Antiferromagnetic resonance in LiMnPO4

J. Phys. Chem. Solids

Pergamon Press 1969. Vol. 30, pp. 1335-I 340.

ANTIFERROMAGNETIC

Printed in Great Britain.

RESONANCE

IN LiMnPO,

P. R. ELLISTON*, J. G. CREER and G. J. TROUP Physics Department, Monash University, Clayton, Victoria, Australia (Received 27 November 1968) Abstract-

Antiferromagnetic resonance at millimetre wavelengths has been observed in singie crystals of LiMnPO,( TN = 35°K). The data have been compared with the Nagamiya-Yosida theory for a collinear orthorhombic antiferromagnet. A best fit to the theory is given by taking (2hK1)“* = 37.9 20.5 kG and 12XK.)1’2= 62a 2 kG at 4.2”K, in good agreement with independent pulsed-field spin-flopdata. . _’

ORTHORHOMBIC LiMnPO,, lithiophilite, is antiferromagnetic below about 35°K [ 11. A variety of studies has been made on this system[ l-41 including spin-flop experiments and preliminary antiferromagnetic resonance experiments reported by us[5,6]. In the present paper we give detailed antiferromagnetic resonance data at millimetre wavelengths in pure single crystals of LiMnPO,, and compare our results with the NagamiyaYosida theory[7-91. Unlike many systems investigated since the early work on CuCIZ .2H,O[lO], LiMnPO, possesses a collinear spin system, and is perfectly orthorhombic. The Nagamiya-Yosida theory should therefore provide a good description of antiferromagnetic resonance in this system, as it does in CuCl, .2H,O. CRYSTAL AND MAGNETIC STRUCTURE

Lithiophilite is isomorphous with olivine, with Li in inversion sites[l l] as in other LiXPO, compounds[4], and Mn in mirrorplane sites. The space group is Pnma with a= 10~46~,b=6~10~andc=4~744~[11]. An antiferromagnetic spin configuration collinear with the a axis was postulated by Mays [ 1I from nuclear magnetic resonance experiments. Mays’ model has been subsequently confirmed by neutron diffraction [2]. *Present uddress: Eaton Electronics McGill University. Montreal, Canada.

Laboratory,

Single crystals of LiMnPO, were synthesized by the flux-melt method[ 121. Orange crystals up to 3 mm in size were obtained. Smaller crystals, about 1 mm, were generally used for the resonance measurements. The larger crystals tended to show structure in the recorded lines (making line-position difficult to determine), while smaller crystals did not; we tentatively ascribe this to propagation effects, although we have not made a detailed study of the effect. Specimens were identified and oriented by back-reflection X-ray photographs, and mounted on a rotatable holder in a broadband millimetre spectrometer [6]. E~E~MENTAL

RESULTS AND DISCUSSION

As previously mentioned, the a axis is the most favoured axis of magnetization in LiMnPO,. The spin-flop data of Ranicar and Elliston[S] further indicate that the least favoured axis is the b axis. In the notation of Nagamiya and Yosida the a and b axes then correspond to the x and z axes respectively. In the paramagnetic state above the N&e1 point an isotropic resonance line with g = 2.00 +O*Ol is observed. This paramagnetic resonance broadens and weakens near 35°K. The Nobel point thus obtained is TN = 34.6 &0*4”K, in agreement with Mays’[l] value (TN = 34.85 -c O.l”K). Since Mn2+ is an S-state ion, a g-value close

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P. R. ELLISTON

to 2 in the paramagnetic state is not unexpected. We take the same g-factor for the antiferromagnetic state, an assumption which has been shown to be quite reasonable for other materials [8,9,13]. Below TN antiferromagnetic resonance is observed. No hysteresis in the data was recorded, although runs were usually made with increasing magnetic field. If a magnetic field Ho is applied along the x axis, the Nagamiya-Yosida theory predicts resonances above and below the critical (spin-flop) field H, [= (cl/a) lj2]. These modes are given by (w/r)‘=

(1/2)[(1+cu2)H,*+~,+~~ ~{(1-a2)2H~4+2(1+~)2H02(~1+~2) + (c~--c,)~}~‘~];

Ho < H,

where the low- and high-frequency given by-and-i- respectively: (w/Y)~ = Ho2-c,;

(1)

modes are

Ho > H,

(2)

and (w/y)” = cz -c,;

Ho > H,

where w is the angular frequency, the gyromagnetic ratio, and

y(= ge/2mc)

Cl = 2hKl, cz = 2X&, CX= 1 - x,,fx i where h(= l/x,) is the molecular field coefficient, K1 and K, are the anisotropy energy constants (K2 > K, > 0). and xII, xI are the parallel and perpendicular susceptibilities. Under certain conditions resonance may also be observed at Ho = H,[8,9]. For H,, along the y axis the resonance condition is (o/r)” = Ho2 -I-cl.

