# Quantum Ferromagnetism and Related Phenomena

For each poster contribution there will be one poster wall (width: 97 cm, height: 250 cm) available. Please do not feel obliged to fill the whole space. Posters can be put up for the full duration of the event.

During the  a committee will choose three poster contributions to receive a poster prize. The final announcement will be made at the workshop dinner on Thursday, 9th May.

### Ferromagnetism in alternating Hubbard ladder

Abdelwahab, Anas

We study alternating 3-leg ladder of bipartite lattice where the number of sites in the first leg alternate every one, two or three rungs. The ladder is described using the Hubbard model. We use the Density Matrix Renormalization Groupe (DMRG) method to determine ground state properties, eg. excitation gaps, charge and spin densities as well as correlation functions at half-filling. We investigate the ladder properties for the noninteracting case and various values of $U$ and hopping terms. We analyze our results in the light of Lieb's theorem of ferromagnetism in bipartite lattice.

### Quantum Critical Phenomena in Ce-based Heavy Fermion Systems with two inequivalent Ce-sites.

Custers, Jeroen

Strongly correlated electron systems with competing interactions provide a fertile ground for discovering exotic states of matter. As a particularly interesting setting we study heavy fermion (HF) systems with two crystallographically inequivalent local moment sites. These may lead to the formation of two Kondo sublattices with largely different Kondo temperatures. We expect such systems to show better tunability towards various kinds of quantum phase transitions than single-site Kondo systems, and to form novel phases. Pressing questions are: Do the two Kondo scales compete or cooperate? Can the interplay lead to Kondo breakdown, partially screened phases, or even fractionalized Fermi liquids? Answers to these and related questions will represent important progress in the fields of HF physics and quantum matter in general. Here we present results on ongoing research on several Ce-based heavy-fermion compounds exhibiting two inequivalent Ce-sites. The most prominent one is Ce$_3$PtIn$_{11}$. The compound crystallizes in the typical tetragonal structure (space group $P4/mmm$) based on the AuPt$_3$-type (CeIn$_3$-block) and PtHg$_2$-type ($T$In$_2$ with $T =$ transition metal) units alternating along the $c$-axis. Ce$_3$PtIn$_{11}$ possesses two inequivalent crystallographic Ce-sites with the Ce1-site occupying the Wyckoff $2g$ position ($4mm$ ($C_{4v}$) symmetry) and the Ce2 resides at $1a$ ($4/mmm$ ($D_{4h}$)) and hence each site spans a layer of equivalent Ce-ions. The Ce2-site experiences a CeIn$_3$ environment, whereas the Ce1-site's surrounding atoms are identical with those Ce-ions in Ce$_2$PtIn$_8$. At ambient pressure the compound exhibits two successive transitions at $T_1 = 2.2$K and $T_N$ = 2K into a possible incommensurate (iAFM) and commensurate (AFM) local moment AFM state, respectively, before becoming superconducting below $T_c$ = 0.32K. A careful entropy analysis promotes the idea that one Ce-sublattice (Ce2) is responsible for the magnetic ordering whereas the second one (Ce1) carries the heavy quasiparticle state. In analogy to UPd$_2$Al$_3$ we conjecture that the unconventional superconductivity originates from the exchange interactions between these two subsystems. The increase of $T_c$ around the compound’s quantum critical point which can be reached by an applied hydrostatic pressure of $p_{c2}$ = 1.5GPa is further evidence for a magnetic origin of the Cooper-pairing. This work is supported by the Czech Science Foundation (GA\v{C}R) under grant number 19-23606S.

### Complex Size-dependence of Oscillating Clusters near Metamagnetic Phase Transitions

Ganesh Hegde, Nagabhushan

$Ca_​3​Co_​2​O_​6$​ is a frustrated Ising-like magnet with uniaxial anisotropy along its crystallographic c-axis. Magnetic field applied along this axis induces a metamagnetic transition with the occurrence of a magnetization plateau at ⅓ of the maximum magnetization. We aim to understand the dynamics of this transition using bulk and microscopic methods, and eliminate compound specific features to identify universal aspects behind them. Here we present a preliminary analysis based on magnetization and AC susceptibility. $(\frac{dM}{dH})_{max}$ calculated from the magnetization measurements were not reflected in AC susceptibility​ indicating complex size-dependence of oscillating clusters. Using these techniques we are currently determining the average size and distribution of magnetic clusters near metamagnetic phase transitions.

