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Spin – orbit coupled molecular quantum magnetism realized in inorganic solid

View Article: PubMed Central - PubMed

ABSTRACT

Molecular quantum magnetism involving an isolated spin state is of particular interest due to the characteristic quantum phenomena underlying spin qubits or molecular spintronics for quantum information devices, as demonstrated in magnetic metal–organic molecular systems, the so-called molecular magnets. Here we report the molecular quantum magnetism realized in an inorganic solid Ba3Yb2Zn5O11 with spin–orbit coupled pseudospin-½ Yb3+ ions. The magnetization represents the magnetic quantum values of an isolated Yb4 tetrahedron with a total (pseudo)spin 0, 1 and 2. Inelastic neutron scattering results reveal that a large Dzyaloshinsky–Moriya interaction originating from strong spin–orbit coupling of Yb 4f is a key ingredient to explain magnetic excitations of the molecular magnet states. The Dzyaloshinsky–Moriya interaction allows a non-adiabatic quantum transition between avoided crossing energy levels, and also results in unexpected magnetic behaviours in conventional molecular magnets.

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Crystallographic structure and magnetization curves of Ba3Yb2Zn5O11.(a) Crystal structure of pyrocholre Ba3Yb2Zn5O11 with cubic space group F3m. Green, red, blue and black spheres represent Ba, Yb, Zn and O ions, respectivley. Two main blocks of Yb4O16 and Zn10O20 are alternated and Ba ions locate in the interstices. (b) Arrays of Yb ions and Yb4 tetrahedrons with alternated Yb–Yb distances in the breathing pyrochlore structure. The inter-tetrahedron (red line) and intra-tetrahedron (grey line) Yb–Yb distances are r=3.30 Å and r′=6.23 Å, respectively. Correponding magnetic exchange couplings are denoted by J and J′. (c) Yb4 tetrahedron and YbO6 octahedron with trigonal distortion (C3v). A blue arrow denotes C3v symmetry axis pointing along the [1 1 1] direction and green arrows indicate the DM vectors d's determined from the Moriya's rule. (d) Field-dependent magnetization M(H) measured for upfield (magenta) and downfield (blue) sweeps with a rate of 15 mT min−1 at T=100 mK, showing the level crossing critical fields of HC1=3.5 T and HC2=8.8 T. A green solid line displays adiabatic simulation results from  with J=0.589 meV, d/J=0.27, g//=3.0 and g∥=2.4. A black dashed line displays simulation results at T=100 mK with HC1=3.7 T and HC2=7.4 T from the conventional Heisenberg magnetic exchange Hamiltonian including the Zeeman term with an exchange coupling constant J=0.554 meV and an isotropic g-factor g=2.569 reported previously24. The inset is a schematic illustration of Landau−Zener transition between two energy states of ψ0 and ψ1 as in Fig. 2d. Adiabatic and non-adiabatic processes as a function of the external magnetic field are presented with solid and dashed lines, respectivley.
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f1: Crystallographic structure and magnetization curves of Ba3Yb2Zn5O11.(a) Crystal structure of pyrocholre Ba3Yb2Zn5O11 with cubic space group F3m. Green, red, blue and black spheres represent Ba, Yb, Zn and O ions, respectivley. Two main blocks of Yb4O16 and Zn10O20 are alternated and Ba ions locate in the interstices. (b) Arrays of Yb ions and Yb4 tetrahedrons with alternated Yb–Yb distances in the breathing pyrochlore structure. The inter-tetrahedron (red line) and intra-tetrahedron (grey line) Yb–Yb distances are r=3.30 Å and r′=6.23 Å, respectively. Correponding magnetic exchange couplings are denoted by J and J′. (c) Yb4 tetrahedron and YbO6 octahedron with trigonal distortion (C3v). A blue arrow denotes C3v symmetry axis pointing along the [1 1 1] direction and green arrows indicate the DM vectors d's determined from the Moriya's rule. (d) Field-dependent magnetization M(H) measured for upfield (magenta) and downfield (blue) sweeps with a rate of 15 mT min−1 at T=100 mK, showing the level crossing critical fields of HC1=3.5 T and HC2=8.8 T. A green solid line displays adiabatic simulation results from with J=0.589 meV, d/J=0.27, g//=3.0 and g∥=2.4. A black dashed line displays simulation results at T=100 mK with HC1=3.7 T and HC2=7.4 T from the conventional Heisenberg magnetic exchange Hamiltonian including the Zeeman term with an exchange coupling constant J=0.554 meV and an isotropic g-factor g=2.569 reported previously24. The inset is a schematic illustration of Landau−Zener transition between two energy states of ψ0 and ψ1 as in Fig. 2d. Adiabatic and non-adiabatic processes as a function of the external magnetic field are presented with solid and dashed lines, respectivley.

