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Huge hyperfine magnetic field of 61Ni in spinel chromites Cu0.9Ni0.1Cr2O4 and Co0.9Ni0.1Cr2O4
a.__
18 December
g F!l
1995
PHYSICS
ELSEVIER
LETTERS
A
Physics Letters A 209 (1995) 241-245
Huge hyperfine magnetic field of 61Ni in spine1 chromites Cu,,Ni,,Cr,O, and Co,.,Ni,.,Cr,O, Takuya Okada a, Yoshihiko
Noro b, Yoshio Kobayashi Fumitoshi Ambe a
a, Hideaki Kitazawa ‘,
a Institute of Physical and Chemical Research (RIKEN), Wake-shi, Saitama 351-01, Japan b Hitachi M.S. R&D Diuision, Tots&-ku, Yokohama-shi, Kanagawa 244, Japan ’ National Research Institute for Metals, I-2-1, Sengen, Tsukuba-shi, Ibaraki 305, Japan Received 20 June 1995; revised manuscript received 21 September 1995; accepted for publication Communicated by A. Lagendijk
5 October
1995
Abstract By means
of ‘tNi
M&batter
measurements,
the
hyperfine
of the spine1 chromite reported for 6’Ni. The large H,, can be elucidated state of Ni2+ ions.
Cu o.sNi,~,Cr,O,
Keywords: Spin-orbit
magnetic
(c/a
< 1) tetrahedral
sites
6’ Ni Miissbauer spectroscopy; coupling; Spine1 chromite
Large hyperfine
magnetic was
field found
H,,
of 6’Ni2+
ions
in the
compressed
to be 800 kOe, which
on the basis of the orbital angular momentum
field; Orbital angular momentum;
is the largest ever in the degenerate ground
Ligand distortion;
Jahn-Teller
effect;
-
1. Introduction A large hyperfine magnetic field H,, of 450 kOe of 61Ni2+ ions in the tetrahedral (A) sites of NiCr,O, with the spine1 structure has been demonstrated by us using 6’Ni Miissbauer spectroscopy [Il. The magnitude of H,, of Ni2+ ions in the A sites is much larger than that of Ni’+ ions in the octahedral (B) sites of NiFe,O, [l], the typical value of which is about 100 kOe. Several groups have reported 61Ni Miissbauer measurements of NiCr,O, and related compounds, and confirmed the large H,, value of “NiZ+ ions in the A sites [l-5]. The origin of this large H,, has been discussed in relation to the degenerate electronic states of Ni” ions in the A sites. Elsevier Science B.V. SSDI 0375-9601(95)00764-4
Goring et al. proposed that the large H,, of Ni*+ ions in the A sites of NiCr,O, was caused by an incompletely quenched orbital angular momentum [2,4]. It is in complete contrast to the situation of Ni2+ ions in the B sites with a completely quenched orbital angular momentum, where H,, is small and originates only from the electron core polarization. Love and Obenshain pointed out the effect of the ligand distortion which removes the orbital degeneracy of Ni2+ ions in the A sites [3]. The distortion can be realized by competitive mechanisms of the Jahn-Teller distortion and the spin-orbit coupling 161. They measured H,, in a NiCr,O,-NiFe,O, system and reported a large H,, of about 600 kOe in NiCr,.,Feo,sO, that is slightly compressed along the c axis giving c/a = 0.99 [7]. This experiment indi-
242
T. Okada et al./ Physics Letters A 209 (1995) 241-245
cates that a small distortion
will result in a large H,,, and therefore the orbital angular momentum which is not perfectly quenched seems to be the origin of the quite large H,, in the A sites. The unquenched orbital angular momentum induces a positive H,, in contrast to a negative contribution of the electron core polarization. Gutlich et al. attempted to clarify the origin of H,, from measuring its sign [5]. They observed the negative sign of H,,; thus, there remains some uncertainty in the orbital angular momentum hypothesis. We attempt to clarify the origin of the large H,, of Ni2’ ions in the A sites of spine1 oxides. The electronic state of Ni*+ ions in the A sites is highly sensitive to the ligand distortion. We can obtain information on the mechanism of H,, from the relation between the ligand distortion and the magnitude of H,,.Love and Obenshain conducted experiments on spine1 oxides with different distortions. However, it seems necessary to obtain more information on the other type of distortion, i.e., opposite distortion to NiCr,O,. It was experimentally proven that the ligand of Ni‘2+ ions in CuCr,O, is distorted not with c/a > 1 as in NiCr,O, but with c/a < 1 [8]. This result indicates that opposite distortion around Ni*+ ions leads to energy gains caused by the Jahn-Teller distortion and reduction of the elastic interaction energy between Ni2+ and Cu2+ ligands. In this paper, we report a Mossbauer study of H,, of 6’Ni2+ ions of a compressed (c/a < 1) spine1 oxide, Cu,,Ni,,,Cr,O,. Furthermore Ni*+ ions in CoCr,O, with a cubic structure are studied as an undistorted case.
