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Magnetic properties of some rare-earth phosphides
Volume 11, number 2
P HYS I C S L E T T E R S
MAGNETIC
PROPERTIES
OF
SOME
15 July 1964
RARE-EARTH
PHOSPHIDES
G. BUSCH, P. SCHWOB and O. VOGT Laboratoriurn f l i t Feslh~rperphysih ETH, Zi~rich, Switzerland and
F. H U L L I G E R Cyanamid European R e s e a r c h Institute, Geneva, Switzerland Received 15 June 1964
The spin s t r u c t u r e s of s o m e r a r e - e a r t h phosphides have been d e t e r m i n e d by Child et al. 1), who found a r a t h e r unusual spin a r r a n g e m e n t in HoP. The s t a b i l i t y of d i f f e r e n t spin a r r a n g e m e n t s in t h e s e compounds has b e e n d i s c u s s e d in detail by T r a m m e l l 2). We have now m e a s u r e d the m a g ne t i c m o m e n t s of TbP, DyP, HoP and E r P , and our e x p e r i m e n t a l r e s u l t s a r e in good a g r e e m e n t with T r a m m e l l ' s a n a l y s i s . Our c r y s t a l s which w e r e grown by t r a n s p o r t r e a c t i o n a r e not l a r g e enough to allow m e a s u r e m e n t s on one single c r y s t a l only. It was n e c e s s a r y , t h e r e f o r e , to fill the s a m p l e h o l d e r with as many as 50 c r y s t a l s . By r e p e a t e d l y exposing them in the f e r r o m a g n e t i c s t a t e to f i e l d s of about 100 kOe we w e r e able to o r i e n t m o s t of the c r y s t a l s with t h e i r e a s y a x i s p a r a l l e l to the applied field. The p a r a m a g n e t i c C u r i e t e m p e r a t u r e 6 p and the e f f e c t i v e n u m b e r of m a g n e t o n s Pelf w e r e der i v e d f r o m the i n v e r s e s u s c e p t i b i l i t y v e r s u s t e m p e r a t u r e c u r v e s . The s h a r p kink found in s o m e of t h e s e c u r v e s is c h a r a c t e r i s t i c for the a n t i f e r i i Bo r magnetons
hi
i
i
i
i
I
I ~
r o m a g n e t i c t r a n s i t i o n at the N~el t e m p e r a t u r e TN. In all t h e s e compounds the e f f e c t i v e magneton n u m b e r s d e t e r m i n e d at t e m p e r a t u r e s well above T N a r e only a few p e r c e n t l o w e r than those of the c o r r e s p o n d i n g f r e e ions. Little o r no quenching of the angular m o m e n t u m , t h e r e f o r e , o c c u r s in the p a r a m a g n e t i c state. The magneton n u m b e r n s in the o r d e r e d f e r r o m a g n e t i c st at e was d e t e r m i n e d at the lowest a v a i l a b l e t e m p e r a t u r e (~ 1.8°K) by an induction method with pulsed f i e l d s of up to 130 kOe. As in GdP, on which we r e p o r t e d e a r l i e r 3), we obtained a l m o s t c o m p l e t e spin alignment in all the phosphides c o n s i d e r e d h e r e . In the a b s e n c e of an e x t e r n a l field the spins in TbP a r e coupled a n t i f e r r o m a g n e t i c a l l y like in MnO 1) and in a s m a l l e x t e r n a l field the m a g n e t i c m o m e n t of this compound shows the m a x i m u m at the N6el point typical of an a n t i : f e r r o m a g n e t i c spin a r r a n g e m e n t . As soon as the applied field e x c e e d s a c r i t i c a l value H c an abrupt t r a n s i t i o n to a diff e r e n t spin s t r u c t u r e o c c u r s (fig. 1). I m m e d i a t e l y above Hc the m a g n e t i c m o m e n t is, h o w e v e r , s t i l l well below the f e r r o m a g n e t i c s a t u r a t i o n value and
i r I Bo r m a g n e t o n s
T-1)87 °K
i
i
I
i
i
i
I
i
I
I
gl f
T- 1,74 ° K
81 71
TbP
HoP
6t 5t
41
6
3) 4
2} 2
0
,~ 2~ 3'0 ,'0
510
I
60
I 70
l, I 80
8 I 90
12 I 100
16 I 110
I I 120 130 H in kOe
Fig. 1. Magnetisation of Tb~ versus magnetic field. 100
o[
H kOe""
ol 0
[
,
,
]
0,2
i
i,~-l,B~o . . . . ~
6
~
|O ] k(..le
,oo ,Io ,~o ,~o H in kOe
Fig. 2. M a g n e t i s a t i o n of HoP v e r s u s m a g n e t i c field.
