1. Temperature Dependence of the Magnetic Hyperfine Field of 181Ta
in Rare Earth-Cobalt Laves Phases RCo2
H. Saitovitch, P. R. J. Silva, J. Th. Cavalcante,
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
P. de la Presa, M. Forker
Helmholtz Institut für Strahlen- und Kernphysik, Universität Bonn, Germany
Magnetic properties of 3d(Stoner)-4f(RKKY) intermetallic compounds.
Itinerant electron metamagnetism
Nature of the phase transitions in light RCo2
Experimental details, results, discussion
Here: 181Ta in TbCo2 and HoCo2
Support:

2. MOTIVATION
Rare Earth-Cobalt Laves Phases RCo2 may be a very suitable series of compounds to study magnetic interactions
well known compounds
Interesting interaction of 3d - 4f electrons
Easy to prepare
Easy doping
Good theoretical knowledge
Here we will focus on the nature of magnetic transition order
RCo2 belongs to the series of 3d-4f intermetallic compounds. It presents the phenomenon of exchange driven itinerant electron metamagnetism which reflects the spin polarization of the itinerant 3d-electrons
RCo2 is a C15 Laves phase with cubic symmetry of the R-site, non-cubic symmetry of the Co site; therefore nuclear probes on the R site experience a pure magnetic interaction, probes on the Co site a combined magnetic + electric interaction.

3. The C15 lattice structure of RCo2
RCo2 belongs to the series of 3d-4f intermetallic compounds. It presents the phenomenon of exchange driven itinerant electron metamagnetism which reflects the spin polarization of the itinerant 3d-electrons
RCo2 is a C15 Laves phase with cubic symmetry of the R-site, non-cubic symmetry of the Co site; therefore nuclear probes on the R site experience a pure magnetic interaction, probes on the Co site a combined magnetic + electric interaction.
Co – non-cubic point symmetry,
combined magnetic and electric hfi
Rare earth – cubic point symmetry,
pure magnetic interaction

4. Experimental detail Probe isotopes Sources preparations PAC equipment
181Hf
181Ta
42.5 d β-
7/2+
5/2+
1/2+
133 keV
482 keV γ2 γ1
t1/2 = ns
Q = 2.53(10) b
µ = 3.34 µN
111In
111Cd
2.81 d EC
7/2+
5/2+
1/2+
172 keV
247 keV γ1
t1/2 =84 ns
Q = 0.83(13) b
µ = µN γ2
Experimental detail
Probe isotopes
Sources preparations
PAC equipment
Temperature variation
Experimental details:
Probes isotopes (above).
Source preparation: arc furnace, annealing
PAC equipment: twelve coincidence spectra.
Ttemperature variation: glass cryostat, closed cycle helium.

5. Previous measured spectra
The temperature dependence of the magnetic hyperfine field of 111Cd in RCo2
Previous measured spectra
PrCo2
GdCo2
DyCo2
In all cases, periodic oscillation of pure magnetic interaction; conclusion: The probe nucleus resides on the cubic R site.
GdCo2: The precession period increases continuously with increasing temperature, i.e. the frequency decreases continuously = SOT. The damping of the oscillations close to Tc reflects a distribution of the Curie temperature of 1-2 K.
DyCo2,PrCo2: The precession period is practically temperature independent, i.e. the frequency remains almost constant up to Tc. At Tc the interaction disappears discontinuously = FOT.
Second-order
transition
First-order
transition

6. Theory of itinerant electron magnetism
Wohlfarth and Rhodes , 1962: Landau expansion of the free energy
a1 < 0 , a3 > 0
a1 < 0 , a3 < 0 FM Md
-Md H
a1> 0, a3 < 0, a5 >0
H = 0
H > 0
M(TC)‏
The Wohlfarth/Rhodes theory of itinerant metamagnetism (YCo2, LuCo2) based on a Landau Expansion of the free energy in powers of the magnetization (Hx = external field), where the nature of the phase transition between the paramagnetic and the ferromagnetic state depends on the sign of the Landau coefficients:
a1<0, a3>0: there is only one minimum, application of an external or exchange field leads to a continuous increase of the magnetization → SOT;
a1<0, a3<0: there are two minima of the free energy, application of an external or exchange field produces a discontinuous jump of the magnetization → FOT.
Consequence: The theory predicts a change of order at a3=0
One minimum:
Continuous, second order
phase transition (SOT)‏
Two minima:
Discontinuous, first order
phase transition (FOT)‏