From powder X-ray analysis, the specimen was found to be of a single phase with a tetragonally distorted spine1 structure with c/a < 1. Ni*+ ions replaced partly with Cu2’ ions occupied the A sites of the spine1 chromite. The specimen had a ferrimagnetic Curie temperature 0, around 135 K. The Co,,Ni,.,Cr,O, specimen prepared at 1300°C had a cubic spine1 structure and 0, around 100 K. As the energy of the Mljssbauer y ray was 67 keV, the source and the absorber were kept at liquid helium temperature to attain a high recoilless fraction. The MGssbauer spectrometer (Wissel Co., Ltd.) was operated in the triangular mode with a multichannel analyzer. The Mossbauer spectra were analyzed with a FACOM M-1800 computer in our institute.
3. Results Miissbauer spectra of Cu,.,Ni,.,Cr,O, and Co,,Ni,.,Cr,O, taken at 5 K are shown in Figs. la and lb respectively. As the nuclear spins in the ground state and the excited state of 6’Ni are 3/2
Cu,.“,‘Ni,., Cr,O,
2. Experimental The single line source of 6’Cu (-+ 6’ Ni) was produced by nuclear reactions, 58Ni ( (Y , p) 6’Cu and 58Ni(a, n> 6’Zn -+61 Cu. A thin Ni-V (84-16%) alloy disk (180 X 1 mm> was irradiated for 3 hours with 25 MeV cr-particles from the RIKEN AVF cyclotron and was used as a source without annealing. A powdered specimen of CU,~~‘N~,,,C~,O, was prepared by the conventional ceramic sintering method. The mixed powders, CuO, 61Ni0 and Cr,O, were heated at 1100°C for 2 days in flowing 0, gas.
I
-20
VeloDcity(mm/s)
I
+20
Fig. 1. 6’Ni Miissbauer spectra of spine1 chromites Cu,,9Ni,,,Cr20, and (b) Co,,,Ni,,,CrzO, measured at 5 K.
(a)
T. Okada
et al./
Physics
Table 1 Hyperfine magnetic fields (H,,r), ratio of lattice parameters Curie temperatures (@I,), and sites occupied by 6’ Ni” various spine1 oxides Specimen 800 540 631 506 450 100
cc/ a), ions in Site
c/a
CG%.P#~ Co,I.gNi0.tCr20~ NiCr,.,Fe,.,Q [31 NiCr,.ssFeO.,$, [31 NiCr,O, [ll NiFe?O, [ll
Letters
0.92 1.oo 0.99 1.02 1.04 1.0
130 100 370 170 80 858
A A A A A B
A 209 f1995)241-245
243
is conspicuously (b) H,, for Cu,., Ni,,Cr,O, large in comparison with H, for the other compounds. cc> H,, for Co,,sNi,,,Cr,O, is larger than that for NiCr,O, but smaller than that for NiCr,,5Feo.s0,. (d) H,, is independent of the Curie temperature (0,). (e) H,, linearly depends on the c/a ratio as shown in Fig. 2.
4. Discussion and S/2, respectively, the absorption spectrum is split into tweIve peaks in the presence of the hyperfine magnetic interaction. One can observe the distinctly split twelve peaks and some unsplit peaks near zero velocity in each spectrum of Fig. 1. The value of H,, in the A sites of Cu,,gNi,.,Cr,O, is 800 kOe, which is the largest ever reported for 61Ni. The value of H,, for Co,,,Ni,,,Cr,O, is 540 kOe. The solid line in Fig. 1 shows the result of the fitting with the twelve peaks. The agreement between the experimental result and the calculated curve is good except for the discrepancy around zero velocity. The value of H,, for the peaks near zero velocity in Fig. 1 is as small as that in the B sites of spine1 oxides. We summarize the experimental results of H,, of ‘1 Ni2+ ions in Table 1, where related characteristics of the compounds are also shown. The following is of note: (a> H,, of 61Ni2t ions is much larger in the A sites than in the B sites. G 900
E %*O” G
.s
700 NiFeasCrt.sOa
s g
600
E ii G 500 ti sR
CoasNio.rCrzO4 NIFeo.1Shd504
400
I
I
0.92
I
I
0.96 1.00 Ligand Distortion (c/al
I
I
1.04
Fig. 2. c/a dependence of the hyperfine magnetic fields (H,,) Ni2+ ions in the A sites of various spine1 oxides.