Volume 11, number 1
PHYSICS LETTERS
15 July 1964
Table 1 Magnetic data of some rare-earth phosphides. The figures in brackets are the free ion values.
9p (OK)
TN~ Peff (g~/J(J+1)) ns (g~ J1 (°K)
J2 (°K) Spin structure H = 0 Critical field Hc (kOe) Spin structure for H = Hc
GdP
TbP
DyP
HoP
ErP
0 15
1 8
6 -
4.2 -
0 4
7.7 (7.9) 7.1 (7.0) 0.12
9.2 (9.7) > 8 (9) 0.10
9.9 (10.6) 7.8 (10) 0.23
10.2 (10.6) 9.2 (10) 0.23
9.3 (9.6) > 8.5 (9) 0.11
-0.25
-0.18
-0.28
-0.28
-0.26
antiferromagnetic 95 ferromagnetic
antiferromagnetic 4.3 HoP type
HoP type
HoP type
17 ferromagnetic
1.9 ferromagnetic
antiferromagnetic 5.2 HoP type
it i s p r o b a b l e that the c o r r e s p o n d i n g spin s t r u c t u r e is s i m i l a r to that met in HoP. As in GdP, one can, by i n c r e a s i n g the m a g n e t i c field, g r a d u a l l y r i s e the m a g n e t i s a t i o n to a l m o s t the s a t u r a tion value gJ = 9 m a g n e t o n s of the f r e e Tb 3+ ion. The s a m e gJ value also i s found for the ground state of E r 3+. It i s not s u r p r i s i n g , t h e r e f o r e , that except for a slight d i f f e r e n c e of Hc (see table 1) the m a g n e t i s a t i o n c u r v e s for E r P and T b P a r e a l m o s t identical. HoP, on the other hand, has a spontaneous m a g n e t i c m o m e n t at low t e m p e r a t u r e s (fig. 2). This r e s u l t is in full a g r e e m e n t with the model p r o p o s e d by Child et al. 1). The t h e o r e t i c a l value of the HoP s t r u c t u r e m a g n e t i c m o m e n t was not, however, r e a c h e d e x p e r i m e n t a l l y , b e c a u s e at 1.9 kOe the applied field changed the HoP-type spin s t r u c t u r e into a n o r m a l f e r r o m a g n e t i c a r r a n g e m e n t long before the d o m a i n s of the HoP type w e r e c o m p l e t e l y oriented. The c o r r e s p o n d ing s a t u r a t i o n m a g n e t i s a t i o n obtained in high fields is about 10% lower than the value c a l c u l a t e d for the f r e e Ho3+ ion at T = 0°K. The ground s t a t e s of Ho 3+ and of Dy 3+ lead to the s a m e gJ value of 10. As in the c a s e of T b P and E r P m e n t i o n e d above, one t h e r e f o r e now finds a close s i m i l a r i t y between the m a g n e t i c p r o p e r t i e s of HoP and DyP. However, the c r i t i c a l field in DyP is about ten t i m e s l a r g e r than in HoP. When plotting the m a g n e t i c m o m e n t of HoP v e r s u s t e m p e r a t u r e as m e a s u r e d in different ext e r n a l fields one finds that even far beyond the C u r i e point the m e a s u r e d v a l u e s a r e lower than the ones c a l c u l a t e d a c c o r d i n g to the C u r i e W e i s s theory with the B r i l l o u l n function for J = 8. This shows that above the C u r i e point as well the HoP
