- Email: [email protected]
Tunnelling of large magnetic moments in a single crystal
~ ~
Journal of Magnetism and Magnetic Materials t77-181 (1998) 962-963
~ , ~ Jollrnal ol magnetism and
magnetic materials
ELSEVIER
Tunnelling of large magnetic moments in a single crystal Nicolas Vernier*, Guy Bellessa Laboraloire de Physiclue des Solides, Bdt. 510, Universitk Paris-Sud, 91405 Orsay, France
Abstract
We report on susceptibility measurements carried out at high frequency on a Dy s +-doped crystal, submitted to a static magnetic field, at very low temperature, We have found a susceptibility peak at low static field, which seems to be a general property of high-spin systems. We have also found evidence for a tunnelling phenomenon of the Dy 3+ -magnetic moments. © 1998 Elsevier Science B.V. All rights reserved. Ke>q,,orcts: Crystal field- RE compounds; Susceptibility- magnetic; Tunnelling
Tunnelling of large spins has been treated theoretically for a long time. It has been shown that such spins, if they have strong enough anisotropy energy, can be reversed along their anisotropy axis [11. Other symmetry conditions than axial one have also been considered [2]. According to all these results, the tunnelling rate decreases quite quickly with the magnitude of the quantum number J. Experimentally, some measurements of magnetic susceptibility and relaxation times at low temperature have been explained by macroscopic tunnelling of the magnetization [3]. Tunnelling of large spins have been observed in glasses doped with rare-earth ions [4]. Here, we report on experiments performed in a simpler system: a single crystal doped with Dy 3÷ ions. It is a good model system because the quantum number J is already quite big (J = 15/2), and the whole system is well defined. We have studied the magnetic susceptibility of a single crystal of LiYo.gvDyo.olF,v The only magnetic ion in this compound is Dy 3 +. It is a Kramers ion (J is half-integer), with a large quantum number J = 15/2. Static susceptibility measurements have shown that there is an easy plane (0, 0, 1) for the direction of the magnetic moment. Moreover, there are two easier directions in the easy plane. This will be important at very low temperature. The magnetic susceptibility was measured with a splitring resonator [51, also called loop-gap resonator. In this device, the oscillating magnetic field B~ is located in the center of the ring, where there is no electric field.
*Corresponding author. Fax: + 33 1 69 I5 60 86; e-mail: [email protected], ft,
The sample was placed in this region, so that we can exclude any dielectric effect. At low temperatures (T < 10 K), without sample, the resonance frequency is 681.444 MHz, and the linewidth is t97 kHz. These characteristics do not change in the temperature range considered here. The sample was almost a parallelepiped of size 4 x 5 x 5 mm 3. From this, we get a filling factor of 0.09, evaluated with a precision evaluated of about 10%. The sample was cooled down to 30 mK with an HeS-He '~ dilution refrigerator. A static magnetic field Bo could be applied with a superconducting coil, Bo was perpendicular to B1, and parallel to the [1, 0, 0"] axis of the crystal. In Fig. 1, we have plotted the real, Z', and imaginary, 5(,", parts of the magnetic susceptibility at 29 mK as a function of the static magnetic field B0, in the range [0, 201 mT. At first, 7," increases as Bo is risen up, reaches a maximum at around 6 roT, then decreases quickly. For the real part, the behavior is quite similar: first Z' increases as Bo is risen up, reaches a maximum at around 9 roT, and then decreases slowly. These peaks seem to be similar to the ones already observed in glasses [6]. Their shapes are similar and the ratio between the values of Bo for the maximum of X' and Z" is the same. So, these peaks seem to be a very general property of high-spin systems, We attribute this broad line to interactions between the different Dy 3 +-ions of the crystal. The nature of these interactions has not been identified yet. It must be pointed out that dipolar interactions are too weak to explain the observed effect, In Fig. 2, we have plotted Z' and 7]' as a function of the magnetic field Bo, in the range [230, 320] mT, at 29 inK. At first. )~" increases slowly, then reaches a maximum at
0304-8853/98/$19.00 .g_,, 1998 Elsevier Science B.¥. Ali rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 7 6 5-8
963
N. Vernier, G. Bellessa / Journal of Magnetism and Magnetic Materials 177-181_ (1998) 962-963 300 ••y
< 200
.< <
,
)00
.
