Self-consistent Renormalization Theory Research Articles

3D-Ising-type magnetic interactions stabilized by the extremely large uniaxial magnetocrystalline anisotropy in layered ferromagnetic Cr2Te3

We investigate the magnetocrystalline anisotropy, critical behavior, and magnetocaloric effect in ferromagnetic-layered Cr2Te3. We have studied the critical behavior around the Curie temperature (TC) using various techniques, including the modified Arrott plot (MAP), the Kouvel-Fisher method (KF), and critical isothermal analysis (CI). The derived critical exponents β = 0.353(4) and γ = 1.213(5) fall in between the three-dimensional (3D) Ising and 3D Heisenberg type models, suggesting complex magnetic interactions by not falling into any single universality class. On the other hand, the renormalization group theory, employing the experimentally obtained critical exponents, suggests 3D-Ising-type magnetic interactions decaying with distance as J(r) = r−4.89. We also observe an extremely large uniaxial magnetocrystalline anisotropy energy (MAE) of Ku = 2065 kJ/m3, the highest ever found in any CrxTey based systems, originating from the noncollinear ferromagnetic ground state as predicted from the first-principles calculations. The self-consistent renormalization theory (SCR) suggests Cr2Te3 to be an out-of-plane itinerant ferromagnet. Further, a maximum entropy change of -ΔSMmax≈ 2.08 J/kg − K is estimated around TC for the fields applied parallel to the c-axis.

Suppressed Fluctuations as the Origin of the Static Magnetic Order in Strained Sr_{2}RuO_{4}.

Combining first-principles density-functional calculations and Moriya's self-consistent renormalization theory, we explain the recently reported counterintuitive appearance of an ordered magnetic state in uniaxially strained Sr_{2}RuO_{4} beyond the Lifshitz transition. We show that strain weakens the quantum spin fluctuations, which destroy the static order, more strongly than the tendency to magnetism. A different rate of decrease of the spin fluctuations vs magnetic stabilization energy promotes the onset of a static magnetic order beyond a critical strain.

The case of itinerant magnetism in CaMn2Al10: self-consistent renormalisation (SCR) theory study

We have applied the powerful self-consistent renormalization theory of spin fluctuations for the system CaMn2Al10 discovered in 2015 and was conjectured to be an itinerant magnet. We have calculated the inverse static i.e. (paramagnetic) susceptibility and have compared it with the experimental data (Steinke et al 2015 Phys. Rev. B 92 020413). The agreement is very good. We have calculated spin fluctuations at various temperatures and have also estimated the strength of the electronic correlation i.e. (U = 0.3136 eV) in the Hubbard Hamiltonian. Based on our quantitative explanation of the inverse static i.e. (paramagnetic) susceptibility data within the framework of self-consistent renormalization theory, we can decisively conclude CaMn2Al10 exhibits the phenomena of itinerant magnetism. Further, our density functional theory (DFT) and DFT + U calculations corroborate the strong Mn-Al hybridization which is the key to the itinerant magnetism in this system. Our estimated correlations strength will provide a foundation for further studies of itinerant magnetism in this system.

Critical behavior in the van der Waals itinerant ferromagnet Fe4GeTe2

The critical phenomenon of the magnetic phase transition in the van der Waals itinerant ferromagnet ${\mathrm{Fe}}_{4}{\mathrm{GeTe}}_{2}$ has been investigated by measuring the dc magnetization. The compound undergoes a continuous paramagnetic to ferromagnetic phase transition at the Curie temperature ${T}_{C}=270.0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. A detailed analysis of magnetization isotherms measured in the vicinity of ${T}_{C}$ with magnetic field $H$ applied parallel to the $ab$ plane yields the asymptotic critical exponents $\ensuremath{\beta}=0.37, \ensuremath{\gamma}=1.20$, and $\ensuremath{\delta}=4.21$, whereas the magnetization isotherms for $H\ensuremath{\parallel}c$ yield $\ensuremath{\beta}=0.34, \ensuremath{\gamma}=1.20$, and $\ensuremath{\delta}=4.52$. Both sets of the critical exponents obey the scaling relation and scaling equation of the magnetic state predicted by the scaling theory. The renormalization group theory analysis for the critical exponents and the analysis based on the self-consistent renormalization theory of spin fluctuations manifest a quasi-two-dimensional itinerant magnetism in the ${\mathrm{Fe}}_{4}{\mathrm{GeTe}}_{2}$ single crystal where the magnetic exchange coupling $J(r)$ is the long-range type that decreases spatially slower than ${r}^{\ensuremath{-}4.76}$. Moreover, a small reduction in the value of $\ensuremath{\beta}$ for $H\ensuremath{\parallel}c$ attests to the observed weak effective uniaxial magnetic anisotropy of ${\mathrm{Fe}}_{4}{\mathrm{GeTe}}_{2}$.