s t r u c t u r e is m o r e stable than n o r m a l f e r r o m a g netic spin a r r a n g e m e n t . Our r e s u l t s a r e s u m m a r i s e d in table 1 together with the data of GdP 3). It is c h a r a c t e r i s t i c for this f a m i l y of compounds that in the p a r a m a g n e t i c as well as in the f e r r o m a g n e t i c r e g i o n the m a g n e t o n n u m b e r s a r e only about 10% s m a l l e r than in the f r e e ion. F o r the a n t i f e r r o m a g n e t i c phosphides TbP and E r P the exchange e n e r g i e s J1 and J 2 between n e a r e s t and next n e a r e s t neighbours, r e s p e c t i v e l y , were calculated a c c o r d i n g to the m o l e c u l a r - f i e l d approximation. T r a m m e l l ' s s t a b i l i t y condition for the HoP-type spin s t r u c t u r e r e a d i l y gives the r a t i o of J1 and J 2 f o r DyP and HoP. S i n c e t h e i r sum can be calculated f r o m the p a r a m a g n e t i c C u r i e t e m p e r a t u r e Op they can be d e t e r m i n e d s e p a r a t e l y also for these compounds. All exchange e n e r g i e s J2 b e tween second n e a r e s t n e i g h b o u r s a r e found to be negative, as is expected for superexchange. It is p e r h a p s s u r p r i s i n g that in spite of the difference in t h e i r m a g n e t i c behaviour the i n v e s t i g a t e d phosphides all have J1 and J2 values of the s a m e o r d e r of magnitude. This would s e e m to s u g g e s t that the exchange e n e r g i e s do not, depend v e r y much on the n u m b e r of f e l e c t r o n s but a r e d e t e r m i n e d l a r g e l y by the c r y s t a l s t r u c t u r e and the lattice spacings.
References 1) H,R.Child, M.K.Wilkinson, J.W.Cable, W.C. Koehler and E.O.Wollan, Phys.Rev. 131 (1963) 922. 2) G.T.Trammell, Phys.Rev. 131 (1963) 932. 3) G.Busch, P.Junod, P.Schwob, O.Vogt and F.Hulliger, Physics Letters 9 (1964) 7.
* * * * *
101
P HYS I C S L E T T E R S
MAGNETIC
PROPERTIES
OF
SOME
15 July 1964
RARE-EARTH
PHOSPHIDES
G. BUSCH, P. SCHWOB and O. VOGT Laboratoriurn f l i t Feslh~rperphysih ETH, Zi~rich, Switzerland and
F. H U L L I G E R Cyanamid European R e s e a r c h Institute, Geneva, Switzerland Received 15 June 1964
The spin s t r u c t u r e s of s o m e r a r e - e a r t h phosphides have been d e t e r m i n e d by Child et al. 1), who found a r a t h e r unusual spin a r r a n g e m e n t in HoP. The s t a b i l i t y of d i f f e r e n t spin a r r a n g e m e n t s in t h e s e compounds has b e e n d i s c u s s e d in detail by T r a m m e l l 2). We have now m e a s u r e d the m a g ne t i c m o m e n t s of TbP, DyP, HoP and E r P , and our e x p e r i m e n t a l r e s u l t s a r e in good a g r e e m e n t with T r a m m e l l ' s a n a l y s i s . Our c r y s t a l s which w e r e grown by t r a n s p o r t r e a c t i o n a r e not l a r g e enough to allow m e a s u r e m e n t s on one single c r y s t a l only. It was n e c e s s a r y , t h e r e f o r e , to fill the s a m p l e h o l d e r with as many as 50 c r y s t a l s . By r e p e a t e d l y exposing them in the f e r r o m a g n e t i c s t a t e to f i e l d s of about 100 kOe we w e r e able to o r i e n t m o s t of the c r y s t a l s with t h e i r e a s y a x i s p a r a l l e l to the applied field. The p a r a m a g n e t i c C u r i e t e m p e r a t u r e 6 p and the e f f e c t i v e n u m b e r of m a g n e t o n s Pelf w e r e der i v e d f r o m the i n v e r s e s u s c e p t i b i l i t y v e r s u s t e m p e r a t u r e c u r v e s . The s h a r p kink found in s o m e of t h e s e c u r v e s is c h a r a c t e r i s t i c for the a n t i f e r i i Bo r magnetons
hi
i
i
i
i
I
I ~
