n , however, the details of the m e c h a n i s m a r e not understood at p r e s e n t . We thank Dr. R. L. Mt~ssbauer for many helpful d i s c u s s i o n s .

Refe/rences 1. R.E.Gegenwarth, J.IoBudnick, S. Skalsi and J.H. Wernick, Phys. Rev. Letters 18 (1967) 9. The value of the magnetic hyperfine field has been reevaluated using ~t= s (Gd-157) = 0.337 ± 0.{}03 ~ . 2. J. Fink,b~.'f. Physik 207 (1967) 225. c~. comment under ref. 1. 3. S.Hitfner, Phys. Rev. Letters 19 (1967) 1034. See this paper for further references. 4. J . F . Elliot, S. Legvold and F. H. Spedding, Phys. Rev. 9 (1953) 28.

STATIONARY SOLUTION OF A FOKKER-PLANCK-EQUATION FOR MULTIMODE LASER-ACTION H. HAKEN I. lnstitut fli~" Theoretische Physik der Universit~t Stuttgart, Germany

Received 27 May 1968

The stationary solution of a Fokker-Planck equation describing the statistics of a multimode laser below, at and above threshold in the adiabatic region is given. Both the saturated gain and the frequency shifts may be power-dependent.

Since it had been shown t h e o r e t i c a l l y [1] and, subsequently, a l s o e x p e r i m e n t a l l y [2] that the s t a t i s t i c a l p r o p e r t i e s of l a s e r light differ b a s i c a l ly f r o m those of light f r o m t h e r m a l s o u r c e s , a g r e a t a m o u n t of work has been spent on the exp l o r a t i o n of the details of l a s e r s t a t i s t i c s [3]. In a l m o s t all c a s e s , the e x p e r i m e n t a l and t h e o r e t i cal i n v e s t i g a t i o n s w e r e c o n f i r m e d to single mode action. In the p r e s e n t l e t t e r we wish to p r e s e n t an exact solution of the F o k k e r - P l a n c k equation, which applies to i m p o r t a n t c l a s s e s of m u l t i m o d e p r o b l e m s in l a s e r theory. The d e r i v a t i o n of such 190

a F o k k e r - P l a n c k equation is now well known: One s t a r t s with the l a s e r - m a s t e r e q u a t i o n of Weidlich and Haake [4], which i s t r a n s f o r m e d [4] into a F o k k e r - P l a n c k equation by u s e of the c o h e r e n t state r e p r e s e n t a t i o n of G l a u b e r [5] and Sudarshan [6] for the field and the r e p r e s e n t a t i o n of Haken et al. [7] for the a t o m s . F o r a region not too far above threshold, the atomic v a r i a b l e s may be e l i m i n a t e d a d i a b a t i c a l l y [8], so that one ends up with a F o k k e r - P l a n c k equation for the complex mode a m p l i t u d e s fl-, fi* alone. A c l o s e r J .? i n s p e c t i o n shows that this equation can in g e n e r a l