of
The hyperfine magnetic field (Hhf) at the nucleus is composed of the following contributions: the Fermi contact term (H,), the orbital angular momentum ( Hl) and the spin dipole interaction ( Hsd>, H,,=H,fH,+H,,.
(1)
The origin of the hyperfine field of Ni*+ ions in the octahedral sites of NiFe,O, has been understood to be the Fermi contact term Hr. However, the observed H,, for 6’ Ni‘*+ ions in the tetrahedral sites (shown in Table 1) are much larger than the value expected by this term only. The spin dipole contribution Hsd is not large enough to explain them [4,91. Therefore, the contribution from the orbital angular momentum (H,> seems to be dominant. We concentrate our discussion on the orbital angular momentum in the tetrahedral sites with the crystal distortion from the cubic symmetry and try to make clear the origin of the huge Hhf at 61Ni and its linear dependence on the c/a ratio. The ground state of the Ni2+ ions in cubic tetrahedral sites is the triply degenerate 3TlU state that is characterized by the fictitious orbital angular momentum L* = 1 and the fictitious factor cr = -3/2 [lo]. In this manifold, we discuss effects of the spin-orbit interaction, the exchange field and the crystal distortion on the orbital angular momentum (L) which is related to the fictitious orbital angular momentum L* as L = - $L*. Since the magnitudes of these terms are of the same order, we have to evaluate these effects rigorously beyond the second order perturbation. We summarize quantitatively the calculated results which will be published in detail elsewhere. The most fundamental and common interaction in this system is the spin-orbit coupling.
T. Okada et al./Physics
244
Letters A 209 (1995) 241-245
and the ligand distortion is to alter the amplitudes, or the weight of I ~5:, S,) terms in the ground state from those for the J * = 0 state. The diagonal matrix elements and the effects of these interactions on the amplitudes of the 1Lz , S,) components in the ground state are qualitatively given in Table 2 where paI& is the exchange field from the neighbor magnetic ions and I D I is the energy splitting of the T,, state caused by the tetragonal distortion. We note here that the diagonal matrix elements do not directly determine the amplitudes but they show a tendency of their effects. From this table, we can understand, for example, the exchange field increases the I Z,: = + 1, S, = - 1) component in the ground state and suppresses I L: = - 1, S, = + 1). Based on this table we will have the following results. (1) c/a = 1. Example: Co,,Ni,,,Cr,O,. The exchange field induces the orbital angular momentum. Its magnitude is determined by the competition of the exchange field and the spin-orbit interaction. The value of the orbital angular momentum is modest; larger than case (2) and smaller than case (3). (2) c/a > 1. Example: NiCr,O,, NiCr,,,,Fe,,,,0,. The effect of the ligand distortion on the angular momentum is opposite to that of the exchange field; it increases the amplitude of the 1L: = 0, S, = 0) state and diminishes that of 1LT = + 1, S, = - 1). So the distortion with c/a > 1 reduces the orbital angular momentum compared to case (1). Therefore the hyperfine field is expected to be smaller than that in the c/a = 1 case. This argument explains also the fact that H,, in NiCr,O, (c/a = 1.04) is smaller
3AA,
/
“Tl
k/...... ‘..,
I 0% -
ZIDI
‘..
Cubic tield
Spin-orbit interaction
c/a=1
Tetragoml tield (with no spin-orbit interaction)
c/a>1
(4
c/a4 04
Fig. 3. Typical energy levels of Ni’+ ions in the A sites. (a) The ligand distortion and the exchange field are 0, and the spin-orbit interaction not; (b) the Iigand distortion is not zero, and the exchange field and the spin-orbit interaction are.