r o m a g n e t i c t r a n s i t i o n at the N~el t e m p e r a t u r e TN. In all t h e s e compounds the e f f e c t i v e magneton n u m b e r s d e t e r m i n e d at t e m p e r a t u r e s well above T N a r e only a few p e r c e n t l o w e r than those of the c o r r e s p o n d i n g f r e e ions. Little o r no quenching of the angular m o m e n t u m , t h e r e f o r e , o c c u r s in the p a r a m a g n e t i c state. The magneton n u m b e r n s in the o r d e r e d f e r r o m a g n e t i c st at e was d e t e r m i n e d at the lowest a v a i l a b l e t e m p e r a t u r e (~ 1.8°K) by an induction method with pulsed f i e l d s of up to 130 kOe. As in GdP, on which we r e p o r t e d e a r l i e r 3), we obtained a l m o s t c o m p l e t e spin alignment in all the phosphides c o n s i d e r e d h e r e . In the a b s e n c e of an e x t e r n a l field the spins in TbP a r e coupled a n t i f e r r o m a g n e t i c a l l y like in MnO 1) and in a s m a l l e x t e r n a l field the m a g n e t i c m o m e n t of this compound shows the m a x i m u m at the N6el point typical of an a n t i : f e r r o m a g n e t i c spin a r r a n g e m e n t . As soon as the applied field e x c e e d s a c r i t i c a l value H c an abrupt t r a n s i t i o n to a diff e r e n t spin s t r u c t u r e o c c u r s (fig. 1). I m m e d i a t e l y above Hc the m a g n e t i c m o m e n t is, h o w e v e r , s t i l l well below the f e r r o m a g n e t i c s a t u r a t i o n value and
i r I Bo r m a g n e t o n s
T-1)87 °K
i
i
I
i
i
i
I
i
I
I
gl f
T- 1,74 ° K
81 71
TbP
HoP
6t 5t
41
6
3) 4
2} 2
0
,~ 2~ 3'0 ,'0
510
I
60
I 70
l, I 80
8 I 90
12 I 100
16 I 110
I I 120 130 H in kOe
Fig. 1. Magnetisation of Tb~ versus magnetic field. 100
o[
H kOe""
ol 0
[
,
,
]
0,2
i
i,~-l,B~o . . . . ~
6
~
|O ] k(..le
,oo ,Io ,~o ,~o H in kOe
Fig. 2. M a g n e t i s a t i o n of HoP v e r s u s m a g n e t i c field.
Volume 11, number 1
PHYSICS LETTERS
15 July 1964
Table 1 Magnetic data of some rare-earth phosphides. The figures in brackets are the free ion values.
9p (OK)
TN~ Peff (g~/J(J+1)) ns (g~ J1 (°K)
J2 (°K) Spin structure H = 0 Critical field Hc (kOe) Spin structure for H = Hc
GdP
TbP
DyP
HoP
ErP
0 15
1 8
6 -
4.2 -
0 4
7.7 (7.9) 7.1 (7.0) 0.12
9.2 (9.7) > 8 (9) 0.10
9.9 (10.6) 7.8 (10) 0.23
10.2 (10.6) 9.2 (10) 0.23
9.3 (9.6) > 8.5 (9) 0.11
-0.25
-0.18
-0.28
-0.28
-0.26
antiferromagnetic 95 ferromagnetic
antiferromagnetic 4.3 HoP type
HoP type
HoP type
17 ferromagnetic
1.9 ferromagnetic
antiferromagnetic 5.2 HoP type
it i s p r o b a b l e that the c o r r e s p o n d i n g spin s t r u c t u r e is s i m i l a r to that met in HoP. As in GdP, one can, by i n c r e a s i n g the m a g n e t i c field, g r a d u a l l y r i s e the m a g n e t i s a t i o n to a l m o s t the s a t u r a tion value gJ = 9 m a g n e t o n s of the f r e e Tb 3+ ion. The s a m e gJ value also i s found for the ground state of E r 3+. It i s not s u r p r i s i n g , t h e r e f o r e , that except for a slight d i f f e r e n c e of Hc (see table 1) the m a g n e t i s a t i o n c u r v e s for E r P and T b P a r e a l m o s t identical. HoP, on the other hand, has a spontaneous m a g n e t i c m o m e n t at low t e m p e r a t u r e s (fig. 2). This r e s u l t is in full a g r e e m e n t with the model p r o p o s e d by Child