### Kondo-lattice ferromagnets and their peculiar order along the magnetically hard axis

Hafner, Daniel

We show that magnetic moments in Ce- and Yb- based Kondo-lattice systems often align spontaneously along the magnetically hard axis of the crystalline electric field (CEF). This counterintuitive phenomenon was believed to be a rare case, but our comparative study suggests that this is rather the general case in these materials. We discuss and review the proposed theoretical scenarios for this kind of perpendicular order by analyzing differences and similarities between all these systems. Differences appear in properties such as Curie temperatures TC, crystalline structures, size of the ordered moment and CEF ground state, while similarities lie in a usual Kondo temperature TK of a few Kelvin, a comparable magnetic anisotropy and a non mean-field like transition in specific heat, hinting at an important role of fluctuations.

### Interplay of Itinerant and Localized Spin Fluctuations in the Ferromagnetic Superconductor UGe$_2$

Haslbeck, Franz

Magnetic quantum critical points (QCP) which occur at zero temperature and as function of a non-thermal control parameter such as doping, pressure or magnetic field are associated with an abundance of critical fluctuations. It is widely believed that these fluctuations are crucial for the emergence of novel states of matter such as nematic electronic textures or unconventional superconductivity. However, their exact nature remains an outstanding question. Most notably, according to theory both the relaxation time and correlation length of the fluctuations are expected to diverge when the QCP is approached. However, to date this has not yet been observed, partially because this requires extreme energy and momentum transfer resolution. For ferromagnetic QCPs this problem may be overcome using the newly developed longitudinal MIEZE (Modulated Intensity by Zero Effort) option available at the instrument RESEDA at MLZ (Garching) that achieves ultra-high energy resolution of 1μeV or better. Using this approach, we have investigated the magnetic fluctuations in the heavy fermion system UGe$_2$ at ambient pressure. Microscopic coexistence of ferromagnetism and unconventional superconductivity renders UGe$_2$ a candidate for spin-triplet superconductivity. To avoid pair-breaking, spin-triplet superconductivity is mediated by longitudinal spin fluctuations. This results in at least partially contradicting requirements; longitudinal spin fluctuations are typically promoted by magnetic Ising anisotropy that arises from localized electrons due to spin-orbit coupling; at the same time the formation of Cooper pairs typically involves spin fluctuations arising from itinerant electrons. Our ultra-high neutron spectroscopy measurements show—for the first time—that this dichotomy may drive spin-triplet superconductivity in UGe$_2$. Notably, they reveal purely longitudinal spin fluctuations in UGe$_2$ with a dual nature arising from 5f electrons that are neither fully itinerant nor fully localized. Local spin fluctuations are perfectly described by the Ising universality class in three dimensions, whereas itinerant spin fluctuations occur over length scales comparable to the superconducting coherence length.

### Dynamic Structure Factor of Disordered Coupled-Dimer Heisenberg models

Hörmann, Max

We investigate the impact of quenched disorder on the zero-temperature dynamic structure factor of coupled-dimer Heisenberg models on the two-leg ladder and the two-dimensional square lattice bilayer. Using perturbative continuous unitary transformations, huge effects on individual quasiparticles but also on composite bound states and two-quasiparticle continua are observed [1]. This leads to intriguing quantum structures in dynamical correlation functions well observable in spectroscopic experiments. M. Hörmann, P. Wunderlich, K. P. Schmidt, Phys. Rev. Lett. 121, 167201 (2018)

### Poor man’s scaling and Lie algebras

Kogan, Eugene

We consider a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, derive the scaling equation and analyse the connection between its explicit form and the symmetry of interaction. On the basis of this analysis we write down explicitly the scaling equation for the interaction acting on $su$(3) Lie algebra and having either $SU$(2) × $U$(1), or $SU$(2) symmetry.

### Multistage Magnetic Detwinning in Eu-based Iron Pnictides

Maiwald, Jannis

Detwinning of magnetic (nematic) domains in Fe-based superconductors has so far only been obtained through mechanical straining, which considerably perturbs the ground state of these materials. The recently discovered nonmechanical detwinning in EuFe$_2$As$_2$ by ultralow magnetic fields offers an entirely different, nonperturbing way to achieve the same goal. However, this way seemed risky due to the lack of a microscopic understanding of the magnetically driven detwinning. Specifically, the following issues remained unexplained: (i) ultralow value of the first detwinning field of approximately 0.1 T, two orders of magnitude below that of BaFe$_2$As$_2$, and (ii) reversal of the preferential domain orientation at approximately 1 T and restoration of the low-field orientation above 10–15 T. On my poster I will present the observed effect as well as a microscopic theory that we recently developed and which quantitatively explains the experimental observations in full. The key ingredient of this theory is a biquadratic coupling between Fe and Eu spins, analogous to the Fe-Fe biquadratic coupling that drives the nematic transition in this family of materials.

