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FIELD-INDUCED TWO-MAGNON NUCLEAR
SPIN-LATTICE RELAXATION IN ORDERED
QUADRATIC-LAYER ANTIFERROMAGNETS
A. J. van der Wal, H. de Wijn
To cite this version:
JOURNAL DE PHYSIQUE Colloque
C6,
supplPment au no8,
Tome39,
aocit1978,
pageC6-757
FIELD-INDUCED TWO-MAGNON NUCLEAR SPIN-LATTICE RELAXATION
IN ORDERED QUADRATIC-LAYER
ANTIFERROMAGNETSA.J. Van Der Wal and H.W. De Wijn.
E'ysisch Laboratorim, R i j k s u n i v e r s i t e i t , P. 0. BOX 80.000, Utrecht, the Netherlands.
Rbsumb.- Le temps de relaxation nucldaire T i 1 deux magnons provoqua par un champ magnctique, a fit6 mesure dans les composes lamellaires K,MnF, et K2NiF4 en fonction de La tempgrature dans le domaine d'arrangement antiferromagndtique. On montre que les resultats sont en accord quantitatif avec un calcul exact fond6 sur la thgorie de Beeman et Pincus.
Abstract.- The field-induced two-magnon relaxation time
T,
has been measured in the quadratic-layer structures K2MnF4and K NiF, in the antiferromagnetic regime as a function of temperature. The re-2
sults are shown to be in quantitative agreement with an exact calculation based on the Beeman and Pincus theory.
In this paper we present experimental data, as well as a rigorous calculation based upon the Beeman and Pincus theory /l/, of the temperature de- pendence of the spin-lattice relaxation time T of the out-of-layer "F ("F') nuclei (I =
4
) ik the two-dimensional (2D) quadratic-layer nearest-neigh- bor Heisenberg antiferromagnets K MnF and K NiF2 4 2 4
in a transverse magnetic field. By virtue of the staggered registry of neighboringlayers, these sys- tems are virtually ideal 2D Heisenbeq antiferroma- gnets. The magnetic structure within the layer is 2D simple quadratic, while the magnetic ordering is along the tetragonal axis / 2 / . Static magnetic proper
ties of these antiferromagnets, such as the sublat- tice magnetization, have already been discussed in detail in terms of spin-wave theory 1 3 1 .
A11 T measurements were done by an NMR tech-
1
nique consisting of first saturating the nuclear spin system, then applying a single a12 pulse, and observing the amplitude of the free induction decay following the latter. The sample was aligned in situ with the c axis perpendicular to the magnetic field with a precision better thah 0.1' by observing coa- lescence of the two "F' NMR branches, correspon- ding to "F' adjacent to up and down sublattices, respectively. The experiments were carried out on single crystals. with typical size 200
mm3,
which we- re grown from the melt by a horizontal zone-melting technique. The concentration of magnetic impurities as detected by atomic absorption was typically less than 50 ppm.The magnetic sylmnetry of the system is such that in zero field the transfer of energy from the
nuclear spins to the magnons is governed by three- magnon processes, enhanced by exchange scattering /4/. However, if a magnetic field perpendicular to the c axis is applidd, the symmetry that the con- serves the total angular momentum of nuclear and electronic spins is broken, and two-magnon relaxa- tion processes become allowed. Upon applying the field, the quantization axis of hhe nuclear spin system is canted over an angle 0 = arctan (Ho/Hhf) from the c axis, where Hhf = AZZ < SZ > is the hy- perfine field at the "FI site. The electronic spins are also canted, but over a much smaller an- gle I$
%
arctan (Ho/2HE) where HE is the exchangefield. In K MnF4, which has its spinflop at H. =
2
54.5 kG 151, we have at H. = 30 kG
4
= 0.8O, as compared to 0 = 38' ; in K NiF,
4
= 0.3' and 0 =2 1.
38'. We therefore ignore canting of the electronic
moments except for adding a small correction pro- portional to to the applied field Ho. Then, by rotating the nuclear quantization axis over an an- gle 0 from the c axis, the part of the hyperfine
24. interaction between neighboring "F' and Mn (or ~i
'+)
producing two-magnon relaxation, may be written asX'=
-
4
A~~I+S' sine, ( 1where S' still refers to the c axis. After using the Holstein-Primakoff transformation application of the golden rule to
K
gives the two-magnon re- laxation rateI t i s noted t h a t t h e f i e l d dependence o f T ( ~ ) i s p r i n c i p a l l y contained i n t h e f a c t o r s i n 2 e . The d i s - p e r s i o n r e l a t i o n E k , t h e o c c u p a t i o n number n k , and t h e Bogoliubov c o e f f i c i e n t s
\
and v k are o n l y wea- k l y dependent o n t h e f i e l d , and t h e s e e f f e c t s have been accounted f o r b y c o r r e c t i o n t e r m s , o f o r d e rl 8PH 2
4
(*).
