Magnetic resonance study of the two-dimensional spin diffusion

in the Heisenberg paramaget (C18H37NH3)2MnCl4

K.W. Leea,b,*, C.E. Leea

aDepartment of Physics, Korea University, Anam-dong, Sungbuk-ku, Seoul 136701, South KoreabNatural Science Research Institute, Jeonju University, Jeonju 560759, South Korea

Received 21 September 2002; received in revised form 8 February 2003; accepted 17 February 2003 by A. Pinczuk

Abstract

1H nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) techniques were employed to study the

perovskite-type layered structure compound (C18H37NH3)2MnCl4 undergoing structural phase transitions. The spin relaxation

was found to sensitively reflect the two-dimensional electron spin diffusion.

q 2003 Elsevier Science Ltd. All rights reserved.

PACS: 76.60. 2 k; 76.30. 2 v; 64.70.kb

Keywords: D. Phase transitions; E. Nuclear resonances

1. Introduction

Perovskite-type layered compounds of general formula

(CnH2nþ1NH3)2MCl4 (CnM for short) show a variety of

structural phase transitions, believed to be governed by the

dynamics of the alkylammonium groups and by the

rotational motions of the MCl4 macroanions about their

crystallographic axes [1]. They can show structural

disorders such as planar disorder in the inorganic layer,

reorientational order–disorder motions of the alkyl chains

about their long axes, and conformational changes leading

to a partial melting of the alkyl chain part. For M ¼ Cd, Cu,

and Mn, the mineral layers are constituted of more or less

distorted corner-sharing MCl6 octahedra forming a two-

dimensional matrix and are sandwiched between hydro-

carbon layers [2]. From NMR studies of (C10H21NH3)2-

CdCl4 (C10Cd), which shows two structural phase

transitions, Blinc et al. have shown that order parameters

used for the liquid crystals, pertinent to the alkylammonium

chains, properly describe the phase transition sequence,

while the inorganic layers play an indirect role [3,4].

The magnetic behavior of CnMn exhibits a two-

dimensional character. The magnetic susceptibility shows a

large anisotropy at the magnetic phase transition [5] and the

EPR linewidth shows an angular dependence characteristic of

the two-dimensional paramagnet in the paramagnetic state [6].

In particular, angular dependence of EPR signals characteristic

of two-dimensional magnetism was explicitly observed in

(CnH2nþ1NH3)2MnCl4 with shorter hydrocarbon chains

(n ¼ 2 and 3) [7]. In K2MnF4 it was shown that in the

presence of two-dimensional spin diffusion the EPR linewidth

shows the same temperature dependence as susceptibility

multiplied by temperature ðxTÞ [8].

CnMn has been intensively studied for the cases of n ¼

1; 2, and 3 [6,9]. However, for n greater than 10, fewer

studies have been done [5,10]. NMR and EPR studies in the

CnMn systems have been confined to the two-dimensional

magnetism [5,11], while those associated with the structural

phase transitions are rare and confined to the short-chain

compounds [12]. This can be attributed to the fact that the

alkylammonium chains are believed to play the main role in

the phase transitions of those systems. It is difficult to detect

the alkyl chain dynamics by Mn2þ electron paramagnetic

resonance (EPR). Besides, NMR is affected by the

0038-1098/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0038-1098(03)00138-8

Solid State Communications 126 (2003) 343–346

www.elsevier.com/locate/ssc

* Corresponding author. Present address: Department of Physics,

Korea University, Anam-dong, Sungbuk-ku, Seoul 136701, South

Korea. Tel.: þ82-2-3290-3098; fax: þ82-2-927-3292.

E-mail address: rscel@korea.ac.kr (K.W. Lee).

paramagnetic electron spins in this paramagnetic system.

Thus, the alkyl chain dynamics has been investigated mainly

by IR (infrared) spectroscopy [10] or by neutron scattering

[13]. The magnetostructural coupling in the CnMn system

below the Neel temperature has been studied by using

neutron scattering [14]. As is generally known, the canted

antiferromagnetism (or weak ferromagnetism) found in the

CnMn system originates from the Dzialoshinsky–Moriya

(DM) interaction, and the neutron scattering study suggests

that it is a strong candidate for the magnetostructural

coupling [14]. While NMR studies of the two-dimensional

magnetism may be more complicated for the long-chain

compounds than for the short-chain ones due to the presence

of many proton interactions, the large separation between

the magnetic layers warrants the two-dimensionality in the

long-chain systems.

