24-P-45 TOKIMEKI211, Nov. 24, 211 Interplay between crystal electric field and magnetic exchange anisotropies in the heavy fermion antiferromagnet under pressure K. Umeo N-BARD, Hiroshima University Collaborators H. Yamane, H. Kubo, Y. Muro, F. Nakamura, T. Suzuki, and T. Takabatake, ADSM, Hiroshima Univ. K. Sengupta, M. K. Forthaus, and M. M. Abd-Elmeguid, Univ. Köln, Germany
T ( K ) Introduction Pressure effect on the magnetism of Yb compounds Applying pressure Ce comp. Yb comp. 2 Ferromagnetic state Quantum critical point (QCP) Change of magnetic state(ybnisn)[2,3] Complex magnetic state 4 3 = JN(E F ) Appearance of another QCP at P* (YbRh 2 Si 2 )[4] YbRh 2 Si 2 2 1 P* 12 9 6 3 P ( GPa )
Yb compounds with the orthorhombic -TiNiSi type structure 3 Magnetization of YbNiSn [2] H II a: Metamagnetic transition, H II c: Ferromagnetism c Yb T X b a YbNiSn (Ferro. T C = 5.6 K)[2,3] YbPtAl (Antiferro. T N = 5.8 K)[5] (Weak ferro. T M = 2.7 K)[1] Complicated magnetic behavior arises from the competition between the anisotropic exchange interaction with the easy c-axis and the CEF anisotropy with the easy a-axis.
Weak ferromagnetism of (T M =2.7K,Mr = 3x1-3 μ B /Yb)[1] 4 a small remanent moment Mr of 3x1-3 μ B /Yb (B//b) 1x1-3 μ B /Yb (B//a, B//c) Maximum in M/B(T) spin flop in M(B) AF arrangement with a canted component
Heavy-fermion behaviour of [1] Inverse susceptibility Electrical resistivity 5 eff =4.4 B In the paramagnetic state, easy axis is a-axis. CEF anisotropy Specific heat Broad maximum at 1 K Kondo effect g = 37 mj/k 2 mol
Purpose 6 Determine pressure dependences of the Kondo and RKKY interactions. Experiments 1. Resistivity ( ) AC 4-terminal method Pressure cell : piston-cylinder type P max =2.5 GPa T :.3 K 3 K Locking nut (Cu-Be) Piston(Cu-Be) Cylinder (Cu-Be) 2. Magnetization (M) SQUID magnetometer (MPMS) B : 5 T Pressure cell : indenter cell [6] Gasket : NiCrAl+Cu-Be P max =2.5 GPa Indenter(ZrO 2 ) Gasket NiCrAl Cu-Be Pressure medium : Daphne oil Home-made indenter cell 6mm
Design of our calorimeter for high pressures [7] 7 To isolate thermally the gasket from the anvil The thermometer is mounted on the felly of the gasket. The sensitivity doesn t change with pressure. 5 mm Bridgman anvil(wc) 3.37 mg In 5.39 mg Cu-Be gasket : 142.92 mg I.d.= 1.6 mm, t =.7 mm Cu-Be plate 16.53 mg t =.5 mm 3 mm The hollow at the anvil top It prevents expansion of the sample space over the anvil top. Pressure superconducting temperature of In. P max =3 GPa..5 < T < 7 K ( 3 He cryostat) Detection of AC component of the sample temperature Lock-in Amp.
Experiments up to 2 GPa 8 1. Resistivity ( ) DC 4-terminal method Pressure cell : a diamond anvil cell (DAC) T : 1.5 K 3 K Pressure determination : ruby luminescence method 2. Pressure dependence of lattice parameters Pressure cell : DAC Pressure medium : N 2 Pressure determination : gold marker in the sample chamber energy-dispersive x-ray diffraction (EDXRD) at the Hamburger Synchrotronstrahlungslabor (HASYLAB)
( cm) Resistivity under pressures 45 4 II a 2.67 T max ( T K ) decreases with pressure. 9 3 T M3 2.7 1.78 For P >1.37 GPa, another magnetic transition occurs at T M2 above T M1. 2 T M2 1.37 T max.34 1 GPa T M1 1 1 1 T(K) (Data sets for each value of P are shifted upward consecutively by 6 cm for clarity).
