Mechanism On The Magnetic And Specific-Heat Anomalies In Rare-Earth Compounds:An Effect Of Crystal-Field-Splitting Order Parameter

Rare-earth elements(R)include 15 Lanthanide elements from NO.57 to NO.71 in the periodic table,as well as Scandium and Yttrium,which are chemically simimlar to Lanthanides at room temperature,Lanthanide rare-earth elements with localized 4 f or-bitals(<1(?))and strong spin-orbit coupling(?0.2-0.4 e V)exhibit paramagnetism which matches perfectly with Hund's three rules.While forming compounds like RMn O₃and RB₁₂,the radii of R ions(<1(?))is much smaller than the bond length(?2-3(?)).That makes the crystal-field-splitting(CFS)energy of R-4 f orbitals is only around 10 me V,which is two orders of magnitude smaller than CFS energy in 3d transition metals.This difference results in the completely different influence of lattice thermal vidration on the stability of CFS,and novel phenomena come from this point of view.The strong CFS of transition metals trends to freeze the orbital momentum,and the weak CFS of R ions brings about some intresting features.As a comparison,LuMnO₃with closed f-shell shows a Mn⁺³related magnetic transition at T_N?35.5 K.And Lu B₁₂shows no magnetic ordering.However,YbMnO₃with Yb⁺³(4 f¹³5d⁰6s⁰)exhibits two magnetic anomaly at 43 K and?3-4 K.The former is just like that in LuMnO₃.The later transition is unsolved together with the anomalies in RB₁₂(R=Tb-Tm),which occur at T_C?22-3 K.The narrow peaks appear in specific-heat of RB₁₂are still unsolved which are all ended with a sharp decline.Based on the bump feature in magnetic susceptibility of YbMnO₃(RB₁₂)at 3-4 K(22-3 K),one may think that the magnetic anomaly comes mostly from the anti-ferromagnetism of rare-earth ions.The measurment of magnetoresistance shows that paramagnetic spin fluctuation is a major cause for electronic scattering above critical temperature,and the scattering of different magnetic moment states is the major cause below the critical temperature.Only the rearrangment of the magnetic moments cannot get the shape of magnetic anomaly.Entropy obtained from the specitic-heat of RB₁₂during the transition calls for the orbital contribution.M?ssbauer spectra reveals that some rare-earth magnetic moments below the bump are induced by thermal excitation of different crystal-field states.All these facts shows that the magnetic anomaly in-volves not only the change of the direction but also the amplitude-modulated nature of magnetic moment.Up to now,no clear magnetic structure was defined by neutron scattering or M?ssbauer experiment.The magnetic anomaly of YbMnO₃and Yb B₁₂at low temperature is unresolved and worth studying.CFS of 4 f-orbitals is two order of magnitude smaller than that of transition-metal3d-orbitals,which is taken as a quantum quantity.The thermal viberation cannot be ignored in rare-earth metals.From above discussions,we propose,at extremely low tempearature away below the magnetic anomaly,CFS of R ions is mutch weaker than spin-orbit coupling but much larger than the thermal fluctuation.The magnetic mo-ment is completely or partially quenched by CFS.With the rising of temperature,ther-mal fluctuation gets larger and the vibration of atoms makes CFS weaker.At a critical temperature,CFS energy is completely killed by thermal fluctuation.Thus,we should treat CFS energy as an order parameter rather than a quantum quantity.The orbital-related magnetic moment is gradually releasing with the decrease of the order param-eter.Above the critical temperature,CFS of rare-earth compounds vanishes entirely and R behave like paramagnetic ions with the total magnetic moment dictated by the Hund's three rules.Based on this picture,we systematically studied the magnetic anomaly in YbMnO₃together with the magnetic and specific-heat anomalies in RB₁₂.And we obtained the following results:Firstly,we used first principles to calculate the magnetic structure of Mn⁺³ions in orthorhombic YbMnO₃,and proved the transition from paramagnetism to antiferromagnetism at T_N?43 K.Secondly,we obtained the thermal vibration of the lattice from Debye model,and successfully estimated the critical temperature of the low temperature anomaly.We qualitatively explained the magnetic susceptibility and specific-heat anomalies at 3-4 K by a single-hole model.Thirdly,we systematically estimated the CFS energy and the critical temperature of RB₁₂(R=Tb-Tm)by using a multi-hole model.The magnetic susceptibility and specific-heat matched qualitatively well with the experiment.Also,considering multiple equilibrium R positions within B₂₄cages of RB₁₂and a 5 me V low frequency Einstein phonon mode,we explained the double peak structure near(1/2,1/2,1/2)from neutron scattering spectra.One can prove or disprove this picture by carrying out the low temperature X-ray diffraction measure-ment.Last but not least,we predicted that YbMnO₃was a regulatable multiferroic material under stress.