純有機ラジカル結晶における磁性の実験的研究

九州大学学術情報リポジトリ

Kyushu University Institutional Repository

純有機ラジカル結晶における磁性の実験的研究

美藤, 正樹

Graduate School of Engineering, Kyushu University

https://doi.org/10.11501/3135018

出版情報：Kyushu University, 1997, 博士（工学）, 課程博士 バージョン：

権利関係：

Chapter ₅

Pressure Effect of

1,3,5-Triphenyl-6-0xoverdazyl with Weak-Ferrolllagnetic

Molllent

5.1 Introduction

The magn tism of 1,3,5-triphenyl-6-oxoverdazyl (TOV) at ambient pressure

(Po)

has been mentioned in chapter

4.

TOV is the two-dimensional (2D) Heisenberg antiferromagnet with the weak-ferromagnetic spontaneous moment below

T

^rv 5

.0

K. Th^e magnitude of intermolecular antiferromagnetic interaction on 2D magnetic pl^ane is estimated to be J

/

^{kB � -4.5 K,} and the Weiss temperature is 8 = -9.9 K. The w ak-ferromagnetic behavior is qualitatively understood with a two-Dzyaloshinsky­

Moriya vector

(D)

model, and its magnetic susceptibility just below 5 K shows the crossover fl·om 2D Heisenberg system to 2D Ising one.

On the other hand, J.B.Jamali et al. reported that the slight dilution of TOV by a non-magnetic TOV-H, in which a nitrogen on the verdazyl ring of TOV is coupled with a hydrogen ^as in Fig. 5.1, changes the negative antiferromagnetic (AF) Weiss temperature to the positive ferr01nagnetic (F) one

[74).

Figure 5.1 shows their experimental results of magnetic susceptibility of (TOVh-x(TOV-H)x

(

^{x =}

0

^rv

0.09).

It is seen that even a few percent of dilution changes 8 from negative (AF) to positive (F); 8 =

2

.6 ±

0.5

K at the impurity of

3.0 ^%,

for example.

We thought that the above transition from AF to F might be brought about by a crystallographic stress (i.e. a chemical pressure) in the diluted system. So we intend d th measurements of ac-magnetic susceptibility

(Xac)

of pure TOV under pressur , expecting the appearance of the transition from AF to F.

89

90CHAPTER 5. PRESSURE EFFECT OF 1,3,5-TRJPHENYI--6-0XOVERDAZYL WITH w

300

250

0 200

...

E _:::l E <U

� ¹⁵⁰

100

50

-o-x-a o

--

^{· x�o 03}

- ._ -X-007

- -•- -X-<J.09

20 40 60

T(K)

80 100 120 140

�. ^;.N-N 0

'=/' �_J==o

Hb

Figure 5.1: Temperature dependence of inverse magnetic susc^eptibility of (TOVh-x(TOV-H)x

(

^{x = 0 rv 0.09) [74]}

.

The Weiss temperature (8) is -12 ± 2 K for ^{x =} 0, and 2.6 ± 0.5 K for ^{x =} 0.03.

5.2 Experimental Results and Discussion

The ac-magnetic susceptibility

(xac)

of pure TOV in the hydrostatic pressure up to 10.9 kbar was measured by the ac-bridge

(Hac

⁼ 1.0 Oe peak-to-peak

and J

=

15.9 Hz). The hydrostatic pressure was attained with the Cu-Be pressure clamp cell (Fig. 2.4), in whkh the polycrystalline sample of TOV

(54.2

mg) mixed with the pressure transmission oil (Apiezon-K grease; 29.6 mg) and some tips of AI (7.6 mg) was enclosed in the teflon sample cell. The absolute value of real pressure at low temperatures was estimated by the pressure dependence of supercoⁿducting transition temperature

Ts(p)

of AI with

Ts(Po)

⁼ 1.17 K [42]. The susceptibility of the blank cell (i.e. the clamp cell, AI etc.) was subtracted from the total susceptibility.

Figures 5.2 and 5.3 show the pressure dependences of

x'

and

x",

respectively, where

x'

^{is a} real component of

Xac

with the same phase as

Hac,

^and

x"

^{is the}

imaginary component of

Xac

with the phase delayed at ninety degrees against

Hac.

It looks easier to detect the transition temperature Tc from the point of intersection of two straight lines extrapolated from above and below around Tc as in Fig. 5.3.

In both figures, the temperature

(Tc)

below which the spontaneous magnetization

5.2. EXPERIMENTAL RESULTS AND DISCUSSION

-

+-' (f) c ::J ..0 _�

...__... ro

><

-

+-' (f) c ::J ..0 _� ...__... ro

><

0

0

T(K) 10

T(K)

0

0 ...

X

0

•

91

p ⁼ 0 kbar 3.3 kbar 5.3 kbar 6.6 kbar 7.5 kbar 10.9 kbar

20

0 p ⁼ 0 kbar 0 3.3 kbar

A. 5.3 kbar

X 6.6 kbar

0 7.5 kbar

• 10.9 kbar

Figure 5.2: Pressure dependence of x' of pure TOV in the pressure region up to 10.9 kbar. The temperature at the intersection of two broken lines stands for Tc at p = Po·

92CHAPTER 5. PRESSURE EFFECT OF 1,3,5-TRTPHENYL-6-0XOVERDAZYL WITH W

p ⁼ 0 kbar

-. +-' (f) c ::J _. ..0 � 8

ro _e

...__... 0

:::: B ⁰

><

�

8

0

Figure 5.3: Pressure dependence of x" of pure TOV in the pressure region up to 10.9 kbar. The temperature at the intersection of two broken lines stands for Tc at each pressure.

5.2. EXPERIMENTAL RESULTS AND DISCUSSION

15

�

�

'--"

,--...

6

�

0 D

D

from from

0 2 4 6 8 10

p (kbar)

93

X' X

^II

12 14

Figure 5.4: Pressure dependence of

Tc(P)

of pure TOV in the pressure region up to 10.9 kbar. 0 and D stand for

Tc(p)

estimated from x' and x", respectively. The solid Hne expresses the relation of eq.5.1.

begins to develop is enhanced toward the high temperature by the pressure;

Tc

at p = Po is estimated to be about 5.0 K and

Tc

at

p

^{= 10.9} kbar exceeds 10.0 K, for example. Figure 5.4 shows the pressure dependence of

Tc(P),

^{which is estimated}

from the experimental results of x' and x", and is characterized with the following positive pressure dependence below 8 kbar,

(

5.1)

The enhancement of

Tc(P)

does not exceed the corresponding results for bulk­

antiferromagnets such ^as TANOL '[75,76], TPV f[76] and p-Cl-BDPA l[76], ^as will be shown in Fig.6.12. This large enhancement of

