ON THE SPONTANEOUS MAGNETIZATION OF MnFe204

Transcription

1 R 550 Philips Res. Repts 20, , 1965 ON THE SPONTANEOUS MAGNETIZATION OF MnFe204 by F. K. LOTGERING Abstract The saturation magnetization of MnFe204 is explained by assuming that the ionic structure at T = 0 "K is represented by Mn 2 +1_.Fe 3 +.IMn 2 +.Fe 3 +2_.I04 and that the 90 0 MnOFe interaction is stronger than the MnOMn interaction. Some attempts to check the model experimentally are described. The data are in reasonable agreement with the predictions, but are not sufficient to establish the model. -, 1. Introduetion 'The spontaneous magnetization at 4 "K of MnFe204, which crystallizes in a mainly normal v-ê) spinel structure, is about 9 % lower 1.3) than the value of 5 flb expected for the Néel coupling scheme. Tentative explanations have been given, based on (a) the presence of divalent iron and trivalent manganese 4) and (b) deviations from the spin-only value of 5 flb for the Fe3+ and Mn2+ ions 5). From the electrical conduction in the mixed crystals Fe304-Mn2Fe04 the author 6) concluded that the concentrations of Fe2+ and Mn3+ at low temperatures are negligibly small and explanation (a) is not correct. In this paper we propose another explanation and describe attempts to check the model experimentally. 2. Tentative explanation of the saturation moment We start with a rough estimation of the antiferromagnetic Fe3+(A)Fe3+(B), Mn 2 +(A)Mn 2 +(B) and Fe3+(A)Mn2+(B)interactions (A and B denote the tetrahedral and octahedral sites, respectively) using the molecular-field approximation. In the usual way 7) the. following equation can be derived for the Curie temperature of a spinel PxAQYAIPxBQYBI04(XA + YA = 1, XB + YB = 2) containing two kinds of ion, Pand Q: - if Aáand BB interactions are neglected. The C's are the molar Curie constants; the Weiss coefficients Wij for the three types of exchange interactions are defined such that the molecular field of six j ions acting on an i ion is given by Hi = - WijMj, where Mj-is the magnetization per mole (Wij positive for

2 'ON THE SPONTANEOUS MAGNETIZATION OF MnFe antiferromagnetic interaction). The coefficients WFeFe and WMnMn are found from the Curie temperatures of Fe3+IFe 3 +3/2Li+1/2104and Mn 2 +IMn 2 +Ti4+I04 (table I). For comparison the Weiss coefficients for the 90 and 180 interactions in MnO are calculated from the Néel point and the asymptotic Curie temperature (table I). The value of W MnFe given in tabl~ I for the Fe(A)Mn(B) interaction in MnFe204 is calculated from eq. (1) with the aid of the values already found for WFeFe and WMnMn~ and Tc = 610 "K measured on Mno.ssFeo.12IMno.12Fel.SsI04(sec. 3 and table ~I). TABLE I Weiss-field coefficients W (defined per 6 neighbours) for Fe3+Fe3+, Mn2+Mn 2 + and Mn2+Fe3+ interactions deduced from Curie temperatures of compounds with spinel and rocksalt structures - compound Tc(OK) eek) interaction type W FeIFe3/2Lh/~I ) - FeFe, Mno.ssFeo.12IMno.12Fel'SsI MnFe, MnlMnTilO4 8IB) - MnMn, MnO MnMn, MnMn, According to this rough estimation, the Mn(A)Mn(B) interaction is much weaker than the Fe(A)Fe(B) and Fe(A)Mn(B) interactions. This suggests the. following explanation of the saturation magnetization of Mn 2 +1_' Fe 3 +' IMn2+.Fe3+2- B I04assuming that the moment of Mn2+ and Fe3+ is 5 (JoB. In the spinellattice B sites have six neighbouringa sites and six neighbouring B sites. We denote an Mn(B) ion with (6 -n) Mn(A)and n Fe(A}neighbours by Mn(6-n,n) and the average number of Mn(6-n,n) per formula unit by Z(6-n,n), where n = 0,..., ~. For a statistical distribution of Mn and Fe ions at A sites, we have' ) Z(6-n,n) - en+1(1':""e)6-n6!/n! (6- n)!. (2) We assume that all A spins and the Fe(B) spins are antiparallelat T = 0 according to Néel's scheme and, consider the spin directions of the Mn(B) ions. If 13 is small, the number of Mn(B) neighbours is small, and the Mn(B) ions interact mainly with Mn(A), Fe(A) and Fe(B) ions. We assume that the 90