### Emergent Random Fields in Frustrated Magnets

Narayanan, Rajesh

A variety of quantum materials hosts low temperature ground states that breaks real space symmetries in addition to the usual symmetries such as spin or phase or gauge symmetries. Notable examples of such states in correlated systems include the stripe phase in superconductors or the Ising nematic state in pnictides. In this talk we investigate the effect of quenched disorder on such ground states which break real space symmetry. By utilizing a simple generalisation of the Ising model called the frustrated $\rm{J_1}-\rm{J_2}$ model we show that uncorrelated disorder is deeply inimical to states that break real space symmetry, leading to its destruction via an emergent random field mechanism. We also show that such symmetry states can be made impervious to disorder fluctuations by building in anti-correlations into the disorder distribution. In other words, the strength of the random field can be tuned to zero via building anticorrelations in the distribution of impurity atoms thereby protecting the states that break real space symmetry.

### Tuning competing ground states in $LuFe_4Ge_2$ using external pressure

Nicklas, Michael

Exotic phenomena and unconventional phases occur at regions of competing energy scales in correlated materials, especially in systems with magnetic frustration. Here, we investigate $LuFe_4Ge_2$ under external pressure in order to better understand the interplay between competing ground states. $LuFe_4Ge_2$ is a frustrated, itinerant magnetic system with antiferromagnetic (AFM) ordering accompanied by a structural transition at 36 K. The pressure dependence of the magneto-elastic transition in $LuFe_4Ge_2$ has been investigated using electrical transport, ac magnetic susceptibility, X-ray diffraction, Mössbauer, and muon-spin resonance ($\mu$SR) measurements under external pressure. External pressure suppresses the first-order magnetic transition (AFM1) at around 1.8 GPa, while the structural transition is largely unaffected by pressure. A new magnetic pressure-induced phase coupled to the structural transition is confirmed by Mössbauer and $\mu$SR experiments. $\mu$SR data reveal that the full sample volume in the pressure-induced phase is long-range magnetically ordered. Mössbauer investigations at 2.9 GPa and in magnetic field indicate that the high pressure phase is also antiferromagnetically ordered (AFM2). In addition, different hyperfine magnetic fields obtained from Mössbauer data in the AFM1 and in the AFM2 region point at a different size of the ordered moment and/or a different magnetic structure in the two regions.

### Magnetic excitations and quantum criticality in spin-chain antiferromagnet YbAlO$_3$

Nikitin, Stanislav

Low-dimensional quantum magnets are interesting because of the emerging collective behavior arising from strong quantum fluctuations. The one-dimensional (1D) $S~=~1/2$ Heisenberg antiferromagnet is a paradigmatic example, whose low-energy excitations, known as spinons, carry fractional spin $S~=~1/2$. Although the considerable progress has been made in the theoretical understanding of one of the simplest quantum many-body systems, good experimental realizations of this model are rare. In this work we explored magnetic excitation spectra and thermodynamic properties of quasi-1D compound, YbAlO$_3$. We found that the material exhibits rather unusual combination of the physical properties: locally, Yb moments have enormous Ising-like anisotropy of $g$-tensor, whereas the Yb-Yb interchain exchange interaction is highly isotropic. This combination along with 1D character of the YbAlO$_3$ give a rise to the gapless spinon continuum above the ordering temperature of $T_{\rm N}~=~0.88$~K, whereas at the ordered phase spinons get confined because of the dipole-dipole intrachain interaction. Application of magnetic field, at first, stabilizes an incommensurate spin-density-wave-like phase, and then induces a quantum phase transition to the field-polarized state. Remarkably, thermodynamic properties of YbAlO$_3$ follow a universal behavior near the QCP and the analysis of the scaling behavior and critical exponents indicates that the quantum critical point is a free fermion fixed point, consistently with expectation for the 1D Tomonaga-Luttinger liquid. Our results represent an intriguing case of quantum spin dynamics in 4$f$-based systems and provide a new experimental system for the future studies of low-dimensional magnets.