Tc(P)

of TOV gives us the great possibility to increase

Tc(P)

more and more by the higher pressure . If a pressure

•2,2,6,6 tetramethyl-4-piperidinol-1-oxyl:Tc(po) = 0.49 K t 1,3,5-triphenylverdazyl: Tc(p0) = 1.70 K

tt,3-bisdiphenylene-2-p-chlorophenyl allyl: Tc(Fo) = 3.25 K

94CHAPTER 5. PRESSURE EFFECT OF 1,3,5-TRIPHENYL-6-0XOVERDAZYL WITII W

o p ⁼ 0 kbar 0 3.3 kbar

- ... 5.3 kbar

(/) )( 6.6 kbar

�

c ⁰

:::J 7.5 kbar

..0 ^• 10.9 kbar

� m

-

><

0 1 3

T/ Tc

Figure 5.5: Pressure dependence of x' of pure TOV in the pressure region up to 10.9 kbar. The temperature of the X-axis is normalized with each

Tc(p).

higher than 20 GPa can be applied without changing the cr ystal symmetry,

T�(p)

of TOY will exceed 100 K.

The hump of x' around 2.0 K observed at ambient pressure ^seems to shift toward higher temperature by the pressure, preserving the w^eak-f^er^romagnetic behavior under pressure. This experimental result indicates that the transition from AF to F does not occur, and the pressurization of TOY enhances the antiferromagnetic intermolecular interaction within the Dzyaloshinsky-Moriya (D-M) mechani^sm.

Figures 5.5 and 5.6 show the pressure dependences of x' and x", respectively,

in which the temperature is normali^zed with

Tc(p).

From Fig. 5. 5, the pressure dependence of x' is understood in the three ways depending on the values of pressure1 at ambient pressure p = PJ and

p �

6.6 kbar. At ambient pressure, ^as mentioned in the previous chapter1 a broad maximum or hump of x is seen around 2.0 K1 and below 2.0 K x' decreases b^ecau^se of the cancellation of weak-ferromagnetic moments which is brought about the competition between

5.2. EXPERIMENTAL RESULTS AND DISCUSSION

--

(/)

�

c ::l ..0 L

-

ro

><

0

���

p ⁼ 0 kbar

.,...) __.

..

^.,._\

'

p = 6.6 kbar

:�\ K

�

⁰

i ^\

^{• ,\ � ()}

t \"'

I /'�"

p ⁼ 10.9 kbar

0.5 1

T/ Tc

1.5

95

2

Figure 5.6: Pressure dependence of x" of pure TOV in the pressure region up to 10.9 kbar. The temperature of the X-axis is normalized with each

Tc(p).

96CHAPTER 5. P^RE^SSURE EFFECT OF 1,3,5-TRIPIIENYL-6-0XOVERDAZYL WITH W

the development of spin-correlation length and the D-M interaction.

By pressurization, however, the two-D-M vector model is supposed to be de­

stroyed by the lowering of local crystal symmetry, weakening the cancellation of the moments at lower temperatures. As the result, the low-temperature increase of

x'

under higher pressure is seen in Fig. 5.5. In the pressure region p

:::;

6.6 kbar, x' shows a shoulder which may be an indication of random co-existence of the D-M interactions with original two D-M vectors and distorted D-M vector. For p

2

_6.6

kbar, x' continues to increase toward low temperatures because the distortion of the D-M vector is enhanced by the pressure. The pressure induced enhancem nt of

Tc(P)

in TOV is reasonably understood by considering the distorted D-M v ctor becomes more dominant, in addition to the enhancement of antiferromagnetic inter­

molecular exchange interaction. This gives an effect to increase

x'

and x" toward higher temperatures than the pure two-D-M vector model does .

On the other hand, in the normalized temperature dependence of

x" (p)

in Fig. 5.6, we can see the energy loss for the development of weak-ferromagnetic moment which may be due to the dominant distortion of D-M interaction at low temperatures.

5.3 Conclusion

The experimental fact that antiferromagnetism of TOV is qualitativ ly turn d to ferromagnetism by doping the non-magnetic derivative is suggestive of the drastic change of the electronic state, referring to our pressure effect of pure TOV.

Our experiment of pressure effect on this sample has not changed antiferromag­

netism in the pressure region up to 10.9 kbar, in spite of our expectation. IIowev r, we have found that the transition temperature increases up to about 10 K, nearly twice of its value at ambient pressure, with weak-ferromagnetic mom nt. This fact is mainly brought about by the pressure induced enhancement of the antiferromagnetic intralayer interaction. This experimental result gives us great hope for realization of the spontaneous magnetization at higher temperature, when we make us of the D-M interaction. The magnetic behavior reflected on x' and x" is understood by the change of the D-M interactions from the type of two D-M vectors at ambi­

ent pressure to that of distorted D-M vector under pressures. The pressurization of TOV plays the roles of distorting the two D-M vectors at ambient pressure, as well ^as enhancing the antiferromagnetic intralayer interaction. On the other hand, the doping of the non-magnetic derivative will change the electronic state drastically.

Chapter ₆

Pressure Effect of

Bulk-Ferrornagne.t /3-phase para-Nitrophenyl Nitronyl Nitroxide

6.1 Introduction

As mentioned in chapter

1,

the ,B-phase

p-NPNN

(para-nitrophenyl nitronyl ni­

troxide) crystal is the first genuine organic bulk-ferromagnet which orders ferro­

magnetically as a whole

(Tc

^{� 0.6 K).} This is a realization of "the through bond strategy" of ferromagnet among a great number of derivatives of nitronyl nitroxide radical synthesized so far: Most of the derivatives are antiferromagnetic, but they give significant information for studying how intermolecular exchange interactions depend on molecular orbitals.

On the other hand, there is another substantial way of understanding intermolec­

ular interactions by giving a continuous change of overlapping of molecular orbitals in a "typical" organic magnet by pressurization.

In this chapter, we reveal first pressure-induced ferro- to antiferromagnetic tran­

sition which occurs in the genuine organic ferromagnet, ;3-phase p-NPNN, and give a quanLitative xplanation based on the change of orbital overlapping under pressure.

Pressure Effect of Organic Molecule-Based Magnets In the experimental study of the pressure effect in organic compounds, there have been a few reports which are limited to antiferromagnet until 1995 [75,76]. These reports about an­

tiferromagn ts show that the bulk( three-dimensional)-antiferromagnetic transition temperature

(T3d)

and/or the antiferromagnetic exchange interaction have been en-

97

98CHAPTER

_6.

PRESSURE EFFECT OF BULK-FERROMAGNET,B-PHJ\SE PARA-NTTR

hanced by pressure. This phenomenon may be simply understood du to th en­

hancement of intermolecular interactions with the shrink of th lattice (i.e. the shrink of intermolecular distances).