0.005
,
0.010
o
•
0.015
0
0.020
B (T) Fig. I. Imaginary tZ') and real (Z" parts of the magnetic susceptibility at the frequency, of 681 MHz, as a function of the static magnetic field B,, in the range [0, 0.0201 T, at T = 29 inK.
1.5
< u5 and 1.0
•
Z"I
•• ••v
~.~. 0.5
0.0
i 0,24
i 0,26
,• 0.28
too
" o.;0
~.3:
B (T)
Fig. 2. Imaginary (Z') and real (7.") parts of'the magnetic susceptibility at the frequency of 68I MHz, as a function of the static magnetic field Bo, in the range [0.23, 0.32] T, at T = 29 inK. Bo = 269 mT and decreases very quickly towards zero. 7/ is very small up to Bo = 260 roT, then increases very quickly, reaches a maximum at Bo = 275 mT and decreases slowly after. The highly non-symmetrical shape of this line is very unusuaI. Indeed, Z" follows a Lorentzian law E7]. Usually, the splitting d of the considered doublet is linear as a function of Bo. This leads to a symmetrical Z". Our effect can be understood if we take into account the tunnelling effect. In this case, A has the following expression [1]: A = x / c 2 + (2.~Js/LjBo cos 0) 2
where 0 is the angle between Bo and the anisotropy axis, and e is the tunnelling contribution, c can be highly non-linear [-1]. F r o m this, we can get an expression of d which increases slowly when Bo is small, and much faster when Bo is higher. Assuming this, Z" increases slowly for low Bo. When d begins to increase faster, everything goes faster: Z" increases faster too, reaches the maximum, and then decreases quickly. In addition to the two preceeding Iines observed, we have found a third one. This line is of very low intensity. To find it, we have used spin echo experiments, which can detect much smaller magnetization than usual Z" measurements. In Fig. 3, we have plotted the initial am-
0:1
0'.2 B (T)
0:3
•
0.4
Fig. 3. Initial amplitude of the spontaneous echo as a function of the static magnetic field Bo. The duration of the RF-pulses was 1.6 bts. The amplitude of the oscillating field B~ was 1 roT, the temperature was T = 30 inK. plitude of the spontaneous echo as a function of Bo. The behavior is similar to the Z"-line of Fig. 2: firstly, the echo amplitude increases slowly for low Bo, reaches a maximum at Bo = 235 roT, and then decreases quite quickly. Since the behavior is the same, we propose the same explanation as before. The existence of two lines, and not only one, can be understood in the following way: in the easy plane, and according to the crystal symmetry, we can expect not one but two easy axis. This will give several possibilities for tunnelling from one easy axis to another one, which can explain the two lines of Figs. 2 and 3. In summary, we have found a new high-spin system with a z-peak in the low magnetic field region. This seems to be a general property of this type of compound. We have also found evidence for tunnelling of the Dy a+magnetic moments: with our technique, we have been able to detect two high-magnetic field lines. The shapes of these lines agree very weli with the occurrence of tunnelling. The existence of such two lines can be explained by the presence of several easy axis for the tunnelling phenomenon. The authors are indebted to L. Bouvot, who made the resonator, and J.M. Godard, who prepared the sample. Laboratoire de Physique des Solides is associated with the Centre National de Ia Recherche Scientifique.
References [1] I.Ya. Korenblit, E.F. Shender, Soy. Phys. JETP 48 (1978) 937. [2] E.M. Chudnovsky, L. Gunther, Phys. Rev. Lett. 60 (1988) 661. [3] P.C.E. Stamp, E.M. Chudnovsky, B. Barbara, Int. J. Mod. Phys. 6 (I992) 1355. [4] N. Vernier, G. BelIessa, D.A. Parshin, Phys. Rev. Lett. 74 (I995) 3459. [5] W.N. Hardy, L.A. Whitehead, Rev. Sci. Instr. 52 (I981) 213. [6] N. Vernier, G. Bellessa, Phys. Rev. Lett. 71 (1993) 4063. [7] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Dover, New York, 1986.