### Discontinuous magnetic phase diagram of UCo$_{1-x}$Ru$_{x}$Al compounds

Opletal, Petr

UCoAl is an itinerant 5f-electron paramagnet with metamagnetic transition and one of the compounds exhibiting the metamagnetic part of discontinuous phase diagram [1-3]. The ferromagnetic transition and tricritical point is predicted to appear at “negative” pressures [4]. Application of uniaxial pressure [5] or doping by some transition metals [6] induces a ferromagnetic order at low temperatures.. We will present results of UCo$_{0.990}$Ru$_{0.010}$Al and UCo$_{0.995}$Ru$_{0.005}$Al on single crystals. UCo$_{0.990}$Ru$_{0.010}$Al is a ferromagnet with T$_{C}$ = 16 K whereas UCo$_{0.995}$Ru$_{0.005}$Al appears in an intermediate state near a first order transition with T$_{C}$ ~ 4.5K [7]. We present results of magnetic and electrical-transport measurement in ambient and high hydrostatic pressure. We examine evolution and disappearance of metamagnetic transition with increasing hydrostatic pressure and discuss together results on UCoAl published in literature. 1. Sechovsky, V., et al., Systematics across the UTX series (T = Ru, Co, Ni; X = Al, Ga, Sn) of high-field and low-temperature properties of non-ferromagnetic compounds. Physica B+C, 1986. 142(3): p. 283-293. 2. Aoki, D., et al., Ferromagnetic Quantum Critical Endpoint in UCoAl. Journal of the Physical Society of Japan, 2011. 80(9). 3. Kimura, N., et al., Quantum critical point and unusual phase diagram in the itinerant-electron metamagnet UCoAl. Physical Review B, 2015. 92(3): p. 035106. 4. Mushnikov, N.V., et al., Magnetic properties of the 5f itinerant electron metamagnet UCoAl under high pressure. Physical Review B, 1999. 59(10): p. 6877-6885. 5. Ishii, Y., et al., Ferromagnetism induced in UCoAl under uniaxial pressure. Physica B: Condensed Matter, 2003. 334(1–2): p. 160-166. 6. Sechovsky, V. and L. Havela, Chapter 1 Magnetism of ternary intermetallic compounds of uranium, in Handbook of Magnetic Materials, K.H.J. Buschow, Editor. 1998, Elsevier. p. 1-289. 7. Opletal, P., et al., Quantum ferromagnet in the proximity of the tricritical point. npj Quantum Materials, 2017. 2(1): p. 29.

### Emergent U(1) Symmetry in a 2D Quantum Clock Model

Patil, Pranay

We propose a quantum clock model on the square lattice built out of a q-state classical clock model with a quantum fluctuation (a generalization of a transverse field) added to it. We see evidence that this model is closely related to the 3D classical clock model through the standard quantum to classical mapping. For q >= 5, we see a continuous phase transition and for q = 6 we show that, at the phase transition, an emergent U(1) symmetry appears, similar to the 3D classical clock models. We address the connection that this emergent symmetry has to a second length scale within the scenario of dangerously irrelevant perturbations of the XY model.

### Quantum fluctuations and magnetic phase transitions in $Fe_xMn_{1-x}Si$

Povzner, Aleksandr

The investigation of the quantum spin fluctuations in chiral helicoidal ferromagnets $Fe_xMn_{1-x}Si$ are based on the direct calculations of the electronic structure. It is shown that the disappearance of the helicoidal long-range order is accompanied by the appearance of a crossover of thermodynamic and quantum transitions with a sharp decrease in the local magnetization and amplitude of zero fluctuations. The suppression of local magnetization by quantum spin fluctuations leads to a concentration-temperature magnetic transition with the disappearance of the helicoidal short-range order. The results of calculations of the local magnetization of the compositions $Fe_xMn_{1-x}Si$ show that at 0.12 $\less$x $\le3ss$0.20 the magnetic state in the thermodynamic limit is characterized by short-range (and not long-range) helicoidal order.