7. Temperature dependence of the Landau coefficients a1 and a3
Based on the analysis of the susceptibility of YCo2
Bloch et al. predict a change of sign of a3 at T0 ~ 150 K
a3(T) = a3(0)(1-T/T0) ; a3(0) < 0 T a3
To ~ 150 K
FOT
SOT
Bloch et al. have extracted the temperature dependence of the Landau coefficients from the susceptibility of YCo2 and come to the conclusion that the coefficient a3 should change sign at ~ 150 K. Consequently, they predict that the order of the phase transition of RCo2 depends on the Tc of the compounds: Tc < 150 K - FOT; Tc > 150 K – SOT
Consequence: The order of the transition depends on the order temperature TC
TC < T0 First-order transition (FOT), TC < T0 : Second-order transition (SOT)

8. Curie temperatures of RCo2LR HR
FOT
SOT
Tc (RCo2) X (spin projection)2.
Bloch et al. predict SOT´s above and FOT´s below the red line.
Experimental data (magnetization, transport, etc.) confirm this prediction for the heavy R elements Er to Gd.
For the light R elements, the situation is less clear. There is no doubt that SmCo2 presents a SOT as predicted. For NdCo2 and PrCo2, recent 111Cd PAC measurements* present clear evidence for a FOT, in agreement with Bloch .
* Forker et al. - PR B68(2003)014409

9. The order of the magnetic phase transitions of RCo2
deduced from the magnetic hyperfine field at 111Cd
SOT
FOT
The 111Cd PAC measurements agree with the Bloch theory:
Continuous SOT for Gd, Tb, Sm which have Tc> 150 K
Discontinuous FOT for Pr, Nd, Er, Ho, Dy which have Tc< 150 K
However, other authors conclude from integrating techniques such as magnetization and calorimetry that the transitions of NdCo2 and PrCo2 are SOT, contrary to Bloch.
For further experimental information on the nature of the RCo2 phase transitions we are presently engaged in a systematic study of the temperature dependence of the magnetic hyperfine field for different non-rare earth nuclei in RCo2 as a function of the R constituent.
Here we report first PAC measurements with the probe nucleus 181Ta.
First results of these studies M. Forker et al., PHYS. REV. B 68, (2003)‏

10. PAC spectra of TbCo2 111Cd:TbCo2 181Ta:TbCo2
Comparison of the PAC spectra of 111Cd and 181Ta in the SOT compound TbCo2
In both cases:
Periodic oscillations of pure magnetic interaction from which we may conclude that these probes resides on the cubic R site ; on the non-cubic Co site one would expect a combined interaction. In the case of 181Ta the is a strong damping at 10 K which is not fully understood;
The precession period increases continuously, i.e. the magnetic frequency decreases continuously;
As one approaches the Tc, the magnetic oscillations become strongly damped which is the consequence of a distribution of the Tc (PR. B68(2003)014409)‏

11. The temperature dependence of the magnetic hyperfine field
of the probe nuclei 111Cd and 181Ta in TbCo2
Temperature dependence of the MHF (normalized) at 111Cd and 181Ta in TbCo2: in both cases one finds a continuous temperature variation of the HF → SOT.
However, in the case of 181Ta, at T/Tc > 0.5, the HF variation with temperature is much faster than in the case of 111Cd.

12. PAC spectra of HoCo2 181Ta:HoCo2 111Cd:HoCo2 HoCo2:
The MHF seen by 111Cd is practically temperature independent.
In the case 181Ta there is slight decrease of the MHF with increasing temperature. In addition, one finds a slight increase of the damping as one approaches Tc.
In both cases the magnetic interaction vanishes discontinuously at Tc → FOT

13. The temperature dependence of the magnetic hyperfine field of the probe nuclei 111Cd and 181Ta in HoCo2
Results for HoCo2:
FOT for both probe nuclei
However, the discontinuity of the order parameter varies with the probe nucleus:
111Cd: B(Tc)/B(0) = 0.9, 181Ta: B(Tc)/B(0) = 0.5
111Cd: the attenuation of the oscillations does not change with temperature; small constant line width.
181Ta: the line width increases towards Tc. This is related to the stronger variation of the magnetic frequency. If this frequency varies with temperature, a distribution of the order temperature leads to an attenuation of the oscillations which is stronger the closer one comes to Tc.
If this frequency does not vary with temperature (as for 111Cd) a variation of Tc leaves the line width unchanged (PR B68(2003)014409).