Journal of Magnetism and Magnetic Materials t77-181 (1998) 962-963
~ , ~ Jollrnal ol magnetism and
magnetic materials
ELSEVIER
Tunnelling of large magnetic moments in a single crystal Nicolas Vernier*, Guy Bellessa Laboraloire de Physiclue des Solides, Bdt. 510, Universitk Paris-Sud, 91405 Orsay, France
Abstract
We report on susceptibility measurements carried out at high frequency on a Dy s +-doped crystal, submitted to a static magnetic field, at very low temperature, We have found a susceptibility peak at low static field, which seems to be a general property of high-spin systems. We have also found evidence for a tunnelling phenomenon of the Dy 3+ -magnetic moments. © 1998 Elsevier Science B.V. All rights reserved. Ke>q,,orcts: Crystal field- RE compounds; Susceptibility- magnetic; Tunnelling
Tunnelling of large spins has been treated theoretically for a long time. It has been shown that such spins, if they have strong enough anisotropy energy, can be reversed along their anisotropy axis [11. Other symmetry conditions than axial one have also been considered [2]. According to all these results, the tunnelling rate decreases quite quickly with the magnitude of the quantum number J. Experimentally, some measurements of magnetic susceptibility and relaxation times at low temperature have been explained by macroscopic tunnelling of the magnetization [3]. Tunnelling of large spins have been observed in glasses doped with rare-earth ions [4]. Here, we report on experiments performed in a simpler system: a single crystal doped with Dy 3÷ ions. It is a good model system because the quantum number J is already quite big (J = 15/2), and the whole system is well defined. We have studied the magnetic susceptibility of a single crystal of LiYo.gvDyo.olF,v The only magnetic ion in this compound is Dy 3 +. It is a Kramers ion (J is half-integer), with a large quantum number J = 15/2. Static susceptibility measurements have shown that there is an easy plane (0, 0, 1) for the direction of the magnetic moment. Moreover, there are two easier directions in the easy plane. This will be important at very low temperature. The magnetic susceptibility was measured with a splitring resonator [51, also called loop-gap resonator. In this device, the oscillating magnetic field B~ is located in the center of the ring, where there is no electric field.
*Corresponding author. Fax: + 33 1 69 I5 60 86; e-mail: [email protected], ft,
The sample was placed in this region, so that we can exclude any dielectric effect. At low temperatures (T < 10 K), without sample, the resonance frequency is 681.444 MHz, and the linewidth is t97 kHz. These characteristics do not change in the temperature range considered here. The sample was almost a parallelepiped of size 4 x 5 x 5 mm 3. From this, we get a filling factor of 0.09, evaluated with a precision evaluated of about 10%. The sample was cooled down to 30 mK with an HeS-He '~ dilution refrigerator. A static magnetic field Bo could be applied with a superconducting coil, Bo was perpendicular to B1, and parallel to the [1, 0, 0"] axis of the crystal. In Fig. 1, we have plotted the real, Z', and imaginary, 5(,", parts of the magnetic susceptibility at 29 mK as a function of the static magnetic field B0, in the range [0, 201 mT. At first, 7," increases as Bo is risen up, reaches a maximum at around 6 roT, then decreases quickly. For the real part, the behavior is quite similar: first Z' increases as Bo is risen up, reaches a maximum at around 9 roT, and then decreases slowly. These peaks seem to be similar to the ones already observed in glasses [6]. Their shapes are similar and the ratio between the values of Bo for the maximum of X' and Z" is the same. So, these peaks seem to be a very general property of high-spin systems, We attribute this broad line to interactions between the different Dy 3 +-ions of the crystal. The nature of these interactions has not been identified yet. It must be pointed out that dipolar interactions are too weak to explain the observed effect, In Fig. 2, we have plotted Z' and 7]' as a function of the magnetic field Bo, in the range [230, 320] mT, at 29 inK. At first. )~" increases slowly, then reaches a maximum at
0304-8853/98/$19.00 .g_,, 1998 Elsevier Science B.¥. Ali rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 7 6 5-8
963
N. Vernier, G. Bellessa / Journal of Magnetism and Magnetic Materials 177-181_ (1998) 962-963 300 ••y
< 200
.< <
,
)00
.
