2
Volume25A. number 7 PHYSICS LETTERS 9October 1967 que u'{f) ne passera jamais par la valeur zdro, ce qui semble en bond accord avec les expdrien- ces publi6es. Nous pouvons aussi remarquer que si nous donnons fi f~l i) la forme d'une fonction de Dirac 6(J i-Jc), ce qui revient ~ consid~rer une seule valeur des forces d'ancrage et donc une vitesse unique pour les vortex, nous retrouvons le r~sultat de Van Ooijen et Van Gurp. Les auteurs remercient les Professeurs Pi- cinbono, Savelli et Dumontet pour d'utiles dis- cussions. Ce travail a pu etre entrepris grace la D. G. R. S.T. (Comit~ Electrotechnique Nou- velle). R~fdrences 1. D.V. Van Ooijen et G.J.Van Gurp. Phys. Letters 17 (1965} 230. 2. D.J.VanOoijen et G.J.VanGurp, Philips Research Reports 21 (1966) 343. 3. J.Baixeras et G.Fournet, J.P.C.S. 28 (1967) 1541. ELECTRON-NUCLEAR DOUBLE RESONANCE OF 55Mn 2+ Y. H. ESKES and H.W. DE WIJN Natuurkundig Laboratorium der Universiteit van Amsterdam. Amsterdam. The Netherlands Received 11 September 1967 IN MgO* ENDOR techniques were used to determine the cubic crystalline field splitting a, and the nuclear spin Hamiltonian parameters A, giI2 N, and U of 55Mn2+ in MgO at 4.2°K. The nuclear magnetic moment of 55Mn has been dereived to be ÷{3.437 ± 0.005) ~N" In this letter we report Electron-Nuclear Double Resonance (ENDOR) measurements on 55Mn 2+ in MgO. The measurements were made with a superheterodyne EPR spectrometer oper- ating near 9.0 GHz [1]. The r.f. power was provided by GR unit oscillators, up to 250 MHz followed by a wide band amplifier. Amplitude modulation of the r.f. power and synchronous detection were employed. The r.f. coil is a single loop, secured in the cavity walls. The relevant terms of the spin Hamiltonian of a 55Mn 2+ ion (S--~ andl =2 ~) in the cubic MgO lattice are !~4 + s~ ÷ s~ - ~ scs÷ s)[3sls÷ ll -11} ÷ + 6 L~X + AS'! + U{S3xIx+S~Iy +S3zlz-~[3SCS+ 1)- 1]S.l} - glgN/'/" I, * Supported by the Netherlands Foundation for Funda- mental Research of Matter (F.O.M.) and the Nether- lands Organization for Pure Scientific Research (z.w.o.). where x, y and z refer to the cubic crystalline axes. The g value was derived from EPR spec- tra, which were analyzed by developing the energy levels and resonant fields in terms of a/g(3H and A/gI3H [2-4]. We found g = 2.0007 i ~- 0.0005 at 4.2°K. The ENDOR measurements were performed with the static magnetic field pointed along the z-axis. All 30 allowed ENDOR transitions were observed. They occur in 6 groups, each group consisting of 5 lines (fig. 1), centered at the ap- proximate frequencies of 620, 390, 155, 90, 340 and 595 MHz. The groups have to be attributed to m S = +~-, +{, +½, -½, -~ and -{, respetively, as is inferred from the detailed calculations. It was found that the ENDOR lines remain observ- able when the static magnetic field is several hundreds of G off the center of the EPR line. About 200 ENDOR frequencies at various magne- tic fields were measured. In the computer program the secular equation of the spin Hamiltonian, including all non-diag- onal elements, was solved by matrix diagonali- zation, and the parameters a, A, gI ~, and U 553

Electron-nuclear double resonance of 55Mn2+ in MgO

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Page 1: Electron-nuclear double resonance of 55Mn2+ in MgO

Volume25A. number 7 P H Y S I C S L E T T E R S 9October 1967

que u'{f) ne p a s s e r a j a m a i s par la va leu r zdro, ce qui semble en bond accord avec les expdr ien- ces publi6es. Nous pouvons auss i r e m a r q u e r que si nous donnons fi f~ l i) la f o rme d'une fonction de Di rac 6(J i - J c ) , ce qui r ev ien t ~ cons id~re r une seule va leu r des fo rce s d ' a n c r a g e et donc une v i t e s s e unique pour les vor tex , nous r e t rouvons le r~sul ta t de Van Ooijen et Van Gurp.