In the report about the bulk-ferromagnet ,B-phase

p-NPNN

in

1995,

_{Takeda et al.}

reported that T3d was decreased by the pressure in the pressure region up to

7.

₇

kbar, and T3d was expected to vanish at the larger pressure of p I"V

20

_kbar

[12,13].

This phenomenon is opposite with those in bulk-antiferromagncts, and it has been thought that this might be the peculiar phenomenon to organic ferromagnets. So we extended the pressure region beyond 7. 7 kbar for the elucidation of the mechanism of exchange interactions in the organic ferromagnet.

This chapter reports the magnetic properties of

,B-p-NPNN

up to

10.4

kbar a11d the change of crystal structure up to

12.6

kbar, which are discussed on the basis of the charge transfer mechanism and the recent ab-initio method for the exchange interaction. Hereafter

Tc

will be used as the bulk-magnetic ord ring temperature, not restricted in the case of ferromagnet.

6.2 Experimental Results

The polycrystalline ;3-phase

p-NPNN,

used in the pr sent experiments, was syn­

thesized by Prof. Kinoshita's group (Tokyo University, Science University of Tokyo in Yamaguchi at present). The ferromagnetism and various physical properties of ;3-

p-NPNN

have been already investigated in detail as mentioned in chapter

1

_{(s ction}

1.1).

The crystal structure of

,B

-p-

NP

N

N

is studied to belong to the space group of F2dd with a =

12.374 _A,

_b =

19.350 _A

_{and c =}

10.960 _A [8].

_The description of molecular arrangement is partially given in chapter

1

_(section

1.4;

_Fig

1.10)

_and

in the following section

6.3.

Here we only give a schematic crystal structure and possible paths of intermolecular interaction as in Fig.

6.1.

6.2.1 Heat Capacity at Ambient Pressure

The heat capacity at ambient pressure

(p

⁼

p0)

in the external magnetic field

(H)

up to

30

kOe was measured with the adiabatic heat pulse method, in order to confirm the bulk-ferromagnetism and estimate the intermolecular exchange interactions in this system. The polycrystalline

,B-p-NPNN (187.1

_{mg) was mixed} with the Apiezon­

N grease

(215.3

mg) for the thermal binder.

Figure

6.2

shows the magnetic field dependences of heat capacity

(Cp)

of {3-p-

NPNN,

and Fig.

6.3

shows that of magnetic entropy (S). Figure

6.4

shows the

6.2. EXPERIMENTAL RESULTS 99

b

a

Figure 6.1: Schematic crystal structure and possible paths of the intermolecular interactions (J12-J14)of ,8-p-NPNN. The character of J1n

(

^{n =}

2-4)

is detailed in section 6.3. An ellipse stands for an molecule of /3-p-NPNN.

lOOCHAPTER 6. P RESSURE EFFECT OF BULK-FERROMAGNET /3-PHASE PARA-NIT

8

⁰

00

0 2

0 0 · 8

0 0 0

4

T(K)

6

o II� 0 Oe

+ 200 Oc

A 500 Oc )( 1000 Oe

v 2500 Oe

o 5 kOe

o 10 kOe

o 30 kOc

0

8 10

Figure 6. 2: External magnetic field dependence of

Cp

of

/3-p-NPNN

_{at p =Po· The}

solid curve expresses the lattice contribution

(C1auice),

which is approximated by the Debye function

/(80

⁼ 132 K, r =

4).

6.2. EXPERIMENTAL RESULTS

6

2

0

- sc � z -

^--

-

��CJOi)Jl.Ql;,)_ ^{.Q- Q_} _Q_ _Q_

0o �...,�� � 8 ^{o o}

AI�,<;:6('h:X)()()OO

0 0 0 0 0 0 0 0 0 0 0 <o 0 ($) 0 0 0 0

0 0

o<f>

^{o 0}

00 0

0 �0

0 0

2

0 0 0 0

4 6

T(K)

o H ^{= 0} Oe

+ 200 Oe

A 500 Oe

x 1000 Oe

v 2500 Oe

o 5 kOe

o

¹⁰ kOe

o 30 kOe

8 10

101

Figure 6.3: External field dependence of magnetic entropy

(S)

of {3-p-NPNN at p

=

Po^· The broken line expresses the value of

S(T

^{= oo}

)

⁼ Nk8 ^ln

(2S

+ ¹

)

^with

S

=

1/2.

102CHAPTER 6. PRESSURE EFFECT OF DULK-FERROMAGNET {3-PIIJ\SE PARA-NIT

10

30 ,._

I o If= 0 Oe

I

P= 0 kbar _I ^I I ^I + 200 Oe

8

^{0 .--20 <D I I I I A 500} _{1 kOc} ^Oe

0 _/ ^I

)(

� ^I 2.5 kOc

::r: ^{/ I v}

...--. 10

,

^/ _{5 kOc}

� / 0

0 ^I

8 6

^{;' I 0 10 kOe}

�

₀ ^LJ___!/ ₁

_

^l___ ₂ ^{Tmax (K)} ₃ ^{0 30 kOe}

---

,.._,

...__....

\..)E 4

2

0

Figure

6.4:

External magnetic field dependence of

Cmag

of {3-p-NPNN at p = Po·

The solid line expresses the Schottky type of heat capacity

(eq.6.l)

^with

6/kn =

^6.4

K. The inset figure shows the external field dependence of the temperature with the maximum of

Cmag·

field dependence of magnetic heat capacity

(Cmag),

which was gotten by subtracting the lattice contribution

(Clattice)

from the total heat capacity

(Cp)·

The lattice contribution is approximated by the Debye function !(80 ⁼ 132 K, ^{r = 4}

)

^{, as in}

chapter 3, and is estimated to be

0.2 %

^of

Cp

^at

1. 0

K, ^81.4

%

^{at 5.1 K, and 94.1}

%

at 10 K. The sharp peak concerned with bulk-magnetic transition is observed at Tc

= 0.64

K in zero external field. As the external field increases, the peak indicating bulk-magnetic ordering becomes broader, and shifts toward higher temperatures as shown in the inset of Fig.

6.4.

The results below 3 kOe are consistent with the previous work by Nakazawa et al.

[6).

Generally in the case of antiferromagnet, the peak shifts toward lower tempera­

ture until the external field reaches the spin-flopping field. On the other hand, the field dependence of ferromagnetic ordering is different from that of antiferromag-

6.2. EXPERIMENTAL RESULTS

103

netic one ^as mentioned in subsection

3.2.3 (eq. 3.11).

In the larger field thru1 the diamagnetic field

(

^�

₁₀₀

Oe), the magnetic order becomes broader and the order­

ing temperature shifts toward higher temperatures with the increasing field. The ext rnal field dependence of

Cmag

of ,8-p-NPNN ^as shown in Fig. 6.4 indicates the character of bulk-ferromagnet.