Correlation between normal state properties and pairing mechanism

The physical quantities in the normal state of a superconductor provide the insight into pairing mechanism responsible for formation of copper pairs. This paper discuss the experimental evidences or physical properties in the normal state of a superconductor. Conventional superconductors show a fermi liquid behavior while a departure from fermi liquid behavior characterizes the unconventional nature of pairing. These anomalous variation in physical properties are well understood within the framework of self-consistent renormalization theory which incorporates the Antiferromagnetic spin fluctuations.

31P NMR studies of an iron-based superconductor Ba0.5Sr0.5Fe2(As1−x P x )2 with T c = 29 K

We report 31P NMR studies of an oriented polycrystalline superconductor of Ba0.5Sr0.5Fe2(As1−x P x )2 with x ∼ 0.4 (T c = 29 K) at T = 14−325 K and B 0 = 1 and 5 T. The 31P Knight shift Kab at B 0 ⊥ c shows a nearly T-independent uniform spin susceptibility above T c and a spin singlet decrease below T c. The 31P nuclear spin-lattice relaxation rate 1/T 1 shows an asymptotic behavior of a + bT (a and b are constants) at T > 100 K and the minimum at 40 K with an upturn toward T c. The a term in 1/T 1 indicates the presence of two-dimensional antiferromagnetic spin fluctuations. The negative θ = −15 K of the Curie-Weiss-type antiferromagnetic spin susceptibility in the analysis of 1/T 1 T suggests antiferromagnetic instability in the superconducting state. Discussions are made from the self-consistent renormalization (SCR) theory for the spin fluctuations with interlayer correlation.

Dual nature of magnetism in MnSi

The temperature dependence of the manganese magnetic moment and the spin-lattice relaxation rate measured by the muon spin relaxation technique in the magnetically ordered phase of the chiral intermetallic cubic MnSi system are both explained in terms of helimagnon excitations of a localized spin model. The two free parameters characterizing the helimagnon dispersion relation are determined. A combined analysis of the two data sets cannot be achieved using the self-consistent renormalization theory of spin fluctuations which assumes the magnetism of MnSi to arise uniquely from electronic bands. As a result of this work, MnSi is proposed to be a dual electronic system composed of localized and itinerant magnetic electrons. Finally we note that the analysis framework can be applied to other helimagnets such as the magnetoelectric compound Cu2OSeO3.

Coexistence of ferromagnetic fluctuations and superconductivity in the actinide superconductor UTe2.

We report low-temperature muon spin relaxation/rotation (μSR) measurements on single crystals of the actinide superconductor UTe2. Below 5 K we observe a continuous slowing down of magnetic fluctuations that persists through the superconducting transition temperature (T c = 1.6 K), but we find no evidence of long-range or local magnetic order down to 0.025 K. The temperature dependence of the dynamic relaxation rate down to 0.4 K agrees with the self-consistent renormalization theory of spin fluctuations for a three-dimensional weak itinerant ferromagnetic metal. Our μSR measurements also indicate that the superconductivity coexists with the magnetic fluctuations.

