FAR INFRARED STUDIES OF THE PAIR MODE IN MnF2 : Fe2+

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FAR INFRARED STUDIES OF THE PAIR MODE IN MnF2 : Fe2+

K. Johnson, R. Weber

To cite this version:

K. Johnson, R. Weber. FAR INFRARED STUDIES OF THE PAIR MODE IN MnF2 : Fe2+. Jour-

nal de Physique Colloques, 1971, 32 (C1), pp.C1-1070-C1-1072. �10.1051/jphyscol:19711385�. �jpa-

00214424�

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JOURNAL D E PHYSIQUE Collogue C 1, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1

-

¹⁰⁷⁰

FAR INFRARED STUDIES OF THE PAIR MODE IN MnF, : Fe2+ (*)

K. JOHNSON and R. WEBER

Cornell University Tthaca, New York, 14850 and 11. Physik Institut University Stuttgart, Germany

R h m 6 . - Une raie active du dip6le MnF2 : Fe+ f a kt6 obsewke par spectroscopic infra-rouge a 1449 cm3

a

1,2 OK. Cette raie apparait seulement dans le cas oh le champ E est paralltle B I'axe optique. La frkquence de la raie dkcroit lorsque la temfirature augmente, et la largeur qui est de quelques cm-1

a

1,2 OK augmente fortement au-dessus de 20 OK.

La loi de variation avec la temperature et avec le champ magnktique indique que cette raie a pour origine un mode de pair dO 21 une excitation simultanke d'un spin Fez+ et d'un spin Mn2.I- voisin. Un calcul par les fonctions de Green permet d'interprkter les rksultats a 1,2 OK par un choix approprik des constantes d'khange impuretks-solvant entre premiers et seconds voisins.

Abstract. - An electric dipole active line in MnFz : Fez+ has been observed by far infrared techn~ques at 144.9 cm-1 at 1.2 OK. The line is observed only for E parallel to the optic axis. With increasing temperature the frequency of the line decreases, while the halfwidth, which is a few cm-1 at 1.2 OK, increases strongly above 20 OK. The temperature dependence of the absorption line and a very small magnetic field dependence indicate that the line is due to a pair mode process consisting of a simultanwus excitation of a Fez+ spin and a next nearest Mn2+ spin. A Green's function calculation is used to fit the 1.2 OK data by appropriate choice of the impurity-host exchange constants between next nearest and nearest neighbors.

Previously reported far infrared investigations of Fez+-doped MnF, revealed the presence of a magnetic local mode [I]. Optical absorption studies have been reported since [2], and Raman scattering measurements [3] have revealed different modes, also of magnetic origin. The observed local mode is of the s, type and is mainly localized on the impurity. The pair modes seen in Raman scattering are of the so

+

^{d type}

and consist primarily of simultaneous excitations on the impurity and its next nearest neighbors. A pair mode of so

+

f symmetry should be infrared active.

We have observed such a mode and now report the experimental results.

ture dependent. This line is centered a t 144.9 cm-'.

The higher frequency wing did not exhibit any temperature dependence, and we therefore assign this part to one phonon induced absorption. I t should be mentioned a t this point that another line a t 113.5 cm-' was observed for E

I

C ; this line did not shift with temperature or magnetic field and must be associated with a resonant phonon mode due t o the Fez+ impu- rities (compare [3]).

The absorption coefficient of the temperature dependent line a t 144.9 cm-' is shown in figure 1.

The measurements were made with a far infrared Michelson interferometer in conjunction with a 1.2 OK-Ga-doped germanium bolometer. At frequencies above 90 cm-' this instrument gives about ten times more energy than the lamellar grating interferometer used in the earlier experiments [I]. Infrared active phonons in MnF, limited investigations t o about 180 cm-' when the E vector of the incident beam was parallel t o the optic axis of the sample, and t o 140 cm-' when it was perpendicular. The spectral resolution was typically 1 cm-' around 145 cm-'.

The crystals were obtained from Optovac, Inc.

The absorption we observed, in addition t o the aforementioned local mode a t 94.8 cm-', is a struc- tured absorption band, of halfwidth 9 cm-', centered around 145 cm-'. Polarization measurements showed

Frequency [cm-'1-

FIG. 1.

-

Far infrared absorption spectrum of MnF2 : FezC around 145 cm-1. The background has been divided out.

that the band is consistent with an electric dipole The line shape is asymmetric, with the absorption transition for E

II

C . Temperature measu- coefficient falling off more slowly on the high fie- rements were made u p to 50 OK ; these data showed quency side. The halfwidth is 3.8 cm-l a t 1.2OK and that only one part of the band is tempera- the absorption strength is 14 cm-2 for a sample doped with 4 U e F , in the melt. With increasing tempera-

(*) This work has been supported by the U. S. Atomic Energy ture the line shifts to lower frequencies, as seen in Commission under Contract NO. (AT 30-11-2391, Technical figure 20. At the same time the halfwidth increases Report No. NYO-2391-120 and by the Advanced Research considerably above 20 OK (see Fig. 2b), while the Projects Agency, through the facilities of the Materials Science

Center at Cornell University, MSC Report 1450. Mr. Johnson strength decreases, making measurements received support from a NASA Traineeship. above 30 OK very difficult. Magnetic fields u p t o 50 k G

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711385

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FAR INFRARED STUDIES OF THE PAIR MODE IN MnF2: Fez'' C 1

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1071

T / T N -

FIG. 2a. - Relative frequency of the 144.9 cm-1 (e) and 94.8 cm-1 lines (0) as a function of temperature.

