Using the bosonization technique, we have studied a spin-1/2 magnetic impurity in Heisenberg chain, and shown that the impurity specific heat and spin susceptibility have an anomalous temperature dependence. The temperature dependence of the impurity specific heat is ${C}_{\mathrm{im}}(T)\ensuremath{\sim}{T}^{\ensuremath{\mu}}$, $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4\ensuremath{-}\frac{1}{g}(1\ensuremath{-}g{)}^{2}$, for ${g}_{c}<g<1$ . The impurity spin susceptibility has the following temperature dependence: ${\ensuremath{\chi}}_{\mathrm{im}}(T)\ensuremath{\sim}{T}^{\ensuremath{\nu}}$, $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ensuremath{-}\frac{1}{g}(1\ensuremath{-}g{)}^{2}$, for ${g}_{c}<g<1$ , and $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$, for $g\ensuremath{\le}{g}_{c}$, where ${g}_{c}$ satisfies ${4g}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({1\ensuremath{-}g}_{c}{)}^{2}$, and $g$ is a dimensionless coupling strength parameter.Using the bosonization technique, we have studied a spin-1/2 magnetic impurity in Heisenberg chain, and shown that the impurity specific heat and spin susceptibility have an anomalous temperature dependence. The temperature dependence of the impurity specific heat is ${C}_{\mathrm{im}}(T)\ensuremath{\sim}{T}^{\ensuremath{\mu}}$, $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4\ensuremath{-}\frac{1}{g}(1\ensuremath{-}g{)}^{2}$, for ${g}_{c}<g<1$. The impurity spin susceptibility has the following temperature dependence: ${\ensuremath{\chi}}_{\mathrm{im}}(T)\ensuremath{\sim}{T}^{\ensuremath{\nu}}$, $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ensuremath{-}\frac{1}{g}(1\ensuremath{-}g{)}^{2}$, for ${g}_{c}<g<1$, and $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$, for $g\ensuremath{\le}{g}_{c}$, where ${g}_{c}$ satisfies ${4g}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({1\ensuremath{-}g}_{c}{)}^{2}$, and $g$ is a dimensionless coupling strength parameter.

arXiv:cond-mat/9706017Physical Review LettersJul 14, 199715 citations

Solitions in a Heisenberg Spin Chain with an Impurity

Raúl Labbé, C. Pereda, Rodrigo Ferrer

physica status solidi (b)Oct 1, 19935 citations

Overcompensated impurities in antiferromagnetic Heisenberg chains

P. Schlottmann

An impurity of spin S′=1/2 is introduced in the Babujian-Takhtajian Heisenberg model of spin S in one dimension. The impurity is located on the mth link of the chain and interacts with both neighboring sites. The interaction between impurity and Heisenberg chain is of a special type so that the integrability is preserved. The diagonalization of the transfer matrices leads to the Bethe ansatz equations of the model. The thermodynamics of the system is studied. For ferromagnetic coupling in the Heisenberg chain, the impurity is locked into the critical behavior of the lattice, i.e., at low temperatures the specific heat is proportional to T1/2 (ferromagnetic magnons) and the susceptibility diverges as T−2 (with logarithmic corrections). For antiferromagnetic coupling and S =1/2 the impurity is just one more site in the chain. If S ≳1/2 the collective properties of impurity and lattice give rise to critical behavior in complete analogy to the overcompensated n-channel Kondo problem. The zero-temperature entropy is finite in zero-field, but zero if the field is nonzero, giving rise to an essential singularity at T=H=0. As a consequence a two-peak structure arises in the specific heat in a small but finite field.An impurity of spin S′=1/2 is introduced in the Babujian-Takhtajian Heisenberg model of spin S in one dimension. The impurity is located on the mth link of the chain and interacts with both neighboring sites. The interaction between impurity and Heisenberg chain is of a special type so that the integrability is preserved. The diagonalization of the transfer matrices leads to the Bethe ansatz equations of the model. The thermodynamics of the system is studied. For ferromagnetic coupling in the Heisenberg chain, the impurity is locked into the critical behavior of the lattice, i.e., at low temperatures the specific heat is proportional to T1/2 (ferromagnetic magnons) and the susceptibility diverges as T−2 (with logarithmic corrections). For antiferromagnetic coupling and S =1/2 the impurity is just one more site in the chain. If S ≳1/2 the collective properties of impurity and lattice give rise to critical behavior in complete analogy to the overcompensated n-channel Kondo problem. The zero-temperature entropy is finite in zero-field, but zero if the field is nonzero, giving rise to an essential singularity at T=H=0. As a consequence a two-peak structure arises in the specific heat in a small but finite field.

