Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-Fermi-liquid systems
In this Letter we show that a strong disorder in the distribution of exchange couplings between magnetic impurities and hosts in quantum spin chains and non-Fermi-liquid rare earth and actinide compounds can be the reason for magnetic orderings in these systems at low temperatures.
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Cite this: | Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-Fermi-liquid systems / A.A. Zvyagin, A.V. Makarova // Физика низких температур. — 2004. — Т. 30, № 10. — С. 1095–1097. — Бібліогр.: 18 назв. — англ. |
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irk-123456789-1200442017-06-11T03:05:02Z Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-Fermi-liquid systems Zvyagin, A.A. Makarova, A.V. Письма pедактоpу In this Letter we show that a strong disorder in the distribution of exchange couplings between magnetic impurities and hosts in quantum spin chains and non-Fermi-liquid rare earth and actinide compounds can be the reason for magnetic orderings in these systems at low temperatures. 2004 Article Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-Fermi-liquid systems / A.A. Zvyagin, A.V. Makarova // Физика низких температур. — 2004. — Т. 30, № 10. — С. 1095–1097. — Бібліогр.: 18 назв. — англ. 0132-6414 PACS: 75.10.Jm, 71.27.+a http://dspace.nbuv.gov.ua/handle/123456789/120044 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Письма pедактоpу Письма pедактоpу Zvyagin, A.A. Makarova, A.V. Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-Fermi-liquid systems Физика низких температур |
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In this Letter we show that a strong disorder in the distribution of exchange couplings between
magnetic impurities and hosts in quantum spin chains and non-Fermi-liquid rare earth and actinide
compounds can be the reason for magnetic orderings in these systems at low temperatures. |
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Zvyagin, A.A. Makarova, A.V. |
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Zvyagin, A.A. Makarova, A.V. |
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Zvyagin, A.A. |
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Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-Fermi-liquid systems |
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Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-Fermi-liquid systems |
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Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-Fermi-liquid systems |
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Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-Fermi-liquid systems |
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Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-Fermi-liquid systems |
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magnetic ordering caused by a disorder in quasi-one-dimensional spin systems and non-fermi-liquid systems |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2004 |
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Magnetic ordering caused by a disorder in
quasi-one-dimensional spin systems
and non-Fermi-liquid systems / A.A. Zvyagin, A.V. Makarova // Физика низких температур. — 2004. — Т. 30, № 10. — С. 1095–1097. — Бібліогр.: 18 назв. — англ. |
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Физика низких температур |
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AT zvyaginaa magneticorderingcausedbyadisorderinquasionedimensionalspinsystemsandnonfermiliquidsystems AT makarovaav magneticorderingcausedbyadisorderinquasionedimensionalspinsystemsandnonfermiliquidsystems |
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2025-07-08T17:08:29Z |
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Fizika Nizkikh Temperatur, 2004, v. 30, No. 10, p. 1095–1097
Letters to the Editor
Magnetic ordering caused by a disorder in
quasi-one-dimensional spin systems
and non-Fermi-liquid systems
A.A. Zvyagin
B. Verkin Institute for Low Temperature Physics and Engineering
of the National Akademy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine
E-mail: zvyagin@ilt.kharkov.ua
A.V. Makarova
Kharkov State Economic University, 9a Lenin Ave., Kharkov 61001, Ukraine
B. Verkin Institute for Low Temperature Physics and Engineering
of the National Akademy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine
Received July 5, 2004
In this Letter we show that a strong disorder in the distribution of exchange couplings between
magnetic impurities and hosts in quantum spin chains and non-Fermi-liquid rare earth and actinide
compounds can be the reason for magnetic orderings in these systems at low temperatures.