It forces the spin and the fictitious orbital angular momentum to couple antiparallel, making the J * = 0 state lowest in energy when there is no exchange field and no ligand distortion as shown in Fig. 3a. The state J * = 0 consists of the following states with equal weight; ) Li = + 1, S, = - l), I L: = -1, S,= +l) and ILf =O, S,=O). Basic properties of the system can be understood by the behavior of these states. The eigenvalues of the z component, L,, of the orbital angular momentum for 1Lz = + 1, S, = -l>, I L: = - 1, S, = +l> and j LS =0, S,=O> are -3/2, +3/2andO, respectively. However, the expectation value for the J * = 0 state is zero because contributions from these terms cancel. The main effect of the exchange field
Table 2 Effects of the exchange field and the ligand distortion diagonal matrix elements IL; = +1, exchange
field
increase
distortion (c/a
> 1)
-/+&r decrease
distortion (c/a
< 1)
+IDI increase
(L,)
S,=
on the amplitudes
-1)
-IDI - 3/2
a I .LI = 0, S, = 0) obtains an energy gain from the exchange field is in the c-plane.
of the
1Lf , S,) components
in the J = 0 ground state and their
I Lf = 0, s; = 0)
IL; = -1, S;= +1>
N” 0 increase
decrease
-2101 decrease f21D1 0”
+lDl increase
field and has orbital angular
+ PB&U decrease
-IDI +3/2 momentum
when the direction
of the exchange
T. Okada et al./ Physics Letters A 209 (1995) 241-245
than that in NiCr,,,, FeO.,sO, (c/u = 1.02). This mechanism of inducing the orbital angular momentum is essentially the same as that proposed by Goring who treated it in the second order perturbation [41. (3) c/a < 1. Example: Cu,sNia.,Cr,O, and NiCr,.,Fe,.,O,. The ligand distortion with c/a < 1 and the exchange field cooperatively stabilize 1Li = + 1, S, = - 1) and make ILz = 0,S,= 0) unstable. Consequently the induced orbital angular momentum is largest in this case. The value of the orbital angular momentum, and hence the hyperfine field, is expected to depend positively on the degree of the ligand distortion. This is realized in the experimental results of Cu,,Ni,,,Cr,O, and NiCr,.jFe,,,O,. The present discussion points out the monotonic relation between the hyperfine field and the ligand distortion. Our experimental results and Love and Obenshain’s ones shown in Fig. 2 can be successfully explained by this argument.
245
2; and (2.2) the change of the orbital angular momentum caused by the ligand distortion successfully accounts for the characteristic shown in Fig. 2. (3) These results demonstrate that the orbital angular momentum is the main origin of H,, for Ni2+ ions in the A sites of spine1 oxides.
Acknowledgement We are deeply indebted to Dr. Y. Yano, Dr. A. Goto, Dr. M. Wakasugi and the staff of the RIKEN cyclotron for the operation of many irradiation runs and also to Professor K. Asai for frequent and helpful discussions.
References 111H. Sekizawa, T. Okada, S. Okamoto and F. Ambe, J. Phys. (Paris) 32 (1971) Cl-326.
121J. Glaring, 2. Naturforsch.
5. Conclusions We arrive at the following conclusions. (1) By means of 61Ni Mossbauer measurements, H,, of 61Ni ions in the A sites of the spine1 chromate Cu,.9Ni,,,Cr,0, was found to be 800 kOe, which is the largest ever reported for 61Ni. N,, of Ni2+ ions in Co,,Ni,,,Cr,O, is 540 kOe which is between the values in NiCr,O, and NiCr,,,Fe,,,O,. (2) These results together with Love and Obenshain’s results show the following: (2.1) the magnitude of H,, of Ni‘2+ ions in the A sites has a linear dependence on the ligand distortion as shown in Fig.
26a (1971) 1929. [31 J.C. Love and F.E. Obenshain, AIP Conf. Proc. 18 (1973) 513. [41 J. GBring, W. Wurtinger and R. Link, J. Appl. Phys. 49 (1978) 269. [51 P. Giitlich, H. Rummel and H. Spiering, J. Phys. (Paris) 41 (1980) Cl-185. [61 J.B. Goodenough, J. Phys. Sot. Japan 17, Suppl. B-l (1962) 185. [71 T.R. McGuire and S.W. Greenwald, in: Proc. Int. Conf. on Solid state physics, Brussels 1958 (Academic Press, New York, 1960), Vol. 3. [81 Y. Kino and S. Miyahara, J. Phys. Sot. Japan 21 (1966) 2732. 191 A. Okiji and J. Kanamori, 3. Phys. Sot. Japan 19 (1964) 908. reso[lOI A. Abragam and B. Bleaney, Electron paramagnetic nance of transition ions (Clarendon, Oxford, 1970).
