Magnetization and spin-flip energy in Cd0.9Mn0.1Se

~

Solid State Communications, Printed in Great Britain.

Vol.44,No.8,

MAGNETIZATION

pp.]243-]245,

]982.

0038-]098/82/44]243-03503.00/0 Pergamon Press Ltd.

AND SPIN-FLIP ENERGY IN Cdo.9Mn0.1Se

Y. Shapira, D. Heiman and S. Foner Francis Bitter National Magnet Laboratory Massachusetts Institute of Technology, Cambridge, MA 02139 (Received 4 August 1982 by Jo Taut)

Magnetization and spin-flip Raman measurements are reported for Cdl_xMnxSe , x = 0.106, at 1.9 < T < 4.2 K and magnetic fields H up to 80 kOe. The high-field results are combined to determine the exchange energy between donor electrons and Mn ++ spins, ~No=261±13 meV. Empirical fits to the magnetization data are described.

In semimagnetic semiconductors there is a large exchange interaction between the spins ~i of the magnetlc ions and the spln s of a free or a loosely bound carrier. ~'2 When a m~gnetic field ~ is applied, the net alignment leads to a spin splitting of the energy of the carrier. This splitting is often much larger than the Zeeman splitting g*PBH caused by the direct action of H on ~. (PB = Bohr magneton, and g* is the g factor for the carrier.) In some (Cd,Mn)Se samples the total spin splitting geff~B H of donor-bound electrons gives effective g-values geff~ 200, compared to g* =0.5. 3,4 Such giant spin effects have also been seen in (Cd,Mn)Te via magnetoreflection, 5 Faraday rotation, 6 and magneto-absorption. 7 For a conduction electron tbe spin s p l i t t i n ~ caused by the exchange interaction with the Mn ~ions is given by &Eex = x~No

,

ments, ~ was parallel to the c axis. Raman data were taken for both ~i£ and ~ il£- The values for AE obtained for both directions were the same within the experimental accuracy. The spin splitting AE was measured using spontaneous spin-flip Raman scattering from donor-bound electrons. The scattered light was collected in a backscattering geometry. A YAG-pumped dye laser produced light pulses having a 5 nsec pulse length at i0 pps. The incident photon energy, ~ m L = 1880 meV, was set just below the absorption edge, to take advantage of resonance enhancement of the scattering cross section. 9 The variation of the spin-flip energy AE as a function of H is shown in Fig. i at two temperatures, T = 1.9 and 4.2 K. ~ne uncertainty in AE is estimated as 0.3 meV, resulting mainly from the large spectral linewidths of approximately I meV. The finite energy at H = 0 is due to the bound magnetic polaron (BMP). 3,~,8,9

(i)

where x is the mole fraction of the Mn ++ ions, N o is the number of cations per unit volume, and is the absolute value of~the average ~ 2~5 Exprescomponent of the Mn " H - spln along H. sions for the total spin splitting AE of a donor-bound electron were given by Dietl and Spalek, 8 and by Heiman, Warnock and Wolff. 9 It will be shown that at high H, AE assumes the simple form

50

I

I

25 T: 1.9K ~ ,

• +

+

E

~T

(2)

io

At lower H there is an additional contribution to AE. By measuring the spin splitting AE and the magnetization M (proportional to x) at high H we have determined =N from Eq. (2). A similar analysis, but base~ on data at lower H, is given in Ref. 8. An analogous determination of =No, based on combining reflectivity and magnetization data, was used earlier in (Cd,Mn)Te. 5 The single crystal of Cdl_xMnxSe was grown by the Bridgman method. Atomic-absorption measurements gave x = 0.106 ± 0.005. This crystal was used in both the Raman and the magnetization measurements. Hall measurements at room temperature gave a donor concentration N D = 3 x 1016 cm -3. In the magnetization measure-

+

•

>Qj,2 0

m15 AE = X~No + g*pB H

I

•

__

• •

+ +

Cd I-X MnxSe

"t-

x = 0.106

~ --•

o o

Figure i.

]243

=4.2K

+

I 2o

I 40 H (kOe)

I 60

Spin-flip Raman energy AE versus applied field H in Cdl_xMnxSe, S x = 0.106. The solid points we_e taken ~t T = 1.9 ± 0 . i K, and the crosses at T = 4.2 ± 0 . i K. These data are for H ! ! .