M/B (emu/mol) M/B (emu/mol) M/B (emu/mol) Magnetic susceptibility M/B(T) for B II a and B II b under various pressures.3.3 2.54 2.2 B II a=.1 T T M3.3.3 B II b=.1t 1.71 2.49 3 1.2 1.59 T M2.2 2.1 1.34.5 GPa T M1. 1 2 3 4 5 6 T (K) P =1.59 GPa Broad maximum at T M2 =3.5 K Increment below 2.7 K P 2.2 GPa Hysteresis of M/B at low T.1 1.55 1.39 1.16.55 P=GPa T M1 T M2 2.33 2.13 1.92 1.71 T M3. 1 2 3 4 5 1 2 3 4 5 6 7 T (K) M/B increases with increasing pressure. P =1.39 GPa : Broad maximum at T M2 =3.5 K Increase of dc for P 2 GPa Ferromagnetic state? 1
M ( B/Yb) Magnetization curves of under various pressures M (1-3 B/Yb) 11 1.4 1.2 1..8.6.4.2. 1..8.6.4.2.8..6.4.2 B II a T=2 K B II b B II c 2.54 1.59 1.34.5 P= GPa 1.71 2.13 2.49 1.39.55 1.75 2.3 1.15. 1 2 3 4 5 B (T) B II a Metamagnetic anomaly shifts from 2.5 T to 1.5 T with P. B II b P 2.5 GPa, ferromagnetic behavior with the Mr of.4 B /Yb B II c P >1.75 GPa, ferromagnetic behavior with the Mr of.3 B /Yb 1 5-5 B//c P=1.39 GPa 3.3K 3.K 2.K >T M1-1 -.5 -.3 -.1.1.3.5 B (T) Weak ferromagnetic moment disappears above T M1.
B/M (mol/emu) T-dependence of B/M under various pressures I PI (K) 12 I PI (K) 2 15 1 5 B II c B II b B II a=1t P=.5 GPa 1.6 2.5 1 2 3 T (K) 15 13 11 9 c-axis b-axis 9 7 5 7 3 a-axis 5 1 2 1 3 P (GPa) p (B//a) and p (B//b) at 2 GPa decrease by 5 % and 2 %, respectively, from the values at GPa. The slop of B/M(T) for P >1K hardly changes with pressure. eff does not change on pressure. p =nt K, n=2~4 [8] T K decreases with pressure.
C/T (J/K 2 mol) Specific heat of under various pressures 13 3 2 2.95 GPa 2.5 T M3 P= The data agrees with the previous one [6]. P=1.5 GPa Thermal hysteresis of C(T) around T M1 1 st order transition P >2 GPa Specific heat jumps become larger. 1 2.5 1.85 1.5.35 P= T M1 T M2 1 2 3 4 5 6 T (K) (Data sets for each value of P are shifted upward consecutively by.5 J/K 2 mol for clarity.)
Sm/(R ln2) Magnetic entropy of under various pressures 14.6.4 1.5 GPa 2.5 GPa S m C()- C(LaRhSb) T C(LaRhSb)=γT+βT 3 γ=6.7 mj/k 2 mol β=.34 mj/k 4 mol dt.2 P= GPa Broken lines:s K (T M /T K ) = S mag (T M ) T K [9] S K ; s=1/2 single-impurity Kondo model. 1 2 3 4 5 6 T (K) S m (T M )/(Rln2)=.24 @ P=.45 @ P=2.5 GPa T K decreases with pressures.
I PI (K) T (K) I PI (K) 5 4 3 17 2 TM1 C Mb Ⅰ TM2 Ⅱ TM3 Ⅲ (a) 4 T - P phase diagram of Minimum of T M at 1.7 GPa Ⅰ:Canted Antifferro. Ⅱ:Antiferro. Ⅲ:Ferro. Mr.3~.4 B /Yb 15 TK (K) 15 13 11 3 2 1 9 15 7 (b) 13 c-axis 9 11 7 9 b-axis 5 7 3 5 a-axis (c) 1 1 2 3 P (GPa) Tmax (K) T K decreases rapidly with increasing pressure, but remains at a constant value above 1.5 GPa. The complicated pressure-induced magnetic phase of is attributed to the enhancement of inter-site exchange interaction causing easy b-c plane anisotropy.
T (K) Model of magnetic structure of 5 4 3 TM1 C Mb Ⅰ TM2 TM3 Canted AF Ferro. 2 1 2 3 P (GPa) P 1.7 GPa 1.7 GPa < P < 2.5 GPa P 2.5 GPa Ⅱ Ⅲ 16 c Rh b a Yb Sb A canted antiferromagnetic structure with ordered moments of.1 B /Yb lying almost parallel to the b axis below T M1 [1]. Ferromagnetic component appears along the c axis below T M3. A ferromagnetic structure with moments of.4 B /Yb lying in the b-c plane.