Next we discuss the magnetic field dependence of

Cmag

quantitatively. The no­

ticeable result in Fig.6.4 is that the maximum values of

Cmag

in H

= 10

^{kOe and}

30

kOe are close to that of the Schottky type of heat capacity

( Csch),

which is expressed as

Nb2exp(b/kBT)

Csch _{= k8T2[1}

₊

exp(b/kBT)]2

^(6.1)

wh r

b

stands for the energy gap in the two-level system. The temperature

Tmax

which gives the maximum value of Csch has the following relation with

b,

Tmax = 0.42 b/kB (6.2)

Generally in organic radical crystals, the orbital angular momentum of molecular orbitals is quenched so that the g-factor has the value close to quite an isotropic value

(g=2.0023)

for any direction in the crystal except low temperatures where som anisotropy such ^as the dipole fields works. In other words, the 1nagnetic mo­

m nt 9J.1BS easily points to the field direction, making its direction the quantum axis. In the limit of strong magnetic field, therefore, the energy levels are domi­

na.Btly d termined from the Zeeman energy, where the system may be treated as

the ensemble of isolated spins under the following effective field Heff,

Heff

= f{

+ Hex ,

(

^6.

3)

where if is the external magnetic field and Hex is the exchange interaction field.

A schematic description for the energy levels is given in Fig. 6.5. The exchange interaction field Hex is the field originated from the surrounding spin via

�j;

(zl

2(S) 9J.1B

zJ ,

Z1 J12

+

z2J13

+

Z3J14)

^(6.4)

wher

i J

is the product of the average coordination number and exchange integral, and (S) is th magnitude of av rage spin induced by the external field. The relation betwe n

b

and Heir can be expressed ^as,

(6.5)

104CHAPTER 6. PRESSURE EFFECT OF BULK-FERROMAGNET {3-PliASE PAHA-NIT

0=9/.ia (H+ Hex)

H

Figure

6.5: A

schematic model of energy level in the st.rong

limit of ext.

rn

a

l m

a

gne

t

.

i

c field (If).

_b

stands for the energy g

ap ^{in th}

e

two-level system, and

.!12 -

^{.!11, do for}

t

he dominant intermolecular interactions (see

Fig. 6.1

and

Fig.6.20). Ifcx expresses the

ex

ch

ange interaction field.

The experimental results of I-I =

30

kOe

a

nd

10

kOe can be

quantitatively repro­

duced by

the theory of

Csch

(

e

q.

^6.1)

with

b

/ k8 =

6. 4 K and 3. 4 K, rcsp tive

l

y.

Above

values of energy gap correspond to the

magn

etic

field of 1 ferr = 47. 7 kOe and 25.4

kOe, from eq.6.5

r

es

p

ec t

iv

el

y.

In the

_case of If= 30 kO

e (7�ax =

2. 7

K),

th

e value of Hex is estimated to be

17.7 kO

e from

eq . 6.3, and in if

=

10 ^{kOe (7�ax =} 1. 5 K), Hex

is estimated to be

15.4

kOe. This value of flex=

16.5 ±

2

kOe beyond

the difference of applied magnetic field is surprising. This implies that (S) in

Pq.G.1 has

nearly the sa

m

e magnitude at II=

30 kOe (Tmax = 2. 7

K)

and 10 kO (1.5

K).

From eq.6.4, the value

of

i] /k8 i

s

estimated under t

h

e

assumption

(S)

⁼ 1/2,

zl/kB =

2.3 K .

(6.6)

When we take

_i = 12

(diamond or face centered cubic s

tru

c

tu

re

⁾

, the value of

^the

averaged exchange integral

has 2

J /

k

8 = 0.8

^K.

More r

i

g

o

ro

u

s

ly

,

it is necessary t

o

consider the temperature

d

epe

nd

e

nce of (S)

in order to reproduce the exp rimental results of Cmag i

n the external fi

el

d

.

The three-dimensional Heisenberg

spi

n

system has the critical

e

ⁿ

tro

^py

8(1�)

⁼

0.6Nk8ln2

for T _:::; Tc, a

n

d

the lower

d

im

ens

io

na

_l

s

y

s

tem

s

have the smaller value

of

S(Tc) [64]. We find S(Tc) =

0.40Nkaln2

for ,8-p-NPNN. T

hi

s means that l12, J13,

and J14 are not potentially identical to construct some low-dimensional magnetic

lattice.

6.2. EXPERIMENTAL RESULTS

0

E

---::J

E

Q)

-

1 2 3

H (Oe)

105

Figure 6.6: Magnetization curves of ,8-p-NPNN up to 5 T at each temperature (1.8

::; T::;

10.0

K; T

= 1.8 K

(

^o

)

^, 3.0 K

(

^•

)

^, 4.0 K

(D),

6.0 K

(•)

and 10.0 K

(.6)).

The solid curves are guides for the eye.

6.2.2 Magnetization at Ambient Pressure

The magnetization (M) of ,8-p-NPNN

(m

⁼ 59.0 mg) at ambient pressure was measured in the magnetic field

(H)

up to 5 T and in the temperature

(T)

region be­

tween 1.8 K and 300 K with the Quantum Design MPMS-58 SQUID magnetometer (Kyushu Institute of Technology).

Figure 6.6 shows the magnetization curves up to 5 T at each constant temperature (1.8::;

T::;

10.0

K).

The rapid growth of M with the decreasing temperature is seen.

Figure 6.

7

shows the magnetization curves, in which His normalized with

T.

Five magnetization curves cannot be reproduced with such a universal curve as a Brillouin function

(eq.6.7)

for a paramagnetic state with S = 1/2 and g = 2.0, since the effect of the exchange interaction cannot be ignored as is so in the thermal analysis.

Generally the mean field theory for exchange coupled spin systems gives the

lOOCHAPTER 6. PRESSURE EFFECT OF BULK-FEiillOMAGNET {3-PIIASE PARA-NIT.

0

---

E

::J

E

Q)

-

6000

�--�--�--�--�--��

Ms

0 1 2

H/T(Oe/K)

Figure

6.7:

Magnetization curves of ,8-p-NPNN, in which His normalized with T, up to 5 T at 1.8::;

T::;

10.0 K

(T

⁼ 1.8 K

(

^o

)

^, 3.0 K

(

^•

)

^, 4.0

K (D),

6

.

0 K

(•)

and 10.0 K

(.6)).

The solid curves are guides for the eye. The broken line expresses the value of the saturation magnetization (Ms = 5593 emujmol).

6.2. EXPERIMENTAL RESULTS

magnetization curve which follows the Brillouin function as M

B

(

x)

9J.LBJ Heif

N

9J.LB] B( kBT

) l

2S + 1 2S + 1 1 1 2S coth

(

2S x

)

- 2S coth

(

2Sx

)

107

(6.7)

where S

stands for the spin value, and B(x) is the Brillouin function. Heif

is

the

effective field (external field H plus exchange field

Hex

at a spin;

Heff = H

+

Hex).