Grüneisen parameter and thermal expansion near magnetic quantum critical points in itinerant electron systems

Complete expressions of the thermal-expansion coefficient $\alpha$ and the Gr\"{u}neisen parameter $\Gamma$ are derived on the basis of the self-consistent renormalization (SCR) theory. By considering zero-point as well as thermal spin fluctuation under the stationary condition, the specific heat for each class of the magnetic quantum critical point (QCP) specified by the dynamical exponent $z=3$ (FM) and $z=2$ (AFM) and the spatial dimension ($d=3$ and $2$) is shown to be expressed as $C_{V}=C_a-C_b$, where $C_a$ is dominant at low temperatures, reproducing the past SCR criticality endorsed by the renormalization group theory. Starting from the explicit form of the entropy and using the Maxwell relation, $\alpha=\alpha_a+\alpha_b$ (with $\alpha_a$ and $\alpha_b$ being related to $C_a$ and $C_b$, respectively) is derived, which is proven to be equivalent to $\alpha$ derived from the free energy. The temperature-dependent coefficient found to exist in $\alpha_b$, which is dominant at low temperatures, contributes to the crossover from the quantum-critical regime to the Curie-Weiss regime and even affects the quantum criticality at 2d AFM QCP. Based on these correctly calculated $C_{V}$ and $\alpha$, Gr\"{u}neisen parameter $\Gamma=\Gamma_a+\Gamma_b$ is derived, where $\Gamma_a$ and $\Gamma_b$ contain $\alpha_a$ and $\alpha_b$, respectively. The inverse susceptibility coupled to the volume $V$ in $\Gamma_b$ gives rise to divergence of $\Gamma$ at the QCP for each class even though characteristic energy scale of spin fluctuation $T_0$ is finite at the QCP, which gives a finite contribution in $\Gamma_a=-\frac{V}{T_0}\left(\frac{\partial T_0}{\partial V}\right)_{T=0}$. General properties of $\alpha$ and $\Gamma$ including their signs as well as the relation to $T_0$ and the Kondo temperature in temperature-pressure phase diagrams of Ce- and Yb-based heavy electron systems are discussed.

Forced magnetostriction of ferromagnetic Heusler alloy Ni2MnGa at the Curie temperature

An investigation on the relationship between magnetostriction and magnetization by means of the self-consistent renormalization (SCR) theory of an itinerant ferromagnet was performed for Ni2MnGa alloy. The magnetization results at the Curie temperature TC suggest that the critical index δ of H ∝ Mδ is 4.7–5.0, and this confirms Takahashi's spin fluctuation theory and the result of Nishihara et al. As a result, at TC, the relation between magnetostriction and M2 deviates from proportionality and the magnetostriction is proportional to M4. At TC, the plot of ΔL/L vs M4 crossed the point of origin. This result is in accordance with Takahashi's spin fluctuation theory.

Grüneisen Parameter and Thermal Expansion by the Self-Consistent Renormalization Theory of Spin Fluctuations

The thermal expansion coefficient $\alpha$ and the Gr\"{u}neisen parameter $\Gamma$ near the magnetic quantum critical point (QCP) are derived on the basis of the self-consistent renormalization (SCR) theory of spin fluctuation. From the SCR entropy, the specific heat $C_{V}$, $\alpha$, and $\Gamma$ are shown to be expressed in a simple form as $C_{V}=C_{\rm a}-C_{\rm b}$, $\alpha=\alpha_{\rm a}+\alpha_{\rm b}$, and $\Gamma=\Gamma_{\rm a}+\Gamma_{\rm b}$, respectively, where $C_{\rm i}$, $\alpha_{\rm i}$, and $\Gamma_{\rm i}$ $({\rm i}={\rm a}, {\rm b})$ are related with each other. As the temperature $T$ decreases, $C_{\rm a}$, $\alpha_{\rm b}$, and $\Gamma_{\rm b}$ become dominant in $C_{V}$, $\alpha$, and $\Gamma$, respectively. The inverse susceptibility of spin fluctuation coupled to the volume $V$ in $\Gamma_{\rm b}$ is found to give rise to the divergence of $\Gamma$ at the QCP for each class of ferromagnetism and antiferromagnetism (AFM) in spatial dimensions $d=3$ and $2$. This $V$-dependent inverse susceptibility in $\alpha_{b}$ and $\Gamma_{\rm b}$ contributes to the $T$ dependences of $\alpha$ and $\Gamma$, and even affects their criticality in the case of the AFM QCP in $d=2$. $\Gamma_{\rm a}$ is expressed as $\Gamma_{\rm a}(T=0)=-\frac{V}{T_0}\left(\frac{\partial T_0}{\partial V}\right)_{T=0}$ with $T_0$ being the characteristic temperature of spin fluctuation, which has an enhanced value in heavy electron systems.