18 December
g F!l
1995
PHYSICS
ELSEVIER
LETTERS
A
Physics Letters A 209 (1995) 241-245
Huge hyperfine magnetic field of 61Ni in spine1 chromites Cu,,Ni,,Cr,O, and Co,.,Ni,.,Cr,O, Takuya Okada a, Yoshihiko
Noro b, Yoshio Kobayashi Fumitoshi Ambe a
a, Hideaki Kitazawa ‘,
a Institute of Physical and Chemical Research (RIKEN), Wake-shi, Saitama 351-01, Japan b Hitachi M.S. R&D Diuision, Tots&-ku, Yokohama-shi, Kanagawa 244, Japan ’ National Research Institute for Metals, I-2-1, Sengen, Tsukuba-shi, Ibaraki 305, Japan Received 20 June 1995; revised manuscript received 21 September 1995; accepted for publication Communicated by A. Lagendijk
5 October
1995
Abstract By means
of ‘tNi
M&batter
measurements,
the
hyperfine
of the spine1 chromite reported for 6’Ni. The large H,, can be elucidated state of Ni2+ ions.
Cu o.sNi,~,Cr,O,
Keywords: Spin-orbit
magnetic
(c/a
< 1) tetrahedral
sites
6’ Ni Miissbauer spectroscopy; coupling; Spine1 chromite
Large hyperfine
magnetic was
field found
H,,
of 6’Ni2+
ions
in the
compressed
to be 800 kOe, which
on the basis of the orbital angular momentum
field; Orbital angular momentum;
is the largest ever in the degenerate ground
Ligand distortion;
Jahn-Teller
effect;
-
1. Introduction A large hyperfine magnetic field H,, of 450 kOe of 61Ni2+ ions in the tetrahedral (A) sites of NiCr,O, with the spine1 structure has been demonstrated by us using 6’Ni Miissbauer spectroscopy [Il. The magnitude of H,, of Ni2+ ions in the A sites is much larger than that of Ni’+ ions in the octahedral (B) sites of NiFe,O, [l], the typical value of which is about 100 kOe. Several groups have reported 61Ni Miissbauer measurements of NiCr,O, and related compounds, and confirmed the large H,, value of “NiZ+ ions in the A sites [l-5]. The origin of this large H,, has been discussed in relation to the degenerate electronic states of Ni” ions in the A sites. Elsevier Science B.V. SSDI 0375-9601(95)00764-4
Goring et al. proposed that the large H,, of Ni*+ ions in the A sites of NiCr,O, was caused by an incompletely quenched orbital angular momentum [2,4]. It is in complete contrast to the situation of Ni2+ ions in the B sites with a completely quenched orbital angular momentum, where H,, is small and originates only from the electron core polarization. Love and Obenshain pointed out the effect of the ligand distortion which removes the orbital degeneracy of Ni2+ ions in the A sites [3]. The distortion can be realized by competitive mechanisms of the Jahn-Teller distortion and the spin-orbit coupling 161. They measured H,, in a NiCr,O,-NiFe,O, system and reported a large H,, of about 600 kOe in NiCr,.,Feo,sO, that is slightly compressed along the c axis giving c/a = 0.99 [7]. This experiment indi-
242
T. Okada et al./ Physics Letters A 209 (1995) 241-245
cates that a small distortion
will result in a large H,,, and therefore the orbital angular momentum which is not perfectly quenched seems to be the origin of the quite large H,, in the A sites. The unquenched orbital angular momentum induces a positive H,, in contrast to a negative contribution of the electron core polarization. Gutlich et al. attempted to clarify the origin of H,, from measuring its sign [5]. They observed the negative sign of H,,; thus, there remains some uncertainty in the orbital angular momentum hypothesis. We attempt to clarify the origin of the large H,, of Ni2’ ions in the A sites of spine1 oxides. The electronic state of Ni*+ ions in the A sites is highly sensitive to the ligand distortion. We can obtain information on the mechanism of H,, from the relation between the ligand distortion and the magnitude of H,,.Love and Obenshain conducted experiments on spine1 oxides with different distortions. However, it seems necessary to obtain more information on the other type of distortion, i.e., opposite distortion to NiCr,O,. It was experimentally proven that the ligand of Ni‘2+ ions in CuCr,O, is distorted not with c/a > 1 as in NiCr,O, but with c/a < 1 [8]. This result indicates that opposite distortion around Ni*+ ions leads to energy gains caused by the Jahn-Teller distortion and reduction of the elastic interaction energy between Ni2+ and Cu2+ ligands. In this paper, we report a Mossbauer study of H,, of 6’Ni2+ ions of a compressed (c/a < 1) spine1 oxide, Cu,,Ni,,,Cr,O,. Furthermore Ni*+ ions in CoCr,O, with a cubic structure are studied as an undistorted case.