The exchange field

Hex

is given as

Hex=

.\M , .\

=

2

zJ N(9J.LB)2

with M

=

NgJ.L8

(

S

)

and eventually

Hetr = H

+ >.M.

(6.8)

Figure 6.8 shows the magnetization curve against

Heif,

which is normalized with T. The five magnetization curves are reproduced with one curve

in

the case of i

J / k8

= 1.8 ±

0. 2

K,

which is close to the value of eq .6.6.

Ilere arises a question whether this universal curve is of the Brillouin function for S

= 1/2.

Then the experimental values are corrected as to approach to the saturation value Ms = N 9J.LB

(

S

)

for the limit

H jT

---t oo, as theoretically reasonable. By this correction

(

� 7

%),

all of the experimental data fall on the universal curve (eq.6.7) for S

=

1

/

2 as in Fig. 6.9.

Above analysis of M based on the mean field theory gives

i]/kB = 1.8

± 0.2 K l

(6.9)

as the value of the effective exchange interaction. The value is more reliable than that of eq.6.6, since there is not necessary to consider the temperature dependence of

(

S

)

in this measurement of magnetization M8

=

N

9J.LB (

S

)

.

108CHAPTER 6. PRESSURE EFFECT OF DULK-FERROM AGNET {3-PIIASE PARA-NIT.

-

E

0

--:::J

E

Q)

-

0

zJ/ks

⁼ 1.8 K

3.0 K

6.0 K

10.0 K

1 ^{2 3}

Ms

(H+ ^"A M)!T (Oe/K) [x1 04]

Figure 6.8: Magnetization curves of {3-p-NPNN agains t

Iferr(= If+ Ifex = If+ )..M),

which is normalized with T, up to 5 Tat 1^.8 S T S 10.0 K

(T =

1.8 K

(

^o

)

^, 3.0 K

(•),

4.0

K (D),

6.0

K (•)

and 10.0

K

(6)). The solid curves are guides for the eye.

The broken line expresses the value of the saturation m agnetization

(Ms =

5593 em

uj

^mol

)

.

6.2. EXPERIMENTAL RESULTS

E

0

-­::::J

E

Q)

...__

4000

� 2000

0

zJ/ks

=

1.8 K

^{, , >,}

"'., "',

' ^{' ' ' '}

112,-:-;,--- --�,'

^3.0

^K

2 ,' ," ,

: / ,' " 4.0

K

I I /

/ ,' _-'

'

s

=

1/2

I I /

I I I

1 I I

1 I I

I I I

1 I I

1 I I

I I I I I I I I I I I I I I ^I I I I

I I ,', I

I I Ill I I I ,'1' Ill I I

Ms

I I

,,, II

1 ^{2 3}

(H+ ^A M)!T (Oe/K) [x1 04]

109

Figure 6.9: Magnetization curve of ,8-p-NPNN against Herr, which is normalized with

T,

up to 5 T at 1.8:::;

T:::; 10.0

K

(T

= 1.8 K

(

o

)

, 3.0 K

(

•

)

, 4.0 K

(D), 6.0

K

(•)

and

10.0

^K

(6)).

The experimental result is corrected to have the experimental value at the lowest temperature

(T

= 1.8 K) and the highest field

(H

= 5 T) equal to the value of the saturation magnetization

(Ms

= 5593 emujmol). The solid curves are guides for the eye. Four dotted lines express the Brillouin function ( eq.6. 7) for S =

1/

2, 1, _{3/2 and 2,} respectively.

110CHAPTER

6. PRESSURE EFFECT OF BULK-FERROMAGNET {3-PHASE P

A

^RA-NIT

6.2.3 Pressure Dependence of Magnetic Susceptibility un­

der the Zero External Magnetic Field

The ac-susceptibility

(xac)

in the hydrostatic pressure up to 10.4 kbar was mea­

sured by the ac-bridge

(Hac

=

0.1

Oe peak-to-peak and f ⁼

1

5_.9

Hz).

The hy­

drostatic pressure was attained with the CuBe pressure clamp cell (Fig.2.1(B)), in which the polycrystalline sample (72.2 mg) of ,8-p-NPNN was mixed with the pres­

sure transmission oil (Apiezon-K grease; 579.8 mg) and some tips of Al metal (31.3 mg). The absolute value of real pressure at low temperatures was estimat d by the pressure dependence of superconductive transition temperature

Ts(P)

of J\l with Ts(Fo) = 1.17 K (Fig.2.2, 2.3) [42]. In order to estimate the correct value of pressure, another tips of Al (35.4 mg) were also set in the outside of the clamp cell (i.e. in the ambient pressure region), as shown in Fig.

6.10.

The susceptibility of the blank clamp cell including Apiezon-K grease was subtracted from the total susceptibility.

Figure 6.11 shows the pressure dependence of Xac in the pressure region up to 10.4 kbar. As the pressure increases from Po =

0

kbar, the magnitude of Xac _is suppress d gradually and the Curie temperature

Tc

shifts toward low temperatures with the initial gradient d

Tc

/d

p

= - 4.8 ^x

10

-2 Kjkbar. This indicates that the pr ssure suppresses the ferromagnetic behavior. In the pressure region up to

p :::; Pc =6.5

kbar, the ferromagnetic state is still preserved, as characterized in the shoulder-like shape of

Xac

around

Tc.

These results in this low pressure region are consist nt with the previous results by Takeda et al. [12,13].

In the higher pressure region above

Pc,

however, the plateau of Xac is drastically suppressed and changing its shape to an antiferromagnetic cusp as shown in the inset of Fig. 6.11. The magnitude of

Xac

below

Tc

is suppressed to about two thirds of the maximum value at

Tc.

These experimental facts at higher pressur s suggest that the magnetic order below

Tc

is of the buJk-antiferromagnet. Furthermore

Tc(P)

turns to increase with the positive

dTc/dp

= + _4.

0

x

10-3

K/kbar, and these results indicate that the antiferromagnetic interaction is enhanced with the increasing pr sure.

Above pressure dependence of

Tc

of {3-p-NPNN in the whole pressure r gion up to

10.4

kbar is shown in Fig. 6.12, together with those of organic bulk-antiferromagnetic radical crystals [75-78]. The quantity a stands for

dTc/ dp,

and

Tc(P)

is expressed as follows:

(6.10)

The pressure dependence of

Tc

of ,8-p-NPNN in the ferromagnetic region below

Pc

is qualitatively opposite from those found in organic bulk-antiferromagnets, but that of {3-p-NPNN in the antiferromagnetic region above

Pc

is qualitatively the same as

6.2. EXP ERIMENTAL RESULTS

Still pumping line

�

Still

�

⁴ He pumping line

3 He input

Nb seal

Matsushita 220 Q AI

Heater

AI Sample

Apiezon-K oil

�Coil

�

Cu-Be clamp

cell

111

Figure 6.10: Setting of ac-susceptibility measurement under pressure in the 3He-4He dilution refrigerator.