Effect of Co substitution on the magnetic properties in Fe1−xCoxGa3

We investigated the effect of Co substitution in Fe1−xCoxGa3 by means of electric resistivity and magnetic measurements. Nearly ferromagnetic behaviors were observed in Fe1−xCoxGa3 system by the chemical substitution of Co for Fe in diamagnetic mother compound FeGa3, accompanying with a semiconducting to metallic transition. With the substitution of Co, the magnetization of Fe1−xCoxGa3 increases first, and then decreases and finally it becomes diamagnetic. The magnetic properties of Fe1−xCoxGa3 were analyzed in terms of self-consistent renormalization (SCR) theory and Takahashi’s theory. The spin-fluctuation parameters, fourth order expansion coefficients of magnetic free energy (), the magnetic susceptibility in the ground state X(0), the spectral widths of the spin fluctuation spectrum T0 and Ta in the frequency and wave-number spaces, respectively, were estimated from the parameters derived from magnetic measurements. The magnetic properties of Fe1−xCoxGa3 can be understood almost quantitatively by the SCR theory and Takahashi’s theory of spin fluctuations.

Towards ferromagnetic quantum criticality inFeGa3−xGex:Ga71NQR as a zero-field microscopic probe

$^{71}\mathrm{Ga}$ NQR, magnetization, and specific-heat measurements have been performed on polycrystalline Ge-doped ${\mathrm{FeGa}}_{3}$ samples. A crossover from an insulator to a correlated local moment metal in the low-doping regime and the evolution of itinerant ferromagnet upon further doping is found. For the nearly critical concentration at the threshold of ferromagnetic order, ${x}_{C}=0.15, ^{71}(1/{T}_{1}T)$ exhibits a pronounced ${T}^{\ensuremath{-}4/3}$ power law over two orders of magnitude in temperature, which indicates three-dimensional quantum critical ferromagnetic fluctuations. Furthermore, for the ordered $x=0.2$ sample (${T}_{C}\ensuremath{\approx}6$ K), $^{71}(1/{T}_{1}T)$ could be fitted well in the frame of Moriya's self-consistent renormalization theory for weakly ferromagnetic systems with $1/{T}_{1}T\ensuremath{\sim}\ensuremath{\chi}$. In contrast to this, the low-doping regime nicely displays local moment behavior where $1/{T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}^{2}$ is valid. For $T\ensuremath{\rightarrow}0$, the Sommerfeld ratio $\ensuremath{\gamma}=(C/T)$ is enhanced $(70\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}/\mathrm{mole}\phantom{\rule{0.28em}{0ex}}{\mathrm{K}}^{2}$ for $x=0.1)$, which indicates the formation of heavy $3d$ electrons.

Static and dynamical magnetic properties of the itinerant ferromagnetLaCo2P2

We synthesized single crystals of an itinerant ferromagnet ${\mathrm{LaCo}}_{2}{\mathrm{P}}_{2}$ with ${\mathrm{ThCr}}_{2}{\mathrm{Si}}_{2}$-type structure and studied their magnetism by magnetization and ${}^{31}\mathrm{P}$ NMR measurements. We measured Knight shift $K$ and spin-lattice relaxation rate divided by temperature $1/{T}_{1}T$ with the applied fields parallel to the $a$ and $c$ axes, and estimated spin fluctuations in the $ab$ plane and $c$. In addition, we evaluated spin fluctuations from the result of magnetization data with a three-dimensional ferromagnetic model. There is little anisotropy in evaluated spin fluctuations in the $ab$ plane and $c$. Spin fluctuations of ${\mathrm{LaCo}}_{2}{\mathrm{P}}_{2}$ have a three-dimensional character and can be understood in the framework of the self-consistent renormalization theory of spin fluctuations.