Les au teurs r e m e r c i e n t les P r o f e s s e u r s P i - cinbono, Savel l i et Dumontet pour d 'u t i l e s d i s -

cuss ions . Ce t r ava i l a pu e t r e e n t r e p r i s g r ace la D. G. R. S . T . (Comit~ E lec t ro techn ique Nou- vel le) .

R~fdrences 1. D.V. Van Ooijen et G.J.Van Gurp. Phys. Letters

17 (1965} 230. 2. D.J.VanOoijen et G.J.VanGurp, Philips Research

Reports 21 (1966) 343. 3. J .Baixeras et G.Fournet, J .P .C .S . 28 (1967)

1541.

E L E C T R O N - N U C L E A R D O U B L E R E S O N A N C E O F 5 5 M n 2+

Y. H. ESKES and H.W. DE WIJN Natuurkundig Laboratorium der Universiteit van Amsterdam.

Amsterdam. The Netherlands

Received 11 September 1967

IN M g O *

ENDOR techniques were used to determine the cubic crystalline field splitting a, and the nuclear spin Hamiltonian parameters A, giI2 N, and U of 55Mn2 + in MgO at 4.2°K. The nuclear magnetic moment of 55Mn has been dereived to be ÷ {3.437 ± 0.005) ~N"

In this l e t t e r we r epo r t E l e c t r o n - N u c l e a r Double Resonance (ENDOR) m e a s u r e m e n t s on 55Mn 2+ in MgO. The m e a s u r e m e n t s were made with a superhe te rodyne EPR s p e c t r o m e t e r o p e r - ating near 9.0 GHz [1]. The r . f . power was provided by GR unit o sc i l l a t o r s , up to 250 MHz followed by a wide band ampl i f i e r . Ampli tude modulat ion of the r . f . power and synchronous detect ion were employed. The r .f . coi l is a s ingle loop, s ecu red in the cavity wal ls .

The r e l evan t t e r m s of the spin Hamil tonian of a 55Mn 2+ ion (S--~ a n d l =2 ~) in the cubic MgO la t t ice a re

! ~ 4 + s~ ÷ s~ - ~ scs÷ s)[3sls÷ ll -11} ÷ + 6 L~X

+ A S ' ! + U{S3xIx+S~Iy +S3zlz-~[3SCS+ 1) - 1 ] S . l }

- glgN/ ' /" I ,

* Supported by the Netherlands Foundation for Funda- mental Research of Matter (F.O.M.) and the Nether- lands Organization for Pure Scientific Research (z.w.o.).

where x, y and z r e f e r to the cubic c rys ta l l ine axes . The g value was de r ived f rom EPR spec - t ra , which were analyzed by developing the energy leve l s and resonant f ie lds in t e r m s of a/g(3H and A/gI3H [2-4]. We found g = 2.0007 i ~- 0.0005 at 4.2°K.

The ENDOR m e a s u r e m e n t s were p e r f o r m e d with the s ta t ic magnet ic f ield pointed along the z - ax i s . All 30 al lowed ENDOR t rans i t ions were observed . They occur in 6 groups , each group cons is t ing of 5 l ines (fig. 1), cen te red at the ap- p rox imate f r equenc ies of 620, 390, 155, 90, 340 and 595 MHz. The groups have to be a t t r ibuted to m S = +~-, +{, +½, -½, -~ and -{, r e spe t ive ly , as is i n f e r r ed f rom the deta i led calcula t ions . It was found that the ENDOR l ines r ema in o b s e r v - able when the s ta t ic magnet ic f ie ld is s e v e r a l hundreds of G off the cen te r of the EPR line. About 200 ENDOR f requenc ie s at va r ious magne - t ic f ie lds were m e a s u r e d .

In the compute r p r o g r a m the secu la r equation of the spin Hamil tonian, including al l non-d iag- onal e l emen t s , was solved by m a t r i x d iagona l i - zation, and the p a r a m e t e r s a, A, gI ~ , and U

553

Page 2: Electron-nuclear double resonance of 55Mn2+ in MgO

Volume 25A, number 7 P H Y S I C S L E T T E R S 9 October 1967

m s = +3/2 A

t •

÷ i i j

ms\-312 ÷ ÷

$ $ * * cu cu ¢~ ¢~

'2 "; ,

J

~p ¢ ¢u

i

Table 1 Spin Hamiltonian p a r a m e t e r s as der ived f rom ENDOR

at 4.2°K.

l l t l r i I i

400 390 380 370 360 350 340 330

F r e q u e n c y (MHz)

Fig. 1. Typical ENDOR spec t ra of 55Mn2+ in MgO. Shown is the m S = - 3 g r o u p , and par t of the m S : +~ group. The microwave frequency is 8964.8 MHz. The stat ic magnetic field is 3371.2 G and di rected along the