112CHAPTER 6. PRESSURE EFFECT OF BULK-FERROMAGNET {3-PIIASE PARA-NIT

2

,--._

... U)

• ...--1

� ;::j

..0

'-t "'

...._,..

u

1

ro

�

0

60 ^-r--,-..-...

·a � _;:j 50 _o

\ !

�

^,

^{... ::-l}

40

30-

\ 20 ^. R.3 kbar 9.3 kbar 10.4 kl>ar

6.7klm ' ^.

: ",

L_,_J_' J ,_!-' I ,_I_'

0.2 0.4 0.6

1

T(K)

,-.,

Figure 6.11: Pressure dependence of Xoc of

,8-p-NPNN

up to 10.4 kbar. Tc of para­

to ferromagnetic transition is decided from the inters^ection between the slope in the paramagnetic region and that in the bulk-ferromag.neLic r^egion^, and Tc of para- to antiferromagnetic transition is done from the position of the cusp.

6.2. EXPERIMENTAL RESULTS

2

Tc(p) Tc(p0)

1

0

113

TANOL (AF)

^a=

+0.15

TPV (AF)

a =

+0.093

p-CI-BDPA (AF)

a=

+0.086

• • •

p-CDTV (AF)

a=

+0.044

a=

+0.004

� -p-NPNN (F)

6 8 10 12 14 p (kbar)

Figure 6.12: Pressure dependence of bulk-magnetic ordering temperature in some organic radical crystals. Here a stands for dTcfdp. The results of TANOL, TPV, p-Cl-BDPA and p-CDTV were referred to the ref.75,76, ref.76, ref.76 and ref.77,78

(see chapter 7), respectively.

114CHAPTER 6. PRESSURE EFFECT OF BULI<-FERROMAGNET/3-PIIASE PARA-NIT.

_...

:t= (/) c

::J

100

...0

..._

.__... ro

u ro

><

0

.....

�.

_�

30 Oe

0.3

•

0 0 0 0 0 ' 0 0

' 0

• _••

0 0 '0

•

0.6

T(K)

p

⁼ 1.2

kbar

0.9

Figure 6.13: External field dependence of Xac of

{3-p-NPNN

at p = 1. 2 kbar

those of bulk-antiferromagnets. The enhancement of Tc of

{3-p-NPNN

above Pc, however, is not as much as those of bulk-antiferromagnets. It will be cleared that the dominant intermolecular interactions of

{3-p-NPNN

in the pressure region above Pc is still ferromagnetic, but the secondary ferromagnetic interaction changes to be antiferromagnetic, as will be discussed in section 6.3.

6.2.4 External Field Dependence of Magnetic Susceptibil­

ity under Pressure

In this subsection, external magnetic field dependences of Xac at representative three pressures are discussed. Figure 6.13, Fig. 6.14 and Fig. 6.15 show the results at p = 1.2 kbar, 4.4 kbar and 6.9 kbar, respectively.

As shown in Fig. 6.13, Xac under zero external field at p = 1. 2 kbar

(

<

Pc)

continues to increas€ down to low temperature, and behaves just as in the case of the bulk-ferromagnets as to be quenched even by a weak field of the order of 100

6.2. EXPERIMENTAL RESULTS

p

= 4.4

kbar

-28 .2

^�-'---�

0.4

^-1.__�

0.6

^---L_---..l...---=:J

0.8

T(K)

Figure 6.14: External field dependence of Xac of /3-�NPNN at p = 4.4 kbar

115 l16CHAPTER 6.

PRESSURE EFFECT OF BULK-FEIU�OMAGNET {3-PHASE

PARA-NIT

u ro

><

18 0.2

H=

0 Oe1

I

50()1.----,-�

0 0 �300

�

^Q_

� l::2oo

0 0

60 oeC:,y, \

¹⁰⁰

o 0 o·'---:o.-'... 1 �:--'-

1200e 150 Oe

o ₀ <t,

0 0

0

200 Oe 1 :

⁰

0 0 0

0

p

=

6.9 kbar 3000e

0.4

0

T(K) 0.6

0 0 0 0

00 a

0.8

Figure 6.15: External field dependence of Xac of /3-�NPNN at p = 6.9 kbar

6.2. EXPERIMENTAL RESULTS 117

Oe. This field dependence of Xac at p = 1.2 kbar is qualitatively same as that at ambient pressure [6].

Also at p = 4.4 kbar

( < Pc),

the behavior of the bulk-ferromagnetic shape of

Xac,

including the suppression of that magnitude by pressure, and its sensitivity to the external field are seen in Fig. 6.14.

At p = 6.9 kbar

(> PeL

however, the characteristic shoulder of Xac for bulk­

fcrromagnets disappears, and the bulk-antiferromagnetic cusp and the decrease to two third of the maximum value at lowest temperature (eq.3.6) appears in the zero field, as shown in Fig. 6.15. These facts suggest that the magnetic state at p

> Pc

belongs to the bulk-antiferromagnet. Furthermore the reduction ofTc by the external field is the strong evidence for the bulk-antiferromagnet, since this phenomenon can be explained by the mean field theory of antiferromagnet [6).

In conclusion of this subsection, the bulk-ferromagnetic state of {3-p-NPNN changes into the bulk-antiferromagnetic state under pressure above

Pc·

6.2.5 Magnetization under Pressure

In order to get the crucial evidence for the pressure-induced ferromagnetic to antiferromagnetic transition besides the experimental results in subsection 6.2.4, the magnetization (M-

H

curve) has been measured in external fields

(H �

500 Oe) at various pressures. This magnetization was gotten by integrating X

ac(

H) (fig. 6.16), which corresponds to dM jdH, against Hat a constant temperature.

Figure 6.17 shows the field dependences of magnetization Mat p = 1.2 kbar, 4.4 kbar, 6.4 kbar, and 9.0 kbar. At p = 1.2 kbar, the ferromagnetic rapid saturation of magnetization near f! � 0 Oe can be seen, and is consistent with the ferromagnetic state as the Nakazawa et al. 's results at ambient pressure [6]. However, the initial gradient of magnetization against H is gradually suppressed with the increasing pressure. Eventually at p = 9.0 kbar, the saturation of M or the peak of

Xac(H)

around H ^rv 0 Oe completely disappears, and the magnetization curve indicates th spin flopping behavior at some H � ± 50 Oe, giving small cusp on

Xac(H)

as in Fig. 6.16. This is the crucial evidence of the antiferromagnet. But also at p = 9.0 kbar, a small hysteresis can be seen. This may suggest that the bulk­

antiferromagnetic ordered state at p = 9.0 kbar has some anisotropy-induced canted weak-ferromagnetic moments.