From powder X-ray analysis, the specimen was found to be of a single phase with a tetragonally distorted spine1 structure with c/a < 1. Ni*+ ions replaced partly with Cu2’ ions occupied the A sites of the spine1 chromite. The specimen had a ferrimagnetic Curie temperature 0, around 135 K. The Co,,Ni,.,Cr,O, specimen prepared at 1300°C had a cubic spine1 structure and 0, around 100 K. As the energy of the Mljssbauer y ray was 67 keV, the source and the absorber were kept at liquid helium temperature to attain a high recoilless fraction. The MGssbauer spectrometer (Wissel Co., Ltd.) was operated in the triangular mode with a multichannel analyzer. The Mossbauer spectra were analyzed with a FACOM M-1800 computer in our institute.
3. Results Miissbauer spectra of Cu,.,Ni,.,Cr,O, and Co,,Ni,.,Cr,O, taken at 5 K are shown in Figs. la and lb respectively. As the nuclear spins in the ground state and the excited state of 6’Ni are 3/2
Cu,.“,‘Ni,., Cr,O,
2. Experimental The single line source of 6’Cu (-+ 6’ Ni) was produced by nuclear reactions, 58Ni ( (Y , p) 6’Cu and 58Ni(a, n> 6’Zn -+61 Cu. A thin Ni-V (84-16%) alloy disk (180 X 1 mm> was irradiated for 3 hours with 25 MeV cr-particles from the RIKEN AVF cyclotron and was used as a source without annealing. A powdered specimen of CU,~~‘N~,,,C~,O, was prepared by the conventional ceramic sintering method. The mixed powders, CuO, 61Ni0 and Cr,O, were heated at 1100°C for 2 days in flowing 0, gas.
I
-20
VeloDcity(mm/s)
I
+20
Fig. 1. 6’Ni Miissbauer spectra of spine1 chromites Cu,,9Ni,,,Cr20, and (b) Co,,,Ni,,,CrzO, measured at 5 K.
(a)
T. Okada
et al./
Physics
Table 1 Hyperfine magnetic fields (H,,r), ratio of lattice parameters Curie temperatures (@I,), and sites occupied by 6’ Ni” various spine1 oxides Specimen 800 540 631 506 450 100
cc/ a), ions in Site
c/a
CG%.P#~ Co,I.gNi0.tCr20~ NiCr,.,Fe,.,Q [31 NiCr,.ssFeO.,$, [31 NiCr,O, [ll NiFe?O, [ll
Letters
0.92 1.oo 0.99 1.02 1.04 1.0
130 100 370 170 80 858
A A A A A B
A 209 f1995)241-245
243
is conspicuously (b) H,, for Cu,., Ni,,Cr,O, large in comparison with H, for the other compounds. cc> H,, for Co,,sNi,,,Cr,O, is larger than that for NiCr,O, but smaller than that for NiCr,,5Feo.s0,. (d) H,, is independent of the Curie temperature (0,). (e) H,, linearly depends on the c/a ratio as shown in Fig. 2.
4. Discussion and S/2, respectively, the absorption spectrum is split into tweIve peaks in the presence of the hyperfine magnetic interaction. One can observe the distinctly split twelve peaks and some unsplit peaks near zero velocity in each spectrum of Fig. 1. The value of H,, in the A sites of Cu,,gNi,.,Cr,O, is 800 kOe, which is the largest ever reported for 61Ni. The value of H,, for Co,,,Ni,,,Cr,O, is 540 kOe. The solid line in Fig. 1 shows the result of the fitting with the twelve peaks. The agreement between the experimental result and the calculated curve is good except for the discrepancy around zero velocity. The value of H,, for the peaks near zero velocity in Fig. 1 is as small as that in the B sites of spine1 oxides. We summarize the experimental results of H,, of ‘1 Ni2+ ions in Table 1, where related characteristics of the compounds are also shown. The following is of note: (a> H,, of 61Ni2t ions is much larger in the A sites than in the B sites. G 900
E %*O” G
.s
700 NiFeasCrt.sOa
s g
600
E ii G 500 ti sR
CoasNio.rCrzO4 NIFeo.1Shd504
400
I
I
0.92
I
I
0.96 1.00 Ligand Distortion (c/al
I
I
1.04
Fig. 2. c/a dependence of the hyperfine magnetic fields (H,,) Ni2+ ions in the A sites of various spine1 oxides.