[001] axis.

w e r e f i t t e d to the m e a s u r e d ENDOR f r e q u e n c i e s w i th l e a s t s q u a r e s a d j u s t m e n t ( t ab le 1). I t i s n o t e d t h a t , a l t h o u g h the c u b i c f i e l d s p l i t t i n g a i s i n d e p e n d e n t of t he n u c l e a r o r i e n t a t i o n , E N D O R m a k e s p o s s i b l e t he d e t e r m i n a t i o n , i n c l u d i n g the s ign . T h i s i s b e c a u s e t he n o n - d i a g o n a l e l e m e n t s of a a r e s u f f i c i e n t l y l a r g e r e l a t i v e to the e l e c t r o - n ic Z e e m a n e n e r g y to p r o d u c e o b s e r v a b l e e f f e c t s on the ENDOR f r e q u e n c i e s .

F r o m g i ~ N / h t h e m a g n e t i c m o m e n t of the 55Mn n u c l e u s , w i thou t s h i e l d i n g c o r r e c t i o n s , i s found to b e

64 = +(3.437 ± 0 .005) ~N.

W i t h a d i a m a g n e t i c c o r r e c t i o n c o n s t a n t cT = = (e2 /3mc2) ( r - l ) = 0.19%, t he c o r r e c t e d v a l u e of +(3.444 + 0 .005 )# N i s d e r i v e d . T h e v a l u e r e p o r - t ed h e r e i s s m a l l e r t h a n the g e n e r a l l y a c c e p t e d v a l u e of +3.4611 PN, a s o b t a i n e d f r o m NMR in

A/h (MHz) -244.426 i 0 . 0 0 2

A/hc (10 -4 cm -1) -81.5318 • 0.0007

gl W'N/h (10-4 MHz/G) ~10.479 • 0.015

U/h (MHz) -0.0012 • 0.0011

a/hc (10 -4 cm -1) +19.83 ± 0.12

The e r r o r s r ep resen t s tandard deviat ions propagated from measu red ENDOR frequencies plus e r r o r propa- gated from inaccuracy of g value. Fo r the hyperfine field pe r unit of e lec t ron spin i ts follows that Hhf s

A/[4I 6IN : -{232.8 ± 0.2) kG.

p e r m a n g a n a t e s [5 ,6] , by a s m u c h a s 0.5%. T h e p r e s e n t r e s u l t s u p p o r t s , h o w e v e r , t he v a l u e r e - c e n t l y p u b l i s h e d by M i m s e t a l . [7]. T h e s e a u t h o r s h a v e s u g g e s t e d t h a t in the p e r m a n g a n a t e s , w h e r e Mn i s b o n d e d in MnO~, s e c o n d o r d e r (Van V l e c k ) o r b i t a l p a r a m a g n e t i s m [8] i s r e s p o n - s i b l e f o r a c o n s i d e r a b l e s h i e l d i n g c o r r e c t i o n . E x p e r i m e n t a l e v i d e n c e fo r s u c h l a r g e e f f e c t s due to Van V l e c k p a r a m a g n e t i s m i s a v a i l a b l e f o r the Co c o m p l e x e s [5,9] . T h e NMR f r e q u e n c i e s of the Co n u c l e u s in t h e s e c o m p l e x e s h a v e b e e n found to d e p e n d on the w a v e l e n g t h of the l o w e s t o p t i c a l t r a n s i t i o n , f r o m w h i c h i t i s c o n c l u d e d t h a t Van V l e c k p a r a m a g n e t i s m g i v e s r i s e to a s h i e l d i n g of t he o r d e r of 1%.

R e f e r e n c e s 1. H.W. de Wijn. Rev. Sci. Inst r . 37 (1966) 1420. 2. W. Low. Phys. Rev. 105 (1957) 793. 3. B.C. Cavenett, Proc. Roy. Soc. (London) 84 {1964)

1. 4. H.W. de Wijn and R. F. van Balderen, J. Chem. Phys

46 (1967) 1381. 5. W.G. P roc to r and F .C . Yu, Phys, Rev. 77 (1950)

716. 6. R.E. Sheriff and D. Will iams, Phys. Rev. 82 (1951)

651. 7. W. B. Mims, G. E. Devlin, S. Geschwind and V. J ac -

carino, Phys. Le t t e r s 24A (1967) 481. 8. N.F. Ramsay, Nuclear moments (John Wiley and

Sons, Inc., New York, 1953), p. 71. 9. J . S. Griffith, The theory of t r ans i t ion -me ta l ions

(Cambridge Univers i ty P r e s s , 1961), p. 374.

554