80

1244

MAGNETIZATION AND SPIN-FLIP ENERGY IN Cd0. 9 Mn0. 1 S e

Magnetization measurements were performed on a 19 mg sample with a vibrating sample magnetometer° Figure 2 shows the magnetization M (per gram) at three temperatures T = 1.92, 3.40 and 4.25 K, all ±0.01 K. At the lowest temperature, the magnetization approaches a constant value M s ~ 6 emu/g at the highest fields. We call M s the technical saturation value. It should be clearly distinguished from the true saturation value M o at H = ~ , where all the antiferromagneti~ally-coupled spins are aligned parallel to H. Assuming g = 2, the calculated value of M o is 15.98 emu/g for x = 0.106.

I CdMnSe

I

I

I

X=O.106

//S

..o.

Vol. 44, No. 8

(Cd,Mn)Te. 2 Also, g* is probably positive, (i.e., the same sign as for a free electron), and is equal to 0.52. 11 Therefore, we assume that the two terms on the right side of Eq. (2) have the same sign. (If g* is negative, our value for ~N o will be affected by only 2%.) We define = AE -

AE

g ~B H

(4)

From Eq. (2) we expect that when technical saturation is approached, the ratio AE*/X will approach ~N o. In Fig. 3, this ratio is plotted as a function of H, for T = 1.9 K. Here the relation = (5/2)M/M o was used. From the high-H portion of Fig. 3 we estimate ~N o = 261 meV. The uncertainty in this value arises almost entirely from the 5% uncertainty in the magnetization. The latter is a combination of a 2% uncertainty in the signal from the sample, and a 3% uncertainty in a scale factor which contains the weight of the sample and the signal from a nickel standard. Thus our value for ~N o is 261 ± 13 meV. This value can be compared with ~No = 280 ± 30 meV obtained by Dietl and Spalek 8 in an x = 0.05 (Cd,Mn)Se sample at fields up to 20 kOe. Both these values are higher than the value ~N o = 220 meV for (Cd,Mn)Te. 5

280

I

I

I Cd I _X MnxS'e x = O. 106

>

E 0

I

I

I

I

20

40

60

80

270

H (kOe) 260

Figure 2.

Magnetization (per gram) M versus H for T = 1.92, 3.40 and 4.25 K. 250

The exchange energy (~No) was determined by comparing the spin-flip energy with the magnetizationo Above a few kOe, AE obeys the meanfield expression 8,9

I 0

Figure 3. AE = EBMp(H) + g pB H + X~No

(3)

The first term corresponds to 2~ of Ref. 8, or P W2/2kT of Ref. 9. It represents the higher local magnetization near the BMP relative to the bulk magnetization. The magnitude of EBM P for our experiments is of order 1 me¥ at H = 0, but it decreases at higher H in proportion to the differential susceptibility 8M/SH. At very high fields (i.e., close to technical saturation), 8M/~H is very small and EBM P is negligible. Physically, the local magnetization near the BMP and the bulk magnetization are then very nearly equal. For our sample, at 1.9 K and H ~ 80 kOe, EBMp/AEs 0.5%. In this case, Eq. (3) is well approximated by Eq. (2). Far-infrared absorption experiments I0 indicate that ~ is positive, as is the case for

20

I 40 H (kOe)

I 60

80

AE*/X versus H at T = 1 . 9 K. AE * is the spin-flip energy AE reduced b~ the bare s~in-flip energy g DB H, with g- = 0.5. is the average z-component of the spin of an Mn ++ ion, as determined from the magnetization. The solid curve is a guide to the eye.