of
The hyperfine magnetic field (Hhf) at the nucleus is composed of the following contributions: the Fermi contact term (H,), the orbital angular momentum ( Hl) and the spin dipole interaction ( Hsd>, H,,=H,fH,+H,,.
(1)
The origin of the hyperfine field of Ni*+ ions in the octahedral sites of NiFe,O, has been understood to be the Fermi contact term Hr. However, the observed H,, for 6’ Ni‘*+ ions in the tetrahedral sites (shown in Table 1) are much larger than the value expected by this term only. The spin dipole contribution Hsd is not large enough to explain them [4,91. Therefore, the contribution from the orbital angular momentum (H,> seems to be dominant. We concentrate our discussion on the orbital angular momentum in the tetrahedral sites with the crystal distortion from the cubic symmetry and try to make clear the origin of the huge Hhf at 61Ni and its linear dependence on the c/a ratio. The ground state of the Ni2+ ions in cubic tetrahedral sites is the triply degenerate 3TlU state that is characterized by the fictitious orbital angular momentum L* = 1 and the fictitious factor cr = -3/2 [lo]. In this manifold, we discuss effects of the spin-orbit interaction, the exchange field and the crystal distortion on the orbital angular momentum (L) which is related to the fictitious orbital angular momentum L* as L = - $L*. Since the magnitudes of these terms are of the same order, we have to evaluate these effects rigorously beyond the second order perturbation. We summarize quantitatively the calculated results which will be published in detail elsewhere. The most fundamental and common interaction in this system is the spin-orbit coupling.
T. Okada et al./Physics
244
Letters A 209 (1995) 241-245
and the ligand distortion is to alter the amplitudes, or the weight of I ~5:, S,) terms in the ground state from those for the J * = 0 state. The diagonal matrix elements and the effects of these interactions on the amplitudes of the 1Lz , S,) components in the ground state are qualitatively given in Table 2 where paI& is the exchange field from the neighbor magnetic ions and I D I is the energy splitting of the T,, state caused by the tetragonal distortion. We note here that the diagonal matrix elements do not directly determine the amplitudes but they show a tendency of their effects. From this table, we can understand, for example, the exchange field increases the I Z,: = + 1, S, = - 1) component in the ground state and suppresses I L: = - 1, S, = + 1). Based on this table we will have the following results. (1) c/a = 1. Example: Co,,Ni,,,Cr,O,. The exchange field induces the orbital angular momentum. Its magnitude is determined by the competition of the exchange field and the spin-orbit interaction. The value of the orbital angular momentum is modest; larger than case (2) and smaller than case (3). (2) c/a > 1. Example: NiCr,O,, NiCr,,,,Fe,,,,0,. The effect of the ligand distortion on the angular momentum is opposite to that of the exchange field; it increases the amplitude of the 1L: = 0, S, = 0) state and diminishes that of 1LT = + 1, S, = - 1). So the distortion with c/a > 1 reduces the orbital angular momentum compared to case (1). Therefore the hyperfine field is expected to be smaller than that in the c/a = 1 case. This argument explains also the fact that H,, in NiCr,O, (c/a = 1.04) is smaller
3AA,
/
“Tl
k/...... ‘..,
I 0% -
ZIDI
‘..
Cubic tield
Spin-orbit interaction
c/a=1
Tetragoml tield (with no spin-orbit interaction)
c/a>1
(4
c/a4 04
Fig. 3. Typical energy levels of Ni’+ ions in the A sites. (a) The ligand distortion and the exchange field are 0, and the spin-orbit interaction not; (b) the Iigand distortion is not zero, and the exchange field and the spin-orbit interaction are.
