Hyperfine Interactions 41 (1988) 505-508 505

THE EFFECT OF MISALIGNMENT ON THE SPIN-FLOP TRANSITION IN K2FeF s

Q.A. PANKHURST*, C.E. JOHNSON, D.H. JONES and M.E THOMAS

Department of Physics, University of Liverpool, L69 3BX, England

Spin-flop transitions in K2FeFs subject to an applied field (i) parallel to the easy axis, and (ii) directed at 33 ~ to the easy axis are found to be (i) abrupt and (ii) smooth, in accordance with theoretical predictions.

I. INTRODUCTION

The spin-flop phase transition occurs when a magnetic field B is directed along the easy anisotropy axis of a weakly anisotropic antlferromagnet. At a critical field Bsf the antiferromagnetic axis of the spins reorients ('flops') to a direction perpendicular to the applied field. According to mean field theory /1,2/ the tran- sition will be abrupt provided B is perfectly aligned with the easy axis; if the misalignment angle between B and the easy axis exceeds a certain value (~o-BA/2B E where B A and BE are the anisotropy and exchange fields) a smooth transition is predicted.

In previous work the present authors have observed spin-flop transitions in the quasi one-dimensional antiferromagnets K2FeFs and RbzFeFs /3,4/. In K2FeFs a field directed along the easy axis provoked an abrupt transition, while in Rb2FeFs a field directed along the crystallographic b axis produced a smooth transition. The ordered magnetic structure of RbzFeFs exhibits four sublattices with the spins lying in the bc-plane at about 25 ~ to the b axis; consequently in our experiment B had been 'misaligned' by 25 ~ from the easy axis. To confirm that this 'misallgnment' accounted for the smooth transition in RbzFeFs we decided to observe the effect of a deliberate misalignment on the spinLflop in K2FeFs.

2. EXPERIMENTAL RESULTS

K2FeFs has an orthorhombic crystal structure with unit cell dimensions a=2.039nm, b=1.284nm and c=0.740nm, in which the ferric ions form zlg-zag chains along the a axis. Below a N~el temperature of 6.95K the spins "align along the magnetically easy b axis. SVFe Mossbauer spectra of an ac-plane single crystal were recorded at 4.2K with both the incident 7-rays and applied field directed at approximately 30 ~ to the b axis, in the bc-plane. These spectra are shown in Figure I, along with the previously reported data for field and 7-rays parallel to the b axis.

Comparing the zero field spectra for the two sets of data, it is apparent that in the 'aligned' case the Am=0 lines (lines two and five of the sextet) are absent, confirming that the 7-rays were aligned with the b axis; whereas in the 'misaligned' case Am=0 lines are present, with an intensity corresponding to an angle of #=33 ~ between the 7-rays and the b axis. In high fields a sextet

*Present address : Department of Physics, university of Manitoba, Winnipeg, R3T 2N2, Canada.

�9 J.C. Baltzer A.G., Scientific Publishing Company

506 Q.A. Pankhorst et aL, Spin-flop transition in K f e F s

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Figure I Mossbauer spectra of KzFeFs at 4.2K with 7-rays and applied field (i) aligned parallel to the b axis, and (ii) misaligned by 33 o from the h axis.

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Figure 2 Applied field dependence of the spin-flopped area and hyper- fine field in the 'aligned' spectra (e), and the rotation angle and hyperfine field in the 'misaligned' spectra (o).

Q.A. Pankhorst et al., Spin-flop transition in KzF. eF 5 507

with intensity ratios of order 3:4:1 in outer:middle:inner pairs of lines is seen in both sets of spectra, indicating a perpendicular orientation of the spins to the 7-ray beam and the completion of the spin-flop.

In the 'aligned' case the intermediate spectra 3.0T<B<3.8T show the coexistence of two phases : unflopped spins contributing a split sextet with 3:0:1 intensity ratio, and flopped spins giving an unsplit 3:4:1 sextet. Computer fitting the spectra shows that the relative area of the flopped component underwent a sharp tran- sition near Bsf=3.65T ~see Figure 2a). In contrast, the intermedi- ate spectra in the 'misaligned' case, 0.0T<B<5.0T show that as B increased all the spectral lines (including the ~m=0 lines) split, and the intensity of the ~m=0 lines increased. This behaviour is in keeping with a gradual rotation (in unison) of the spins away from the field as it was increased. Computer analysis of the spectra showed that the AFM axis of the spins had rotated from ~=33" to the applied field to #=90 ~ in a gradual transition centered at Bs{=4.3T (see Figure 2a).