### Single-particle properties of the antiferromagnetic quantum critical metal: From cold to lukewarm to hot electrons

Schlief Raether, Andrés Felipe

We study the single-particle properties of hot, lukewarm and cold electrons that coexist in the two-dimensional antiferromagnetic quantum critical metal within a unified theory. We generalize the theory that describes the interaction of critical spin-density wave fluctuations and electrons near the hot spots on the Fermi surface (hot electrons) by including electrons far away from the hot spots (lukewarm and cold electrons). In doing so, we engineer an analytically tractable functional renormalization group scheme that provides an exact universal description of electrons on extended regions of the Fermi surface. We show that low-energy electrons are characterized by a universal momentum-dependent quasi-particle weight that decays to zero as the hot spots are approached along the Fermi surface, owing to the coexistence of quasiparticle and non-quasiparticle excitations within the same metallic state. We further characterize how the global shape of the Fermi surface is renormalized due to the strong interaction between the electrons and the critical spin fluctuations. These predictions are testable through angle-resolved photoemission spectroscopy (ARPES). This work provides a general framework for theories of metals with or without quasiparticles whose universal low-energy properties are phrased in terms of an infinite number of low-energy degrees of freedom. Finally, some comments on the two-particle properties of the state will be provided with special emphasis on the superconducting instability of the system.

### Spin Density Wave and Vector Chiral Order in the Heisenberg Model for $\beta$-TeVO$_4$

Singhania, Ayushi

Frustrated spin systems hosts variety of magnetic phases which appear due to a combination of lattice geometry and competing interactions. One dimensional fustrated spin models provides platform to study such unconventional orders with high accuracy. The simplest frustrated spin system is a zigzag spin-1/2 chain with competing nearest neighbor (J$_1$) and next nearest neighbor interactions (J$_2$). Magnetic phase diagram of this model in the limit where J1 is ferromagnetic and J2 is antiferromagnetic is studied using sophisticated theoretical tools such as DMRG, bosoniation, etc. The phase diagram is rich and includes phases with spin density waves, vector chiral and multipolar ordering. Numerous materials are believed to be close realizations of this model, e.g. LiCuVO$_4$, PbCu(OH)$_2$SO$_4$, β-TeVO$_4$, etc. While theoretical results have provided some insight, the effect of inter-chain coupling, temperature and magnetic field is not completely understood for real materials. Here, we attempt to provide understanding of the magnetic phase diagram of β-TeVO$_4$ obtained experimentally [1,2]. We use cluster mean field approach to capture quantum correlations, and show that the high-temperature paramagnet gives way to a spin-density wave phase and finally to a vector chiral ordered state upon reducing temperature. Magnetic field and anisotropy effects in the minimilistic two-dimensional Heisenberg model are in agreement with the experiments. Signatures of spin nematic/quadrupolar phases are noticed in the magnetization response to magnetic fied. Our results suggest that the cluster mean field is an appropriate approach for a number of quasi-two dimensional systems with long-range ordered magnetic ground states. [1] Pregelj, M., et al. Spin-stripe phase in a frustrated zigzag spin-1/2 chain. Nature Communications, page 7255, June 2015. [2] F. Weickert, et al. Magnetic anisotropy in the frustrated spin-chain compound β − TeVO$_4$. Phys. Rev. B, 94:064403, Aug 2016.

### Elastic neutron diffraction investigation of the non-Fermi liquid incommensurate magnet $UAu_2$ and development of a magnetic susceptometer for high pressure studies

Stevens, Callum

We discuss experiments on the frustrated incommensurate antiferromagnet UAu$_2$, showing non-Fermi liquid behaviour below 20K and a return to Fermi liquid scaling below 420mK. Elastic neutron diffraction measurements are presented on the magnetic structure of UAu$_2$, compared to behaviour seen in heat capacity and resistivity measurements. We compare our current experimental measurements to theoretically motivated phase diagrams. The design and intended future measurements of an AC susceptometer for high pressure studies of UAu$_2$ are discussed. Experimental data on the superconductor U$_6$Fe is presented to demonstrate functionality.

### Site dependence of the Kondo scale in CePd$_{1−x}$Rh$_x$

Stockert, Ulrike

CePd$_{1−x}$Rh$_x$ undergoes a continuous evolution from ferromagnetic order in CePd to an intermediate-valent ground state for CeRh. Close to the disappearance of magnetic order at a critical Rh content of $x_{cr} = 0.87$ various physical properties exhibit unusual temperature dependencies. This was attributed to a broad distribution of local Kondo temperatures due to the disorder introduced by Pd-Rh exchange and to the possible formation of a quantum Griffith’s phase (QGP) for $0.8 \leq x \leq 0.9$. The thermopower $S(T)$ is very sensitive to Kondo scattering, even in highly diluted systems. Therefore it is an ideal tool to study a distribution of Kondo scales. By thermopower measurements between 2 K and 300 K we could indeed confirm a site-dependent Kondo scale in CePd$_{1−x}$Rh$_x$. Close to $x_{cr}$, $S(T)$ vs.~$T$ assumes a power-law dependence down to 2 K. First measurements at lower $T$ on a sample with possible QGP formation ($x = 0.9$) show a crossover to a logarithmic divergence $S/T ~ \log T_0/T$ down to about 0.2 K.