(3)

With a microwave frequency of 676 Gcis 24.1 kG) and H,, along the a axis we observe two resonances in LiMnPO,, (w/y=

et al.

at low temperatures. The linewidths between inffexion points at 4~2°K are about 250 G for the low-field line and about 400G for the high-field line. We identify these resonances with two of the modes given above: the lowfrequency mode of (l), and (2). The high-field mode, equation (2), allows a direct determination of cX at the temperature of measurement, providing the g-factor, or y, is known. From equation (2) we obtain, at 4*2X, ctliz = 37.9 +-0.5 kG, in good agreement with spin-flop measurements[fi]. Knowing c11/2 we can determine c.~“~ from the low-field mode, provided (Yis known. Rather than determine (Y from molecular lield theory, it is usually obtained experimentally, since this generally gives better agreement between theory and the resonance data [ 143. Mays[ l] gives cx at 4~2°K obtained from NMR and direct susceptibility measurements. We arbitrarily take cy= 0.95 at 4*2”K, a value between those given by Mays. Actually, at this temperature (where (Yis of the order of unity) the resonance expressions are somewhat insensitive to the choice of (Y. From equation (1) we then obtain c211z= 622 2 kG at 4*2”K, taking c1112= 37*9rrt:O*5kG. This value of c211*is in good agreement with the value of 65 & 3 kG obtained from spin-flop measurements in the ah plane [5]. Knowing c,, c~, (Y,and y, all the parameters in the Nagamiya-Yosida theory are specified. The frequency dependence of the various resonances for w/r < 60kG is shown in Fig. 1. The 67.6 Gc/s points are, of course, those from which c1 and cz (and hence the theoretical curves) have been determined. No resonance at the critical field is predicted for this temperature at the frequencies used, in agreement with observation, The 135.5 Gc/s (w/r= 48.4 kG) data for H0 along the c axis are in good accord with equation (3). The angular dependence of the resonances in the ac plane is shown in Fig. 2. The theoretical expressions for this plane are complicated; they were solved, using an iterative technique, with the aid of a computer. The

ANTIFERROMAGNETIC 60

I

RESONANCE

1337

IN LiMnPO,

I

1

/

”

I

(kG)

0

I

I

I

0

\I

I

20

I

1

60

40

Fig. 1. Frequency dependence of antiferromagnetic resonance at 4.2”K. Open circles are for Ho along a axis, and full circles for HO along c axis. Curves are from Nagamiya-Yosida theory with (c,)*‘~ = 37.9 kG and (c,)“* = 62 kG.

60

I

I

I

50

135.5 40

Gc/s

-

H0

\k

(kG)

l

30 -

”

\

-t 20 c

IO L 0” 0 axis

I

I

3o”

60”

90' 14axts

Fig. 2. Angular dependence of antiferromagnetic resonance with Ho in UCplane. Open circles are for 4,2”K, and full circles for 18.5”K. Curves are from NagamiyaYosida theory.

1338

et al.

P. R. ELLISTON

theoretical curves for the above values of cl, cz and a! are shown as solid lines in Fig. 2; the agreement with the data is good. It appears likely that close to the a axis the high-field line at 67.6 Gels shows a small ‘dip’ in the resonance field value similar to that which has been observed in CuCl, .2H,O [15,16] and NiCl,. 6H,0[17]. In CuCl, .2H,O Yamazaki and Date[l6] have observed an anomalously broad line in the region of the dip; this also occurs in LiMnPO,, although experimentally we were not able to study the behaviour in detail. The origin of the dip in these materials is not clear. The angular dependence in the ab plane at 67.6 Gels is shown in Fig. 3 for T = 4*2”K. Again we obtain good agreement between theory and experiment, using c,, c2 and (Y as before. Finally, the temperature dependence of the resonances at 67.6 Gc/s is shown in Fig. 4. Resonance for Ho along the c axis is observed

H0

40

-

30

-

at this frequency for T greater than about 28°K. Above T = 32°K broad resonances are also observed for H, along the a axis; these correspond to the high frequency (+) mode of equation (1). In order to compare the temperaturedependence data with theory we need to know CY ( T) . In the absence of published data we proceed as follows: the critical field H, is given by Hc2 = 2hKJa = 2K,/axI so that generally a(T) = ~K,(T)IH,YT)xI(T). Assuming that a(0) = 1 and x1(T) is constant below TN (expected for a simple antiferromagnet) we have

a(T) = K,(T)H,2(0)/K,(0)H,2(T).