0.005
,
0.010
o
•
0.015
0
0.020
B (T) Fig. I. Imaginary tZ') and real (Z" parts of the magnetic susceptibility at the frequency, of 681 MHz, as a function of the static magnetic field B,, in the range [0, 0.0201 T, at T = 29 inK.
1.5
< u5 and 1.0
•
Z"I
•• ••v
~.~. 0.5
0.0
i 0,24
i 0,26
,• 0.28
too
" o.;0
~.3:
B (T)
Fig. 2. Imaginary (Z') and real (7.") parts of'the magnetic susceptibility at the frequency of 68I MHz, as a function of the static magnetic field Bo, in the range [0.23, 0.32] T, at T = 29 inK. Bo = 269 mT and decreases very quickly towards zero. 7/ is very small up to Bo = 260 roT, then increases very quickly, reaches a maximum at Bo = 275 mT and decreases slowly after. The highly non-symmetrical shape of this line is very unusuaI. Indeed, Z" follows a Lorentzian law E7]. Usually, the splitting d of the considered doublet is linear as a function of Bo. This leads to a symmetrical Z". Our effect can be understood if we take into account the tunnelling effect. In this case, A has the following expression [1]: A = x / c 2 + (2.~Js/LjBo cos 0) 2
where 0 is the angle between Bo and the anisotropy axis, and e is the tunnelling contribution, c can be highly non-linear [-1]. F r o m this, we can get an expression of d which increases slowly when Bo is small, and much faster when Bo is higher. Assuming this, Z" increases slowly for low Bo. When d begins to increase faster, everything goes faster: Z" increases faster too, reaches the maximum, and then decreases quickly. In addition to the two preceeding Iines observed, we have found a third one. This line is of very low intensity. To find it, we have used spin echo experiments, which can detect much smaller magnetization than usual Z" measurements. In Fig. 3, we have plotted the initial am-
0:1
0'.2 B (T)
0:3
•
0.4
Fig. 3. Initial amplitude of the spontaneous echo as a function of the static magnetic field Bo. The duration of the RF-pulses was 1.6 bts. The amplitude of the oscillating field B~ was 1 roT, the temperature was T = 30 inK. plitude of the spontaneous echo as a function of Bo. The behavior is similar to the Z"-line of Fig. 2: firstly, the echo amplitude increases slowly for low Bo, reaches a maximum at Bo = 235 roT, and then decreases quite quickly. Since the behavior is the same, we propose the same explanation as before. The existence of two lines, and not only one, can be understood in the following way: in the easy plane, and according to the crystal symmetry, we can expect not one but two easy axis. This will give several possibilities for tunnelling from one easy axis to another one, which can explain the two lines of Figs. 2 and 3. In summary, we have found a new high-spin system with a z-peak in the low magnetic field region. This seems to be a general property of this type of compound. We have also found evidence for tunnelling of the Dy a+magnetic moments: with our technique, we have been able to detect two high-magnetic field lines. The shapes of these lines agree very weli with the occurrence of tunnelling. The existence of such two lines can be explained by the presence of several easy axis for the tunnelling phenomenon. The authors are indebted to L. Bouvot, who made the resonator, and J.M. Godard, who prepared the sample. Laboratoire de Physique des Solides is associated with the Centre National de Ia Recherche Scientifique.
References [1] I.Ya. Korenblit, E.F. Shender, Soy. Phys. JETP 48 (1978) 937. [2] E.M. Chudnovsky, L. Gunther, Phys. Rev. Lett. 60 (1988) 661. [3] P.C.E. Stamp, E.M. Chudnovsky, B. Barbara, Int. J. Mod. Phys. 6 (I992) 1355. [4] N. Vernier, G. BelIessa, D.A. Parshin, Phys. Rev. Lett. 74 (I995) 3459. [5] W.N. Hardy, L.A. Whitehead, Rev. Sci. Instr. 52 (I981) 213. [6] N. Vernier, G. Bellessa, Phys. Rev. Lett. 71 (1993) 4063. [7] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Dover, New York, 1986.