Mentions: With strong spin–orbit coupling (SOC), the magnetic quantum spin is given by the total angular momentum J, rather than the spin S. The degenerate J-state is split by a crystal field (CF), and the ground-state quantum spin can be represented by a modified J, the so-called pseudospin, as discussed in lanthanide-based molecular magnets171819202122. The strong 4f SOC combined with a subtle CF contributes strong magnetic anisotropy to yield a simple model Hamiltonian with Ising-like or XY-like anisotropic magnetic exchange between the molecular pseudospins. Recently, Ba3Yb2Zn5O11 was reported to be a geometrically frustrated breathing pyrochlore system with two distinct Yb–Yb distances2324. Ba3Yb2Zn5O11 consists of two alternating main blocks of Yb4O16 and Zn10O20 (Fig. 1a). The magnetic Yb3+ ions in Yb4O16 form a tetrahedron connected with another one through corner-sharing in the three-dimensional framework. Remarkably, the inter-tetrahedron Yb–Yb distance r′=6.23 Å is much larger than the intra-tetrahedron one r=3.30 Å. Thus, the inter-magnetic exchange energy J′ becomes negligible in comparison with the intra-exchange energy J, that is, J′/J∼0 (Fig. 1b). As can be seen in the detailed ionic arrangements of the tetrahedron Yb4O16 (Fig. 1c), each Yb ion is surrounded by six oxygens to form an octahedron (YbO6) with a trigonal distortion (C3v symmetry), and the C3v symmetry axis is towards the tetrahedron center. The Yb3+ ion (4f13) effectively has a pseudospin-½ ground state of a Kramers doublet separated by the CF splitting energy of 38.2 meV (=443 K-kB) without any magnetic long-range order even below sub-Kelvin in spite of the considerable Curie–Weiss temperature ΘCW=−6.7 K (refs 24, 25), indicating possible formation of decoupled molecular spin states.