PACS: 75.10.Jm, 71.27.+a
Low-dimensional quantum spin systems and
heavy-fermion systems are of a great interest of physi-
cists, because in those systems an interaction between
quantum particles plays an important role. Such an in-
teraction manifests itself in many characteristics of
those systems. It is important to point out that in
heavy-fermion systems, as well as in many compounds
with the properties of quantum spin chains, quantum
spin fluctuations often define their low-energy proper-
ties. For low-dimensional spin systems quantum spin
fluctuations are enhanced. According to the Mer-
min—Wagner theorem [1] isotropic Heisenberg mag-
nets have no magnetic order in one and two space di-
mensions at any nonzero temperature. In rare earth
and actinide compounds exhibiting properties of
heavy fermions [2] and so-called non-Fermi-liquids
[3] a hybridization of rare earth or actinide localized
electrons of 4f or 5f states with conduction electron
band(s) usually produces the Kondo effect [4], i.e.,
the screening of the spin of a localized electron (mag-
netic impurity) by spins of conduction electrons. In
heavy-fermion compounds it also gives rise to spin
fluctuations of localized spin moments, which are
completely screened below some characteristic energy
(the Kondo temperature, TK), i.e., the ground state is
a singlet with a finite magnetic susceptibility. Due to
this effect, effective masses of carriers are enhanced,
comparing to normal metals. It manifests itself in
large values of the low-temperature magnetic suscepti-
bility, linear in temperature Sommerfeld coefficient of
the electron specific heat, and low-temperature coeffi-
cient of the resistivity. Such a behavior can be de-
scribed in the framework of a standard Fermi liquid
theory [5] with a heavy effective electron mass. On
the other hand, for non-Fermi-liquid compounds the
magnetic susceptibility and the Sommerfeld coeffi-
cient of the specific heat are usually divergent at low
temperatures. It turns out that there is often no mag-
netic ordering in heavy-fermion systems (they are
metals with zero order parameter). However, very of-
ten, by tuning some parameters, like a concentration
of impurities, such systems are undergone phase tran-
sitions to ordered magnetic or superconducting states
[2,3]. Sometimes such phase transitions happen only
at zero temperature, i.e., they are quantum critical
transitions.
© A.A. Zvyagin and A.V. Makarova, 2004
In both of these two classes magnetic impurities play
an important role. For example, according to two
known scenarios the non-Fermi-liquid behavior in rare
earth and actinide compounds is caused either by the
so-called multi-channel Kondo effect (the spin of the
magnetic impurity is overscreened by spins of electrons
from several channels), or by the disorder in the distri-
bution of Kondo temperatures of magnetic impurities*.
The idea of (nonscreened) magnetic moments existing
in disordered metallic systems and quantum spin chains
has been formulated in [6–8]. It was proposed that the
change in interactions between the impurity sites and
the host spins can be considered as a modification of the
Kondo temperature. The same characteristic, i.e. TK ,
can be introduced for the description of the behavior of
magnetic impurities in quantum spin chains [8–10].
The random distribution of magnetic characteristics of
impurities renormalizes the single universal parameter,
TK , which characterizes the state of each magnetic im-
purity. Later it was pointed out that the problem of the
behavior of magnetic impurities with random distribu-
tions of their Kondo temperatures in metals can be
solved exactly, with the help of the Bethe ansatz
[8–10]. It was shown also [9–12] that distributions of
effective Kondo temperatures for each magnetic impu-
rity can cause divergencies of the magnetic susceptibil-
ity and the Sommerfeld coefficient of the specific heat
for quasi-one-dimensional organic conductors and
quantum spin chains, where such a behavior was obser-
ved experimentally [13–16]. To explain power law di-
vergencies of magnetic susceptibilities and Sommerfeld
coefficients of rare earth and actinide compounds, as
well as quasi-one-dimensional organic conductors and
quantum spin chains, it was necessary to use the distri-
bution of Kondo temperatures (the strong disorder dis-
tribution, for which «tails» were large enough), which
starts with the term P T G TK K( ) ( )� � �� � 1 (� � 1)
valid till some energy scale G for the lowest values of
TK [9,10,12]. Such a distribution was recently derived
from the first principles in [17].
Let us consider a number of quantum spin chains,
weakly coupled with each other (quasi-one-dimen-
sional system). Then the magnetic susceptibility of
the three-dimensional set of one-dimensional spin
chains is determined by the Dyson’s formula
�
�
�
set ( )
( )
( )
T
T
zJ T
�
� �
1
11
, (1)
where J� is the constant of the interaction between
spin chains, z is the number of the nearest neighbor-
ing chains, and �1 is the magnetic susceptibility of
the chain. In a similar way one can calculate the mag-
netic susceptibility of an ensemble of weakly coupled
between each other magnetic impurities in a metal (in
such a case �1 describes the magnetic susceptibility of
magnetic impurities in a metal without interaction
between them, and J� defines the interaction between
impurtities). Notice that the interaction between each
impurity and the host (a quantum spin chain, or a
metal for non-Fermi-liquid systems) is considered ex-
actly in our approach; it defines �1. Obviously, the
denominator in Eq. (1) becomes zero at the point of
the phase transition to a magnetically ordered state,
and the critical temperature is determined from the
condition: �1 1( )T zJc � � .