3 322 F. K. LOTGERING Fig. 1. Saturation moment m at T = 0 and Curie temperature Tc calcu.lated for Mn2+1_.Fe. IMn 2 +.Fe 3 +2_.I04 as functions of e. Measuring points: (a) quenched, polycr. sample,(b) annealed, polycr. sample, (c) original single er, and (d) single cr. after heat treatment under high pressure b c ; x --'!,...-- f- OḄ. 'nr. "'i- D koe d K Fig. 2. Magnetization u at 4 2 "K as a function of the external field (top) and 172 as a function of the temperature (bottom) for samples a-d. For the meaning of a-d, see fig. I:

4 ON THE SPONTANEOUS MAGNETIZATION OF MnFe Fe(B)Mn(B) interaction is negative and,introduce the corresponding Weiss coefficient as an unknown parameter WBB. The exchange field acting on the Mn(6-n,n) ions depends on n. If WBB > WMnMn, the resulting exchange field. for an Mn (6,0) ion is antiparallel to the Fe(B) spins. The interaction of an Mn(6-n,n) spin with the B spins is independent ofn but the interaction with the A spins increases for increasing n because weak Mn(A)Mn(B) interactions are replaced by much stronger Fe(A)Mn(B) interactions (table I). If. all Mn(B) spins are parallel to the Fe(B) spins except the Mn(6,0) spins, which have the opposite direction. Then the moment per formula unit at T = 0 is mo = [5-10 Z(6,0)] [LB = [5-10 e (1- e)6] [LB. (4) Figure 1 gives the mo vs e curve calculated from eq. (4) and the Tn-e curve computed from eq. (1) using the values of WFeFe, WMnFe and WMnMn in table I (using the molecular-field approximation, calculations show thattc(e) is mainly determined by the strongest interactions Fe(A)Fe(B) and Fe(A)Mn(B), and hardly depends on the weaker interactions Mn(A)Mn(B), Fe(B)Mn(B), and Fe(B)Fe(B)). (3) 3. Attempts to check the model experimentally Polycrystalline MnFe204 was prepared with the normal ceramic technique. A stoichiometrie sample was obtained by a heat treatment at 1400 oe in C02 followed by quenching. Then the material was heated for 1 hr at 1150 oe in an evacuated silica tube, slowly cooled and annealed for 3 hrs at 1000 oe, 17 hrs at 900 oe and 17 hrs at 700 oe. Part of the material obtained was again heated for 1 hr at 1150 oe in a silica tube and quenched. The oxygen content of both samples was ideal within the error of analysis (1%0). Figure 2 shows a2-t curves and a-h curves at 4 2 "K measured on the quenched and annealed samples. From' these data we found the values for m(4 2 OK) and Tc given in table 11. The values of e have been determined on these samples by Driessens 10) with the aid of an X-ray-diffraction method based on anomalous dispersion of X-rays. He found lower e values (table 11) than reported in the literature 1,2) and attributed the differences to different preparation methods and chemical compositions. The two experimental mee) values fit well on the mo-e curve calculated (fig. 1, points a and b). The fact that the two values of T c( e) agree less well with the calculated T c-e curve seems to us no serious objection against the model because here the method of calculation is only a rough approximation.

5 324 F. K. LOTGERING TABLE, 11 Curie temperature To, saturation magnetization a per gramme at 4 2 ok and corresponding moment m per formula unit measured on two polycrystalline samples and a single crystal; amount e o(mn at B sites according to X-ray work by Driessens 10) a at 4 2 "K mat4'1 K sample heat treatment Tc(OK) (gauss ([JoB) cm3g-1) e 1150 C, quenched '5±0'2 4 49±0 OI 0,11-0'12 polycr C, slowly cooled and annealed at 1000, 900 and 700 C '8±0'2 4'6I±0'OI 0,05-0,08 rapidly cooled from melting point ± ±0 OI single er Cunder pressure of I06 8± ± bars, rapidly cooled -, A straightforward check of the model could be obtained from the magnetic properties of MnFe204 samples with s values considerably larger than 0,1-0,2, for which the model predicts higher mo and To values than observed so far(fig.i). Since an inverse spinel has a smaller lattice parameter than a normal spinel U) we tried to increase ë in the following way. Dr W. J. Witteman heated a cylindrical single crystal of MnFe204 at C under a pressure of bars. The specimen was c~oled rapidly. Unfortunately it was not possible to determine the oxygen content and e because of the smallness of the crystal. The magnetic properties were measured before and after the procedure (fig. 2, table II). The observed change L1To = 35 o~ caused by the treatment shows clearly that the Mn distribution among A and B sites has changed, but the change of e is probably small. We adjusted the experimental To values to the dotted line in fig. 1, which is drawn through the measuring points a and b for the two polycrystalline samples. Using the e values obtained in this way we found 'the mee) points c and d (fig. 1) near to the calculated mo-e curve for the single crystal.