2. Experiment

The (C18H37NH3)2MnCl4 powder sample was made

according to the reaction 2C18H37NH3Cl þ MnCl4·4H2O

!(C18H37NH3)2MnCl4. The powder was twice recrystallized

and then vacuum dried. The room temperature X-ray powder

diffraction shows well aligned (00l) peaks with an orthorhom-

bic-like lattice with some other very weak peaks. The

interlayer distance between the inorganic layers is about

39 A, which is compatible with that of C18Cu [1]. The spin–

lattice relaxation time ðT1Þ measurements were made at the

Larmor frequency of 200 MHz by means of the conventional

inversion recovery method. For the X-band (9.4 GHz) Mn2þ

EPR measurements, a Bruker ESP 300 spectrometer was

employed, and the magnetic susceptibility x was measured by

a superconducting quantum interference device (SQUID,

Quantum Design MMPS5).

3. Results and discussion

In our preliminary studies of C18Mn, three successive

structural phase transitions were found [15]; a major phase

transition at 346 K ðTc1Þ accompanied by the largest thermal

entrance in the differential scanning calorimetry (DSC)

measurements, a minor one at 359 K ðTc2Þ; and an intermediate

one at 370 K ðTc3Þ:1H NMR second moment measurements,

shown in Fig. 1, show a large reduction at Tc1 and a smaller one

at Tc3; respectively, which were attributed to the alkylammo-

nium chain dynamics. On the other hand, the phase transition

at Tc2; which showed anomalies in the EPR and magnetic

susceptibility measurements but not in the NMR second

moment measurements, was ascribed to the magnetic

inorganic layers. It is the purpose of this work to investigate

the spin relaxation and magnetic properties in this complicated

two-dimensional paramagnetic system undergoing structural

phase transitions.

The proton NMR spin–lattice relaxation pattern was

nearly of a single exponential form. Fig. 2 shows the

temperature dependence of the spin–lattice relaxation rate

ðT211 Þ; in which a discontinuity is prominent at the

conformational phase transition temperature Tc1; revealing

a first-order nature. The dipolar hyperfine interaction

between the electron spins of Mn2þ and the proton spins,

which is about three orders greater than the proton dipole–

dipole interaction, is expected to dominate the spin–lattice

relaxation in C18Mn [16,17]. The paramagnetic centers

directly relax the nuclei via the dipolar hyperfine inter-

action, and at the same time, develop a spin temperature

gradient over the nuclear spin system, giving rise to the

nuclear spin diffusion [18,19].

Fig. 1. Temperature dependence of the 1H NMR second moment.

Fig. 2. Temperature dependence of the 200 MHz proton NMR

spin–lattice relaxation rate measured (B) and that calculated (W)

according to Eq. (8).

K.W. Lee, C.E. Lee / Solid State Communications 126 (2003) 343–346344

In the NMR theory of spin–lattice relaxation in a dilute

paramagnet, several characteristic lengths are important,

such as the internuclear spacing a; the impurity separation R;

the pseudopotential radius b; and the diffusion barrier radius

b [20]. The impurity separation is commonly defined by

R ¼3

4pNp

!1=3

; ð1Þ

where Np is the impurity concentration. The pseudopotential

radius b is a radius at which direct relaxation (due to the

dipolar hyperfine interaction) and nuclear spin diffusion

give the same contributions. It is defined by

b ¼C

D

� �1=4

: ð2Þ

Here, the nuclear spin diffusion coefficient [21] D .ð1=30Þ

ffiffiffiffiM2

pa2; where M2 is the NMR second moment, and

C is defined by

C ¼2

5"2g2

Pg2I SðS þ 1Þ

tc

1 þ v2ot

2c

; ð3Þ

where gP; gI; S; tc; and vo are the electron gyromagnetic

ratio, the nuclear gyromagnetic ratio, the electron spin, the

electron correlation time, and the nuclear Larmor frequency,

respectively. The electron correlation time tc is equal to the

electron spin–lattice relaxation time T1e when the electron

spin–spin relaxation time T2e is longer than T1eðT2e q T1eÞ;

and is equal to T2e when T2e is shorter than T1eðT2e p T1eÞ

[21]. C and D represent the contribution to the nuclear spin–

lattice relaxation rate from the direct relaxation and that

from the nuclear spin diffusion, respectively. Inside the

diffusion barrier radius, nuclear spin diffusion is completely

quenched, and there is only direct relaxation of the nuclear

spin system due to the dipolar hyperfine interaction between

the electron spins and the nuclear spins. The diffusion

barrier radius is defined as the distance from the para-

magnetic center at which the change of Bp; the magnetic

field of the paramagnetic center, is of the order of the local

field Bl produced by a nucleus, at the sites of other nuclei.