FIG. 2b.

-

Halfwidth of the 144.9 cm-1 line as a function of temperature.

were applied, and no splitting of the line was observed.

A slight extension of the absorption band to lower frequencies did result, from which the g factor was estimated to be smaller than 0.3. A more accurate determination was not possible because of the phonon contribution to the absorption band.

The experimental results lead us to argue that the line at 144.9 cm-' is due to an excitation of the infrared active pair mode of the so

+

f type. This conclusion is also supported by the Raman scattering measurements [3], which revealed pair modes in the same frequency region.

The frequency of the so

+

f mode can be estimated by means of a molecular field picture using the measured so mode frequency [I]. Taking into account next nearest and nearest exchange coupling constants we can write

o s o , = o s o - 2(znnn - 1) Jnnn S

+

²^Znn^{Jnn S}

^-

^{2 JAnn(S1}

^-

¹⁾

+

^O, (1) where

Jnnn and Jnn are the exchange constants between next nearest and nearest neighbors, respectively, w, is the host lattice anisotropy energy, and S is the host spin ; the corresponding quantities for the impurity site are denoted by a prime. Znnn and Znn refer to the number of next nearest and nearest neighbors, and are equal to eight and two, respectively.

Using the measured value o,, = 94.8 cm-' and the quantities J i n n =

-

1.86 cm-' and w,. = 19.5 cm-' from [I], and the values Jnnn =

-

1.226 cm-', J,, = 0.226 cm-l, and o, = 0.8 cm-' from [5], one gets o,,, = 144.6 cm-'. This result is in good agree- ment with the measured value of 144.9 cm-'.

It should be noted, however, that the calculation of Jinn in ref. [I] did not take into account the supposedly small nearest neighbor coupling. On the other hand, equations (1) and (2) above should in principle be

sufficient to determine JA,, and JA, separately. It is obvious from these equations, however, that only a reliable theory can give reliable values for both J;,, and Ji,. The reason for this is that a small error in cal- culating JAnn from (1) results in a very large error in J;,, due to the large coefficient of JA,, in (2). The simple approximation used above is certainly not appropriate since it neglects transverse components of the exchange energy.

Although there are no complete Green's function results for MnF, : Fe2+, we adopt the Green's function calculation of Thorpe [6] which gives the frequency o;

(w;

= 46.9 cm-') of a magnetic vacancy in MnF, in order to obtain a better estimate of the exchange constants. Adding a term 2 Jinn(S1 - 1) which takes the Fe2+ impurity into account, we obtain for the so f mode

Wsof N OSO

+

^{W ;}^-2 JAnn(S'

-

1)

.

For a,, we can write, in a good approximation [7],

+

2 Ji,, S'

-

^2(znnn^-¹⁾^{Jnnn Ss'}

Z,,, S - S'

From these equations we find the values

and JAn = 0.87 cm-'. Although the absolute numbers should be taken with care, it seems clear that JAn is ferromagnetic and larger than in pure MnF2.

A few comments should be made about the temperature dependence of the pair mode line. The line shifts to lower frequencies more slowly with increasing temperatures than the zone boundary magnons [8], and the relative frequency shift is even slightly smaller than that of the so mode. A simple cluster approximation, first used by Holden and al. [8], and based on equations (1) and (2) for the defect site, fits the so mode data satisfactorily. However, this approximation gives a larger relative frequency shift for the pair mode than for the so mode, contrary to our results.

Also, no model is available for the analysis of the temperature dependence of the linewidth and absorp tion strength.

At sufficiently high temperatures the f mode excitation of next nearest neighbors about the impurity site might become localized above the spin wave band, and therefore become more easily observable due to a decreasing halfwidth as it moves away from the band. We have searched for this mode without success.

In conclusion, we have found an electric dipole active line in MnF, : ~ eat ~144.9 cm-' which can + be assigned to a pair mode of the so

+

f type. The data indicate that the impurity-host exchange constant is antiferromagnetic between next nearest neighbors and ferromagnetic between nearest neighbors.

The authors would like to thank A. J. Sievers and U. Diirr for useful discussions. They are indebted to H. Ziegler for the performance of computer calcu- lations.

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C 1

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1072 K. JOHNSON AND R. WEBER

References

[I] WEBER (R.), Phys. Rev. Letters, 1968, 21, 1260. [6] THORPE (M. F.), to be published and private commu- SCHIRMER ( 0 . F.), SCHNADT (R.), Sol. State Comm.,

1969, 7. 1159.

OSEROFF (A.), PERSHAN (P. S.), Phys. Rev. Letters, 1968, 21, 1593.

To get data gbove 30 OK measurements with higher doped MnF2 samples are planned.

NIKOBM (O.), LINDGARD (P. A.), DIETRICH ( 0 . W.), J. Phys., 1969, C . 2 , 1168.

nication.

The antiferromagnetic term has been derived by Thorpe [6] for so modes in doped RbMnF,. I t can also be obtained by a semiclassical cluster approximation [I]. In a similar way the ferro- magnetic term can be derived, the numerical results being in agreement with those of SHILLS (E.), HONE (D.). J. Phvs. SOC. Jan.. 1970. 28. 51.

HOLDEN (T: M.), B ~ Y E R S (w. j . ' ~ . ) ,

STEVENSON

(R. W. H.), J . Appl. Phys., 1969, 40, 991.