Spin – orbit coupled molecular quantum magnetism realized in inorganic solid
Crystallographic structure and magnetization curves of Ba3Yb2Zn5O11.(a) Crystal structure of pyrocholre Ba3Yb2Zn5O11 with cubic space group F3m. Green, red, blue and black spheres represent Ba, Yb, Zn and O ions, respectivley. Two main blocks of Yb4O16 and Zn10O20 are alternated and Ba ions locate in the interstices. (b) Arrays of Yb ions and Yb4 tetrahedrons with alternated Yb–Yb distances in the breathing pyrochlore structure. The inter-tetrahedron (red line) and intra-tetrahedron (grey line) Yb–Yb distances are r=3.30 Å and r′=6.23 Å, respectively. Correponding magnetic exchange couplings are denoted by J and J′. (c) Yb4 tetrahedron and YbO6 octahedron with trigonal distortion (C3v). A blue arrow denotes C3v symmetry axis pointing along the [1 1 1] direction and green arrows indicate the DM vectors d's determined from the Moriya's rule. (d) Field-dependent magnetization M(H) measured for upfield (magenta) and downfield (blue) sweeps with a rate of 15 mT min−1 at T=100 mK, showing the level crossing critical fields of HC1=3.5 T and HC2=8.8 T. A green solid line displays adiabatic simulation results from  with J=0.589 meV, d/J=0.27, g//=3.0 and g∥=2.4. A black dashed line displays simulation results at T=100 mK with HC1=3.7 T and HC2=7.4 T from the conventional Heisenberg magnetic exchange Hamiltonian including the Zeeman term with an exchange coupling constant J=0.554 meV and an isotropic g-factor g=2.569 reported previously24. The inset is a schematic illustration of Landau−Zener transition between two energy states of ψ0 and ψ1 as in Fig. 2d. Adiabatic and non-adiabatic processes as a function of the external magnetic field are presented with solid and dashed lines, respectivley.
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f1: Crystallographic structure and magnetization curves of Ba3Yb2Zn5O11.(a) Crystal structure of pyrocholre Ba3Yb2Zn5O11 with cubic space group F3m. Green, red, blue and black spheres represent Ba, Yb, Zn and O ions, respectivley. Two main blocks of Yb4O16 and Zn10O20 are alternated and Ba ions locate in the interstices. (b) Arrays of Yb ions and Yb4 tetrahedrons with alternated Yb–Yb distances in the breathing pyrochlore structure. The inter-tetrahedron (red line) and intra-tetrahedron (grey line) Yb–Yb distances are r=3.30 Å and r′=6.23 Å, respectively. Correponding magnetic exchange couplings are denoted by J and J′. (c) Yb4 tetrahedron and YbO6 octahedron with trigonal distortion (C3v). A blue arrow denotes C3v symmetry axis pointing along the [1 1 1] direction and green arrows indicate the DM vectors d's determined from the Moriya's rule. (d) Field-dependent magnetization M(H) measured for upfield (magenta) and downfield (blue) sweeps with a rate of 15 mT min−1 at T=100 mK, showing the level crossing critical fields of HC1=3.5 T and HC2=8.8 T. A green solid line displays adiabatic simulation results from with J=0.589 meV, d/J=0.27, g//=3.0 and g∥=2.4. A black dashed line displays simulation results at T=100 mK with HC1=3.7 T and HC2=7.4 T from the conventional Heisenberg magnetic exchange Hamiltonian including the Zeeman term with an exchange coupling constant J=0.554 meV and an isotropic g-factor g=2.569 reported previously24. The inset is a schematic illustration of Landau−Zener transition between two energy states of ψ0 and ψ1 as in Fig. 2d. Adiabatic and non-adiabatic processes as a function of the external magnetic field are presented with solid and dashed lines, respectivley.
Mentions: With strong spin–orbit coupling (SOC), the magnetic quantum spin is given by the total angular momentum J, rather than the spin S. The degenerate J-state is split by a crystal field (CF), and the ground-state quantum spin can be represented by a modified J, the so-called pseudospin, as discussed in lanthanide-based molecular magnets171819202122. The strong 4f SOC combined with a subtle CF contributes strong magnetic anisotropy to yield a simple model Hamiltonian with Ising-like or XY-like anisotropic magnetic exchange between the molecular pseudospins. Recently, Ba3Yb2Zn5O11 was reported to be a geometrically frustrated breathing pyrochlore system with two distinct Yb–Yb distances2324. Ba3Yb2Zn5O11 consists of two alternating main blocks of Yb4O16 and Zn10O20 (Fig. 1a). The magnetic Yb3+ ions in Yb4O16 form a tetrahedron connected with another one through corner-sharing in the three-dimensional framework. Remarkably, the inter-tetrahedron Yb–Yb distance r′=6.23 Å is much larger than the intra-tetrahedron one r=3.30 Å. Thus, the inter-magnetic exchange energy J′ becomes negligible in comparison with the intra-exchange energy J, that is, J′/J∼0 (Fig. 1b). As can be seen in the detailed ionic arrangements of the tetrahedron Yb4O16 (Fig. 1c), each Yb ion is surrounded by six oxygens to form an octahedron (YbO6) with a trigonal distortion (C3v symmetry), and the C3v symmetry axis is towards the tetrahedron center. The Yb3+ ion (4f13) effectively has a pseudospin-½ ground state of a Kramers doublet separated by the CF splitting energy of 38.2 meV (=443 K-kB) without any magnetic long-range order even below sub-Kelvin in spite of the considerable Curie–Weiss temperature ΘCW=−6.7 K (refs 24, 25), indicating possible formation of decoupled molecular spin states.

View Article: PubMed Central - PubMed

ABSTRACT

Molecular quantum magnetism involving an isolated spin state is of particular interest due to the characteristic quantum phenomena underlying spin qubits or molecular spintronics for quantum information devices, as demonstrated in magnetic metal–organic molecular systems, the so-called molecular magnets. Here we report the molecular quantum magnetism realized in an inorganic solid Ba3Yb2Zn5O11 with spin–orbit coupled pseudospin-½ Yb3+ ions. The magnetization represents the magnetic quantum values of an isolated Yb4 tetrahedron with a total (pseudo)spin 0, 1 and 2. Inelastic neutron scattering results reveal that a large Dzyaloshinsky–Moriya interaction originating from strong spin–orbit coupling of Yb 4f is a key ingredient to explain magnetic excitations of the molecular magnet states. The Dzyaloshinsky–Moriya interaction allows a non-adiabatic quantum transition between avoided crossing energy levels, and also results in unexpected magnetic behaviours in conventional molecular magnets.

No MeSH data available.


Related in: MedlinePlus