These results conclusively indicate that the bulk-magnetic ordered state at p

< Pc

is of the f rromagnet, and that at p

> Pc

is of the a.ntiferromagnet.

118CHAPTER 6. PRESSURE EFFECT OF BULK-FERROMAGNET {3-PHASE PARA-NIT

p ⁼⁼ 1.2 kbar T= 0.34 K

� _{__....} � ..._ ^l1f1

0.44 K_... .. - ---...-...,.._..,...,--., ____ • .,.,� 6.7 kbar

... - ·� ....

500

Figure 6.16: External field dependences of Xac of {3-p-NPNN at p = ^1. 2 kbar, 4.4 kbar, 6.4 kbar and 9.0 kbar in the small field

(IHI �

500 Oc) at a constant ^temperatur^e.

6.2. EXPERIMENTAL RESULTS

- +--1 (f) c :J

..0 L

�

ro

^-0.2

-0.4

0.1

� -0.1

-500

-100

o p = 1 .2 kbar

( T=0.34 K)

+ p = 4.4 kbar

(T=0.35 K)

A p = 6.4 kbar

(T=0.26 K)

• p = 9.0 kbar

(T=0.41 K)

H(Oe) 0 ⁵⁰⁰

0

A p = 6.4 kbar

(T=0.26 K)

• p = 9.0 kbar

{T=0.41 K)

100 200

H (Oe)

1 19

Figure 6.17: External field dependences of magnetization (M) of /3-p-N PNN at p

= 1.2 kbar, 4.4 kbar, 6.4 kbar and 9.0 kbar in the small field (IHI

�

500 Oe) at a constant temperature.

120CHAPTER 6.

PRESSURE EFFECT OF BULK-FERROMAGNET {3-PHASE PARA-NIT

-+--1

c ::J u 0

2

::::--1

I

• - , <

:-

.· ..

"'·

.. ;

.

.

·�

p = 0 kbar

40

Figure 6.18: Pressure dependence of the powdered X-ray diffraction pattern of {3-p­

NPNN at room temperature.

6.2.6 X-ray Diffraction under Pressure

Representative three powdered X-ray diffraction patterns of {3-p-NPNN in the pressure region up to p = 12.6 kbar at room temperature are shown in Fig. 6.18.

Here the rapid X-ray analysis with imaging plate and diamond anvil cell js utilized.

The fluorine oil was used as the pressure transmission oil, and the pre..c;sure was estimated by the Ruby fluorescence [43]. The crystal structure at ambient pressure belongs to the space group of F2dd with a = 1 2.374

.i1,

b = 1 9.350

A

and c = 10.960

A

[8]. The diffraction patterns at each pressure shift toward the direction of wide angle with nearly the same signal pattern as shown in Fig. 6. 1 8, indicating the initial crystal symmetry may be preserved in this pressurized state. Each lattice constant was estimated by the Rietveld method [37] on the assumption that the initial space group is preserved, and these pressure dependences, as well as the unit

6.2. EXPERIMENTAL RESULTS

+-' c

+-' cu (f) c 0 0

Q) 0

B

cu

u Q) N cu

E

L...

0

z

0.95 0

o

a-axis

•

b-axis

o

c-axis

•

volume

2 4 6 8 10

p (kbar)

12

Q)

E

:::J 0

>

u Q) N cu

E

L...

0

z

0.90

14

121

Figure 6.19: Pressure dependences of each lattice constant and the volwne at room temperature.

cell volume, are shown in Fig. 6.19. Each lattice constant seems to shrink in the two ways depending on the pressure range p

�

5kbar. The ratio of the shrink, which amounts at most 4.5

%

along the c-axis, exceeds the thermal expansion between 6 K and 300 K which shows the biggest shrink of 2.1

%

along the c-a.xis of the three axes [10].

Around p = 5 kbar in Fig. 6.19, the change of the slopes which may concern the ferro-antiferromagnetic transition can be seen. However the direct correspondence between above two phenomena may be difficult, since they are measured in the dif­

ferent temperature regions.

122CHAPTER 6. PRESSURE EFFECT OF BULK-FERROMAGNET {3-PHASE PARA-NCT

6.3 Discussion

Recent development of molecular-orbital (MO) calculation gives the r liable esti­

mation of spin and charge densities on each constituent atomic site in the molecule on the basis of the unrestricted Hartree-Fock (different orbitals for different spins) approximations, as well as energy levels of each MO. With the help of advanced technique for topological analysis of crystal structures as well, the individual contri­

bution of MO's to the magnetic interactions has been detailed in the charge transfer mechanism [24,25] or in the ab-initio methods [79,80], which await the check from the experimental side.

Okumura et al. calculated some possible exchange interactions considering the details of the crystal structure [8] by the approximate unrestricted Hartree-Fock calculation [79,80], in which the effective exchange interaction Jab is given by the following Hamiltonian,

(6.11)

According to their reports, the crystal structure of {3-p-NPNN with the space sym­

metry of F2dd indicates that twelve nearest neighboring p-N NN molecules xist around the central

p-NPNN

molecule, and they are classified into three groups as shown in Fig. 6.20 (or Fig. 6.1). Therefore the effective exchange integrals betwe n the central p-NPNN and the nearest neighbors are divided into thr e kinds of .J1n ( n=2-4). The lattice distances ^r1n between the lattice points 1 and n (n-2-1) are given with the lattice constants (a, b, ^c

)

as follows:

�

(a2 + c2)1/2 ⁼ 11.49

A,

2

!

^{(a2 + b2 +} c2) 1/2 ⁼ 6.37

A,

4

�

(a2 + b2 + 9c2)1/2 = 10.04

A,

4

where a = 12.36

A,

_b = 19.36

A

_{and c = 10.97}

A.

(6.12)

Figure 6.21 shows the spin densities and net charges of p-NPNN reported by Okumura et al. [80]. Figure 6.22 shows the molecular stacking in the ac-plane, which illustrates that the oxygen atom (01) of the nitronyl nitroxide group of p­

NPNN

interacts with the nitro group (N1-02-03) of its nearest neighbor in the ac-plane [79]. Judging from the spin densities, the so-called McConnell-type spin density product

(SDP)

term (eq.1.13) between the 01-N1 pair should exhibit the small antiferromagnetic interaction. According to the report of Yamaguchi et al.

[81], the face-to-face molecular stacking of p-NPNN exhibits the antiferromagnetic

6.3. DISCUSSION

123

Figure

6.20:

Possible interaction paths in ,8-phase

p-NPNN.

