Journal of Magnetism and Magnetic Materials 104-107 (1992) 1311-1312 North-Holland

study of PrCo2Si 2 in pulsed high magnetic field

H. Nojiri a, M. Motokawa a, K. Nishiyama b K. Nagamine b and T. Shigeoka c Department of Physics, Faculty of Science, Kobe Unil,ersity, Rokkodai, Nada, Kobe 657, Japan

b Meson Science Laboratory, Faculty of Science, Unil~ersity of Tokyo, Bunkyo-ku, Tokyo 113, Japan c Department of Physics, Faculty of Science, Yamaguchi Unicersity, Yamaguchi 753, Japan

IxSR experiments have been performed on metamagnetic PrCo2Si 2 at zero field at various temperatures down to 4.2 K and at high magnetic fields up to 13 T, well above the saturation field at 4.2 K. Large changes of the relaxation rates have been observed at the critical temperatures, where the magnetic structure changes. At high field, the relaxation rates have been found to be large. This effect is considered to be due to the spin fluctuations which occur in the long-period structure phases.

txSR is one of the me thods to invest igate the dy- namic proper t i es of a spin system and has been used for s tudies of various kinds of magne t ic mater ia ls but mainly at zero or weak fields. It has been cons idered that if a high field is available for I.tSR exper iments , m e a s u r e m e n t s of the field d e p e n d e n c e of T 1 near the phase boundary , where a f ie ld- induced magnet ic phase t rans i t ion occurs, must be in teres t ing as well as the critical behav ior of T] nea r the critical t empera tu re . W e have developed a high-field I~SR system to per- form this kind of exper iment [1]. On the o the r hand, it is known tha t some ra re -ea r th in termeta l l ic compounds show me tamagne t i c t rans i t ions induced by external fields. PrCo2Si 2 is one of this kind of magnet ic mater i - als and shows four-s tep m e t am agne t i c t ransi t ions at 1.2, 3.8, 6.7 and the sa tura t ion field 12.2 T when an external field is appl ied along the c-axis [2]. It also shows magnet ic s t ructure changes at 9 and 17 K below the N6el t empera tu re , 30 K. The magnet ic momen t s come only from Pr a toms and they couple fe r romagne t - ically in the c-p lane to each other . T h e n this can be t rea ted as a one-d imens iona l model as shown in fig. 1. The high-field magne t i za t ion m e a s u r e m e n t and zero [3,4] and high-field n e u t r o n scat ter ing exper iments [5] suggest tha t the magnet ic s t ructure along the c-axis is an t i f e r romagne t i c below 9 K or 1.2 T and two kinds of long-per iod s t ruc tures with p ropaga t ion vectors k = 0.926 and 0.777 exist be tween 9 and 17 K and be tween 17 and 30 K or be tween 1.2 and 3.8 and be tween 3.8 and 12.2 T, respectively, as is shown in fig. 1. The exper iment was pe r fo rmed by using the surface muon at the Meson Science Laboratory , Universi ty of Tokyo in KEK. The field di rect ion was parallel to the c-axis of the sample and also to the beam axis to measure the longi tudinal re laxat ion t ime T 1. The details of the exper imenta l m e t h o d are descr ibed in ref. [1].

(i) Zero field. Above 100 K, the re laxat ion curve is an exponent ia l type and it changes below 100 K to a Gauss ian type which is due to the dipole field f rom the nuclei. The cxponent ia l type above 100 K is cons idered

to be due to the diffusion effect of the muon. Below 50 K, the relaxat ion curve becomes of the exponent ia l type ag, ain and the in terac t ion with the Pr a tomic momen t s is cons idered to be impor tant . The tempera- ture d e p e n d e n c e of the relaxat ion rate o-= 1 / T 1 is p lo t ted in fig. 2. tr is very small below 9 K, but it increases drastically at 9 K and still more at 17 K with increasing t empera tu re . But no divergence is observed at bo th 9 and 17 K and even at the NEel t empe ra tu r e 30 K, while it seems to show a max imum a round 25 K. In the usual Ising-like an t i fe r romagnet , for example in the case of CoF 2 [6], o- shows divergent behavior at the NEel t empe ra tu r e and the spin f luctuat ions decrease rapidly below it. Ou r resul t is unusua l f rom this point of view. We consider this is due to the large spin f luctuat ions which occur in the long-per iod phases. As a ma t t e r of fact, the long-per iod magne t ic s t ructure is a kind of domain s t ruc ture along the c-axis and the domain boundary can move easily wi thout energy dissi- pa t ion like a soliton. In this case, the a tomic dipole

~_. 12.2 - ' - - ' ~ ~d )

.~_

,c)\ ~ 3.8

9 17 30 Temperature(K)

Fig. 1. Magnetic phase diagram and suggested spin structures (a), (b), (c) at zero field. (d) is the paramagnetic or forced ferromagnetic phase. Each arrow is the representative of one ferromagnetic c-plane. The direction of the arrows is changed for convenience. At a high field, the anti-phase domains indicated by the shadowed circles are supposed to point in the

direction of the applied magnetic field.