Resistivity of under various pressures up to 2 GPa 1.1 1. (T) (29K) 17.8.6.4 1 2 27529 T (K) ρ(t, P) shows a double maximum structure. 3.2 GPa 5.2 8 13.5 16.5 2.4 The broad maximum at high temperatures is suggested to be due to an incoherent scattering of the conduction electrons at the first excited crystal field level. With increasing pressure, the maximum at high temperature (around 15 K at ambient pressure) is shifted to higher temperatures.
d 2 /dt 2 (arb. units) (T) (29K) Pressure dependence of T M3 18 1.1 1. 8 8.8.6 4..4 3.2 5.2 13.5 16.5 2.4 GPa (a) TM 3 (K) 6 4 2 5 1 15 2 P (GPa) 3. 1.5 5.2 2.4 GPa 13.5 8 T M3 steeply increases up about 7 K, showing a broad maximum, and then slightly decreases with increasing pressure above 8 GPa.. 3.2 (b) -1.5 5 1 15 T (K)
V (A 3 ) c (A ) b (A ) a (A ) 7. T=3 K 6.9 6.8 Pressure dependence of lattice parameters 19 6.7 6.6 4.5 4.4 (a) We obtain a smooth variation of the lattice parameters (a, b and c) and the volume which exclude any structural changes up to 19 GPa. bulk modulus B =114(9) GPa and its pressure derivative db /dp = 5(1) 4.3 (b) 7.7 7.6 7.5 25 (c) 24 23 22 (d) 21 5 1 15 2 P (GPa)
Volume dependence of T M for and YbNiSn T (K) 2 8 Pressure 6 4 2 245 V (YbNiSn) 24 23 22 21 A 3 V ( ) (present work) YbNiSn (Ref. 14) At higher pressures, we find that T M3 for exhibits qualitatively similar pressure dependence as the Curie temperature (T C ) of YbNiSn.
SummaryⅠ Pressure-induced ferromagnetic order in T (K) For a weak ferromagnet witht M1 = 2.7 K at P =, resistivity, DC magnetization and specific heat have been measured on a single crystal under pressures up to 2.5 GPa. For.9 < P < 1.5 GPa, another magnetic transition occurs at T M2 above T M1, and T M1 has a deep minimum of 2.5 K at P C = 1.7 GPa. T K decreases rapidly with increasing pressure, but remains at a constant value above 1.5 GPa. For P 2.5 GPa, a ferromagnetic state is induced with ordered moments lying in the b-c plane. In the ferromagnetic state, the magnetization curve for B a exhibits a sharp metamagnetic transition at around 1.5 T. The change of the magnetically ordered state arises from the competition among the Kondo effect (T K ), anisotropic RKKY interaction (T RKKY ), and CEF anisotropic energy (T ). The above competition among the three interactions determine the complex magnetism of Yb compounds. Future studies CAFM Canted AF (b) 2 1 2 3 P (GPa) Magnetic structures under pressures Neutron diffraction and Mössbauer spectroscopy TK (K) 17 15 13 11 9 757 4 3 TM1 C Mb T K >T RKKY T TM2 AFM TM3 Ferro FM (a) 21 4 3 2 1 T RKKY >T >T K Tmax (K)
Summary Ⅱ Ferromagnetic order in at high pressures The pressure dependence of the ordering temperature T M3 of the FM state has been further investigated up to about 2 GPa using electrical resistivity measurements. We found that for P > 2.5 GPa T M3 rapidly increases to about 7 K, going through a broad maximum, and then slightly decreases with increasing pressure above 8 GPa. No the structural change up to 19 GPa was observed by x-ray diffraction measurements at room temperature. The enhancement of T M3 for P > 2.5 GPa is attributed to an increase of the CEF anisotropy with respect to magnetic exchange anisotropy. The obtained magnetic phase diagram of as a function of the unit cell volume has been compared with that of the isostructural HF ferromagnet YbNiSn. 22
References 22 [1] Y. Muro, K. Umeo et al., Phys. Rev. B 69 (24) 241(R). [2] M. Kasaya et al., J. Phys. Soc. Jpn. 6 (1991) 3145. [3] K. Drescher et al., Phys. Rev. Let. 77 (1996) 3228. [4] G. Knebel et al., J. Phys. Soc. Jpn. 75 (26) 11479 [5] C. Schank et al., J. Magn. Magn. Mater. 14-144 (1995) 1237. [6] T. C. Kobayashi et al., Rev. Sci. Instrum. 78 (27) 2399. [7] H. Kubo, K. Umeo and T. Takabatake: J. Phys. Soc. Jpn. 76 (27) Suppl. A, 221. [8] G. Grüner and A. Zawadowski, Rept. Prog. Phys. 37 (1974) 1497. [9] H. Mori et al., J. Low Temp, Phys, 58 (1985) 513. [1] H. Tou, private communications.