Journal of Magnetism and Magnetic Materials 31-34 (1983) 1183-1184 1183

DYNAMICS OF IMPURITY EXCITATIONS IN Q U A D R A T I C - L A Y E R A N T I F E R R O M A G N E T S

H V A N D E R V L I S T , W . C M. C L A A S S E N , A . F M. A R T S a n d H . W . D E W I J N

Fvslsch Laboratortum, Rtjksunivervtteit Utrecht, PO Box 80 000, 3508 TA Utrecht, The Netherland~

The spin autocorrelatlons of N* lmpurmes m K2MnF 4 and Mn lmpurmes m K2NIF 4 were examined by measuring the nuclear spm-lamce relaxation of out-of-layer 19F, and found to be dlmimshed and enhanced relanve to the host systems, respectively This was confirmed by Green's-funcnons calculations

We examined, m the ordered regime, the local spin autocorrelatxons associated with subst i tut ional impuri- ties m quadranc- layer antfferromagnets of the K2NIF 4 family by measuring the sp in- la t t i ce relaxation of the out-of-layer 19FI nucle~ adjacent to the ~mpunty. The systems studied were K z M n l _ ~ N I ~ F 4 and its reverse K2Nt 1 ~ M n , F 4 (x = 0.01), in which the impuri ty exci- ta t ions have energies well above and low within the band, respectively

The measurements were carried out with an \ M R spectrometer employing a single ~r/2 pulse for satura- t ion followed by a ~r/2, ~r sequence for detection, and opera t ing at about 170 MHz The measured 19FI sp in- la t t i ce relaxation rimes TI with the external field parallel to the c axis (fig 1) vary in KzMn1_~NI~F4 over four decades in the range 2 20 K, and m K2NI 1 ~Mn~F 4 over five decades up to 30 K

The s p m - l a t n c e relaxation rate of nuclei coupled by hyperfme interact ion to the electron spms of a magnetic system is propor t ional to the Fourier componen t of the autocorre la t ton func t |on of the electron spins at the Larmor frequency [1] In case the external field is along the c ax~s we have for the present system

= A~ f+OOdt cos o % t ( ( S o ( t ) S o }), (1) 1

Tt 2h 2 - ~

where ( ) denotes taking the symmetrlzed product , A, is the transverse hyperf ine coupling constant , So ± are com- ponen t s of the impuri ty spin, and ~o 0 ~s the Larmor frequency Since the decay rime of the corre lanons ts of the order of the reciprocal exchange frequency, o : l = h / J - 1 0 -12 s, T, in effect probes the static Fourier componen t (cos o:ot = 1)

F rom eq. (1) we see that we may use the measured T 1 to relate, at various temperatures, the transverse auto- correlat ion of the ~mpurity spin with that of the host spin at large &stances, or equivalently the pure system, by scahng T, in the latter [2] with the squared rano of the hype r f Inecons t an t s Thus T(N') m K z M n l _ ~ N I ~ F 4

10 3 ,

F~g 1 Spin-lattice relaxation times T I versus temperature of ~gFI Dashed hnes represent the experimental T 1 In the corre- sponding host systems after scaling of the hyperfme interac- tions to allow comparison of spin autocorrelanon functions

- o ~

~o

lO 2

v

"~ 101 l--

Z o

x

LH n-

LH

I-- IF

~, 10 °

n u3

10 -1

10-2I o

0 3 0 4 - 8 8 5 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 (*~ 1983 N o r t h - H o l l a n d

' I i I

\ \ \ \

\T~N~ so) \ \ K2NqF4

\ \

T(Mn) I

K2Nh-×Mn×F4

T(NI) ~ ~ c 1

K2Mnl.×NIxF 4

T(Mn,5¢) \ --1 \ c K2MnF 4 ~\\\ (%~

', x t k i I

10 2 0 T E M P E R A T U R E

\ \ \ \ \ \ \

J

(K)

\ \

\

30

1184

Is to be compared with T~ Mn's~)= (A~Mn)/A~N'))ZTI I n

K 2 M n F 4, and T( Mm m K 2 N l l _ x M n , F 4 with T( N' '~)= (A]N1)/A]M"))2TI in K2N1F 4. The Tl's of the pure sys-

tems scaled m this way are entered m fig. 1, where we see that m the N~-based system the spin autocorrelat~on ~s enhanced at the M n ~mpunty by say a factor of 70, and m the Mn-based system reduced at the N~ ~mpurlty by an order of magnitude.

For a calculation, the autocorrelat~on functions oc- curring m eq. (1) may first be writ ten m terms of H o l s t e i n - P n m a k o f f spm-dewat~on operators a 0 Be- cause of energy conservation, the leading process ~s the o n e d e s c r i b e d b y t he c o r r e l a t i o n f u n c t i o n

(ato(t)ao(t)ao(t)aeoatoao} After decouphng to a prod- uct of two-dewat~on correlations, and passage to the energy domain, we find

1 1 h JJf fdEIdEze~E'+E2)/knr TI 4~r: So

ImGo(&) Imaoo(E~) linGo(E, + E2) × , (2)

e E h / k n T - 1 e E 2 / k B T - 1 e ( E I + E 2 ) / k B T - 1

where G00 ( E ) s tands for the Green 's function ( ( a 0 , at0}), and S o ~s the impuri ty spin

The Green 's functxons Goo(E) for K 2 M n ~ :N~F,~ and the pure systems have already been calculated by Van Lu0k et al [3], who found ImGo0(E) at the N~ s~te to be substantmlly dl rmmshed relative to pure K 2 M n F 4 due to the occurrence of an s mode above the spin-wave band. In compar ing the Mn-based systems eq (2) y~elds

t t van der Vhst et al / lmpurtty e}:utattons m quadratt~ -layer anttferromagnet~

with the calculated ImG00(E) T}N~)/T( Mn'~)= 8 at 6 K, m agreement w~th the experiment, at 12 K the calcu- lated and expemmental ratios are 10 and 14, respec- tively Here, the approximat ion has also been made that the exchange enhancement [4] does not vary when going from one compound to the other lmG00(E) for KzNI 1 , M n ~ F 4 has been evaluated m an accompan 5- rag paper [5], and appeared to be increased by an s mode low wltl'un the band For the ratio T(Mnl/TI ~' " ' eq (2) gwes 0005 at 20 K, of the rtght order ol magmtude compared to the expermaental ratio 0 014

A d d m o n a l measurements , conf i rming the above findings, have been performed wnh the external field or iented perpen&cular to the ~ ax~s Here, because the tetragonal symmetry Is broken [2] T~ t probes a lower-

order correlat ion function, vlz, (a~( t )ao( t )a~ao} In K z M n l_ NI~F 4 t h e r e , s a s l o w m g - d o w n o f the relaxa- t ion of ~9Fl adjacent to N1 by a factor of 3 at 8 K relative to ~gF~ m the pure system, again after ap- propr ia te scahng of the hyperfme interact ion

References

{1] V Jaccarmo, m Magnetism (Vol I1A), eds G T Rado and H Suht (Academic, New York, 1965) p 307

[2] A J van der Wal and H W de Won, Phys Rev B20 (1979) 3712

[3] J A van Lu0k, A F M Arts and HW deWijn, Phys Rev B21 (1981) 1963

[4] D Beeman and P Pmcus, Phys Rev 166 (1968) 359 [5] H vanderVhst , A F M Arts and HW deWun, J Magn

Magn Mat 31-34 (1983) 1185