(kG)

-I

-66

-46

-20”

0”

20’

60’

40’

a axis

Fig. 3. Angular

dependence of antiferromagnetic resonance with Ho in ab plane at 67.6Gcls T = 4.2”K. Curves are from Nagamiya-Yosida theory.

and

ANTIFERROMAGNETIC

RESONANCE

IN LiMnPO,

1339

H, CkG)

t

T (“K) Fig. 4. Temperature dependence of antiferromagnetic resonance at 67.6 Gels. Open circles are for H, along a axis, and full circles for Ho along c axis. The curves are explained in the text.

Following assume K,(T)IK,(O)

Abkowitz

and

=&(7-)/&(O)

Honig[ 141 we = %,(TIT‘V)

where B5,& T/T,) is the reduced Brillouin function for the spin 5/2 appropriate to Mn*+ in LiMnPO,. Hence a(T)

= %(TITN)

- Hc*(O)lHc*(n.

H, ( T) has been experimentally determined by Ranicar and Elliston[S]; using their data we can predict CV(T). Implicit in the above assumptions are the variations of c,(T) and c,(T):

c,(T)lc,(O)

= K,(T)IK,(O)

= B&(V’,V) =

~2(T)/c2(0).

Knowing c1 (T) , cz ( T) and CY(T) , we can now compare the experimental data with the

Nagamiya-Yosida theory. The theoretical curves, taking TN = 34_6”K, are shown in Fig. 4, with [c,(4*2)]“* = 37.9 kG, and [c2(4*2)11/* = 62 kG. The curve starting at about 40 kG for T = O”K, and shown as a solid line above 17*4”K, is a best fit to the spin-flop phase boundary determined by Ranicar and Elliston. Above 17*4”K, the spinflop mode given by equation (2) is not observed; instead, the resonance occurs at the critical field. The exchange field HE in an antiferromagnet can be determined from the perpendicular susceptibility, since HE = MO/XI (where M,, is the sublattice magnetization). At 4*2”K, using ~~(4.2) = O-043 cm3/mole[l], we obtain HE = 320 kG for LiMnPO,. The anisotropy field HA = KIM, can be determined from HE and cl, since c1 = 2HEHA. With cll’* = 37.9 kG we obtain H.., = 2.2 kG. A necessary requirement of the NagamiyaYosida theory is that the exchange field be

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P. R. ELLISTON

much greater than the applied and anisotropy fields; this requirement is therefore well satisfied in LiMnPO,. CONCLUSIONS

Antiferromagnetic resonance in LiMnPO, is well described by the Nagamiya-Yosida theory. At 4*2”K, the parameters chosen to give the best agreement between theory and experiment are cI1’*= 37.9 Ir:O-5 kG and c21j2= 62 & 2 kG, in good agreement with independent pulsed-field magnetization measurements. Acknowledgements-We are grateful to Mr. A. Vas for growing single crystals of LiMnPO,. One of us (P. R. Elliston) acknowledges a Radio Research Board grant. REFERENCES 1. MAYS J. M.,Phys. Rev. 131.38 (1963). 2. NEWNHAM R. E., SANTORO R. P. and REDMAN M. J., J. Phys. Chem. Solids 26, 445 (1965).

et al.

MERCIER M. and GAREYTE J., Solid State Commun. 5,139 (1967). SANTORO R. P. and NEWNHAM R. E., Acta crystallogr. 22, 344 (1967). J. H. and ELLlSTON P. R.. Phys. 5. RANICAR Lert. 25A, 720 (1967). 6. ELLISTON P. R. and TROUP G. J., Proc. phys. Sot. 92,104O (1967). 7, YOSIDA K., Prog. theor. Phys. 7,425 (1952). 8. NAGAMIYA T., Prog. theor. Phys. 11,309 (1954). NAGAMIYAT., Prog. theor. Phys. 15,306 (1956). 1z: for references see Foner S., In Magnetism (Edited by G. T. Rado and H. Suhl), Vol. 1, p. 408. Academic Press, New York (1963). 11. GELLER S. and DURAND J. L.. Acta crystallogr. 13,325 (1960). F. and MALOSSI L., Z. Kristallogr. 12. ZAMBONINI 80,442 (19311. 13. FONER S., Phys. Rev. 130,183 (1963). M. and HONIG A., Phys. Rev. 136, 14. ABKOWITZ Al003 (1964). H. J.. Physica 22, 1.5. GARBER M. and GERRITSEN 189(1956). 16. YAMAZAKI H. and DATE M., J. phys. Sot. Japan 21,16 15 (1966). M., J. phys. Sot. 17. DATE M. and MOTOKAWA Japan 22,165 (1967).

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