Journal of Applied PhysicsNov 15, 19910 citations

The heat capacities of linear Heisenberg chains

Henk W. J. Blöte

PhysicaDec 1, 197438 citations

Spin- S impurities with XXZ anisotropy in a spin- 12 Heisenberg chain

Ayushi Singhania, Masahiro Kadosawa, Y. Ohta +2 more

We study the effect of anisotropy of spin- $S$ impurities on an antiferromagnetic SU(2) Heisenberg chain. The magnetic impurities are assumed to have an XXZ-type anisotropic exchange with their neighboring sites. First, using density-matrix renormalization group technique, we examine spin-spin correlation function, instability of N\'eel order, and local spin susceptibility in the presence of a single spin- $S$ impurity. Based on the results, we find that the types of spin- $S$ impurities are classified into two groups: (i) nonmagnetic and $S=1$ impurities enhance only short-range antiferromagnetic correlation and (ii) $S=\frac{1}{2}$ and $S>1$ impurities can, in contrast, stabilize a long-range N\'eel order in the disordered SU(2) Heisenberg chain. Then, we focus on the case of $S=\frac{1}{2}$ impurity as a representative of (ii) and investigate the evolution of some experimentally observable quantities such as magnetization, specific heat, and magnetic susceptibility, as a function of concentration and XXZ anisotropy strength of the impurity. We confirm that the N\'eel order is induced in the bulk spin chain in the presence of finite amount of easy-axis XXZ $S=\frac{1}{2}$ impurities. Furthermore, we recover some of the aforementioned features using cluster mean-field theory, which allows us to present results on experimentally accessible quantities at finite temperatures. Interestingly, in the presence of uniform magnetic field, the total magnetization exhibits a pseudogap behavior for low values of applied field. We also discuss the dependence of NMR spectrum on various XXZ impurities and identify that the spin state of Co impurity in ${\mathrm{SrCu}}_{0.99}{\mathrm{Co}}_{0.01}{\mathrm{O}}_{2}$ is $S=\frac{3}{2}$ .We study the effect of anisotropy of spin-$S$ impurities on an antiferromagnetic SU(2) Heisenberg chain. The magnetic impurities are assumed to have an XXZ-type anisotropic exchange with their neighboring sites. First, using density-matrix renormalization group technique, we examine spin-spin correlation function, instability of N\'eel order, and local spin susceptibility in the presence of a single spin-$S$ impurity. Based on the results, we find that the types of spin-$S$ impurities are classified into two groups: (i) nonmagnetic and $S=1$ impurities enhance only short-range antiferromagnetic correlation and (ii) $S=\frac{1}{2}$ and $S>1$ impurities can, in contrast, stabilize a long-range N\'eel order in the disordered SU(2) Heisenberg chain. Then, we focus on the case of $S=\frac{1}{2}$ impurity as a representative of (ii) and investigate the evolution of some experimentally observable quantities such as magnetization, specific heat, and magnetic susceptibility, as a function of concentration and XXZ anisotropy strength of the impurity. We confirm that the N\'eel order is induced in the bulk spin chain in the presence of finite amount of easy-axis XXZ $S=\frac{1}{2}$ impurities. Furthermore, we recover some of the aforementioned features using cluster mean-field theory, which allows us to present results on experimentally accessible quantities at finite temperatures. Interestingly, in the presence of uniform magnetic field, the total magnetization exhibits a pseudogap behavior for low values of applied field. We also discuss the dependence of NMR spectrum on various XXZ impurities and identify that the spin state of Co impurity in ${\mathrm{SrCu}}_{0.99}{\mathrm{Co}}_{0.01}{\mathrm{O}}_{2}$ is $S=\frac{3}{2}$.

arXiv:2109.00777Physical review. B./Physical review. BDec 6, 20210 citations

{g}_{c}<g<1

. The impurity spin susceptibility has the following temperature dependence: ${\ensuremath{\chi}}_{\mathrm{im}}(T)\ensuremath{\sim}{T}^{\ensuremath{\nu}}$, $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ensuremath{-}\frac{1}{g}(1\ensuremath{-}g{)}^{2}$, for

{g}_{c}<g<1

, and $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$, for $g\ensuremath{\le}{g}_{c}$, where

{g}_{c}

satisfies ${4g}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({1\ensuremath{-}g}_{c}{)}^{2}$, and

g

is a dimensionless coupling strength parameter.

We study the effect of anisotropy of spin-

S

impurities on an antiferromagnetic SU(2) Heisenberg chain. The magnetic impurities are assumed to have an XXZ-type anisotropic exchange with their neighboring sites. First, using density-matrix renormalization group technique, we examine spin-spin correlation function, instability of N\'eel order, and local spin susceptibility in the presence of a single spin-

S

impurity. Based on the results, we find that the types of spin-

S

impurities are classified into two groups: (i) nonmagnetic and

S=1

impurities enhance only short-range antiferromagnetic correlation and (ii)

S=\frac{1}{2}

and

S>1

impurities can, in contrast, stabilize a long-range N\'eel order in the disordered SU(2) Heisenberg chain. Then, we focus on the case of

S=\frac{1}{2}

impurity as a representative of (ii) and investigate the evolution of some experimentally observable quantities such as magnetization, specific heat, and magnetic susceptibility, as a function of concentration and XXZ anisotropy strength of the impurity. We confirm that the N\'eel order is induced in the bulk spin chain in the presence of finite amount of easy-axis XXZ

S=\frac{1}{2}

impurities. Furthermore, we recover some of the aforementioned features using cluster mean-field theory, which allows us to present results on experimentally accessible quantities at finite temperatures. Interestingly, in the presence of uniform magnetic field, the total magnetization exhibits a pseudogap behavior for low values of applied field. We also discuss the dependence of NMR spectrum on various XXZ impurities and identify that the spin state of Co impurity in

{\mathrm{SrCu}}_{0.99}{\mathrm{Co}}_{0.01}{\mathrm{O}}_{2}

S=\frac{3}{2}