Several comments should be made concerning our determination of ~No: (i) The factor x which enters in this determination is practically unaffected by the uncertainty in x because is inversely proportional to Mo, and M o (per gram) is very nearly proportional to x for x near 0.i. Thus, the uncertainty in x has practically no influence on ~N o. (ii) Because the value of aN o is based on data near technical

Vol. 44, No. 8

MAGNETIZATION

AND SPIN-FLIP ENERGY IN Cd0. 9 Mn0. I Se

saturation, the small difference (<0.I K) in the temperatures at which AE and M were measured has a negligible effect. (iii) The H-dependence of the ratio AE*/X in Fig. 3 arises mainly from the terms EBM P in Eq. (3). This term becomes negligible near technical saturation. (iv) A plot similar to that in Fig. 3 can also be made by using the data at 4.2 K, instead of 1.9 K. In this case, however, the term EBM P is more significant, because AE was measured only up to 60 kOe where M was still ~20% below technical saturation. By making an approximate correction for EBM P we obtained ~N o m 267 meV from the data at 4.2 K. This value is less reliable than the one obtained at 1.9 K. It has been shown by Gaj et al. 5 that magnetization data up to 155 kOe in the (Cd,Mn)Te system are well described by a Brillouin function M : MsB5/2(y)

,

(5)

where y = 5~BH/kTef f. Here, M s is a technical saturation value (which differs from Mo) , and Tef f = T + T o is an effective temperature. The temperature T o is chosen to fit the data. Although Eq. (5) has no theoretical basis, we find that it does give a good empirical fit to the magnetization curves in Fig. 2. This fit is obtained with M s = 6.1 emu/g (i.e., Ms/M<) = 0.38) and T O = 2.5 K. These values should be

1245

compared to M$/M o = 0.43 and T O = 3.84 K for Cdo 9Mn0.1Te. A second empirical fit was made to the low-H susceptibility X in the range 1.9 < T < 4 . 2 5 K. Here, we used a Curie-Weiss relation X = C/(T + TAF)

(6)

This simple equation has no theoretical justification in the present situation, because the sample contains Mn a-N clusters of various sizes. Nevertheless, Eq. (6) is useful for an empirical description of the susceptibility over a limited temperature interval. The data give TAF = 2 . 1 ± 0.4 K, and C = (9.28±0.9) x 1 0 -4 emu K/g. If the latter value is used with the standard expression for the Curie constant, an effective Mn concentration E = 3.9% is obtained. The ratio x/x = 0.37 is comparable to Ms/M o = 0.38. The Raman data at low H, in the region of the MBP, were also analyzed. The obtained values for TAF were comparable to that given above. 4 Acknowledgements--We wlsh to thank R.L. Aggarwal, J.K. Furdyna and A.K. Ramdas for the sample, and P.A. Wolff for stimulating discussions. The National Magnet Laboratory is supported by the National Science Foundation. Partial support for this work was obtained from the Office of Naval Research Contract No. N0001481-K-0654.

References

io

2.

R.R. Galazka, Proc. XIV Int. Conf. Phys. Semicond., Inst. Physo Conf. Sero 43, 133 (1979); T. Dietl, in "Physics in High Magnetic Fields, edited by So Chikazumi and N. Miura, (Springer Verlag, Berlin, 1981), p.344. J.A. Gaj, Proc. XV Int. Conf. Phys. Semicond., J. Phys. Soc. Japan (Suppl. A) 49,

797 (1980). 3.

M. Nawrocki, R. Planel, G. Fishman and R.R. Galazka, Phys. Rev. Lett. 46, 735

4.

D. Heiman, P.A. Wolff and J. Warnock, Proc. XVI Int. Conf. Phys. Semicond., Montpellier, France, Sept. 1982 (to he published). J.A. Gaj, R. Planel and Go Fishman, Solid State Commun. 2__99,435 (1979).

(1981).

5.

6. 7. 8o 9. i0.

ii.

J.A. Gaj, R. Ro Galazka and Mo Nawrocki, Solid State Connnun. 25, 193 (1978) o A. Twardowski, M. Nawrocki and J. Ginter, Phys. Stat. Solo B96, 497 (1979)o T. Dietl and J. Spalek, Phys. Rev. Letto 48, 355 (1982)o Do Heiman, Jo Warnock and PoA. Wolff, to be published. M. Dobrowolska, H.D. Drew, J.K. Furdyna, T. Ichiguchi, A. Witowski and P.A. Wolff, to be published in Phys. Rev. Lett. B. Segall and D.T.F. Marple, in "Physics and Chemistry of Semiconductor II-VI Compounds," edited by M. Aven and J.S. Prener, (North Holland, Amsterdam, 1967), p.357; C.H. Henry, K. Nassau and J.W. Shiever, Phys. Rev. B~, 458 (1972).