It forces the spin and the fictitious orbital angular momentum to couple antiparallel, making the J * = 0 state lowest in energy when there is no exchange field and no ligand distortion as shown in Fig. 3a. The state J * = 0 consists of the following states with equal weight; ) Li = + 1, S, = - l), I L: = -1, S,= +l) and ILf =O, S,=O). Basic properties of the system can be understood by the behavior of these states. The eigenvalues of the z component, L,, of the orbital angular momentum for 1Lz = + 1, S, = -l>, I L: = - 1, S, = +l> and j LS =0, S,=O> are -3/2, +3/2andO, respectively. However, the expectation value for the J * = 0 state is zero because contributions from these terms cancel. The main effect of the exchange field
Table 2 Effects of the exchange field and the ligand distortion diagonal matrix elements IL; = +1, exchange
field
increase
distortion (c/a
> 1)
-/+&r decrease
distortion (c/a
< 1)
+IDI increase
(L,)
S,=
on the amplitudes
-1)
-IDI - 3/2
a I .LI = 0, S, = 0) obtains an energy gain from the exchange field is in the c-plane.
of the
1Lf , S,) components
in the J = 0 ground state and their
I Lf = 0, s; = 0)
IL; = -1, S;= +1>
N” 0 increase
decrease
-2101 decrease f21D1 0”
+lDl increase
field and has orbital angular
+ PB&U decrease
-IDI +3/2 momentum
when the direction
of the exchange
T. Okada et al./ Physics Letters A 209 (1995) 241-245
than that in NiCr,,,, FeO.,sO, (c/u = 1.02). This mechanism of inducing the orbital angular momentum is essentially the same as that proposed by Goring who treated it in the second order perturbation [41. (3) c/a < 1. Example: Cu,sNia.,Cr,O, and NiCr,.,Fe,.,O,. The ligand distortion with c/a < 1 and the exchange field cooperatively stabilize 1Li = + 1, S, = - 1) and make ILz = 0,S,= 0) unstable. Consequently the induced orbital angular momentum is largest in this case. The value of the orbital angular momentum, and hence the hyperfine field, is expected to depend positively on the degree of the ligand distortion. This is realized in the experimental results of Cu,,Ni,,,Cr,O, and NiCr,.jFe,,,O,. The present discussion points out the monotonic relation between the hyperfine field and the ligand distortion. Our experimental results and Love and Obenshain’s ones shown in Fig. 2 can be successfully explained by this argument.
245
2; and (2.2) the change of the orbital angular momentum caused by the ligand distortion successfully accounts for the characteristic shown in Fig. 2. (3) These results demonstrate that the orbital angular momentum is the main origin of H,, for Ni2+ ions in the A sites of spine1 oxides.
Acknowledgement We are deeply indebted to Dr. Y. Yano, Dr. A. Goto, Dr. M. Wakasugi and the staff of the RIKEN cyclotron for the operation of many irradiation runs and also to Professor K. Asai for frequent and helpful discussions.
References 111H. Sekizawa, T. Okada, S. Okamoto and F. Ambe, J. Phys. (Paris) 32 (1971) Cl-326.
121J. Glaring, 2. Naturforsch.
5. Conclusions We arrive at the following conclusions. (1) By means of 61Ni Mossbauer measurements, H,, of 61Ni ions in the A sites of the spine1 chromate Cu,.9Ni,,,Cr,0, was found to be 800 kOe, which is the largest ever reported for 61Ni. N,, of Ni2+ ions in Co,,Ni,,,Cr,O, is 540 kOe which is between the values in NiCr,O, and NiCr,,,Fe,,,O,. (2) These results together with Love and Obenshain’s results show the following: (2.1) the magnitude of H,, of Ni‘2+ ions in the A sites has a linear dependence on the ligand distortion as shown in Fig.
26a (1971) 1929. [31 J.C. Love and F.E. Obenshain, AIP Conf. Proc. 18 (1973) 513. [41 J. GBring, W. Wurtinger and R. Link, J. Appl. Phys. 49 (1978) 269. [51 P. Giitlich, H. Rummel and H. Spiering, J. Phys. (Paris) 41 (1980) Cl-185. [61 J.B. Goodenough, J. Phys. Sot. Japan 17, Suppl. B-l (1962) 185. [71 T.R. McGuire and S.W. Greenwald, in: Proc. Int. Conf. on Solid state physics, Brussels 1958 (Academic Press, New York, 1960), Vol. 3. [81 Y. Kino and S. Miyahara, J. Phys. Sot. Japan 21 (1966) 2732. 191 A. Okiji and J. Kanamori, 3. Phys. Sot. Japan 19 (1964) 908. reso[lOI A. Abragam and B. Bleaney, Electron paramagnetic nance of transition ions (Clarendon, Oxford, 1970).