et al. 1). The t h e o r e t i c a l value of the HoP s t r u c t u r e m a g n e t i c m o m e n t was not, however, r e a c h e d e x p e r i m e n t a l l y , b e c a u s e at 1.9 kOe the applied field changed the HoP-type spin s t r u c t u r e into a n o r m a l f e r r o m a g n e t i c a r r a n g e m e n t long before the d o m a i n s of the HoP type w e r e c o m p l e t e l y oriented. The c o r r e s p o n d ing s a t u r a t i o n m a g n e t i s a t i o n obtained in high fields is about 10% lower than the value c a l c u l a t e d for the f r e e Ho3+ ion at T = 0°K. The ground s t a t e s of Ho 3+ and of Dy 3+ lead to the s a m e gJ value of 10. As in the c a s e of T b P and E r P m e n t i o n e d above, one t h e r e f o r e now finds a close s i m i l a r i t y between the m a g n e t i c p r o p e r t i e s of HoP and DyP. However, the c r i t i c a l field in DyP is about ten t i m e s l a r g e r than in HoP. When plotting the m a g n e t i c m o m e n t of HoP v e r s u s t e m p e r a t u r e as m e a s u r e d in different ext e r n a l fields one finds that even far beyond the C u r i e point the m e a s u r e d v a l u e s a r e lower than the ones c a l c u l a t e d a c c o r d i n g to the C u r i e W e i s s theory with the B r i l l o u l n function for J = 8. This shows that above the C u r i e point as well the HoP
s t r u c t u r e is m o r e stable than n o r m a l f e r r o m a g netic spin a r r a n g e m e n t . Our r e s u l t s a r e s u m m a r i s e d in table 1 together with the data of GdP 3). It is c h a r a c t e r i s t i c for this f a m i l y of compounds that in the p a r a m a g n e t i c as well as in the f e r r o m a g n e t i c r e g i o n the m a g n e t o n n u m b e r s a r e only about 10% s m a l l e r than in the f r e e ion. F o r the a n t i f e r r o m a g n e t i c phosphides TbP and E r P the exchange e n e r g i e s J1 and J 2 between n e a r e s t and next n e a r e s t neighbours, r e s p e c t i v e l y , were calculated a c c o r d i n g to the m o l e c u l a r - f i e l d approximation. T r a m m e l l ' s s t a b i l i t y condition for the HoP-type spin s t r u c t u r e r e a d i l y gives the r a t i o of J1 and J 2 f o r DyP and HoP. S i n c e t h e i r sum can be calculated f r o m the p a r a m a g n e t i c C u r i e t e m p e r a t u r e Op they can be d e t e r m i n e d s e p a r a t e l y also for these compounds. All exchange e n e r g i e s J2 b e tween second n e a r e s t n e i g h b o u r s a r e found to be negative, as is expected for superexchange. It is p e r h a p s s u r p r i s i n g that in spite of the difference in t h e i r m a g n e t i c behaviour the i n v e s t i g a t e d phosphides all have J1 and J2 values of the s a m e o r d e r of magnitude. This would s e e m to s u g g e s t that the exchange e n e r g i e s do not, depend v e r y much on the n u m b e r of f e l e c t r o n s but a r e d e t e r m i n e d l a r g e l y by the c r y s t a l s t r u c t u r e and the lattice spacings.
References 1) H,R.Child, M.K.Wilkinson, J.W.Cable, W.C. Koehler and E.O.Wollan, Phys.Rev. 131 (1963) 922. 2) G.T.Trammell, Phys.Rev. 131 (1963) 932. 3) G.Busch, P.Junod, P.Schwob, O.Vogt and F.Hulliger, Physics Letters 9 (1964) 7.
* * * * *
101