We know [18] that for a set of homogeneous quan-
tum spin chains the magnetic susceptibility �1 as a func-
tion of temperature has a maximum with the value (we
consider units in which g-factors and Bohr’s magneton
are equal to 1) ~ . /| |014 J , where J is the exchange con-
stant along the quantum spin chain. Hence, for weak
enough interactions J J z� � | |/ .014 the quasi-one-dimen-
sional spin system never undergoes a phase transition to
the ordered state. The same is true for spin chains with
single impurities and for spin chains with a weak disor-
der in the distribution of their Kondo temperatures: In
those cases the ground state is a singlet, and the mag-
netic susceptibility of those spin chains is finite at low
temperatures. Thus, for small enough values of
interchain couplings ( )J TK� � const , the denominator
in Eq. (1) never becomes zero, and there is no phase
transition to a magnetically ordered state. On the other
hand, for a strong disorder in the distribution of Kondo
temperatures of magnetic impurities in quantum spin
chains the magnetic susceptibility of each chain is diver-
gent at low temperatures, and any, even infinitely weak
interchain interaction has to produce a phase transition
to a magnetically ordered state. For example, for the
distribution of Kondo temperatures, derived in [17] the
magnetic susceptibility of a spin chain with disordered
magnetic impurities is � �
1
1� �T . This is why, the criti-
cal temperature of the magnetic transition can be esti-
mated as T zJc ~ ( ) /( )� �1 1 � . For the special case � � 0
one has �1 � � lnT and the critical temperature is ap-
proximately T /zJc ~ exp( )� �1 . Obviously, we can
made similar conclusions about the possibility of phase
transitions to magnetically ordered states for rare earth
or actinide compounds, which exhibit non-Fermi-liquid
behavior: Any, even infinitely weak interaction between
magnetic impurities with the strong disorder in the dis-
1096 Fizika Nizkikh Temperatur, 2004, v. 30, No. 10
A.A. Zvyagin and A.V. Makarova
* Another reason, which can cause the non-Fermi-liquid behavior, is the presence of a quantum critical point:
Fluctuations of an order parameter interact with itinerant electrons and can cause low-temperature divergencies of
thermodynamic characteristics [2,3].
tribution of their Kondo temperatures has to produce a
phase transition to a magnetically ordered state. On the
other hand, for heavy-fermion systems and for metals
with single Kondo impurities and impurities with a
weak disorder in the distribution of their Kondo tempe-
ratures there exist critical values of impurity-impurity
couplings J�. In those cases, if the coupling J� is smaller
than the critical one, the total system cannot undergo a
phase transition to a magnetically ordered phase. The
reason for weak inter-chain or impurity-impurity cou-
plings can be the magnetic dipole-dipole interaction,
present in any magnetic system; it is weak and long-range
one. Notice that the presence of a phase transition at low
temperatures Tc � 0 for rare earth or actinide systems
with non-Fermi-liquid behavior obviously questions the
applicability of the «quantum critical point» scenario in
those cases.
Summarizing, in this Letter we have shown that
due to a strong disorder in the distribution of charac-
teristics of magnetic impurities (Kondo temperatures)
in quantum spin chains and non-Fermi-liquid rare
earth and actinide compounds any weak interaction
between spin chains or between magnetic impurities in
non-Fermi-liquid systems can produce a phase transi-
tion to a magnetically ordered state. On the other
hand, for homogeneous spin chains, spin chains and
heavy-fermion systems with a weak disoder of the dis-
tribution of Kondo temperatures, there exists a criti-
cal value of the coupling, below which there is no such
a phase transition.
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Magnetic ordering caused by a disorder in quasi-one-dimensional spin systems
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