'"ti o tl tltlIt tltlt t t t tltlt l

• • o

' ° ' ttttttlt tlIt. t

0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

1312 H. Nojiri et al. / IxSR study of PrCo2Si 2

1.0

u 0.8

0.6

O ' ~ 0.4

"~ 0.2 o o

o.o ~ © i

1o

I I I I

± I I

I i

O

J

20 30

o

i

40 50

Temperature(K)

Fig. 2. Temperature dependence of the relaxation rate at zero field. Dotted'lines indicate the phase transition temperatures.

field f luctuates and cont r ibu tes to the muon spin relax- ation.

(ii) High magnetic field. The relaxat ion ra te in high magnet ic field a round the sa tura t ion field is shown in fig. 3. The sample t e m p e r a t u r e which is initially 4.2 K increases up to 12 K when a pulsed magnet ic field of 13 T is appl ied because of the eddy cur ren t heat ing. It is difficult to measure o- below 8 T due to exper imenta l l imitations, o- is apparen t ly large in this field region compared to tha t observed at zero field and the field d e p e n d e n c e seems to be not so s t rong by taking into account the large exper imenta l error . The relaxat ion rate of the m u o n spin caused by the fast f luctuat ing a tomic dipole in terac t ion is expressed as [7]

2 2 2 1] (1) h , , ) , c + ,

where ~'c is the corre la t ion t ime of the a tomic spin fluctuations, y is the muon gyromagnet ic ratio, w o is

1.0 u

=L 0.8

0.6 t- O

' ~ 0.4 X

-~ 0.2

0.0'

H//c

5 10 12,2

M a g n e t i c f ie ld(T)

Fig. 3. Magnetic field dependence' of the relaxation rate. The open and closed circle indicate the zero-field relaxation rate at 12 K (long-period phase) and 4.2 K (antiferromagnetic phase), respectively. The dotted line shows the saturation

field.

the muon Larmor frequency, hll and h • are the inter- nal fields at the muon site paral lel and perpendicu la r to the beam axis, respectively. If the muon spins are forced to align to the field direct ion by a s trong field, f requent spin flip is unexpec ted when % is longer than 1/o~ 0. This effect results in a small re laxat ion rate. In our case, however, the large o- suggests tha t r c is considerably fast and the spin f luctuat ions in a high field are fairly strong. F rom the condi t ion 1/~ c > wo, supposed to hold in this case, % is es t imated to be below 1 x 10- ~0 s. Finally we men t ion the muon site in the crystal, to es t imate h ± and then to evaluate r c theoretically. A muon has a positive charge and usually stays at the interst i t ial site where the Made lung energy has a min imum. We calculated it and found that the energy min imum posit ion is (½,0,0). This is in accord- ance with one of the th ree sites p roposed by Dalmas de R6ot ie r et al. for YC02Si2, which is the nonmag- net ic compound isostructural with PrC02Si 2 [8]. How- ever, the min imum of the potent ia l is shallow and there still remains an ambiguity in the muon site. If we assume the muon is located at (½,0,0), h I = 0 at this posi t ion when the Pr momen t s in the c-plane point to the e-axis. If the direct ion of all the momen t s is per- pendicu la r to the c-axis, h • is es t imated to be 0.1 T and then ~'c is in the o rder of 10 ~ s when ~r is 0.6 ~xs ]. However, this spin conf igurat ion may not bc realized.

This work was suppor ted by a Grand- in -Aid for Scientific Resea rch from the Ministry of Educat ion , Science and Cul ture of Japan.

R e f e r e n c e s

[1] M. Motokawa, H. Nojiri, M. Uchi, S. Watamura, K. Nishiyama and K. Nagamine, Hyperfine Interactions 65 (1990) 1089.

[2] T. Shigeoka, H. Fujii, K. Yonenobu, K. Sugiyama and M. Date, J. Phys. Soc. Jpn. 58 (1989) 394.

[3] T. Shigeoka, N. Iwata, H. Fujii, T. Okamoto and Y. Hashimoto, J. Magn. Magn. Mater. 70 (1987) 239.

[4] T. Shigeoka, N. Iwata, Y. Hashimoto, Y. Andoh and H. Fujii, Physica B 156&157 (1989) 741.

[5] H. Nojiri, M. Uchi, S. Watamura, M. Motokawa, H. Kawai, Y. Endoh and T. Shigeoka, J. Phys. Soc. Jpn., to be published.

[6] R. De Renzi, G. Guidi, C. Bucci, P. Podini, R. Tedeschi and S.F.J. Cox, Hyperfine Interactions 17-19 (1984) 479.

[7] A Schenck, Muon Spin Rotation Spectroscopy (Adam Hilger, Bristol).

[8] P. Dalmas de R~otier, J.P. Sanchez, A. Yaouanc, B. Chevalier, P. ChaudoEt and R. Madar, Hyperfine Interac- tions 65 (1990) 457.