THE SPIN-FLOP TRANSITION IN MnF2 : Fe2+

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THE SPIN-FLOP TRANSITION IN MnF2 : Fe2+

M. Lowe, A. Misetich, C. Abeledo

To cite this version:

M. Lowe, A. Misetich, C. Abeledo. THE SPIN-FLOP TRANSITION IN MnF2 : Fe2+. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-1068-C1-1069. �10.1051/jphyscol:19711384�. �jpa-00214423�

JOURNAL DE PHYSIQUE Colloque C I , supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 1068

THE SPIN-FLOP TRANSITION IN ^: Fez+

M. A. LOWE

Department of Chemistry, Boston University, Boston, Mass.

A. MISETICH

Francis Bitter National Magnet Laboratory (*), M. I. T., Cambridge, Mass.

C . R. ABELEDO

Department of Chemistry, Brandeis University, Waltham, Mass.

R6sum6. - Un accroissement du champ de basculement (spin flop) de MnF2 est observk lorsque ce compose est dopk avec Fez+. Cet accroissement a BtB suivi par spectroscopie optique en fonction de la concentration de Fez+. On a trouvk que l'accroissement observe peut Stre expliquk en prenant comme valeur de l'anisotropie de champ cristallin pour l'ion Fez+, D = 8,6 cm-1.

Abstract. - A significant increase is observed in the flopping field of MnF2 upon doping with Fez+. We have follo- wed this increase as a function of Fez+ concentration by optical spectroscopy. A value of D = 8.6 cm-1 for the Fez+

single ion anisotropy accounts for the observed shifts.

The magnetic properties of MnF, below the N6el temperature, TN = 67 ^{O K ,} are well described as those of an ideal uniaxial two sublattice antiferromagnet with the magnetic moment of each sublattice directed along the c-axis [I]. When a magnetic field applied along the c-axis reaches a certain critical value, H,,, a realignment of the sublattice magnetizations takes place to a direction nearly perpendicular to the c-axis.

This rotation of the sublattice magnetization is known as the spin-flop transition and in pure MnF, at 4.2 OK takes place at 93 kG 121. We have studied the depen- dence on Fez+ concentration of the spin-flop transi- tion of Fez+ doped MnF, by measuring shifts in the optical absorption of MnF, as a function of magnetic field. Since the behavior of the spin-flop transition

Re. 1. -Mametic field behavior of the 28.163 cm-1 line of the MnFz ibsorption in MnFz/Fez+ at 4.2 K. A : pure ; B :

0.095 mol % Fe ; C : 0.28 % ; D : 0.80 0/,

depends on the anisotropy energy, it is thus possible t o obtain a value for the single ion anisotropy of ~ e ' + in the MnF, host.

The optical spectrum of pure MnF, has been studied as a function of magnetic field through the spin-flop transition [3]. The far infrared spectrum has been followed through the spin-flop transition for pure and for doped samples [4, 51. Rather large shifts in the optical absorption energies at H,, are observed for some of the transitions (**). Measurement of the magnetic field at which these shifts occur can thus be used to identify the spin-flop transition in MnF, and in Fez+ doped samples of MnF,. We have followed the MnF, absorption in the 18,400 cm-I region and in the 28,000 cm-I region as a function of magnetic field for various concentrations of Fez'. Spectra were taken at 4.2 OK and were recorded photographically using a Bausch and Lomb grating tspectrograph.

Typical behavior in the 28,000 cm-' region is shown in figure 1 for the magnon sideband at 28,163 cm-l.

Data from both spectral regions give the same concen- tration dependence of H,,, shown in figure 2.

The broadness of the spin-flop transition is probably due primarily to crystal misalignment. If the external magnetic field is not aligned exactly along the c-axis, the rotation of the magnetic sublattices takes place over a finite magnetic field interval which increases with angle. All measurements were made relative to a pure MnF, crystal and relative alignments are within l o .

The field a t which the spin-flop transition takes place can be obtained from molecular field parameters and anisotropy by equating the free energy in the flopped and unflopped state. For a simple two sublat- tice system such as MnF,, the transition is given by

Hsf =

c2

(*) Supported by the U. S. Air Force Office of Scientific ^(**) The large shifts observed in the optical spectrum have Research. been attributed to spin-orbit coupling. See reference 3.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711384

THE SPIN-FLOP TRANSITION IN MnF2 : Fez+ C1-1069

mol % Fe

FIG. 2. - Change in HSr with Fezf doping. Circles : cxperi- mental points at 4.2 ^OK. Lines represent the theoretical pre-

dictions : u, for D =-= 8.6 cm-1, b, for D = 6.5 cm-1.