Its value is given by

b ¼ ð3akmplz=BlÞ1=4 ¼ ð3kmplz=mnÞ

1=4a; ð4Þ

where kmplz is the average magnetic moment of the

paramagnetic ion that is effective in quenching the nuclear

spin diffusion and mn is the nuclear magnetic moment. At

high temperatures kmpl2z is given by Ref. [22]

kmpl2z ¼

1

3mp2 2

ptan21 tc

T2

� �� �ð5Þ

where mp and T2 are the electron magnetic moment and the

nuclear spin–spin relaxation time, respectively. Another

characteristic length bo needs to be noticed, inside of which

the resonance lines of the nuclei are broadened too much to

be observed. It is given by Ref. [20]

bo ¼ ðkmplz=BlÞ1=3 ¼ ðkmplz=mnÞ

1=3a: ð6Þ

There can be three limiting cases depending on the relative

magnitudes of the characteristics lengths, i.e. R; b; and b

[20]; the rapid spin diffusion case, the diffusion limited case,

and the diffusion vanishing case. In the rapid spin diffusion

limit, the nuclear energy transfer due to the nuclear spin

diffusion is much faster than the direct relaxation and so the

nuclear spin–lattice relaxation rate is completely deter-

mined by the direct relaxation. In the diffusion vanishing

limit, there is no nuclear spin diffusion and so the nuclear

spin–lattice relaxation occurs only through the direct

relaxation. In the diffusion limited case, the dominant

spin–lattice relaxation mechanism is the direct relaxation

for the short-time region, and the nuclear spin diffusion for

the long-time region.

In the presence of strong exchange interaction as in this

system, T2e is nearly the same as T1e [18,19], and thus tc is

equal to T2e [22]. The electron spin–spin relaxation rate

calculated from the EPR linewidth is about 90 MHz [15].

With S ¼ 5=2; a ¼ 1 �A; vo ¼ 2p £ 200 MHz; T212e ¼ 170

MHz; and M2 ¼ 23 G2; which is the low temperature NMR

second moment as measured by us, the pseudopotential

radius b is estimated to be about 1.8 A. The nuclear spin–

spin relaxation time T2 for a Gaussian lineshape is , 2=ffiffiffiffiM2

p

[18,19]. The diffusion barrier radius b in Eq. (4) is calculated

to be about 1.8 A, and bo defined by Eq. (6) about 1.5 A. The

average separation between the electron spins, R; can be

assumed to be close to the interlayer distance, 39 A, along

which nuclear spin diffusion occurs [2].

The rapid spin diffusion limit is described by d ¼

0:5 £ ðb=bÞ2 , 1 [20], which is valid in our case. In the case

of rapid spin diffusion ðR . b q bÞ; the nuclear spin–

lattice relaxation rate T211 is given by Ref. [20]

T211 ø

4p

3

NpC

b31 þ

b3o 2 b3

R32

1

4

b4

b4

" #ð7Þ

In the limit votc q 1 as in our case, Eq. (7) is reduced to

T211 / Npa23dn11=8

e M23=162 v22

o ; ð8Þ

which shows a strong dependence on the EPR linewidth dne

as well as on M2:

The EPR lineshape was nearly of a Lorentzian form over

the temperature range investigated, indicating a strong

exchange narrowing. In Fig. 3, it is seen that the EPR

linewidth and the magnetic susceptibility multiplied by

temperature ðxTÞ show very similar temperature dependen-

cies, including anomalies at the transition temperatures Tc1

and Tc2: In fact, in the presence of two-dimensional spin

diffusion, the EPR linewidth is expected to follow the

temperature dependence of xT [8]. Thus, the temperature

dependence of EPR linewidth arises from the two-

dimensional electron spin diffusion, and the anomalies in

the EPR linewidth can be attributed to those in the magnetic

susceptibility [15]. Besides, comparison of Figs. 2 and 3

indicates that the overall temperature dependence of the

K.W. Lee, C.E. Lee / Solid State Communications 126 (2003) 343–346 345

200 MHz proton spin–lattice relaxation rate, up to around

the magnetic phase transition temperature Tc2; resembles

that of the EPR linewidth, as indicated by Eq. (8). In fact,

Fig. 2 shows that with a properly chosen proportionality

constant, the measured spin–lattice relaxation rate follows

the M23=162 and dn11=8

e dependencies using the M2 and dne

data in Figs. 1 and 3, respectively. On the other hand, above

Tc2; a drastic deviation is noticed, in agreement with the

magnetic nature of the high temperature phase transition at

Tc2; through which the magnetic interactions undergo a

substantial change.

In summary, we have studied the spin relaxation in the

two-dimensional Heisenberg paramagnet (C18H37NH3)2-

MnCl4 undergoing structural phase transitions associated

with the organic and the inorganic layers. The 200 MHz

NMR spin–lattice relaxation was identified in the frame-

work of the theory of the nuclear magnetic relaxation by

dilute magnetic impurities, and was found to reflect the

magnetic properties of the system, as revealed by the EPR

and the magnetic susceptibility measurements, via the two-

dimensional electron spin diffusion.

Acknowledgements

This work was supported by the KISTEP (National

Research Laboratory and M102KS010001-02K1901-

01814) and by the Korea Research Foundation (BK21).

Measurements at the Korea Basic Science Institute (KBSI)

are acknowledged.

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K.W. Lee, C.E. Lee / Solid State Communications 126 (2003) 343–346346