Weak itinerant antiferromagnetism in PuIn3 explored using 115In nuclear quadrupole resonance

The results of 115In nuclear quadrupole resonance (NQR) measurements on PuIn3 are reported. Three of the four NQR lines of 115In expected for nuclear spin I = 9/2 are observed. The equal spacing of these lines at 20 K yields the NQR frequency of νQ = 10.45 MHz, and the asymmetry parameter of the electric field gradient η = 0. The NQR line profile and the nuclear spin–lattice relaxation rate 1/T1 display an abrupt change at 14 K, which is associated with the onset of long-range antiferromagnetic order. The temperature dependences of the staggered magnetization MQ(T), extracted from the NQR spectra, and 1/T1 below TN = 14 K are well explained by the self-consistent renormalization (SCR) theory for spin fluctuations. In addition, the scaling between T1T and MQ(T)/MQ(0) is also consistent with the predictions of SCR theory, providing further evidence that PuIn3 is a weak itinerant antiferromagnet in which spin fluctuations around the antiferromagnetic wavevector play a major role in the system’s behavior at finite temperatures.

Magnetic properties in layeredACo2Se2(A =K, Rb, Cs) with the ThCr2Si2-type structure

The magnetic properties of ThCr${}_{2}$Si${}_{2}$-type single crystals $A$Co${}_{2}$Se${}_{2}$ ($A=\text{K}$, Rb, and Cs) were investigated by means of magnetic susceptibilities and isothermal magnetizations measurements. The ferromagnetic phase transition temperatures are $\ensuremath{\approx}$74 and 76 K for $A=\text{K}$ and Rb, respectively. A possible antiferromagnetic phase transition occurs around 80 K in susceptibility and a metamagnetismlike behavior is first discovered at a field of $\ensuremath{\approx}$3.5 T for $H\ensuremath{\parallel}ab$ plane in CsCo${}_{2}$Se${}_{2}$ below 62 K. The susceptibilities in the paramagnetic state obey the modified Curie-Weiss law quite well in all samples. Moreover, the derived effective magnetic moments of the Co atom are about 2.21, 2.04, and 2.04 ${\ensuremath{\mu}}_{B}$/Co for $A=\text{K}$, Rb, and Cs, respectively. The generalized Rhodes-Wohlfarth ratio indicates an itinerant magnetism in this series. Finally, we discussed the magnetic properties in this series within the frameworks of the self-consistent renormalization and Takahashi's theory of spin fluctuations.

Local electromagnetic properties of magnetic pnictides: a comparative study probed by NMR measurements

75As and 31P NMR studies are performed in PrCoAsO and NdCoPO respectively. The Knight shift data in PrCoAsO indicate the presence of an antiferromagnetic interaction between the 4f moments along the c axis in the ferromagnetic state of Co 3d moments. We propose a possible spin structure in this system. The 75As quadrupolar coupling constant, νQ, increases continuously with decrease of temperature and is found to vary linearly with the intrinsic spin susceptibility, Kiso. This indicates the possibility of the presence of a coupling between charge density and spin density fluctuations. Further, the 31P NMR Knight shift and spin–lattice relaxation rate (1/T1) in the paramagnetic state of NdCoPO indicate that the differences of LaCoPO and NdCoPO from SmCoPO are due to the decrement of the interlayer separation and not due to the moments of the 4f electrons. The nuclear spin–lattice relaxation time (T1) in NdCoPO shows weak anisotropy at 300 K. Using the self-consistent renormalization (SCR) theory of itinerant ferromagnets, it is shown that in the ab plane, the spin fluctuations are three-dimensional ferromagnetic in nature. From SCR theory the important spin-fluctuation parameters (T0, TA, ) are evaluated. The similarities and dissimilarities of the NMR results in As and P based systems with different rare earths are also discussed.