The anisotropy energy can originate from the inter- ionic magnetic dipolar interactions or from coupling between the spin and orbital motions of electrons.

In MnF,, the predominant source of the magnetic anisotropy is the magnctic dipolar interaction and the calculated K [6] is in good agreement with the experimental value K = 1.83 cm-' [2]. In FeF,, which also behaves as a two sublattice antiferroma- gnet, the anisotropy arises primarily from the singlc ion spin-orbit interactions. The predominant aniso- tropic term in the Hamiltonian of an ion in a uniaxial field is given by

and the contribution to the anisotropy energy is fournd to be [7]

For FeF,, the single ion crystal field anisotropy, D, has been estimated by Kanamori and Minatono [7]

to be 6.5 cm-'. Combining this with the observed HE for FeF,, H,. is calculated to be 300 kG. This transition has not yet been observed in FeF,.

To describe the behavior of the ~ e , + doped MnF, we use a simple molccular field model, in which the

Fe2+ sees the effective field due to its interaction with neighbouring Mn ions. Below the spin-flop the spins are parallel to the c-axis, while after the transi- tion they are slightly canted from a plane perpendicu- lar to the c-axis. We first assume that all Mn ions are canted by the same angle. If cp is the angle between the moment of a Mn ion and the plane perpendicular to c and q' is similarly defined for Fe2+, by equating the torques on the ions to zero we obtain

sin cp = Ho(2HE - KIgPS,)

H , cos q' - H;, sin (cp'

+

+

2 K ' .

+

where H , is the applied field, HE, K and S, are the exchange field, anisotropy constant and spin of the unperturbed Mn ions, HL1 and HA2 are the exchange fields acting on the Fe ions due to interactions with the same and opposite sublattice Mn ions respectively and K' and Sl are the Fez+ anisotropy constant (dipole and single ion) and spin.

With the canting angles given by eq. (3), one can calculatc the energy of the flopped phase as a function of concentration and magnetic field. As above, the spin-flop transition occurs when the energy of the flopped phase becomes equal to that of the unflopped phase. Equating energies in this way, we have calcu- lated the change in H,, with Fez+ concentration, using for HE the value calculated with the exchange para- meters measured by Low, et al. [8], for K the value given above and for HL1 and Hi,, the Fe-Mn exchange parameters reported by Butler et al. [9]. By fitting the experimental results with the theoretical predictions we derive, using eq. (2), D = 8.6 cm-', which is very close to the value in FeF, of 6.5 cm-'.

The solid lines in figure-2 are calculated using these two values of D. The theoretical curves are very insensitive to changes in the Fe-Mn exchange values.

We have extended the model by allowing the first and second neighbors to an Fe ion to have different canting angles, cp" and cp"', from the rest of the host ions at the angle cp. This improvement in the model introduces very little change, less than 0.2 % in the theoretical curves of figure 2. Our results suggest that the distortions at the Fez+ site in MnF, are very similar to those found in FeF, rather than those in MnF,.

References [I] FONER (S.), Magnetism, ed. by G . T. Rado and H.

Suhl (Academic Press Inc., N. Y., 1963), Vol. I,

1183

[2] S H A P I ~ ~ ~ ( Y . ) and ZAK (J.), Phys., Rev., 1968, 170, 503.

[3] MELTZER (R.) and LOHR (L.), J. Chem. Phys., 1968, 49,541 ; MELTZER (R.), LOWE (M.) and MCCLURE

@.), Phys. Rev., 1969, 180, 561.

[4] BLEWITT (R.) and WEBER (R.), J. Appl. Phys., 1970, 41, 884.

[5] BERNSTEIN (T.), MISETICH (A.) and LAX (B.), to be

published.

KEFFER (F.). P ~ Y s . Rev.. 1952. 87. 608.

KANAMORI '(J.) -and M~NATONO (H.), J. ~ h y s . SOC.

Japan, 1962, 17, 1759.

Low (G.), OKAZAKI (A.), STEVENSON (R.) and TURBER-

FIELD (K.), J. Appl. P h y ~ . , 1964, 35, 998.

BUTLER (M.). JACCARMO (V.). KAPLAN (N.) and GUGGENHEIM (H.), phys ~ e v . B, 1970,' 1,' 3058.