The four equivalent p-NPNN molecules are denoted by the white, shaded, and black circles

[79].

(0.114)

H

^-0023

{0.024} N

N 0.274

o,.,. 'o

{-0.289} (0.152) -0.569 0.563 (0.076) 0.150 {-0.018) -0.150

(0.033) 0.100

(0.032) -0. 136 (0.439) N o.022

/ '

(-0.353) 0 0 -0.015

Figure

6.21:

Spin densities and net charges (in parentheses) obtained for

p-NPNN [80].

124CHAPTER 6. PRESSURE EFFECT OF BULK-FERROMAGNET(3-PHASE PARA-NIT

(8}

Figure

6.22:

Interaction paths between adjacent

{3-p-NPNN

molecules in the ac­

plane. The dotted lines indicate important interaction paths. (B) shows the side view for emphasizing the nonorthogonality between the nitro and nitroxide groups.

The interatomic distances for the

01-Nl, 01-02

_and

01-03

pairs are 3.368, 3.435, and

3.671 A,

respectively.

6.3. DISCUSSION 125

{A)

figure 6. 23: Three dimensional intermolecular interactions between ,8-p-NPN N. The dotted lines in (A) indicate important interaction paths, and the interactions for the 01-Cl and 01-C2 are antiferromagnetic and ferromagnetic, respectively. The inter­

atomic distances for the Ol-C1 and 01-C2 pairs are 3.219 and 3.247

A,

respectively.

The van der Waals interactions between the methyl and nitro groups are shown in

(B)

by the circles

intermolecular interaction via the 01-Nl contact, and the introduction of nonpla­

narity induces the inversion from the negative

lab

to the positive

lab·

The molecular stacking in the ac-plane ^as shown in Fig. 6.22 indicates the nonorthogonal conforma­

tion between nitronyl nitroxide and nitro groups, which is predominantly important for the ferromagnetic intermolecular interaction

J12,

and estimated to be 0.18 cm-1.

Next, the three-dimensional interactions are shown in Fig. 6.23. The effective exchange integral

J13

for the clusters in Fig. 6.20 is estimated to be ferromagnetic (about 0.08 cm-1). The spin density population indicates that the SDP terms be­

tween the 01-Cl and 01-C2 atomic pairs ^as illustrated in Fig. 6.23(A) are positive and negative, respectively. The so-called McConnell-type SDP terms

(eq.l.l3)

for th 01-Cl pair and the 01-C2 one are antiferromagnetic and ferromagnetic, re­

spectively. These mutual cancellation leads the ferromagnetic net interaction

}13.

The l14-value for the clusters in Fig. 6.20 is slightly antiferromagnetic (-0.014 cm-1) because of the weak van der Waals interaction between methyl and nitro groups ^as shown in Fig. 6.23(B). However, this weak interaction is overcome with the other fer­

romagnetic interaction

l13.

Therefore net interlayer interaction

(113+114)

becomes positive (ferromagnetic). The magnitude of

113 + 114

is about one third of

112

in the ac-plane, and the exchange integrals for other radical pairs except for the pairs

126CHAPTER 6. PRESSURE EFFECT OF BULK-FERROMAGNET ,8-PHASE PARA-NIT

examined above are negligible.

From the appearance of short range order in the heat capacity measurement at

p

= 7.2 kbar [13], the pressure-induced reduction of the magnetic dimensionality from the three- to two-dimensional Heisenberg system is pointed out. W ith the pr ent notation

l12, l13

and

114,

the transition temperature

Tc

in such a r duced system can be written ^as

(6.13)

from the mean field theory, where

6ct

is the spin correlation length in the ac-plane, in which the ferromagnetic interaction of

112 �

0.4 K is estimated at

p

= 7.2 kbar

(13].

The pressure-induced antiferromagnetic behavior, which has b en found here, is therefore considered to originate from the pressure-induced inversion of the sign of interlayer exchange interaction

113

according to eq.l.17. Another interlayer inter­

action

l14,

pointed out to have an initial negative sign, must remain also anti� r­

romagnetic under pressure to explain the present experimental results. At ambient pressure, we estimate the following relation from the magnetization,

zl

¹

kB ⁼ kB

(4J12 + 4113

⁺

4114)

^{= 1.8 K (6.14)}

On the other hand, the theory predicts

112

^� 2113, I

1141

<< 113. Considering th mean field theory (eq.6.13) and observed value of

Tc(p),

in addition to above results, we get the possible pressure dependence of

11n

(n ⁼ 2-4) ^as in Fig. 6.24 from the experimental point of view. The spin flopping field of the order 50 Oe is relevant to the magnitude of the interlayer interactions

113

and

J14,

^as well as the anisotropy probably due to the dipole-dipole interaction [12].

According to the theoretical ab-initio study,

112

is dominantly ferromagnetic (0.18 cm

-1 ), l13

is secondarily (0. 07 cm-1), and

114

is antiferromagnetic ( -0.014 cm-1) at ambient pressure [79,80]. From Fig. 6.19, the shrink of intermolecular distance for

112

is expected less than 2

%

_around

p � Pc·

It is difficult for

112

to change its value so much including its sign. Takeda

et

al. 's previous work indicates

112 �

0.4 K

(>

0) at 7. 2 kbar (13]. Recent calculation by Yamaguchi

et

al. suggests the possibility of inversion of the sign of

113

for a few percent of the shrink along the c-axis [82].

6.4. CONCLUSION

0.4

�--�----�--��--�--�--�

T-

I E

.£.

�

C\J I

II

0.1

.s

c ...--

J

-0.10

2

Ferro. Antiferro.

4 6 8

P (kbar)

1 0 12

127

Figure 6.24: Possible pressure dependences of intermolecular interactions in {3-p­

NPNN.

6.4 Conclusion

Pressure induced ferro- to antiferromagnetic or antiferro- to ferromagnetic transi­

tion has already been observed in several inorganic compounds, and explained by the change of band structure of itinerant electron or the crystal structure etc.

[83-89]

* .

The pressure induced ferro- to antiferromagnetic transition in the genuine organic compounds has been observed for the fust time in this {3-phase para-nitrophenyl nitronyl nitroxide

(p-NPNN)

crystal with Tc =

0.61

K _and

i] /kB

=

1.8

±

0.2

K at ambient pressure. Tltis pressure induced ferro- to antiferromagnetic transition in {3-phase

p-NPNN

is brought about from the change of the balance of ferromag­

netic and antiferromagnetic components of various overlapping of molecular orbitals among the

p-NPNN

molecules, which is Wlderstood on the basis of the charge trans­

fer mechanism and the recent ab-initio calculation for the exchange interactions.

•FeP[83], CeTl[84], Hf0.9T<l<:u Fe2[85], CeZn[86], EuSe[87], K2CuF 4[88], EuTe[89]