6 ON THE SPONTANEOUS MAGNETIZATION OF MnFc Discussion Although the experimental data agree reasonably with our model (fig. 1) we feel that the model is far from established. Our attempts to confirm or exclude the model using classical methods have failed because we are not able to prepare samples with a sufficient amount of Mn at B sites. A neutron diffraction study on a carefully prepared and analysed single crystal may be able to solve the problem. A difficulty of the model is the fact that acceptable values of the unknown parameter WBB lie between rather narrow limits for reasons which we will now consider. According to the essential condition (3), the exchange fields H(6,0) and H(5,1) acting on Mn(6,0) and Mn(5,1) are mutually antiparallel and have magnitudes equal to (WBB- WMnllln)Moand (5 WMnMn)+ WMnFe-6WBBMo/6, respectively, at T = 0, where Mo = 5N!LB ~ gauss cm 3 /mole. Using the W values in table I, we have IH(6,0) I + IH(5,1)1 = (WMnFe- WlIlnMn)Mo/6= 320 koe. (5) This estimation is of course very rough and probably too small being obtained from Curie temperatures and by means of the molecular-field approximation. Values up to 500 koe seem to us still acceptable. The Mn(6,0) or Mn(5,1) spins will be weakly coupled for small values of H(6,0) or H(5,1), respectively. This would 'give the a-t curve an anomalous shape at low temperatures and the a-h curve at 4 "K an observable slope, especially for high fields. Such a behaviour is not found experimentally. Moruzzi 3) measures a slope of (0'7 ± 0'5). 10-4gauss/oersted at 4 1 OK in fields up to 70 koe, and from our measurements (fig. 2) it can only be concluded that the slope is smaller.than 10-4 gauss/oersted. Simple calculations show that values of ~ 200 koe or larger must be assigned to H(6,0) and H(5,1) if the model is not to disagree with these experimental data. According to eq. (5) this requires a WBB value which is not too far from the mean value of the limits given by condition (3), i.e. WBB ~ 25. Although we are not able to estimate WBB with any accuracy, we think that this rather high value is not impossible. Since Mn2+ and Pe 3 + are both 6S ions, one may speculate that the Mn2+Pe3+ interaction is about the average value of the Mn 2 +Mn 2 + and Pe 3 +Pe 3 + interactions. Por the 125 AB interactions this is true because (WMnMn + WFeFe)/2 = = (17'5 + 19}/2 = 97, i.e, near to WMnFe = 86 6 (table I). In this way we find for the 90 Mn2+Pe3+ interaction that WMnMn,90 = (56 + WFeFe,9o) /2> 28. The possibility that the ionic moments deviate from the spin-only value cannot be excluded 12) (cf. introduction). An explanation of the saturation moment of MnFe204 based exclusively on such deviations seems unlikely to us. One would then expect the saturation to depend not at all or.only weakly on e, and it would be difficult to explain the difference between the magnetic properties of the quenched and annealed polycrystalline samples (table I, fig. 2).

7 326 F. K. LOTGERING Acknowledgement The author is indebted to Prof. J. Smit, formerly of this laboratory, for stimulating discussions, to Mr J. F. Fast for performing the magnetic measurements and to Mr J. Verberkt for preparing the samples. Eindhoven, February 1965 REFERENCES 1) J. M. Hastings and t, M. Corliss, Phys, Rev. 104, 328, ) I. I. Yamzin, N. V. Belov and Y. Z. Nozik, J. phys. Soc. Japan 17, SuppI. B-III, 55, ) V. L. Moruzzi, J. appi. Phys, 32, 59S, ) F. W. Harrison, W. P. Osmo nd and R. W. Teaie, Phys. Rev. 106, 865, ) S; E. Harrison,. C. J. Kriesman and S. R. Pollack, Phys. Rev. 110, 844, ) F. K. Lotgering, J. Phys. Chem. Solids 25, 95, ) J. Smit and H. P. J. Wijn, Ferrites, Centrex, Eindhoven, ) D. G. Wickam, N. Menuijk and K. Dwight, J. Phys. Chem. Solids 20,316, ) H. Bizette, J. Phys, Radium 12, 161, ) F. C. M. Driessens, Thesis, Eindhoven, 1964, p ) E. J. W. Verwey and E. L. Heilmann, J. chem. Phys, 15,174, ) N. Menuijk and K. Dwight, Preprint Conf. Magnetism, Minneapolis, 1964,H 10.