14. SUMMARY / REMARKS
For T/Tc ≥ 0.5 the MHF of 181Ta decreases much faster with temperature than that of 111Cd, both in SOT compounds (TbCo2) and FOT compounds (HoCo2); probably because 111Cd is closed shells, so MHF is mainly caused by the spin polarization of the s-conduction electrons.
In contrast, 181Ta has an open 5d-shell with a finite 5d spin which may produce a core polarization contribution to the MHF. It is conceivable that the expectation values of this core polarization depends on coupling of the 5d spin to the host magnetization.
If the coupling is weak, the 5d spin possibly fluctuates, resulting in a decrease of the time averaged core polarization part of the field which should be stronger the closer one comes to Tc.
Probe isotope 140La/140Ce
Conclusions
Starting at T/TC ≥ 0.5 the MHF of 181Ta decreases much faster with temperature than that of 111Cd, both in SOT compounds (TbCo2) and FOT compounds (HoCo2).
Possible interpretation: 111Cd is closed shell probe nucleus, so MHF is mainly caused by the spin polarization of the s- conduction electrons.
In contrast, 181Ta has an open 5d-shell with a finite 5d spin. This 5d spin may produce a R core polarization contribution to the MHF. It is conceivable that the expectation values of this core polarization depends on coupling of the 5d spin to the R host magnetization. If the coupling is weak, the 5d spin possibly fluctuates, resulting in a decrease of the time averaged core polarization part of the field which should be stronger the closer one comes to Tc.

16. Magnetic elements
3d elements: Mn…Ni - unclosed 3d shell : (Ar) 3dm
Rare earth (4f) elements : (Xe) 4fn 5d2 6s1 ; in solids: mostly R3+ - (Xe) 4f n
except Ce, Eu, Yb
There are 2 groups of pure metals which present spontaneous magnetic order:
In the 3d-elements Mn, Fe, Co, Ni the itinerant 3d electrons are responsible for spontaneous magnetic order (Stoner magnetism)
In the Rare earth Ce to Tm magnetic order is due to the interaction of between the localized 4f electrons (RKKY coupling)‏
In intermetallic compounds RxMy envolving rare earth (R) and 3d-elements M = Mn.
Fe,Co,Ni the interaction between itinerant 3d- and localized 4f- electrons leads to complex magnetic properties. These compounds have been studied for decades; still there are many open questions to be answered. n:

17. Itinerant electron metamagnetism
T. Goto et al.
Solid State Commun.72, 945 (1989)‏
magnetic field H
magnetization
What is Metamagnetism?
Answer: Application of a strong magnetic field induces a transition to a state of high magnetization.
Example YCo2 and LuCo2. Without applied field these compounds are enhanced Pauli paramagnets: No spontaneous magnetization of the 3d band. External fields of the order of 70 T induce a transition to a state of high magnetization of the Co 3d-band of YCo2. First observed by Goto et al. using external fields up to 100 T = 1 Mgauss (for the production of such strong external fields see the Goto paper)‏

18. Magnetic properties of trivalent rare earth (R) ionsJ
(g-1)J
Russel-Saunders
Coupling
When Y or Lu are substituted by a magnetic rare earth element (R= Ce, …Yb), spontaneous magnetization of the Co 3d band may occur even without applying an external. In this case the metamagnetic transition is driven by the exchange interaction between 3d and 4f electrons.
The rare elements are characterized by the incomplete 4f shell with orbital angular momentum L and spin S. The constant of motion is the projetion (g-1)J of S onto the total angular momentum.
The exchange interaction between 2 spins may be described by a phenomemological molecular (or exchange) field Bmol. In the case of the Rare earths, the exchange field is proportional to Bmol ~ (g-1)J, since the projetion (g-1)J of S onto the total angular momentum J and not S itself is the constant of motion.

19. RCo2: metamagnetism driven by the 4f-exchange field ~ (g-1)J
As one goes from Tm to Gd the molecular field increases linearly, since (g-1) J increases and at (g-1)J ~ 1 (between Tm and Er) the 4f molecular field reaches the critical value to induce a spontaneous magnetization in the Co 3d band