E x p e r i m e n t a l l y , a t a g i v e n temperature E,'=
t h e flepd-induced two-magnon Raman process can be e x t r a c t e d from t h e measured r e l a x a t i o n r a t e s a t va- r i o u s t r a n s v e r s e magnetic f i e l d s , b y p l o t t i n g t h e r e s u l t s f o r t h e observed T - ' v e r s u s s i n 2 e . The i n i - t i a l s l o p e s T ( ' ) s i n 2 8 thu: obtained are p l o t t e d as a f u n c t i o n o f temperature i n f i g u r e I f o r b o t h K MnF and K N i F
.
2 C 2 4
F i g . 1 : The f ield-induced two-magnon Raman r e l a x a - t i o n t i m e T , ( ~ ) s i n 2 8 o f t h e 1 9 ~ 1 n u c l e i i n K2MnF, and K 2 N i F 4 as a f u n c t i o n o f temperature i n t h e l i - m i t o f zero f i e l d . The d a t a p o i n t s are derived from e x p e r i m e n t a l T;' v e r s u s a t r a n s v e r s e magnetic f i e l d . The f u l l c u r v e s a r e c a l c u l a t e d from Eq.(2) w i t h e x a c t i n t e g r a t i o n o v e r t h e B r i l l o u i n zone.
NMR measurements / 3 / , w h i l e E+, n+, U+ and v+, or
k k k k
a l t e r n a t i v e l y t h e exchange parameter J and t h e ani- s o t r o p y c o n s t a n t a , are determined from previous spin-wave a n a l y s i s / 3 / , / 6 / . Considering t h i s , t h e two-magnon r e l a x a t i o n c a l c u l a t e d from Eq. ( 2 ) i s found t o e x c e l l e n t l y agree w i t h t h e e x p e r i m e n t a l da- t a over t h r e e decades i n T
,
up t o temperatures1
c l o s e t o t h o s e corresponding w i t h t h e spin-wave ener- g y gaps (7.4 and 27.5 K i n KMnF and K N i F
,
r e s -2 4 2 '1
p e c t i v e l y ) . Another p o i n t o f i n t e r e s t i s t h a t two- magnon r e l a x a t i o n , i f n o t f o r b i d d e n by symmetry
.
(0 = 0 ) , is much f a s t e r t h a n t h r e e and higher-order magnon r e l a x a t i o n , and i n f a c t predominates above, s a y , s i n 2 0 = 0.01. T h u s , K MnF and K N i F provide
2 4 2 4
e x c e l l e n t examples i n which d i r e c t two-magnon r e l a - x a t i o n can b e separated from a l l o t h e r magnon r e l a - x a t i o n p r o c e s s e s . The s i m p l i c i t y o f t h e q u a d r a t i c - l a y e r s t r u c t u r e f u r t h e r allowed e x a c t c a l c u l a t i o n t o be done, l e a d i n g t o q u a n t i t a t i v e c o n f i r m a t i o n o f t h e a s s e r t i o n s o f t h e Beeman and Pincus t h e o r y .
R e f e r e n c e s
/ I / Beeman, D. and P i n c u s , P - , Phys. Rev.
166
( 1 968) 359. ,/ 2 / For a r e v i e w : De Jongh, L . J . and Miedema, A.R., Adv- Phys.
3
( 1 9 7 4 ) 1 ./ 3 / De W i j n , H . W . , W a l k e r , L.R. and W a l s t e d t , R.E., Phys. Rev. (1973) 2 8 5 .
/ 4 / Van Der Wal, A.J., S c h u l t e , B . and De W i j n , H.W. Proceedings-XIX Congress AmpSre ( ~ e i d e l b e r g ) 1976, p . 4 8 3 .
/ 5 / A r t s , A.F.M., Van U i j e n , C.M.J. and De W i j n , H . W . , Phys. Rev.
B15
( 1 9 7 7 ) 4360./ 6 / Birgeneau, R.J., Guggenheim, H.J. and S h i r a n e , G . , Phys. Rev. ( 1 9 7 3 ) 304.