Muon spin relaxation and susceptibility measurements of an itinerant-electron system Sr1−xCaxRuO3: Quantum evolution from ferromagnet to paramagnet

Muon spin relaxation ($\ensuremath{\mu}$SR) and magnetic susceptibility measurements have been performed in the itinerant-electron magnet Sr${}_{1\ensuremath{-}x}$Ca${}_{x}$RuO${}_{3}$, with $x=$ 0.0, 0.3, 0.5, 0.65, 0.7, 0.75, 0.8, 0.9, and 1.0. SrRuO${}_{3}$ is a ferromagnet with the critical temperature ${T}_{c}\ensuremath{\sim}160$ K. Upon (Sr, Ca) substitution, ${T}_{c}$ decreases monotonically with increasing Ca concentration $x$ and the ferromagnetic order disappears around $x=$ 0.7. Very weak static magnetism is observed in the $x=$ 0.75 and 0.8 systems, while the $x=$ 0.9 and 1.0 systems remain paramagnetic in their full volume. Phase separation between volumes with and without static magnetism was observed in the $x=$ 0.65, 0.7, 0.75, and 0.8 systems, near the magnetic crossover around $x=$ 0.7. In this concentration region, $\ensuremath{\mu}$SR measurements revealed discontinuous evolution of magnetic properties in contrast to magnetization measurements, which exhibit seemingly continuous evolution. Unlike the volume-integrated magnetization measurements, $\ensuremath{\mu}$SR can separate the effects of the ordered moment size and the volume fraction of magnetically ordered regions. The muon spin relaxation rate $1/{T}_{1}$ exhibits critical slowing down of spin fluctuations near ${T}_{c}$ in the ferromagnetic systems with $x=$ 0.0--0.65, consistent with the behavior expected in the self-consistent renormalization theory of itinerant electron ferromagnets. The lack of maximum of $1/{T}_{1}$ in the $x=$ 0.7 system indicates the disappearance of critical slowing down. These results demonstrate a first-order quantum evolution in the ferromagnet to paramagnet crossover near $x=$ 0.7.

Anisotropic and excellent magnetocaloric properties of La0.7Ca0.3MnO3 single crystal with anomalous magnetization

Abstract Magnetic properties and the magnetocaloric effect (MCE) have been investigated in La 0.7 Ca 0.3 MnO 3 single crystal with applied field along both the ab -plane and the c -direction. Due to the magnetocrystalline anisotropy, the crystal exhibits anisotropy in the MCE. Upon application of a 5 T field, the magnetic entropy changes (Δ S M ), reaching values of 7.668 J/(kg K) and 6.412 J/(kg K) for both the ab -plane and the c -direction, respectively. A magnetic entropy change of 3.3 J/(kg K) was achieved for a magnetic field change of 1.5 T at the Curie temperature, T C = 245 K. Due to the absence of grains in the single crystal, the Δ S M distribution here is much more uniform than for gadolinium (Gd) and other polycrystalline manganites, which is desirable for an Ericsson-cycle magnetic refrigerator. For a field change of 5 T, the relative cooling power, RCP, reached 358.17 J/kg, while the maximum adiabatic temperature change of 5.33 K and a magnetoresistance (MR) ratio of 507.88% at T C were observed. We analysed the magnetization of La 0.7 Ca 0.3 MnO 3 single crystal at T C and estimated several parameters of spin fluctuation on the basis of a self-consistent renormalization theory of spin fluctuations, with reciprocal susceptibility above T C . We found that the magnetic property of La 0.7 Ca 0.3 MnO 3 is weakly itinerant ferromagnetic. A large reversible MCE and no hysteresis loss with a considerable value of refrigerant capacity indicate that La 0.7 Ca 0.3 MnO 3 single crystal is a potential candidate as a magnetic refrigerant.

Enhancement of the Curie temperature in small particles of weak itinerant ferromagnets

Self-consistent renormalization theory of itinerant ferromagnets is used to calculate the Curie temperature of clusters down to approximately 100 atoms in size. In these clusters the electrons responsible for the magnetic properties are assumed to be (weakly) itinerant. It is shown that the Curie temperature can be larger than in the bulk. The effect originates from the phenomenon of level repulsion in chaotic quantum systems, which suppresses spin fluctuations. Since the latter destroy the magnetic order the resulting Curie temperature increases, contrary to expectations of the na\"{\i}ve Stoner picture. The calculations are done assuming that the energy levels of the cluster are described by the Gaussian Orthogonal Ensemble of random matrix theory.