### Muon site determination in $NbFe_2$

Süllow, Stefan

By means of angular dependent muSR experiments in weak transverse magnetic fields we have determined the site symmetry of the muon stopping site in the weak ferromagnet/spin density wave system $NbFe_2$. By modelling the angular dependence we have determined the muon site and have reanalyzed the muon spin relaxation data determined for this compound [1]. This way, we can fully describe the experimental data both in the spin density wave and ferromagnetic phase assuming two distinct muon sites. [1] D. Rauch, M. Kraken, F. J. Litterst, S. Süllow, H. Luetkens, M. Brando, T. Förster, J. Sichelschmidt, A. Neubauer, C. Pfleiderer, W. J. Duncan, F.M. Grosche: Phys. Rev. B 91 (2015) 174404/1-7; arXiv:condmat:1312.2357

### Ferromagnetic to paramagnetic transition of $SrRuO_3$ under pressure

Tong, Anh

Ferromagnetic to paramagnetic transition of $SrRuO_3$ under pressure Anh Tong, Pau Jorba, Marc Seifert, Markus Braden, Jim Schilling, Christian Pfleiderer In the Ruddlesden-Popper perovskite series, Sr$_{n+1}$Ru$_n$O$_{3n+1}$, intense experimental and theoretical efforts have been dedicated to unravel the nature of unconventional superconductivity in single-layer Sr$_2$RuO$_4$ ($n=1$) as well as a putative electronic nematic phase masking the quantum critical end-point in the double-layer itinerant metamagnet Sr$_3$Ru$_2$O$_7$ ($n=2$). We report an experimental study of the zero temperature ferromagnetic to paramagnetic transition under pressures up to 20\,GPa in high quality single crystals of the infinite layer itinerant ferromagnet SrRuO$_3$ ($n=\infty$). Our study aims to reconcile the properties of Sr$_3$Ru$_2$O$_7$ and Sr$_2$RuO$_4$ with the generic temperature-pressure-magnetic field phase diagram of itinerant ferromagnets.

### Anisotropic magnetic fluctuations in ferromagnetic YbNi$_4$P$_2$

Tou, Hideki

We report on $^{31}$ NMR measurements below 1 K on single crystalline YbNi$_4$P$_2$, which was reported to be a ferromagnetic heavy fermion system with a ferromagnetic transition at $T_C=$0.17 K. It has been discussed that the quasi-one-dimensional Yb chains along the c direction in the tetragonal crystal structure is a key to understand the magnetic ground state in this material. We found that in-plane magnetic fluctuations are pronounced at low fields and dvelop with decreasing temperature. We will discuss the relationship between anisotropic magnetic fluctuation and the crystal electrical field effect in YbNi$_4$P$_2$.

### Benchmark study of two-dimensional large U Hubbard model with one hole by full configuration interaction quantum Monte Carlo

Yun, Sujun

A new method, full configuration interaction quantum Monte Carlo (FCIQMC) with non-unitary similarity transformations (ST-FCIQMC) in real space, is introduced to calculate the ground-state energy of two-dimensional large U Hubbard model with one hole. By the non-unitary similarity transformations of Hamiltonian the new one is a non-Hermitian effective Hamiltonian and has some new two-body terms, which can be projected by FCIQMC very well. It is because these new two-body terms that makes spin flip much easier, leads to a higher convergence rate and a smaller target walker number. These advantages can be validated when ST-FCIQMC is used to study the instability of Nagaoka's Ferromagnetism on limited lattice system. Corresponding to 16, 18 and 24 sites, the critical value Uc are 68.0,92.0 and 150.0. It is the first time to answer the question that how large U should be in order to get the saturated Nagaoka's Ferromagnetism on a given square lattice system. Meanwhile, results in this paper can be also as new benchmark results of large U Hubbard model with one hole on the lattice system which is beyond the range of exact diagonalization that can be calculated.