A further notable feature of the transitions was revealed in the computer analysis : in both the 'aligned' and 'misaligned' cases a significant minimum was observed in the hyperfine field as a function of applied field (see Figure 2b). Such behaviour is characteristic of the field-dependent spin-reduction observable in antiferromagnets with low N~el temperatures. At first sight the sharpness of the minimum in the 'misaligned' spectra seems to be at odds with the observed smoothness of the spin-flop in that case, but the magnitude of the hyperfine field is sensitive to the fluc- tuations in the spin directions which, as mentioned later, have a maximum at the spin-flop field.

3. DISCUSSION

The character of the spin-flop transition in K2FeFs was found to be dependent on the degree of misalignment between the applied field and the easy anisotropy axis. With the applied field parallel to the easy axis the transition is seen as a coexistence of unflopped and flopped phases over a range of fields ~B=0.4T cen- tered at Bsf=3.65T. This coexistence is probably a re'sult of a small degree of randomness in the crystal giving rise to a distri- bution of local critical field values. The spin-flop at each indi- vidual ferric ion appears to be abrupt, with no evidence of an intermediate rotated phase being observed in the spectra. In con- trast, with the applied field directed at #=33 ~ to the easy axis the spin-flop is seen as a gradual rotation of the spins away from the field, with the mid-point of the transition occuring near Bs{=4.3T. Comparing the 'aligned' and 'misaligned' critical fields it is evident that Bsf=Bs{cos#, implying that the 'misaligned' spin-flop takes place when the component of the applied field par- allel to the easy axis is in the vicinity of Bsf .

Mean field theory predicts that the spin-flop transition will be of second-order (smooth) if the misalignment angle exceeds a critical angle ~o which, assuming uniaxial anisotropy, is given approximately by tan-'(BA/2B E) /1,2/. In K~FeFs at 4.2K the aniso- tropy and exchange fields are BA=0.08T and BE=83.0T, giving ~o=0.03 ~ This is clearly much less than the 33 ~ of the 'misaligned' experimens so that the observed smooth transition is in accord with mean field theory. The estimated uncertainty in the alignment achieved in the 'aligned' experiment, • ~ is also larger than ~o, implying that although the spin-flop appeared to be 'abrupt' it may not, strictly speaking, have been a 'first-order' transition.

508 QA. Pankhorst et al., Spin-flop transition in KyFeF 5

The hyperfine field minima observed in both the 'aligned' and 'misaligned' experiments may be understood in terms of spin-wave theory 75/. An applied field B<Bsf parallel to the easy axis pro- motes the thermal excitation of spin-waves in the magnetic chains, with the increased spin fluctuations being seen as a reduced hyper- fine field. The fluctuations are maximal at B=Bsf. For B>Bsf the spin axis is perpendicular to the applied field and spin-waves are inhibited so that the hyperfine field increases. Although this dis- tinct hyperfine field minimum is usually associated with an abrupt spin-flop transition, recent numerical computations /5/ have shown that a definite (albeit smaller) minimum may occur for applied fields significantly removed from the easy axis. This would appear to be the case in the 'misaligned' K2FeFs experiment. In conclusion it is interesting to note that the hyperfine field minimum provided a convenient indication of the critical spin-flop field in both the 'aligned' and 'misaligned' transitions.

ACKNOWLEDGEMENTS

The authors are indebted to Mrs. B.M. Wanklyn of the Clarendon Laboratory, Oxford, for the single crystal sample used in this work. Q.A. Pankhurst would like to thank the Commonwealth Scholar- ship Commission UK for their support during his time at Liverpool.

References

/I/ H. Rohrer and H. Thomas, J. Appl. Phys. 40 (1969) 1025. ~ D.H. Jones and Q.A. Pankhurst, J. Phys. C 20 (1987)2453.

Q.A. Pankhurst, C.E. Johnson and M.F. Thomas, J. Phys. C 18 (1985) 3249.

/4/ Q.A. Pankhurst, C.E. Johnson an d M.F. Thomas, Hyp. Int. 29 (1986) 1361.

/5/ D.H. Jones, Q.A. Pankhurst and C.E. Johnson, to appear in J. Phys. C (1987).